[{"data":1,"prerenderedAt":35874},["ShallowReactive",2],{"note:cs\u002Fdm\u002Fnote\u002Fchap12":3,"site-search-catalogue":35873},{"id":4,"title":5,"body":6,"description":15,"extension":35866,"meta":35867,"navigation":35868,"path":35869,"seo":35870,"stem":35871,"__hash__":35872},"notes\u002Fsource\u002Fcs\u002Fdm\u002Fnote\u002Fchap12.md","第十二章总线索",{"type":7,"value":8,"toc":35749},"minimark",[9,12,16,146,149,168,171,283,286,413,416,505,508,512,517,520,609,611,714,721,727,729,733,737,740,820,899,902,950,953,1010,1071,1073,1077,1080,1141,1218,1220,1284,1287,1342,1344,1348,1352,1361,1363,1585,1588,1590,1594,1599,1602,1605,1607,1611,1699,1776,1850,1852,1856,1862,1864,1942,2002,2004,2008,2014,2016,2244,2400,2402,2406,2412,2415,2492,2495,2497,2501,2507,2509,2731,2911,2913,2917,2923,2926,2928,2932,2936,2942,2945,3002,3004,3008,3014,3016,3020,3026,3029,3031,3035,3041,3151,3154,3156,3160,3166,3199,3277,3280,3478,3510,3722,3725,3850,3852,3856,3860,3895,3943,3975,3978,4079,4082,4084,4088,4091,4095,4127,4208,4211,4243,4320,4323,4504,4506,4510,4513,4559,4594,4596,4642,4676,4678,4682,4748,4750,4758,4760,4764,4767,4875,5084,5087,5092,5095,5098,5100,5104,5107,5251,5254,5257,5260,5349,5352,5354,5358,5361,5604,5606,5769,5867,5869,5873,5966,6086,6089,6209,6304,6306,6310,6312,6399,6402,6489,6586,6588,6593,6595,6599,6602,6689,6758,6840,6843,6848,6850,6854,6856,6942,6948,7028,7030,7034,7124,7179,7243,7330,7332,7336,7367,7421,7486,7573,7575,7579,7610,7664,7666,7670,7674,7677,7682,7684,7688,7778,7849,7881,7884,7990,7993,8101,8104,8253,8255,8259,8263,8359,8362,8504,8598,8686,8688,8692,8695,8716,8718,8722,8724,8760,8767,8770,8772,8786,8788,8792,8795,8797,8801,8803,8879,8882,9268,9270,9610,9613,9704,9706,9710,9713,10003,10006,10182,10184,10188,10194,10197,10199,10203,10213,10216,10305,10308,10310,10314,10317,10453,10462,10464,10468,10474,10476,10480,10486,10488,10492,10581,10584,10586,10590,10649,10653,10656,10765,10768,10881,10883,10887,10890,10981,10984,10986,10990,10994,11055,11086,11089,11120,11123,11126,11179,11181,11183,11187,11190,11193,11195,11199,11201,11232,11235,11266,11268,11299,11301,11332,11335,11366,11368,11399,11402,11404,11408,11542,11685,11688,11745,11909,12056,12221,12365,12506,12649,12651,12655,12658,12965,12968,12970,12974,12978,13009,13043,13045,13049,13052,13058,13061,13109,13140,13209,13211,13215,13224,13227,13334,13365,13368,13373,13375,13379,13385,13387,13493,13524,13526,13530,13533,13537,13582,13635,13637,13688,13694,13696,13701,13703,13707,13751,13801,13803,13853,13858,13860,13864,13870,13872,13876,14008,14011,14013,14024,14026,14030,14034,14040,14042,14046,14052,14054,14058,14064,14066,14070,14073,14084,14086,14090,14093,14096,14110,14112,14116,14119,14208,14210,14434,14658,14661,14716,14719,14722,14724,14728,14731,14905,14907,15575,15578,15586,15588,15592,15606,15608,15612,15615,15618,16484,16487,16632,16634,16638,16641,16730,16732,16955,16958,17012,17014,17016,17020,17023,17193,17195,17297,17468,17471,17573,17575,17579,17581,17682,17851,17853,17857,17888,17899,17901,17987,17989,17993,17995,17998,18276,18308,18311,18586,18617,18620,18924,18926,18930,18933,18964,18967,19030,19076,19318,19320,19373,19545,19547,19550,19552,19693,19696,19842,19844,19848,19851,19856,19859,19891,20004,20006,20543,20545,20549,20551,20653,20655,20791,20793,20795,20897,20900,20902,20906,20988,20991,21238,21240,21412,21415,21589,21592,21594,21598,21630,21715,21718,21720,21821,21824,21929,21932,22004,22007,22079,22082,22084,22088,22091,22093,22207,22209,22421,22424,22526,22528,22581,22583,22687,22689,22693,22696,22702,22704,22708,22711,22714,22725,22728,22839,22841,22845,22848,22857,22889,22937,22940,22960,22962,22966,22969,22972,23170,23172,23477,23479,23483,23486,23575,23578,23580,23584,23587,23670,23673,23771,23832,23834,23838,23910,23914,24024,24027,24648,24650,24654,24784,24786,24790,24933,25232,25235,25533,25535,25539,25599,25601,25605,25608,25625,25627,25631,25634,25723,25726,25728,25732,25735,25925,25927,26035,26171,26174,26304,26306,26359,26361,26493,26495,26499,26502,27020,27022,27140,27172,27174,27178,27181,27278,27281,27284,27361,27364,27366,27370,27400,27403,27509,27511,27515,27519,27522,27525,27725,27728,27731,27733,27737,27743,27746,27751,27753,27757,27983,28259,28261,28266,28268,28272,28275,28279,28282,28299,28301,28305,28378,28471,28544,28547,28662,28665,28983,29125,29127,29131,29203,29297,29370,29373,29549,29551,29868,30009,30011,30015,30018,30112,30118,30121,30123,30127,30130,30133,30136,30138,30141,32087,32089,32092,32096,32099,32119,32122,32211,32300,32302,32306,32308,32316,32318,32329,32331,32335,32338,32341,32397,32400,32403,32406,32459,32461,32465,32468,32627,32630,32633,32635,32639,32642,32662,32665,32668,32670,32674,32677,32788,32791,32918,32920,32924,32927,32980,32983,32986,33039,33042,33044,33048,33051,33222,33225,33344,33346,33350,33353,33594,33597,33599,33603,33606,33694,33697,33785,33787,33790,33794,33830,33833,33922,33924,33928,33960,33962,33966,34055,34144,34233,34235,34239,34283,34285,34289,34316,34318,34321,34324,34413,34502,34591,34680,34769,34772,34962,35051,35180,35515,35643,35743],[10,11,5],"h1",{"id":5},[13,14,15],"p",{},"图论研究的是：",[17,18,21],"span",{"className":19},[20],"katex-display",[17,22,25,63],{"className":23},[24],"katex",[17,26,29],{"className":27},[28],"katex-mathml",[30,31,34],"math",{"xmlns":32,"display":33},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[35,36,37,58],"semantics",{},[38,39,40],"mrow",{},[41,42,44],"menclose",{"notation":43},"box",[45,46,49],"mstyle",{"scriptlevel":47,"displaystyle":48},"0","false",[45,50,51],{"scriptlevel":47,"displaystyle":48},[45,52,54],{"scriptlevel":47,"displaystyle":53},"true",[55,56,57],"mtext",{},"对象之间的连接关系",[59,60,62],"annotation",{"encoding":61},"application\u002Fx-tex","\\boxed{\\text{对象之间的连接关系}}",[17,64,67],{"className":65,"ariaHidden":53},[66],"katex-html",[17,68,71,76],{"className":69},[70],"base",[17,72],{"className":73,"style":75},[74],"strut","height:1.3633em;vertical-align:-0.34em;",[17,77,80],{"className":78},[79],"mord",[17,81,85,137],{"className":82},[83,84],"vlist-t","vlist-t2",[17,86,89,132],{"className":87},[88],"vlist-r",[17,90,94,120],{"className":91,"style":93},[92],"vlist","height:1.0233em;",[17,95,97,102],{"style":96},"top:-3.3633em;",[17,98],{"className":99,"style":101},[100],"pstrut","height:3.3633em;",[17,103,106],{"className":104},[105],"boxpad",[17,107,109],{"className":108},[79],[17,110,112],{"className":111},[79],[17,113,116],{"className":114},[79,115],"text",[17,117,57],{"className":118},[79,119],"cjk_fallback",[17,121,123,126],{"style":122},"top:-3.0233em;",[17,124],{"className":125,"style":101},[100],[17,127],{"className":128,"style":131},[129,130],"stretchy","fbox","height:1.3633em;border-style:solid;border-width:0.04em;",[17,133,136],{"className":134},[135],"vlist-s","​",[17,138,140],{"className":139},[88],[17,141,144],{"className":142,"style":143},[92],"height:0.34em;",[17,145],{},[13,147,148],{},"比如：",[150,151,152,156,159,162,165],"ul",{},[153,154,155],"li",{},"城市之间有没有路；",[153,157,158],{},"人和人之间是否认识；",[153,160,161],{},"程序是否等待某个资源；",[153,163,164],{},"任务之间谁必须先完成；",[153,166,167],{},"两个点之间最短路线是多少。",[13,169,170],{},"图的基本结构就是：",[17,172,174],{"className":173},[20],[17,175,177,217],{"className":176},[24],[17,178,180],{"className":179},[28],[30,181,182],{"xmlns":32,"display":33},[35,183,184,214],{},[38,185,186,190,194,197,200,203,206,208,211],{},[187,188,189],"mi",{},"G",[191,192,193],"mo",{},"=",[191,195,196],{"stretchy":48},"⟨",[187,198,199],{},"V",[191,201,202],{"separator":53},",",[187,204,205],{},"E",[191,207,202],{"separator":53},[187,209,210],{},"φ",[191,212,213],{"stretchy":48},"⟩",[59,215,216],{"encoding":61},"G=\\langle V,E,\\varphi\\rangle",[17,218,220,243],{"className":219,"ariaHidden":53},[66],[17,221,223,227,231,236,240],{"className":222},[70],[17,224],{"className":225,"style":226},[74],"height:0.6833em;",[17,228,189],{"className":229},[79,230],"mathnormal",[17,232],{"className":233,"style":235},[234],"mspace","margin-right:0.2778em;",[17,237,193],{"className":238},[239],"mrel",[17,241],{"className":242,"style":235},[234],[17,244,246,250,254,258,262,266,270,273,276,279],{"className":245},[70],[17,247],{"className":248,"style":249},[74],"height:1em;vertical-align:-0.25em;",[17,251,196],{"className":252},[253],"mopen",[17,255,199],{"className":256,"style":257},[79,230],"margin-right:0.2222em;",[17,259,202],{"className":260},[261],"mpunct",[17,263],{"className":264,"style":265},[234],"margin-right:0.1667em;",[17,267,205],{"className":268,"style":269},[79,230],"margin-right:0.0576em;",[17,271,202],{"className":272},[261],[17,274],{"className":275,"style":265},[234],[17,277,210],{"className":278},[79,230],[17,280,213],{"className":281},[282],"mclose",[13,284,285],{},"其中：",[287,288,289,302],"table",{},[290,291,292],"thead",{},[293,294,295,299],"tr",{},[296,297,298],"th",{},"符号",[296,300,301],{},"含义",[303,304,305,341,376],"tbody",{},[293,306,307,338],{},[308,309,310],"td",{},[17,311,313,326],{"className":312},[24],[17,314,316],{"className":315},[28],[30,317,318],{"xmlns":32},[35,319,320,324],{},[38,321,322],{},[187,323,199],{},[59,325,199],{"encoding":61},[17,327,329],{"className":328,"ariaHidden":53},[66],[17,330,332,335],{"className":331},[70],[17,333],{"className":334,"style":226},[74],[17,336,199],{"className":337,"style":257},[79,230],[308,339,340],{},"顶点集",[293,342,343,373],{},[308,344,345],{},[17,346,348,361],{"className":347},[24],[17,349,351],{"className":350},[28],[30,352,353],{"xmlns":32},[35,354,355,359],{},[38,356,357],{},[187,358,205],{},[59,360,205],{"encoding":61},[17,362,364],{"className":363,"ariaHidden":53},[66],[17,365,367,370],{"className":366},[70],[17,368],{"className":369,"style":226},[74],[17,371,205],{"className":372,"style":269},[79,230],[308,374,375],{},"边集",[293,377,378,410],{},[308,379,380],{},[17,381,383,397],{"className":382},[24],[17,384,386],{"className":385},[28],[30,387,388],{"xmlns":32},[35,389,390,394],{},[38,391,392],{},[187,393,210],{},[59,395,396],{"encoding":61},"\\varphi",[17,398,400],{"className":399,"ariaHidden":53},[66],[17,401,403,407],{"className":402},[70],[17,404],{"className":405,"style":406},[74],"height:0.625em;vertical-align:-0.1944em;",[17,408,210],{"className":409},[79,230],[308,411,412],{},"关联函数，说明每条边连接哪些顶点",[13,414,415],{},"最直观一句话：",[17,417,419],{"className":418},[20],[17,420,422,445],{"className":421},[24],[17,423,425],{"className":424},[28],[30,426,427],{"xmlns":32,"display":33},[35,428,429,442],{},[38,430,431],{},[41,432,433],{"notation":43},[45,434,435],{"scriptlevel":47,"displaystyle":48},[45,436,437],{"scriptlevel":47,"displaystyle":48},[45,438,439],{"scriptlevel":47,"displaystyle":53},[55,440,441],{},"顶点表示对象，边表示对象之间的关系",[59,443,444],{"encoding":61},"\\boxed{\\text{顶点表示对象，边表示对象之间的关系}}",[17,446,448],{"className":447,"ariaHidden":53},[66],[17,449,451,454],{"className":450},[70],[17,452],{"className":453,"style":75},[74],[17,455,457],{"className":456},[79],[17,458,460,497],{"className":459},[83,84],[17,461,463,494],{"className":462},[88],[17,464,466,486],{"className":465,"style":93},[92],[17,467,468,471],{"style":96},[17,469],{"className":470,"style":101},[100],[17,472,474],{"className":473},[105],[17,475,477],{"className":476},[79],[17,478,480],{"className":479},[79],[17,481,483],{"className":482},[79,115],[17,484,441],{"className":485},[79,119],[17,487,488,491],{"style":122},[17,489],{"className":490,"style":101},[100],[17,492],{"className":493,"style":131},[129,130],[17,495,136],{"className":496},[135],[17,498,500],{"className":499},[88],[17,501,503],{"className":502,"style":143},[92],[17,504],{},[506,507],"hr",{},[10,509,511],{"id":510},"_121-图与子图","12.1 图与子图",[513,514,516],"h2",{"id":515},"一图的定义","一、图的定义",[13,518,519],{},"图通常记作：",[17,521,523],{"className":522},[20],[17,524,526,555],{"className":525},[24],[17,527,529],{"className":528},[28],[30,530,531],{"xmlns":32,"display":33},[35,532,533,553],{},[38,534,535,537,539,541,543,545,547,549,551],{},[187,536,189],{},[191,538,193],{},[191,540,196],{"stretchy":48},[187,542,199],{},[191,544,202],{"separator":53},[187,546,205],{},[191,548,202],{"separator":53},[187,550,210],{},[191,552,213],{"stretchy":48},[59,554,216],{"encoding":61},[17,556,558,576],{"className":557,"ariaHidden":53},[66],[17,559,561,564,567,570,573],{"className":560},[70],[17,562],{"className":563,"style":226},[74],[17,565,189],{"className":566},[79,230],[17,568],{"className":569,"style":235},[234],[17,571,193],{"className":572},[239],[17,574],{"className":575,"style":235},[234],[17,577,579,582,585,588,591,594,597,600,603,606],{"className":578},[70],[17,580],{"className":581,"style":249},[74],[17,583,196],{"className":584},[253],[17,586,199],{"className":587,"style":257},[79,230],[17,589,202],{"className":590},[261],[17,592],{"className":593,"style":265},[234],[17,595,205],{"className":596,"style":269},[79,230],[17,598,202],{"className":599},[261],[17,601],{"className":602,"style":265},[234],[17,604,210],{"className":605},[79,230],[17,607,213],{"className":608},[282],[13,610,285],{},[150,612,613,649,683],{},[153,614,615,643,644,648],{},[17,616,618,631],{"className":617},[24],[17,619,621],{"className":620},[28],[30,622,623],{"xmlns":32},[35,624,625,629],{},[38,626,627],{},[187,628,199],{},[59,630,199],{"encoding":61},[17,632,634],{"className":633,"ariaHidden":53},[66],[17,635,637,640],{"className":636},[70],[17,638],{"className":639,"style":226},[74],[17,641,199],{"className":642,"style":257},[79,230]," 是非空有限集合，元素叫",[645,646,647],"strong",{},"顶点","；",[153,650,651,679,680,648],{},[17,652,654,667],{"className":653},[24],[17,655,657],{"className":656},[28],[30,658,659],{"xmlns":32},[35,660,661,665],{},[38,662,663],{},[187,664,205],{},[59,666,205],{"encoding":61},[17,668,670],{"className":669,"ariaHidden":53},[66],[17,671,673,676],{"className":672},[70],[17,674],{"className":675,"style":226},[74],[17,677,205],{"className":678,"style":269},[79,230]," 是有限集合，元素叫",[645,681,682],{},"边",[153,684,685,713],{},[17,686,688,701],{"className":687},[24],[17,689,691],{"className":690},[28],[30,692,693],{"xmlns":32},[35,694,695,699],{},[38,696,697],{},[187,698,210],{},[59,700,396],{"encoding":61},[17,702,704],{"className":703,"ariaHidden":53},[66],[17,705,707,710],{"className":706},[70],[17,708],{"className":709,"style":406},[74],[17,711,210],{"className":712},[79,230]," 把每条边对应到某个顶点对。",[13,715,716,717,720],{},"如果边没有方向，叫",[645,718,719],{},"无向图","。",[13,722,723,724,720],{},"如果边有方向，叫",[645,725,726],{},"有向图",[506,728],{},[513,730,732],{"id":731},"二无向边与有向边","二、无向边与有向边",[513,734,736],{"id":735},"_1-无向边","1. 无向边",[13,738,739],{},"无向边连接两个顶点，不分起点终点。",[13,741,742,743,773,774,819],{},"如果边 ",[17,744,746,760],{"className":745},[24],[17,747,749],{"className":748},[28],[30,750,751],{"xmlns":32},[35,752,753,758],{},[38,754,755],{},[187,756,757],{},"e",[59,759,757],{"encoding":61},[17,761,763],{"className":762,"ariaHidden":53},[66],[17,764,766,770],{"className":765},[70],[17,767],{"className":768,"style":769},[74],"height:0.4306em;",[17,771,757],{"className":772},[79,230]," 连接 ",[17,775,777,797],{"className":776},[24],[17,778,780],{"className":779},[28],[30,781,782],{"xmlns":32},[35,783,784,794],{},[38,785,786,789,791],{},[187,787,788],{},"u",[191,790,202],{"separator":53},[187,792,793],{},"v",[59,795,796],{"encoding":61},"u,v",[17,798,800],{"className":799,"ariaHidden":53},[66],[17,801,803,806,809,812,815],{"className":802},[70],[17,804],{"className":805,"style":406},[74],[17,807,788],{"className":808},[79,230],[17,810,202],{"className":811},[261],[17,813],{"className":814,"style":265},[234],[17,816,793],{"className":817,"style":818},[79,230],"margin-right:0.0359em;","，可以写作：",[17,821,823],{"className":822},[20],[17,824,826,854],{"className":825},[24],[17,827,829],{"className":828},[28],[30,830,831],{"xmlns":32,"display":33},[35,832,833,851],{},[38,834,835,837,839,842,844,846,848],{},[187,836,757],{},[191,838,193],{},[191,840,841],{"stretchy":48},"(",[187,843,788],{},[191,845,202],{"separator":53},[187,847,793],{},[191,849,850],{"stretchy":48},")",[59,852,853],{"encoding":61},"e=(u,v)",[17,855,857,875],{"className":856,"ariaHidden":53},[66],[17,858,860,863,866,869,872],{"className":859},[70],[17,861],{"className":862,"style":769},[74],[17,864,757],{"className":865},[79,230],[17,867],{"className":868,"style":235},[234],[17,870,193],{"className":871},[239],[17,873],{"className":874,"style":235},[234],[17,876,878,881,884,887,890,893,896],{"className":877},[70],[17,879],{"className":880,"style":249},[74],[17,882,841],{"className":883},[253],[17,885,788],{"className":886},[79,230],[17,888,202],{"className":889},[261],[17,891],{"className":892,"style":265},[234],[17,894,793],{"className":895,"style":818},[79,230],[17,897,850],{"className":898},[282],[13,900,901],{},"或者理解成无序对：",[17,903,905],{"className":904},[20],[17,906,908,926],{"className":907},[24],[17,909,911],{"className":910},[28],[30,912,913],{"xmlns":32,"display":33},[35,914,915,923],{},[38,916,917,919,921],{},[187,918,788],{},[191,920,202],{"separator":53},[187,922,793],{},[59,924,925],{"encoding":61},"{u,v}",[17,927,929],{"className":928,"ariaHidden":53},[66],[17,930,932,935],{"className":931},[70],[17,933],{"className":934,"style":406},[74],[17,936,938,941,944,947],{"className":937},[79],[17,939,788],{"className":940},[79,230],[17,942,202],{"className":943},[261],[17,945],{"className":946,"style":265},[234],[17,948,793],{"className":949,"style":818},[79,230],[13,951,952],{},"例如：",[17,954,956],{"className":955},[20],[17,957,959,978],{"className":958},[24],[17,960,962],{"className":961},[28],[30,963,964],{"xmlns":32,"display":33},[35,965,966,975],{},[38,967,968,970,973],{},[187,969,788],{},[191,971,972],{},"−",[187,974,793],{},[59,976,977],{"encoding":61},"u-v",[17,979,981,1001],{"className":980,"ariaHidden":53},[66],[17,982,984,988,991,994,998],{"className":983},[70],[17,985],{"className":986,"style":987},[74],"height:0.6667em;vertical-align:-0.0833em;",[17,989,788],{"className":990},[79,230],[17,992],{"className":993,"style":257},[234],[17,995,972],{"className":996},[997],"mbin",[17,999],{"className":1000,"style":257},[234],[17,1002,1004,1007],{"className":1003},[70],[17,1005],{"className":1006,"style":769},[74],[17,1008,793],{"className":1009,"style":818},[79,230],[13,1011,1012,1013,1041,1042,1070],{},"表示 ",[17,1014,1016,1029],{"className":1015},[24],[17,1017,1019],{"className":1018},[28],[30,1020,1021],{"xmlns":32},[35,1022,1023,1027],{},[38,1024,1025],{},[187,1026,788],{},[59,1028,788],{"encoding":61},[17,1030,1032],{"className":1031,"ariaHidden":53},[66],[17,1033,1035,1038],{"className":1034},[70],[17,1036],{"className":1037,"style":769},[74],[17,1039,788],{"className":1040},[79,230]," 和 ",[17,1043,1045,1058],{"className":1044},[24],[17,1046,1048],{"className":1047},[28],[30,1049,1050],{"xmlns":32},[35,1051,1052,1056],{},[38,1053,1054],{},[187,1055,793],{},[59,1057,793],{"encoding":61},[17,1059,1061],{"className":1060,"ariaHidden":53},[66],[17,1062,1064,1067],{"className":1063},[70],[17,1065],{"className":1066,"style":769},[74],[17,1068,793],{"className":1069,"style":818},[79,230]," 相连。",[506,1072],{},[513,1074,1076],{"id":1075},"_2-有向边","2. 有向边",[13,1078,1079],{},"有向边有方向，有起点和终点。",[13,1081,1082,1083,1111,1112,1140],{},"如果边从 ",[17,1084,1086,1099],{"className":1085},[24],[17,1087,1089],{"className":1088},[28],[30,1090,1091],{"xmlns":32},[35,1092,1093,1097],{},[38,1094,1095],{},[187,1096,788],{},[59,1098,788],{"encoding":61},[17,1100,1102],{"className":1101,"ariaHidden":53},[66],[17,1103,1105,1108],{"className":1104},[70],[17,1106],{"className":1107,"style":769},[74],[17,1109,788],{"className":1110},[79,230]," 指向 ",[17,1113,1115,1128],{"className":1114},[24],[17,1116,1118],{"className":1117},[28],[30,1119,1120],{"xmlns":32},[35,1121,1122,1126],{},[38,1123,1124],{},[187,1125,793],{},[59,1127,793],{"encoding":61},[17,1129,1131],{"className":1130,"ariaHidden":53},[66],[17,1132,1134,1137],{"className":1133},[70],[17,1135],{"className":1136,"style":769},[74],[17,1138,793],{"className":1139,"style":818},[79,230],"，记作：",[17,1142,1144],{"className":1143},[20],[17,1145,1147,1173],{"className":1146},[24],[17,1148,1150],{"className":1149},[28],[30,1151,1152],{"xmlns":32,"display":33},[35,1153,1154,1170],{},[38,1155,1156,1158,1160,1162,1164,1166,1168],{},[187,1157,757],{},[191,1159,193],{},[191,1161,196],{"stretchy":48},[187,1163,788],{},[191,1165,202],{"separator":53},[187,1167,793],{},[191,1169,213],{"stretchy":48},[59,1171,1172],{"encoding":61},"e=\\langle u,v\\rangle",[17,1174,1176,1194],{"className":1175,"ariaHidden":53},[66],[17,1177,1179,1182,1185,1188,1191],{"className":1178},[70],[17,1180],{"className":1181,"style":769},[74],[17,1183,757],{"className":1184},[79,230],[17,1186],{"className":1187,"style":235},[234],[17,1189,193],{"className":1190},[239],[17,1192],{"className":1193,"style":235},[234],[17,1195,1197,1200,1203,1206,1209,1212,1215],{"className":1196},[70],[17,1198],{"className":1199,"style":249},[74],[17,1201,196],{"className":1202},[253],[17,1204,788],{"className":1205},[79,230],[17,1207,202],{"className":1208},[261],[17,1210],{"className":1211,"style":265},[234],[17,1213,793],{"className":1214,"style":818},[79,230],[17,1216,213],{"className":1217},[282],[13,1219,285],{},[150,1221,1222,1253],{},[153,1223,1224,1252],{},[17,1225,1227,1240],{"className":1226},[24],[17,1228,1230],{"className":1229},[28],[30,1231,1232],{"xmlns":32},[35,1233,1234,1238],{},[38,1235,1236],{},[187,1237,788],{},[59,1239,788],{"encoding":61},[17,1241,1243],{"className":1242,"ariaHidden":53},[66],[17,1244,1246,1249],{"className":1245},[70],[17,1247],{"className":1248,"style":769},[74],[17,1250,788],{"className":1251},[79,230],"：起点；",[153,1254,1255,1283],{},[17,1256,1258,1271],{"className":1257},[24],[17,1259,1261],{"className":1260},[28],[30,1262,1263],{"xmlns":32},[35,1264,1265,1269],{},[38,1266,1267],{},[187,1268,793],{},[59,1270,793],{"encoding":61},[17,1272,1274],{"className":1273,"ariaHidden":53},[66],[17,1275,1277,1280],{"className":1276},[70],[17,1278],{"className":1279,"style":769},[74],[17,1281,793],{"className":1282,"style":818},[79,230],"：终点。",[13,1285,1286],{},"画图时用箭头表示：",[17,1288,1290],{"className":1289},[20],[17,1291,1293,1312],{"className":1292},[24],[17,1294,1296],{"className":1295},[28],[30,1297,1298],{"xmlns":32,"display":33},[35,1299,1300,1309],{},[38,1301,1302,1304,1307],{},[187,1303,788],{},[191,1305,1306],{},"→",[187,1308,793],{},[59,1310,1311],{"encoding":61},"u\\to v",[17,1313,1315,1333],{"className":1314,"ariaHidden":53},[66],[17,1316,1318,1321,1324,1327,1330],{"className":1317},[70],[17,1319],{"className":1320,"style":769},[74],[17,1322,788],{"className":1323},[79,230],[17,1325],{"className":1326,"style":235},[234],[17,1328,1306],{"className":1329},[239],[17,1331],{"className":1332,"style":235},[234],[17,1334,1336,1339],{"className":1335},[70],[17,1337],{"className":1338,"style":769},[74],[17,1340,793],{"className":1341,"style":818},[79,230],[506,1343],{},[10,1345,1347],{"id":1346},"三图的基本术语","三、图的基本术语",[513,1349,1351],{"id":1350},"_1-顶点","1. 顶点",[13,1353,1354,1355,1357,1358,720],{},"图中的点叫",[645,1356,647],{},"，也叫",[645,1359,1360],{},"结点",[13,1362,952],{},[17,1364,1366],{"className":1365},[20],[17,1367,1369,1414],{"className":1368},[24],[17,1370,1372],{"className":1371},[28],[30,1373,1374],{"xmlns":32,"display":33},[35,1375,1376,1411],{},[38,1377,1378,1380,1382],{},[187,1379,199],{},[191,1381,193],{},[38,1383,1384,1393,1395,1402,1404],{},[1385,1386,1387,1389],"msub",{},[187,1388,793],{},[1390,1391,1392],"mn",{},"1",[191,1394,202],{"separator":53},[1385,1396,1397,1399],{},[187,1398,793],{},[1390,1400,1401],{},"2",[191,1403,202],{"separator":53},[1385,1405,1406,1408],{},[187,1407,793],{},[1390,1409,1410],{},"3",[59,1412,1413],{"encoding":61},"V={v_1,v_2,v_3}",[17,1415,1417,1435],{"className":1416,"ariaHidden":53},[66],[17,1418,1420,1423,1426,1429,1432],{"className":1419},[70],[17,1421],{"className":1422,"style":226},[74],[17,1424,199],{"className":1425,"style":257},[79,230],[17,1427],{"className":1428,"style":235},[234],[17,1430,193],{"className":1431},[239],[17,1433],{"className":1434,"style":235},[234],[17,1436,1438,1441],{"className":1437},[70],[17,1439],{"className":1440,"style":406},[74],[17,1442,1444,1493,1496,1499,1539,1542,1545],{"className":1443},[79],[17,1445,1447,1450],{"className":1446},[79],[17,1448,793],{"className":1449,"style":818},[79,230],[17,1451,1454],{"className":1452},[1453],"msupsub",[17,1455,1457,1484],{"className":1456},[83,84],[17,1458,1460,1481],{"className":1459},[88],[17,1461,1464],{"className":1462,"style":1463},[92],"height:0.3011em;",[17,1465,1467,1471],{"style":1466},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[17,1468],{"className":1469,"style":1470},[100],"height:2.7em;",[17,1472,1478],{"className":1473},[1474,1475,1476,1477],"sizing","reset-size6","size3","mtight",[17,1479,1392],{"className":1480},[79,1477],[17,1482,136],{"className":1483},[135],[17,1485,1487],{"className":1486},[88],[17,1488,1491],{"className":1489,"style":1490},[92],"height:0.15em;",[17,1492],{},[17,1494,202],{"className":1495},[261],[17,1497],{"className":1498,"style":265},[234],[17,1500,1502,1505],{"className":1501},[79],[17,1503,793],{"className":1504,"style":818},[79,230],[17,1506,1508],{"className":1507},[1453],[17,1509,1511,1531],{"className":1510},[83,84],[17,1512,1514,1528],{"className":1513},[88],[17,1515,1517],{"className":1516,"style":1463},[92],[17,1518,1519,1522],{"style":1466},[17,1520],{"className":1521,"style":1470},[100],[17,1523,1525],{"className":1524},[1474,1475,1476,1477],[17,1526,1401],{"className":1527},[79,1477],[17,1529,136],{"className":1530},[135],[17,1532,1534],{"className":1533},[88],[17,1535,1537],{"className":1536,"style":1490},[92],[17,1538],{},[17,1540,202],{"className":1541},[261],[17,1543],{"className":1544,"style":265},[234],[17,1546,1548,1551],{"className":1547},[79],[17,1549,793],{"className":1550,"style":818},[79,230],[17,1552,1554],{"className":1553},[1453],[17,1555,1557,1577],{"className":1556},[83,84],[17,1558,1560,1574],{"className":1559},[88],[17,1561,1563],{"className":1562,"style":1463},[92],[17,1564,1565,1568],{"style":1466},[17,1566],{"className":1567,"style":1470},[100],[17,1569,1571],{"className":1570},[1474,1475,1476,1477],[17,1572,1410],{"className":1573},[79,1477],[17,1575,136],{"className":1576},[135],[17,1578,1580],{"className":1579},[88],[17,1581,1583],{"className":1582,"style":1490},[92],[17,1584],{},[13,1586,1587],{},"表示图有三个顶点。",[506,1589],{},[513,1591,1593],{"id":1592},"_2-边","2. 边",[13,1595,1596,1597,720],{},"图中连接顶点的线叫",[645,1598,682],{},[13,1600,1601],{},"无向图的边没有方向。",[13,1603,1604],{},"有向图的边有方向。",[506,1606],{},[513,1608,1610],{"id":1609},"_3-关联","3. 关联",[13,1612,742,1613,1641,1642,1041,1670,1698],{},[17,1614,1616,1629],{"className":1615},[24],[17,1617,1619],{"className":1618},[28],[30,1620,1621],{"xmlns":32},[35,1622,1623,1627],{},[38,1624,1625],{},[187,1626,757],{},[59,1628,757],{"encoding":61},[17,1630,1632],{"className":1631,"ariaHidden":53},[66],[17,1633,1635,1638],{"className":1634},[70],[17,1636],{"className":1637,"style":769},[74],[17,1639,757],{"className":1640},[79,230]," 连接顶点 ",[17,1643,1645,1658],{"className":1644},[24],[17,1646,1648],{"className":1647},[28],[30,1649,1650],{"xmlns":32},[35,1651,1652,1656],{},[38,1653,1654],{},[187,1655,788],{},[59,1657,788],{"encoding":61},[17,1659,1661],{"className":1660,"ariaHidden":53},[66],[17,1662,1664,1667],{"className":1663},[70],[17,1665],{"className":1666,"style":769},[74],[17,1668,788],{"className":1669},[79,230],[17,1671,1673,1686],{"className":1672},[24],[17,1674,1676],{"className":1675},[28],[30,1677,1678],{"xmlns":32},[35,1679,1680,1684],{},[38,1681,1682],{},[187,1683,793],{},[59,1685,793],{"encoding":61},[17,1687,1689],{"className":1688,"ariaHidden":53},[66],[17,1690,1692,1695],{"className":1691},[70],[17,1693],{"className":1694,"style":769},[74],[17,1696,793],{"className":1697,"style":818},[79,230],"，则称：",[1700,1701,1702],"blockquote",{},[13,1703,1704,1705,1733,1734,1775],{},"边 ",[17,1706,1708,1721],{"className":1707},[24],[17,1709,1711],{"className":1710},[28],[30,1712,1713],{"xmlns":32},[35,1714,1715,1719],{},[38,1716,1717],{},[187,1718,757],{},[59,1720,757],{"encoding":61},[17,1722,1724],{"className":1723,"ariaHidden":53},[66],[17,1725,1727,1730],{"className":1726},[70],[17,1728],{"className":1729,"style":769},[74],[17,1731,757],{"className":1732},[79,230]," 与顶点 ",[17,1735,1737,1754],{"className":1736},[24],[17,1738,1740],{"className":1739},[28],[30,1741,1742],{"xmlns":32},[35,1743,1744,1752],{},[38,1745,1746,1748,1750],{},[187,1747,788],{},[191,1749,202],{"separator":53},[187,1751,793],{},[59,1753,796],{"encoding":61},[17,1755,1757],{"className":1756,"ariaHidden":53},[66],[17,1758,1760,1763,1766,1769,1772],{"className":1759},[70],[17,1761],{"className":1762,"style":406},[74],[17,1764,788],{"className":1765},[79,230],[17,1767,202],{"className":1768},[261],[17,1770],{"className":1771,"style":265},[234],[17,1773,793],{"className":1774,"style":818},[79,230]," 关联。",[13,1777,1778,1779,1820,1821,1849],{},"也说 ",[17,1780,1782,1799],{"className":1781},[24],[17,1783,1785],{"className":1784},[28],[30,1786,1787],{"xmlns":32},[35,1788,1789,1797],{},[38,1790,1791,1793,1795],{},[187,1792,788],{},[191,1794,202],{"separator":53},[187,1796,793],{},[59,1798,796],{"encoding":61},[17,1800,1802],{"className":1801,"ariaHidden":53},[66],[17,1803,1805,1808,1811,1814,1817],{"className":1804},[70],[17,1806],{"className":1807,"style":406},[74],[17,1809,788],{"className":1810},[79,230],[17,1812,202],{"className":1813},[261],[17,1815],{"className":1816,"style":265},[234],[17,1818,793],{"className":1819,"style":818},[79,230]," 是边 ",[17,1822,1824,1837],{"className":1823},[24],[17,1825,1827],{"className":1826},[28],[30,1828,1829],{"xmlns":32},[35,1830,1831,1835],{},[38,1832,1833],{},[187,1834,757],{},[59,1836,757],{"encoding":61},[17,1838,1840],{"className":1839,"ariaHidden":53},[66],[17,1841,1843,1846],{"className":1842},[70],[17,1844],{"className":1845,"style":769},[74],[17,1847,757],{"className":1848},[79,230]," 的端点。",[506,1851],{},[513,1853,1855],{"id":1854},"_4-邻接顶点","4. 邻接顶点",[13,1857,1858,1859,720],{},"如果两个顶点之间有边相连，就称它们是",[645,1860,1861],{},"邻接顶点",[13,1863,952],{},[17,1865,1867],{"className":1866},[20],[17,1868,1870,1897],{"className":1869},[24],[17,1871,1873],{"className":1872},[28],[30,1874,1875],{"xmlns":32,"display":33},[35,1876,1877,1894],{},[38,1878,1879,1881,1883,1885,1887,1889,1892],{},[191,1880,841],{"stretchy":48},[187,1882,788],{},[191,1884,202],{"separator":53},[187,1886,793],{},[191,1888,850],{"stretchy":48},[191,1890,1891],{},"∈",[187,1893,205],{},[59,1895,1896],{"encoding":61},"(u,v)\\in E",[17,1898,1900,1933],{"className":1899,"ariaHidden":53},[66],[17,1901,1903,1906,1909,1912,1915,1918,1921,1924,1927,1930],{"className":1902},[70],[17,1904],{"className":1905,"style":249},[74],[17,1907,841],{"className":1908},[253],[17,1910,788],{"className":1911},[79,230],[17,1913,202],{"className":1914},[261],[17,1916],{"className":1917,"style":265},[234],[17,1919,793],{"className":1920,"style":818},[79,230],[17,1922,850],{"className":1923},[282],[17,1925],{"className":1926,"style":235},[234],[17,1928,1891],{"className":1929},[239],[17,1931],{"className":1932,"style":235},[234],[17,1934,1936,1939],{"className":1935},[70],[17,1937],{"className":1938,"style":226},[74],[17,1940,205],{"className":1941,"style":269},[79,230],[13,1943,1944,1945,1041,1973,2001],{},"则 ",[17,1946,1948,1961],{"className":1947},[24],[17,1949,1951],{"className":1950},[28],[30,1952,1953],{"xmlns":32},[35,1954,1955,1959],{},[38,1956,1957],{},[187,1958,788],{},[59,1960,788],{"encoding":61},[17,1962,1964],{"className":1963,"ariaHidden":53},[66],[17,1965,1967,1970],{"className":1966},[70],[17,1968],{"className":1969,"style":769},[74],[17,1971,788],{"className":1972},[79,230],[17,1974,1976,1989],{"className":1975},[24],[17,1977,1979],{"className":1978},[28],[30,1980,1981],{"xmlns":32},[35,1982,1983,1987],{},[38,1984,1985],{},[187,1986,793],{},[59,1988,793],{"encoding":61},[17,1990,1992],{"className":1991,"ariaHidden":53},[66],[17,1993,1995,1998],{"className":1994},[70],[17,1996],{"className":1997,"style":769},[74],[17,1999,793],{"className":2000,"style":818},[79,230]," 邻接。",[506,2003],{},[513,2005,2007],{"id":2006},"_5-邻接边","5. 邻接边",[13,2009,2010,2011,720],{},"如果两条边有公共端点，则称它们是",[645,2012,2013],{},"邻接边",[13,2015,148],{},[17,2017,2019],{"className":2018},[20],[17,2020,2022,2076],{"className":2021},[24],[17,2023,2025],{"className":2024},[28],[30,2026,2027],{"xmlns":32,"display":33},[35,2028,2029,2073],{},[38,2030,2031,2037,2039,2041,2043,2045,2047,2049,2051,2054,2060,2062,2064,2066,2068,2071],{},[1385,2032,2033,2035],{},[187,2034,757],{},[1390,2036,1392],{},[191,2038,193],{},[191,2040,841],{"stretchy":48},[187,2042,788],{},[191,2044,202],{"separator":53},[187,2046,793],{},[191,2048,850],{"stretchy":48},[191,2050,202],{"separator":53},[234,2052],{"width":2053},"1em",[1385,2055,2056,2058],{},[187,2057,757],{},[1390,2059,1401],{},[191,2061,193],{},[191,2063,841],{"stretchy":48},[187,2065,793],{},[191,2067,202],{"separator":53},[187,2069,2070],{},"w",[191,2072,850],{"stretchy":48},[59,2074,2075],{"encoding":61},"e_1=(u,v),\\quad e_2=(v,w)",[17,2077,2079,2136,2219],{"className":2078,"ariaHidden":53},[66],[17,2080,2082,2086,2127,2130,2133],{"className":2081},[70],[17,2083],{"className":2084,"style":2085},[74],"height:0.5806em;vertical-align:-0.15em;",[17,2087,2089,2092],{"className":2088},[79],[17,2090,757],{"className":2091},[79,230],[17,2093,2095],{"className":2094},[1453],[17,2096,2098,2119],{"className":2097},[83,84],[17,2099,2101,2116],{"className":2100},[88],[17,2102,2104],{"className":2103,"style":1463},[92],[17,2105,2107,2110],{"style":2106},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[17,2108],{"className":2109,"style":1470},[100],[17,2111,2113],{"className":2112},[1474,1475,1476,1477],[17,2114,1392],{"className":2115},[79,1477],[17,2117,136],{"className":2118},[135],[17,2120,2122],{"className":2121},[88],[17,2123,2125],{"className":2124,"style":1490},[92],[17,2126],{},[17,2128],{"className":2129,"style":235},[234],[17,2131,193],{"className":2132},[239],[17,2134],{"className":2135,"style":235},[234],[17,2137,2139,2142,2145,2148,2151,2154,2157,2160,2163,2167,2170,2210,2213,2216],{"className":2138},[70],[17,2140],{"className":2141,"style":249},[74],[17,2143,841],{"className":2144},[253],[17,2146,788],{"className":2147},[79,230],[17,2149,202],{"className":2150},[261],[17,2152],{"className":2153,"style":265},[234],[17,2155,793],{"className":2156,"style":818},[79,230],[17,2158,850],{"className":2159},[282],[17,2161,202],{"className":2162},[261],[17,2164],{"className":2165,"style":2166},[234],"margin-right:1em;",[17,2168],{"className":2169,"style":265},[234],[17,2171,2173,2176],{"className":2172},[79],[17,2174,757],{"className":2175},[79,230],[17,2177,2179],{"className":2178},[1453],[17,2180,2182,2202],{"className":2181},[83,84],[17,2183,2185,2199],{"className":2184},[88],[17,2186,2188],{"className":2187,"style":1463},[92],[17,2189,2190,2193],{"style":2106},[17,2191],{"className":2192,"style":1470},[100],[17,2194,2196],{"className":2195},[1474,1475,1476,1477],[17,2197,1401],{"className":2198},[79,1477],[17,2200,136],{"className":2201},[135],[17,2203,2205],{"className":2204},[88],[17,2206,2208],{"className":2207,"style":1490},[92],[17,2209],{},[17,2211],{"className":2212,"style":235},[234],[17,2214,193],{"className":2215},[239],[17,2217],{"className":2218,"style":235},[234],[17,2220,2222,2225,2228,2231,2234,2237,2241],{"className":2221},[70],[17,2223],{"className":2224,"style":249},[74],[17,2226,841],{"className":2227},[253],[17,2229,793],{"className":2230,"style":818},[79,230],[17,2232,202],{"className":2233},[261],[17,2235],{"className":2236,"style":265},[234],[17,2238,2070],{"className":2239,"style":2240},[79,230],"margin-right:0.0269em;",[17,2242,850],{"className":2243},[282],[13,2245,2246,2247,2275,2276,2001],{},"它们都经过 ",[17,2248,2250,2263],{"className":2249},[24],[17,2251,2253],{"className":2252},[28],[30,2254,2255],{"xmlns":32},[35,2256,2257,2261],{},[38,2258,2259],{},[187,2260,793],{},[59,2262,793],{"encoding":61},[17,2264,2266],{"className":2265,"ariaHidden":53},[66],[17,2267,2269,2272],{"className":2268},[70],[17,2270],{"className":2271,"style":769},[74],[17,2273,793],{"className":2274,"style":818},[79,230],"，所以 ",[17,2277,2279,2305],{"className":2278},[24],[17,2280,2282],{"className":2281},[28],[30,2283,2284],{"xmlns":32},[35,2285,2286,2302],{},[38,2287,2288,2294,2296],{},[1385,2289,2290,2292],{},[187,2291,757],{},[1390,2293,1392],{},[191,2295,202],{"separator":53},[1385,2297,2298,2300],{},[187,2299,757],{},[1390,2301,1401],{},[59,2303,2304],{"encoding":61},"e_1,e_2",[17,2306,2308],{"className":2307,"ariaHidden":53},[66],[17,2309,2311,2314,2354,2357,2360],{"className":2310},[70],[17,2312],{"className":2313,"style":406},[74],[17,2315,2317,2320],{"className":2316},[79],[17,2318,757],{"className":2319},[79,230],[17,2321,2323],{"className":2322},[1453],[17,2324,2326,2346],{"className":2325},[83,84],[17,2327,2329,2343],{"className":2328},[88],[17,2330,2332],{"className":2331,"style":1463},[92],[17,2333,2334,2337],{"style":2106},[17,2335],{"className":2336,"style":1470},[100],[17,2338,2340],{"className":2339},[1474,1475,1476,1477],[17,2341,1392],{"className":2342},[79,1477],[17,2344,136],{"className":2345},[135],[17,2347,2349],{"className":2348},[88],[17,2350,2352],{"className":2351,"style":1490},[92],[17,2353],{},[17,2355,202],{"className":2356},[261],[17,2358],{"className":2359,"style":265},[234],[17,2361,2363,2366],{"className":2362},[79],[17,2364,757],{"className":2365},[79,230],[17,2367,2369],{"className":2368},[1453],[17,2370,2372,2392],{"className":2371},[83,84],[17,2373,2375,2389],{"className":2374},[88],[17,2376,2378],{"className":2377,"style":1463},[92],[17,2379,2380,2383],{"style":2106},[17,2381],{"className":2382,"style":1470},[100],[17,2384,2386],{"className":2385},[1474,1475,1476,1477],[17,2387,1401],{"className":2388},[79,1477],[17,2390,136],{"className":2391},[135],[17,2393,2395],{"className":2394},[88],[17,2396,2398],{"className":2397,"style":1490},[92],[17,2399],{},[506,2401],{},[513,2403,2405],{"id":2404},"_6-自环","6. 自环",[13,2407,2408,2409,720],{},"一条边的两个端点相同，叫",[645,2410,2411],{},"自环",[13,2413,2414],{},"形式：",[17,2416,2418],{"className":2417},[20],[17,2419,2421,2447],{"className":2420},[24],[17,2422,2424],{"className":2423},[28],[30,2425,2426],{"xmlns":32,"display":33},[35,2427,2428,2444],{},[38,2429,2430,2432,2434,2436,2438,2440,2442],{},[187,2431,757],{},[191,2433,193],{},[191,2435,841],{"stretchy":48},[187,2437,793],{},[191,2439,202],{"separator":53},[187,2441,793],{},[191,2443,850],{"stretchy":48},[59,2445,2446],{"encoding":61},"e=(v,v)",[17,2448,2450,2468],{"className":2449,"ariaHidden":53},[66],[17,2451,2453,2456,2459,2462,2465],{"className":2452},[70],[17,2454],{"className":2455,"style":769},[74],[17,2457,757],{"className":2458},[79,230],[17,2460],{"className":2461,"style":235},[234],[17,2463,193],{"className":2464},[239],[17,2466],{"className":2467,"style":235},[234],[17,2469,2471,2474,2477,2480,2483,2486,2489],{"className":2470},[70],[17,2472],{"className":2473,"style":249},[74],[17,2475,841],{"className":2476},[253],[17,2478,793],{"className":2479,"style":818},[79,230],[17,2481,202],{"className":2482},[261],[17,2484],{"className":2485,"style":265},[234],[17,2487,793],{"className":2488,"style":818},[79,230],[17,2490,850],{"className":2491},[282],[13,2493,2494],{},"画图时就是顶点上绕一圈的边。",[506,2496],{},[513,2498,2500],{"id":2499},"_7-重边","7. 重边",[13,2502,2503,2504,720],{},"如果两个顶点之间有多条边相连，这些边叫",[645,2505,2506],{},"重边",[13,2508,952],{},[17,2510,2512],{"className":2511},[20],[17,2513,2515,2567],{"className":2514},[24],[17,2516,2518],{"className":2517},[28],[30,2519,2520],{"xmlns":32,"display":33},[35,2521,2522,2564],{},[38,2523,2524,2530,2532,2534,2536,2538,2540,2542,2544,2546,2552,2554,2556,2558,2560,2562],{},[1385,2525,2526,2528],{},[187,2527,757],{},[1390,2529,1392],{},[191,2531,193],{},[191,2533,841],{"stretchy":48},[187,2535,788],{},[191,2537,202],{"separator":53},[187,2539,793],{},[191,2541,850],{"stretchy":48},[191,2543,202],{"separator":53},[234,2545],{"width":2053},[1385,2547,2548,2550],{},[187,2549,757],{},[1390,2551,1401],{},[191,2553,193],{},[191,2555,841],{"stretchy":48},[187,2557,788],{},[191,2559,202],{"separator":53},[187,2561,793],{},[191,2563,850],{"stretchy":48},[59,2565,2566],{"encoding":61},"e_1=(u,v),\\quad e_2=(u,v)",[17,2568,2570,2625,2707],{"className":2569,"ariaHidden":53},[66],[17,2571,2573,2576,2616,2619,2622],{"className":2572},[70],[17,2574],{"className":2575,"style":2085},[74],[17,2577,2579,2582],{"className":2578},[79],[17,2580,757],{"className":2581},[79,230],[17,2583,2585],{"className":2584},[1453],[17,2586,2588,2608],{"className":2587},[83,84],[17,2589,2591,2605],{"className":2590},[88],[17,2592,2594],{"className":2593,"style":1463},[92],[17,2595,2596,2599],{"style":2106},[17,2597],{"className":2598,"style":1470},[100],[17,2600,2602],{"className":2601},[1474,1475,1476,1477],[17,2603,1392],{"className":2604},[79,1477],[17,2606,136],{"className":2607},[135],[17,2609,2611],{"className":2610},[88],[17,2612,2614],{"className":2613,"style":1490},[92],[17,2615],{},[17,2617],{"className":2618,"style":235},[234],[17,2620,193],{"className":2621},[239],[17,2623],{"className":2624,"style":235},[234],[17,2626,2628,2631,2634,2637,2640,2643,2646,2649,2652,2655,2658,2698,2701,2704],{"className":2627},[70],[17,2629],{"className":2630,"style":249},[74],[17,2632,841],{"className":2633},[253],[17,2635,788],{"className":2636},[79,230],[17,2638,202],{"className":2639},[261],[17,2641],{"className":2642,"style":265},[234],[17,2644,793],{"className":2645,"style":818},[79,230],[17,2647,850],{"className":2648},[282],[17,2650,202],{"className":2651},[261],[17,2653],{"className":2654,"style":2166},[234],[17,2656],{"className":2657,"style":265},[234],[17,2659,2661,2664],{"className":2660},[79],[17,2662,757],{"className":2663},[79,230],[17,2665,2667],{"className":2666},[1453],[17,2668,2670,2690],{"className":2669},[83,84],[17,2671,2673,2687],{"className":2672},[88],[17,2674,2676],{"className":2675,"style":1463},[92],[17,2677,2678,2681],{"style":2106},[17,2679],{"className":2680,"style":1470},[100],[17,2682,2684],{"className":2683},[1474,1475,1476,1477],[17,2685,1401],{"className":2686},[79,1477],[17,2688,136],{"className":2689},[135],[17,2691,2693],{"className":2692},[88],[17,2694,2696],{"className":2695,"style":1490},[92],[17,2697],{},[17,2699],{"className":2700,"style":235},[234],[17,2702,193],{"className":2703},[239],[17,2705],{"className":2706,"style":235},[234],[17,2708,2710,2713,2716,2719,2722,2725,2728],{"className":2709},[70],[17,2711],{"className":2712,"style":249},[74],[17,2714,841],{"className":2715},[253],[17,2717,788],{"className":2718},[79,230],[17,2720,202],{"className":2721},[261],[17,2723],{"className":2724,"style":265},[234],[17,2726,793],{"className":2727,"style":818},[79,230],[17,2729,850],{"className":2730},[282],[13,2732,2733,2734,2910],{},"且 ",[17,2735,2737,2765],{"className":2736},[24],[17,2738,2740],{"className":2739},[28],[30,2741,2742],{"xmlns":32},[35,2743,2744,2762],{},[38,2745,2746,2752,2756],{},[1385,2747,2748,2750],{},[187,2749,757],{},[1390,2751,1392],{},[191,2753,2755],{"mathvariant":2754},"normal","≠",[1385,2757,2758,2760],{},[187,2759,757],{},[1390,2761,1401],{},[59,2763,2764],{"encoding":61},"e_1\\neq e_2",[17,2766,2768,2864],{"className":2767,"ariaHidden":53},[66],[17,2769,2771,2775,2815,2818,2861],{"className":2770},[70],[17,2772],{"className":2773,"style":2774},[74],"height:0.8889em;vertical-align:-0.1944em;",[17,2776,2778,2781],{"className":2777},[79],[17,2779,757],{"className":2780},[79,230],[17,2782,2784],{"className":2783},[1453],[17,2785,2787,2807],{"className":2786},[83,84],[17,2788,2790,2804],{"className":2789},[88],[17,2791,2793],{"className":2792,"style":1463},[92],[17,2794,2795,2798],{"style":2106},[17,2796],{"className":2797,"style":1470},[100],[17,2799,2801],{"className":2800},[1474,1475,1476,1477],[17,2802,1392],{"className":2803},[79,1477],[17,2805,136],{"className":2806},[135],[17,2808,2810],{"className":2809},[88],[17,2811,2813],{"className":2812,"style":1490},[92],[17,2814],{},[17,2816],{"className":2817,"style":235},[234],[17,2819,2821,2854,2858],{"className":2820},[239],[17,2822,2824],{"className":2823},[239],[17,2825,2828],{"className":2826},[79,2827],"vbox",[17,2829,2832],{"className":2830},[2831],"thinbox",[17,2833,2836,2839,2850],{"className":2834},[2835],"rlap",[17,2837],{"className":2838,"style":2774},[74],[17,2840,2843],{"className":2841},[2842],"inner",[17,2844,2846],{"className":2845},[79],[17,2847,2849],{"className":2848},[239],"",[17,2851],{"className":2852},[2853],"fix",[17,2855],{"className":2856},[234,2857],"nobreak",[17,2859,193],{"className":2860},[239],[17,2862],{"className":2863,"style":235},[234],[17,2865,2867,2870],{"className":2866},[70],[17,2868],{"className":2869,"style":2085},[74],[17,2871,2873,2876],{"className":2872},[79],[17,2874,757],{"className":2875},[79,230],[17,2877,2879],{"className":2878},[1453],[17,2880,2882,2902],{"className":2881},[83,84],[17,2883,2885,2899],{"className":2884},[88],[17,2886,2888],{"className":2887,"style":1463},[92],[17,2889,2890,2893],{"style":2106},[17,2891],{"className":2892,"style":1470},[100],[17,2894,2896],{"className":2895},[1474,1475,1476,1477],[17,2897,1401],{"className":2898},[79,1477],[17,2900,136],{"className":2901},[135],[17,2903,2905],{"className":2904},[88],[17,2906,2908],{"className":2907,"style":1490},[92],[17,2909],{},"，它们就是重边。",[506,2912],{},[513,2914,2916],{"id":2915},"_8-孤立点","8. 孤立点",[13,2918,2919,2920,720],{},"如果某个顶点没有任何边与它关联，则称它是",[645,2921,2922],{},"孤立点",[13,2924,2925],{},"孤立点的度为 0。",[506,2927],{},[10,2929,2931],{"id":2930},"四图的分类","四、图的分类",[513,2933,2935],{"id":2934},"_1-零图","1. 零图",[13,2937,2938,2939,720],{},"只含一些孤立点、没有边的图，叫",[645,2940,2941],{},"零图",[13,2943,2944],{},"也就是：",[17,2946,2948],{"className":2947},[20],[17,2949,2951,2970],{"className":2950},[24],[17,2952,2954],{"className":2953},[28],[30,2955,2956],{"xmlns":32,"display":33},[35,2957,2958,2967],{},[38,2959,2960,2962,2964],{},[187,2961,205],{},[191,2963,193],{},[187,2965,2966],{"mathvariant":2754},"∅",[59,2968,2969],{"encoding":61},"E=\\varnothing",[17,2971,2973,2991],{"className":2972,"ariaHidden":53},[66],[17,2974,2976,2979,2982,2985,2988],{"className":2975},[70],[17,2977],{"className":2978,"style":226},[74],[17,2980,205],{"className":2981,"style":269},[79,230],[17,2983],{"className":2984,"style":235},[234],[17,2986,193],{"className":2987},[239],[17,2989],{"className":2990,"style":235},[234],[17,2992,2994,2998],{"className":2993},[70],[17,2995],{"className":2996,"style":2997},[74],"height:0.6633em;vertical-align:-0.0817em;",[17,2999,2966],{"className":3000},[79,3001],"amsrm",[506,3003],{},[513,3005,3007],{"id":3006},"_2-平凡图","2. 平凡图",[13,3009,3010,3011,720],{},"只有一个孤立顶点的图，叫",[645,3012,3013],{},"平凡图",[506,3015],{},[513,3017,3019],{"id":3018},"_3-多重图","3. 多重图",[13,3021,3022,3023,720],{},"含有重边的图叫",[645,3024,3025],{},"多重图",[13,3027,3028],{},"教材里含重边的图称为多重边图。",[506,3030],{},[513,3032,3034],{"id":3033},"_4-简单图","4. 简单图",[13,3036,3037,3038,720],{},"不含自环，也不含重边的图，叫",[645,3039,3040],{},"简单图",[17,3042,3044],{"className":3043},[20],[17,3045,3047,3070],{"className":3046},[24],[17,3048,3050],{"className":3049},[28],[30,3051,3052],{"xmlns":32,"display":33},[35,3053,3054,3067],{},[38,3055,3056],{},[41,3057,3058],{"notation":43},[45,3059,3060],{"scriptlevel":47,"displaystyle":48},[45,3061,3062],{"scriptlevel":47,"displaystyle":48},[45,3063,3064],{"scriptlevel":47,"displaystyle":53},[55,3065,3066],{},"简单图 = 无自环 + 无重边",[59,3068,3069],{"encoding":61},"\\boxed{\\text{简单图 = 无自环 + 无重边}}",[17,3071,3073],{"className":3072,"ariaHidden":53},[66],[17,3074,3076,3080],{"className":3075},[70],[17,3077],{"className":3078,"style":3079},[74],"height:1.4467em;vertical-align:-0.4233em;",[17,3081,3083],{"className":3082},[79],[17,3084,3086,3142],{"className":3085},[83,84],[17,3087,3089,3139],{"className":3088},[88],[17,3090,3092,3130],{"className":3091,"style":93},[92],[17,3093,3095,3099],{"style":3094},"top:-3.4467em;",[17,3096],{"className":3097,"style":3098},[100],"height:3.4467em;",[17,3100,3102],{"className":3101},[105],[17,3103,3105],{"className":3104},[79],[17,3106,3108],{"className":3107},[79],[17,3109,3111,3114,3118,3122,3126],{"className":3110},[79,115],[17,3112,3040],{"className":3113},[79,119],[17,3115,3117],{"className":3116},[79]," = ",[17,3119,3121],{"className":3120},[79,119],"无自环",[17,3123,3125],{"className":3124},[79]," + ",[17,3127,3129],{"className":3128},[79,119],"无重边",[17,3131,3132,3135],{"style":122},[17,3133],{"className":3134,"style":3098},[100],[17,3136],{"className":3137,"style":3138},[129,130],"height:1.4467em;border-style:solid;border-width:0.04em;",[17,3140,136],{"className":3141},[135],[17,3143,3145],{"className":3144},[88],[17,3146,3149],{"className":3147,"style":3148},[92],"height:0.4233em;",[17,3150],{},[13,3152,3153],{},"这是后面讨论很多定理时最常用的图。",[506,3155],{},[513,3157,3159],{"id":3158},"_5-完全图","5. 完全图",[13,3161,3162,3163,720],{},"如果一个简单图中任意两个不同顶点之间都有边相连，则叫",[645,3164,3165],{},"完全图",[13,3167,3168,3169,3198],{},"含 ",[17,3170,3172,3186],{"className":3171},[24],[17,3173,3175],{"className":3174},[28],[30,3176,3177],{"xmlns":32},[35,3178,3179,3184],{},[38,3180,3181],{},[187,3182,3183],{},"n",[59,3185,3183],{"encoding":61},[17,3187,3189],{"className":3188,"ariaHidden":53},[66],[17,3190,3192,3195],{"className":3191},[70],[17,3193],{"className":3194,"style":769},[74],[17,3196,3183],{"className":3197},[79,230]," 个顶点的无向完全图记作：",[17,3200,3202],{"className":3201},[20],[17,3203,3205,3224],{"className":3204},[24],[17,3206,3208],{"className":3207},[28],[30,3209,3210],{"xmlns":32,"display":33},[35,3211,3212,3221],{},[38,3213,3214],{},[1385,3215,3216,3219],{},[187,3217,3218],{},"K",[187,3220,3183],{},[59,3222,3223],{"encoding":61},"K_n",[17,3225,3227],{"className":3226,"ariaHidden":53},[66],[17,3228,3230,3234],{"className":3229},[70],[17,3231],{"className":3232,"style":3233},[74],"height:0.8333em;vertical-align:-0.15em;",[17,3235,3237,3241],{"className":3236},[79],[17,3238,3218],{"className":3239,"style":3240},[79,230],"margin-right:0.0715em;",[17,3242,3244],{"className":3243},[1453],[17,3245,3247,3269],{"className":3246},[83,84],[17,3248,3250,3266],{"className":3249},[88],[17,3251,3254],{"className":3252,"style":3253},[92],"height:0.1514em;",[17,3255,3257,3260],{"style":3256},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[17,3258],{"className":3259,"style":1470},[100],[17,3261,3263],{"className":3262},[1474,1475,1476,1477],[17,3264,3183],{"className":3265},[79,230,1477],[17,3267,136],{"className":3268},[135],[17,3270,3272],{"className":3271},[88],[17,3273,3275],{"className":3274,"style":1490},[92],[17,3276],{},[13,3278,3279],{},"无向完全图的边数是：",[17,3281,3283],{"className":3282},[20],[17,3284,3286,3325],{"className":3285},[24],[17,3287,3289],{"className":3288},[28],[30,3290,3291],{"xmlns":32,"display":33},[35,3292,3293,3322],{},[38,3294,3295],{},[41,3296,3297],{"notation":43},[45,3298,3299],{"scriptlevel":47,"displaystyle":48},[45,3300,3301],{"scriptlevel":47,"displaystyle":48},[45,3302,3303],{"scriptlevel":47,"displaystyle":53},[3304,3305,3306,3320],"mfrac",{},[38,3307,3308,3310,3312,3314,3316,3318],{},[187,3309,3183],{},[191,3311,841],{"stretchy":48},[187,3313,3183],{},[191,3315,972],{},[1390,3317,1392],{},[191,3319,850],{"stretchy":48},[1390,3321,1401],{},[59,3323,3324],{"encoding":61},"\\boxed{\\frac{n(n-1)}{2}}",[17,3326,3328],{"className":3327,"ariaHidden":53},[66],[17,3329,3331,3335],{"className":3330},[70],[17,3332],{"className":3333,"style":3334},[74],"height:2.793em;vertical-align:-1.026em;",[17,3336,3338],{"className":3337},[79],[17,3339,3341,3469],{"className":3340},[83,84],[17,3342,3344,3466],{"className":3343},[88],[17,3345,3348,3456],{"className":3346,"style":3347},[92],"height:1.767em;",[17,3349,3351,3355],{"style":3350},"top:-4.793em;",[17,3352],{"className":3353,"style":3354},[100],"height:4.793em;",[17,3356,3358],{"className":3357},[105],[17,3359,3361],{"className":3360},[79],[17,3362,3364],{"className":3363},[79],[17,3365,3367,3371,3453],{"className":3366},[79],[17,3368],{"className":3369},[253,3370],"nulldelimiter",[17,3372,3374],{"className":3373},[3304],[17,3375,3377,3444],{"className":3376},[83,84],[17,3378,3380,3441],{"className":3379},[88],[17,3381,3384,3397,3408],{"className":3382,"style":3383},[92],"height:1.427em;",[17,3385,3387,3391],{"style":3386},"top:-2.314em;",[17,3388],{"className":3389,"style":3390},[100],"height:3em;",[17,3392,3394],{"className":3393},[79],[17,3395,1401],{"className":3396},[79],[17,3398,3400,3403],{"style":3399},"top:-3.23em;",[17,3401],{"className":3402,"style":3390},[100],[17,3404],{"className":3405,"style":3407},[3406],"frac-line","border-bottom-width:0.04em;",[17,3409,3411,3414],{"style":3410},"top:-3.677em;",[17,3412],{"className":3413,"style":3390},[100],[17,3415,3417,3420,3423,3426,3429,3432,3435,3438],{"className":3416},[79],[17,3418,3183],{"className":3419},[79,230],[17,3421,841],{"className":3422},[253],[17,3424,3183],{"className":3425},[79,230],[17,3427],{"className":3428,"style":257},[234],[17,3430,972],{"className":3431},[997],[17,3433],{"className":3434,"style":257},[234],[17,3436,1392],{"className":3437},[79],[17,3439,850],{"className":3440},[282],[17,3442,136],{"className":3443},[135],[17,3445,3447],{"className":3446},[88],[17,3448,3451],{"className":3449,"style":3450},[92],"height:0.686em;",[17,3452],{},[17,3454],{"className":3455},[282,3370],[17,3457,3459,3462],{"style":3458},"top:-3.767em;",[17,3460],{"className":3461,"style":3354},[100],[17,3463],{"className":3464,"style":3465},[129,130],"height:2.793em;border-style:solid;border-width:0.04em;",[17,3467,136],{"className":3468},[135],[17,3470,3472],{"className":3471},[88],[17,3473,3476],{"className":3474,"style":3475},[92],"height:1.026em;",[17,3477],{},[13,3479,3480,3481,3509],{},"因为 ",[17,3482,3484,3497],{"className":3483},[24],[17,3485,3487],{"className":3486},[28],[30,3488,3489],{"xmlns":32},[35,3490,3491,3495],{},[38,3492,3493],{},[187,3494,3183],{},[59,3496,3183],{"encoding":61},[17,3498,3500],{"className":3499,"ariaHidden":53},[66],[17,3501,3503,3506],{"className":3502},[70],[17,3504],{"className":3505,"style":769},[74],[17,3507,3183],{"className":3508},[79,230]," 个顶点中任意选两个顶点连一条边：",[17,3511,3513],{"className":3512},[20],[17,3514,3516,3558],{"className":3515},[24],[17,3517,3519],{"className":3518},[28],[30,3520,3521],{"xmlns":32,"display":33},[35,3522,3523,3555],{},[38,3524,3525,3535,3537],{},[3526,3527,3528,3531,3533],"msubsup",{},[187,3529,3530],{},"C",[187,3532,3183],{},[1390,3534,1401],{},[191,3536,193],{},[3304,3538,3539,3553],{},[38,3540,3541,3543,3545,3547,3549,3551],{},[187,3542,3183],{},[191,3544,841],{"stretchy":48},[187,3546,3183],{},[191,3548,972],{},[1390,3550,1392],{},[191,3552,850],{"stretchy":48},[1390,3554,1401],{},[59,3556,3557],{"encoding":61},"C_n^2=\\frac{n(n-1)}{2}",[17,3559,3561,3632],{"className":3560,"ariaHidden":53},[66],[17,3562,3564,3568,3623,3626,3629],{"className":3563},[70],[17,3565],{"className":3566,"style":3567},[74],"height:1.1111em;vertical-align:-0.247em;",[17,3569,3571,3574],{"className":3570},[79],[17,3572,3530],{"className":3573,"style":3240},[79,230],[17,3575,3577],{"className":3576},[1453],[17,3578,3580,3614],{"className":3579},[83,84],[17,3581,3583,3611],{"className":3582},[88],[17,3584,3587,3599],{"className":3585,"style":3586},[92],"height:0.8641em;",[17,3588,3590,3593],{"style":3589},"top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;",[17,3591],{"className":3592,"style":1470},[100],[17,3594,3596],{"className":3595},[1474,1475,1476,1477],[17,3597,3183],{"className":3598},[79,230,1477],[17,3600,3602,3605],{"style":3601},"top:-3.113em;margin-right:0.05em;",[17,3603],{"className":3604,"style":1470},[100],[17,3606,3608],{"className":3607},[1474,1475,1476,1477],[17,3609,1401],{"className":3610},[79,1477],[17,3612,136],{"className":3613},[135],[17,3615,3617],{"className":3616},[88],[17,3618,3621],{"className":3619,"style":3620},[92],"height:0.247em;",[17,3622],{},[17,3624],{"className":3625,"style":235},[234],[17,3627,193],{"className":3628},[239],[17,3630],{"className":3631,"style":235},[234],[17,3633,3635,3639],{"className":3634},[70],[17,3636],{"className":3637,"style":3638},[74],"height:2.113em;vertical-align:-0.686em;",[17,3640,3642,3645,3719],{"className":3641},[79],[17,3643],{"className":3644},[253,3370],[17,3646,3648],{"className":3647},[3304],[17,3649,3651,3711],{"className":3650},[83,84],[17,3652,3654,3708],{"className":3653},[88],[17,3655,3657,3668,3676],{"className":3656,"style":3383},[92],[17,3658,3659,3662],{"style":3386},[17,3660],{"className":3661,"style":3390},[100],[17,3663,3665],{"className":3664},[79],[17,3666,1401],{"className":3667},[79],[17,3669,3670,3673],{"style":3399},[17,3671],{"className":3672,"style":3390},[100],[17,3674],{"className":3675,"style":3407},[3406],[17,3677,3678,3681],{"style":3410},[17,3679],{"className":3680,"style":3390},[100],[17,3682,3684,3687,3690,3693,3696,3699,3702,3705],{"className":3683},[79],[17,3685,3183],{"className":3686},[79,230],[17,3688,841],{"className":3689},[253],[17,3691,3183],{"className":3692},[79,230],[17,3694],{"className":3695,"style":257},[234],[17,3697,972],{"className":3698},[997],[17,3700],{"className":3701,"style":257},[234],[17,3703,1392],{"className":3704},[79],[17,3706,850],{"className":3707},[282],[17,3709,136],{"className":3710},[135],[17,3712,3714],{"className":3713},[88],[17,3715,3717],{"className":3716,"style":3450},[92],[17,3718],{},[17,3720],{"className":3721},[282,3370],[13,3723,3724],{},"如果是有向完全图，每一对不同顶点之间有两个相反方向的有向边，则边数是：",[17,3726,3728],{"className":3727},[20],[17,3729,3731,3765],{"className":3730},[24],[17,3732,3734],{"className":3733},[28],[30,3735,3736],{"xmlns":32,"display":33},[35,3737,3738,3762],{},[38,3739,3740],{},[41,3741,3742],{"notation":43},[45,3743,3744],{"scriptlevel":47,"displaystyle":48},[45,3745,3746],{"scriptlevel":47,"displaystyle":48},[45,3747,3748],{"scriptlevel":47,"displaystyle":53},[38,3749,3750,3752,3754,3756,3758,3760],{},[187,3751,3183],{},[191,3753,841],{"stretchy":48},[187,3755,3183],{},[191,3757,972],{},[1390,3759,1392],{},[191,3761,850],{"stretchy":48},[59,3763,3764],{"encoding":61},"\\boxed{n(n-1)}",[17,3766,3768],{"className":3767,"ariaHidden":53},[66],[17,3769,3771,3775],{"className":3770},[70],[17,3772],{"className":3773,"style":3774},[74],"height:1.68em;vertical-align:-0.59em;",[17,3776,3778],{"className":3777},[79],[17,3779,3781,3841],{"className":3780},[83,84],[17,3782,3784,3838],{"className":3783},[88],[17,3785,3788,3828],{"className":3786,"style":3787},[92],"height:1.09em;",[17,3789,3791,3795],{"style":3790},"top:-3.68em;",[17,3792],{"className":3793,"style":3794},[100],"height:3.68em;",[17,3796,3798],{"className":3797},[105],[17,3799,3801],{"className":3800},[79],[17,3802,3804,3807,3810,3813,3816,3819,3822,3825],{"className":3803},[79],[17,3805,3183],{"className":3806},[79,230],[17,3808,841],{"className":3809},[253],[17,3811,3183],{"className":3812},[79,230],[17,3814],{"className":3815,"style":257},[234],[17,3817,972],{"className":3818},[997],[17,3820],{"className":3821,"style":257},[234],[17,3823,1392],{"className":3824},[79],[17,3826,850],{"className":3827},[282],[17,3829,3831,3834],{"style":3830},"top:-3.09em;",[17,3832],{"className":3833,"style":3794},[100],[17,3835],{"className":3836,"style":3837},[129,130],"height:1.68em;border-style:solid;border-width:0.04em;",[17,3839,136],{"className":3840},[135],[17,3842,3844],{"className":3843},[88],[17,3845,3848],{"className":3846,"style":3847},[92],"height:0.59em;",[17,3849],{},[506,3851],{},[10,3853,3855],{"id":3854},"五顶点的度","五、顶点的度",[513,3857,3859],{"id":3858},"_1-无向图中的度","1. 无向图中的度",[13,3861,3862,3863,3891,3892,1140],{},"在无向图中，一个顶点 ",[17,3864,3866,3879],{"className":3865},[24],[17,3867,3869],{"className":3868},[28],[30,3870,3871],{"xmlns":32},[35,3872,3873,3877],{},[38,3874,3875],{},[187,3876,793],{},[59,3878,793],{"encoding":61},[17,3880,3882],{"className":3881,"ariaHidden":53},[66],[17,3883,3885,3888],{"className":3884},[70],[17,3886],{"className":3887,"style":769},[74],[17,3889,793],{"className":3890,"style":818},[79,230]," 的",[645,3893,3894],{},"度",[17,3896,3898],{"className":3897},[20],[17,3899,3901,3922],{"className":3900},[24],[17,3902,3904],{"className":3903},[28],[30,3905,3906],{"xmlns":32,"display":33},[35,3907,3908,3919],{},[38,3909,3910,3913,3915,3917],{},[187,3911,3912],{},"d",[191,3914,841],{"stretchy":48},[187,3916,793],{},[191,3918,850],{"stretchy":48},[59,3920,3921],{"encoding":61},"d(v)",[17,3923,3925],{"className":3924,"ariaHidden":53},[66],[17,3926,3928,3931,3934,3937,3940],{"className":3927},[70],[17,3929],{"className":3930,"style":249},[74],[17,3932,3912],{"className":3933},[79,230],[17,3935,841],{"className":3936},[253],[17,3938,793],{"className":3939,"style":818},[79,230],[17,3941,850],{"className":3942},[282],[13,3944,3945,3946,3974],{},"表示与 ",[17,3947,3949,3962],{"className":3948},[24],[17,3950,3952],{"className":3951},[28],[30,3953,3954],{"xmlns":32},[35,3955,3956,3960],{},[38,3957,3958],{},[187,3959,793],{},[59,3961,793],{"encoding":61},[17,3963,3965],{"className":3964,"ariaHidden":53},[66],[17,3966,3968,3971],{"className":3967},[70],[17,3969],{"className":3970,"style":769},[74],[17,3972,793],{"className":3973,"style":818},[79,230]," 关联的边数。",[13,3976,3977],{},"注意：",[17,3979,3981],{"className":3980},[20],[17,3982,3984,4011],{"className":3983},[24],[17,3985,3987],{"className":3986},[28],[30,3988,3989],{"xmlns":32,"display":33},[35,3990,3991,4008],{},[38,3992,3993],{},[41,3994,3995],{"notation":43},[45,3996,3997],{"scriptlevel":47,"displaystyle":48},[45,3998,3999],{"scriptlevel":47,"displaystyle":48},[45,4000,4001],{"scriptlevel":47,"displaystyle":53},[38,4002,4003,4006],{},[55,4004,4005],{},"自环对度的贡献是 ",[1390,4007,1401],{},[59,4009,4010],{"encoding":61},"\\boxed{\\text{自环对度的贡献是 }2}",[17,4012,4014],{"className":4013,"ariaHidden":53},[66],[17,4015,4017,4020],{"className":4016},[70],[17,4018],{"className":4019,"style":75},[74],[17,4021,4023],{"className":4022},[79],[17,4024,4026,4071],{"className":4025},[83,84],[17,4027,4029,4068],{"className":4028},[88],[17,4030,4032,4060],{"className":4031,"style":93},[92],[17,4033,4034,4037],{"style":96},[17,4035],{"className":4036,"style":101},[100],[17,4038,4040],{"className":4039},[105],[17,4041,4043],{"className":4042},[79],[17,4044,4046,4057],{"className":4045},[79],[17,4047,4049,4053],{"className":4048},[79,115],[17,4050,4052],{"className":4051},[79,119],"自环对度的贡献是",[17,4054,4056],{"className":4055},[79]," ",[17,4058,1401],{"className":4059},[79],[17,4061,4062,4065],{"style":122},[17,4063],{"className":4064,"style":101},[100],[17,4066],{"className":4067,"style":131},[129,130],[17,4069,136],{"className":4070},[135],[17,4072,4074],{"className":4073},[88],[17,4075,4077],{"className":4076,"style":143},[92],[17,4078],{},[13,4080,4081],{},"因为自环的两个端点都在同一个顶点上。",[506,4083],{},[513,4085,4087],{"id":4086},"_2-有向图中的出度和入度","2. 有向图中的出度和入度",[13,4089,4090],{},"在有向图中：",[4092,4093,4094],"h3",{"id":4094},"出度",[13,4096,4097,4098,4126],{},"从顶点 ",[17,4099,4101,4114],{"className":4100},[24],[17,4102,4104],{"className":4103},[28],[30,4105,4106],{"xmlns":32},[35,4107,4108,4112],{},[38,4109,4110],{},[187,4111,793],{},[59,4113,793],{"encoding":61},[17,4115,4117],{"className":4116,"ariaHidden":53},[66],[17,4118,4120,4123],{"className":4119},[70],[17,4121],{"className":4122,"style":769},[74],[17,4124,793],{"className":4125,"style":818},[79,230]," 发出的边数叫出度，记作：",[17,4128,4130],{"className":4129},[20],[17,4131,4133,4159],{"className":4132},[24],[17,4134,4136],{"className":4135},[28],[30,4137,4138],{"xmlns":32,"display":33},[35,4139,4140,4156],{},[38,4141,4142,4150,4152,4154],{},[4143,4144,4145,4147],"msup",{},[187,4146,3912],{},[191,4148,4149],{},"+",[191,4151,841],{"stretchy":48},[187,4153,793],{},[191,4155,850],{"stretchy":48},[59,4157,4158],{"encoding":61},"d^+(v)",[17,4160,4162],{"className":4161,"ariaHidden":53},[66],[17,4163,4165,4169,4199,4202,4205],{"className":4164},[70],[17,4166],{"className":4167,"style":4168},[74],"height:1.0713em;vertical-align:-0.25em;",[17,4170,4172,4175],{"className":4171},[79],[17,4173,3912],{"className":4174},[79,230],[17,4176,4178],{"className":4177},[1453],[17,4179,4181],{"className":4180},[83],[17,4182,4184],{"className":4183},[88],[17,4185,4188],{"className":4186,"style":4187},[92],"height:0.8213em;",[17,4189,4190,4193],{"style":3601},[17,4191],{"className":4192,"style":1470},[100],[17,4194,4196],{"className":4195},[1474,1475,1476,1477],[17,4197,4149],{"className":4198},[997,1477],[17,4200,841],{"className":4201},[253],[17,4203,793],{"className":4204,"style":818},[79,230],[17,4206,850],{"className":4207},[282],[4092,4209,4210],{"id":4210},"入度",[13,4212,4213,4214,4242],{},"进入顶点 ",[17,4215,4217,4230],{"className":4216},[24],[17,4218,4220],{"className":4219},[28],[30,4221,4222],{"xmlns":32},[35,4223,4224,4228],{},[38,4225,4226],{},[187,4227,793],{},[59,4229,793],{"encoding":61},[17,4231,4233],{"className":4232,"ariaHidden":53},[66],[17,4234,4236,4239],{"className":4235},[70],[17,4237],{"className":4238,"style":769},[74],[17,4240,793],{"className":4241,"style":818},[79,230]," 的边数叫入度，记作：",[17,4244,4246],{"className":4245},[20],[17,4247,4249,4273],{"className":4248},[24],[17,4250,4252],{"className":4251},[28],[30,4253,4254],{"xmlns":32,"display":33},[35,4255,4256,4270],{},[38,4257,4258,4264,4266,4268],{},[4143,4259,4260,4262],{},[187,4261,3912],{},[191,4263,972],{},[191,4265,841],{"stretchy":48},[187,4267,793],{},[191,4269,850],{"stretchy":48},[59,4271,4272],{"encoding":61},"d^-(v)",[17,4274,4276],{"className":4275,"ariaHidden":53},[66],[17,4277,4279,4282,4311,4314,4317],{"className":4278},[70],[17,4280],{"className":4281,"style":4168},[74],[17,4283,4285,4288],{"className":4284},[79],[17,4286,3912],{"className":4287},[79,230],[17,4289,4291],{"className":4290},[1453],[17,4292,4294],{"className":4293},[83],[17,4295,4297],{"className":4296},[88],[17,4298,4300],{"className":4299,"style":4187},[92],[17,4301,4302,4305],{"style":3601},[17,4303],{"className":4304,"style":1470},[100],[17,4306,4308],{"className":4307},[1474,1475,1476,1477],[17,4309,972],{"className":4310},[997,1477],[17,4312,841],{"className":4313},[253],[17,4315,793],{"className":4316,"style":818},[79,230],[17,4318,850],{"className":4319},[282],[4092,4321,4322],{"id":4322},"总度",[17,4324,4326],{"className":4325},[20],[17,4327,4329,4377],{"className":4328},[24],[17,4330,4332],{"className":4331},[28],[30,4333,4334],{"xmlns":32,"display":33},[35,4335,4336,4374],{},[38,4337,4338,4340,4342,4344,4346,4348,4354,4356,4358,4360,4362,4368,4370,4372],{},[187,4339,3912],{},[191,4341,841],{"stretchy":48},[187,4343,793],{},[191,4345,850],{"stretchy":48},[191,4347,193],{},[4143,4349,4350,4352],{},[187,4351,3912],{},[191,4353,4149],{},[191,4355,841],{"stretchy":48},[187,4357,793],{},[191,4359,850],{"stretchy":48},[191,4361,4149],{},[4143,4363,4364,4366],{},[187,4365,3912],{},[191,4367,972],{},[191,4369,841],{"stretchy":48},[187,4371,793],{},[191,4373,850],{"stretchy":48},[59,4375,4376],{"encoding":61},"d(v)=d^+(v)+d^-(v)",[17,4378,4380,4407,4460],{"className":4379,"ariaHidden":53},[66],[17,4381,4383,4386,4389,4392,4395,4398,4401,4404],{"className":4382},[70],[17,4384],{"className":4385,"style":249},[74],[17,4387,3912],{"className":4388},[79,230],[17,4390,841],{"className":4391},[253],[17,4393,793],{"className":4394,"style":818},[79,230],[17,4396,850],{"className":4397},[282],[17,4399],{"className":4400,"style":235},[234],[17,4402,193],{"className":4403},[239],[17,4405],{"className":4406,"style":235},[234],[17,4408,4410,4413,4442,4445,4448,4451,4454,4457],{"className":4409},[70],[17,4411],{"className":4412,"style":4168},[74],[17,4414,4416,4419],{"className":4415},[79],[17,4417,3912],{"className":4418},[79,230],[17,4420,4422],{"className":4421},[1453],[17,4423,4425],{"className":4424},[83],[17,4426,4428],{"className":4427},[88],[17,4429,4431],{"className":4430,"style":4187},[92],[17,4432,4433,4436],{"style":3601},[17,4434],{"className":4435,"style":1470},[100],[17,4437,4439],{"className":4438},[1474,1475,1476,1477],[17,4440,4149],{"className":4441},[997,1477],[17,4443,841],{"className":4444},[253],[17,4446,793],{"className":4447,"style":818},[79,230],[17,4449,850],{"className":4450},[282],[17,4452],{"className":4453,"style":257},[234],[17,4455,4149],{"className":4456},[997],[17,4458],{"className":4459,"style":257},[234],[17,4461,4463,4466,4495,4498,4501],{"className":4462},[70],[17,4464],{"className":4465,"style":4168},[74],[17,4467,4469,4472],{"className":4468},[79],[17,4470,3912],{"className":4471},[79,230],[17,4473,4475],{"className":4474},[1453],[17,4476,4478],{"className":4477},[83],[17,4479,4481],{"className":4480},[88],[17,4482,4484],{"className":4483,"style":4187},[92],[17,4485,4486,4489],{"style":3601},[17,4487],{"className":4488,"style":1470},[100],[17,4490,4492],{"className":4491},[1474,1475,1476,1477],[17,4493,972],{"className":4494},[997,1477],[17,4496,841],{"className":4497},[253],[17,4499,793],{"className":4500,"style":818},[79,230],[17,4502,850],{"className":4503},[282],[506,4505],{},[513,4507,4509],{"id":4508},"_3-奇顶点和偶顶点","3. 奇顶点和偶顶点",[13,4511,4512],{},"如果：",[17,4514,4516],{"className":4515},[20],[17,4517,4519,4538],{"className":4518},[24],[17,4520,4522],{"className":4521},[28],[30,4523,4524],{"xmlns":32,"display":33},[35,4525,4526,4536],{},[38,4527,4528,4530,4532,4534],{},[187,4529,3912],{},[191,4531,841],{"stretchy":48},[187,4533,793],{},[191,4535,850],{"stretchy":48},[59,4537,3921],{"encoding":61},[17,4539,4541],{"className":4540,"ariaHidden":53},[66],[17,4542,4544,4547,4550,4553,4556],{"className":4543},[70],[17,4545],{"className":4546,"style":249},[74],[17,4548,3912],{"className":4549},[79,230],[17,4551,841],{"className":4552},[253],[17,4554,793],{"className":4555,"style":818},[79,230],[17,4557,850],{"className":4558},[282],[13,4560,4561,4562,4590,4591,720],{},"是奇数，则 ",[17,4563,4565,4578],{"className":4564},[24],[17,4566,4568],{"className":4567},[28],[30,4569,4570],{"xmlns":32},[35,4571,4572,4576],{},[38,4573,4574],{},[187,4575,793],{},[59,4577,793],{"encoding":61},[17,4579,4581],{"className":4580,"ariaHidden":53},[66],[17,4582,4584,4587],{"className":4583},[70],[17,4585],{"className":4586,"style":769},[74],[17,4588,793],{"className":4589,"style":818},[79,230]," 是",[645,4592,4593],{},"奇顶点",[13,4595,4512],{},[17,4597,4599],{"className":4598},[20],[17,4600,4602,4621],{"className":4601},[24],[17,4603,4605],{"className":4604},[28],[30,4606,4607],{"xmlns":32,"display":33},[35,4608,4609,4619],{},[38,4610,4611,4613,4615,4617],{},[187,4612,3912],{},[191,4614,841],{"stretchy":48},[187,4616,793],{},[191,4618,850],{"stretchy":48},[59,4620,3921],{"encoding":61},[17,4622,4624],{"className":4623,"ariaHidden":53},[66],[17,4625,4627,4630,4633,4636,4639],{"className":4626},[70],[17,4628],{"className":4629,"style":249},[74],[17,4631,3912],{"className":4632},[79,230],[17,4634,841],{"className":4635},[253],[17,4637,793],{"className":4638,"style":818},[79,230],[17,4640,850],{"className":4641},[282],[13,4643,4644,4645,4590,4673,720],{},"是偶数，则 ",[17,4646,4648,4661],{"className":4647},[24],[17,4649,4651],{"className":4650},[28],[30,4652,4653],{"xmlns":32},[35,4654,4655,4659],{},[38,4656,4657],{},[187,4658,793],{},[59,4660,793],{"encoding":61},[17,4662,4664],{"className":4663,"ariaHidden":53},[66],[17,4665,4667,4670],{"className":4666},[70],[17,4668],{"className":4669,"style":769},[74],[17,4671,793],{"className":4672,"style":818},[79,230],[645,4674,4675],{},"偶顶点",[506,4677],{},[513,4679,4681],{"id":4680},"_4-正则图","4. 正则图",[13,4683,4684,4685,4716,4717,720],{},"如果无向图中所有顶点的度都等于 ",[17,4686,4688,4702],{"className":4687},[24],[17,4689,4691],{"className":4690},[28],[30,4692,4693],{"xmlns":32},[35,4694,4695,4700],{},[38,4696,4697],{},[187,4698,4699],{},"k",[59,4701,4699],{"encoding":61},[17,4703,4705],{"className":4704,"ariaHidden":53},[66],[17,4706,4708,4712],{"className":4707},[70],[17,4709],{"className":4710,"style":4711},[74],"height:0.6944em;",[17,4713,4699],{"className":4714,"style":4715},[79,230],"margin-right:0.0315em;","，则称它是 ",[645,4718,4719,4747],{},[17,4720,4722,4735],{"className":4721},[24],[17,4723,4725],{"className":4724},[28],[30,4726,4727],{"xmlns":32},[35,4728,4729,4733],{},[38,4730,4731],{},[187,4732,4699],{},[59,4734,4699],{"encoding":61},[17,4736,4738],{"className":4737,"ariaHidden":53},[66],[17,4739,4741,4744],{"className":4740},[70],[17,4742],{"className":4743,"style":4711},[74],[17,4745,4699],{"className":4746,"style":4715},[79,230]," 正则图",[13,4749,952],{},[150,4751,4752,4755],{},[153,4753,4754],{},"所有顶点度都是 2：2 正则图；",[153,4756,4757],{},"所有顶点度都是 3：3 正则图。",[506,4759],{},[10,4761,4763],{"id":4762},"六握手定理","六、握手定理",[13,4765,4766],{},"这是本章最重要公式之一。",[13,4768,4769,4770,4844,4845,4874],{},"设无向图 ",[17,4771,4773,4799],{"className":4772},[24],[17,4774,4776],{"className":4775},[28],[30,4777,4778],{"xmlns":32},[35,4779,4780,4796],{},[38,4781,4782,4784,4786,4788,4790,4792,4794],{},[187,4783,189],{},[191,4785,193],{},[191,4787,196],{"stretchy":48},[187,4789,199],{},[191,4791,202],{"separator":53},[187,4793,205],{},[191,4795,213],{"stretchy":48},[59,4797,4798],{"encoding":61},"G=\\langle V,E\\rangle",[17,4800,4802,4820],{"className":4801,"ariaHidden":53},[66],[17,4803,4805,4808,4811,4814,4817],{"className":4804},[70],[17,4806],{"className":4807,"style":226},[74],[17,4809,189],{"className":4810},[79,230],[17,4812],{"className":4813,"style":235},[234],[17,4815,193],{"className":4816},[239],[17,4818],{"className":4819,"style":235},[234],[17,4821,4823,4826,4829,4832,4835,4838,4841],{"className":4822},[70],[17,4824],{"className":4825,"style":249},[74],[17,4827,196],{"className":4828},[253],[17,4830,199],{"className":4831,"style":257},[79,230],[17,4833,202],{"className":4834},[261],[17,4836],{"className":4837,"style":265},[234],[17,4839,205],{"className":4840,"style":269},[79,230],[17,4842,213],{"className":4843},[282],"，边数为 ",[17,4846,4848,4862],{"className":4847},[24],[17,4849,4851],{"className":4850},[28],[30,4852,4853],{"xmlns":32},[35,4854,4855,4860],{},[38,4856,4857],{},[187,4858,4859],{},"m",[59,4861,4859],{"encoding":61},[17,4863,4865],{"className":4864,"ariaHidden":53},[66],[17,4866,4868,4871],{"className":4867},[70],[17,4869],{"className":4870,"style":769},[74],[17,4872,4859],{"className":4873},[79,230],"，则：",[17,4876,4878],{"className":4877},[20],[17,4879,4881,4931],{"className":4880},[24],[17,4882,4884],{"className":4883},[28],[30,4885,4886],{"xmlns":32,"display":33},[35,4887,4888,4928],{},[38,4889,4890],{},[41,4891,4892],{"notation":43},[45,4893,4894],{"scriptlevel":47,"displaystyle":48},[45,4895,4896],{"scriptlevel":47,"displaystyle":48},[45,4897,4898],{"scriptlevel":47,"displaystyle":53},[38,4899,4900,4914,4916,4918,4920,4922,4924,4926],{},[4901,4902,4903,4906],"munder",{},[191,4904,4905],{},"∑",[38,4907,4908,4910,4912],{},[187,4909,793],{},[191,4911,1891],{},[187,4913,199],{},[187,4915,3912],{},[191,4917,841],{"stretchy":48},[187,4919,793],{},[191,4921,850],{"stretchy":48},[191,4923,193],{},[1390,4925,1401],{},[187,4927,4859],{},[59,4929,4930],{"encoding":61},"\\boxed{\\sum_{v\\in V}d(v)=2m}",[17,4932,4934],{"className":4933,"ariaHidden":53},[66],[17,4935,4937,4941],{"className":4936},[70],[17,4938],{"className":4939,"style":4940},[74],"height:3.0517em;vertical-align:-1.6617em;",[17,4942,4944],{"className":4943},[79],[17,4945,4947,5075],{"className":4946},[83,84],[17,4948,4950,5072],{"className":4949},[88],[17,4951,4954,5062],{"className":4952,"style":4953},[92],"height:1.39em;",[17,4955,4957,4961],{"style":4956},"top:-5.0517em;",[17,4958],{"className":4959,"style":4960},[100],"height:5.0517em;",[17,4962,4964],{"className":4963},[105],[17,4965,4967],{"className":4966},[79],[17,4968,4970,5032,5035,5038,5041,5044,5047,5050,5053,5056,5059],{"className":4969},[79],[17,4971,4975],{"className":4972},[4973,4974],"mop","op-limits",[17,4976,4978,5023],{"className":4977},[83,84],[17,4979,4981,5020],{"className":4980},[88],[17,4982,4985,5007],{"className":4983,"style":4984},[92],"height:1.05em;",[17,4986,4988,4992],{"style":4987},"top:-1.8557em;margin-left:0em;",[17,4989],{"className":4990,"style":4991},[100],"height:3.05em;",[17,4993,4995],{"className":4994},[1474,1475,1476,1477],[17,4996,4998,5001,5004],{"className":4997},[79,1477],[17,4999,793],{"className":5000,"style":818},[79,230,1477],[17,5002,1891],{"className":5003},[239,1477],[17,5005,199],{"className":5006,"style":257},[79,230,1477],[17,5008,5010,5013],{"style":5009},"top:-3.05em;",[17,5011],{"className":5012,"style":4991},[100],[17,5014,5015],{},[17,5016,4905],{"className":5017},[4973,5018,5019],"op-symbol","large-op",[17,5021,136],{"className":5022},[135],[17,5024,5026],{"className":5025},[88],[17,5027,5030],{"className":5028,"style":5029},[92],"height:1.3217em;",[17,5031],{},[17,5033],{"className":5034,"style":265},[234],[17,5036,3912],{"className":5037},[79,230],[17,5039,841],{"className":5040},[253],[17,5042,793],{"className":5043,"style":818},[79,230],[17,5045,850],{"className":5046},[282],[17,5048],{"className":5049,"style":235},[234],[17,5051,193],{"className":5052},[239],[17,5054],{"className":5055,"style":235},[234],[17,5057,1401],{"className":5058},[79],[17,5060,4859],{"className":5061},[79,230],[17,5063,5065,5068],{"style":5064},"top:-3.39em;",[17,5066],{"className":5067,"style":4960},[100],[17,5069],{"className":5070,"style":5071},[129,130],"height:3.0517em;border-style:solid;border-width:0.04em;",[17,5073,136],{"className":5074},[135],[17,5076,5078],{"className":5077},[88],[17,5079,5082],{"className":5080,"style":5081},[92],"height:1.6617em;",[17,5083],{},[13,5085,5086],{},"意思是：",[1700,5088,5089],{},[13,5090,5091],{},"所有顶点度数之和 = 边数的 2 倍。",[13,5093,5094],{},"为什么？",[13,5096,5097],{},"因为每条普通边贡献两个端点，自环也贡献 2。",[506,5099],{},[513,5101,5103],{"id":5102},"推论奇度顶点个数一定为偶数","推论：奇度顶点个数一定为偶数",[13,5105,5106],{},"因为：",[17,5108,5110],{"className":5109},[20],[17,5111,5113,5151],{"className":5112},[24],[17,5114,5116],{"className":5115},[28],[30,5117,5118],{"xmlns":32,"display":33},[35,5119,5120,5148],{},[38,5121,5122,5134,5136,5138,5140,5142,5144,5146],{},[4901,5123,5124,5126],{},[191,5125,4905],{},[38,5127,5128,5130,5132],{},[187,5129,793],{},[191,5131,1891],{},[187,5133,199],{},[187,5135,3912],{},[191,5137,841],{"stretchy":48},[187,5139,793],{},[191,5141,850],{"stretchy":48},[191,5143,193],{},[1390,5145,1401],{},[187,5147,4859],{},[59,5149,5150],{"encoding":61},"\\sum_{v\\in V}d(v)=2m",[17,5152,5154,5238],{"className":5153,"ariaHidden":53},[66],[17,5155,5157,5161,5214,5217,5220,5223,5226,5229,5232,5235],{"className":5156},[70],[17,5158],{"className":5159,"style":5160},[74],"height:2.3717em;vertical-align:-1.3217em;",[17,5162,5164],{"className":5163},[4973,4974],[17,5165,5167,5206],{"className":5166},[83,84],[17,5168,5170,5203],{"className":5169},[88],[17,5171,5173,5193],{"className":5172,"style":4984},[92],[17,5174,5175,5178],{"style":4987},[17,5176],{"className":5177,"style":4991},[100],[17,5179,5181],{"className":5180},[1474,1475,1476,1477],[17,5182,5184,5187,5190],{"className":5183},[79,1477],[17,5185,793],{"className":5186,"style":818},[79,230,1477],[17,5188,1891],{"className":5189},[239,1477],[17,5191,199],{"className":5192,"style":257},[79,230,1477],[17,5194,5195,5198],{"style":5009},[17,5196],{"className":5197,"style":4991},[100],[17,5199,5200],{},[17,5201,4905],{"className":5202},[4973,5018,5019],[17,5204,136],{"className":5205},[135],[17,5207,5209],{"className":5208},[88],[17,5210,5212],{"className":5211,"style":5029},[92],[17,5213],{},[17,5215],{"className":5216,"style":265},[234],[17,5218,3912],{"className":5219},[79,230],[17,5221,841],{"className":5222},[253],[17,5224,793],{"className":5225,"style":818},[79,230],[17,5227,850],{"className":5228},[282],[17,5230],{"className":5231,"style":235},[234],[17,5233,193],{"className":5234},[239],[17,5236],{"className":5237,"style":235},[234],[17,5239,5241,5245,5248],{"className":5240},[70],[17,5242],{"className":5243,"style":5244},[74],"height:0.6444em;",[17,5246,1401],{"className":5247},[79],[17,5249,4859],{"className":5250},[79,230],[13,5252,5253],{},"一定是偶数。",[13,5255,5256],{},"偶数度顶点加起来还是偶数，所以奇数度顶点的个数必须是偶数。",[13,5258,5259],{},"结论：",[17,5261,5263],{"className":5262},[20],[17,5264,5266,5289],{"className":5265},[24],[17,5267,5269],{"className":5268},[28],[30,5270,5271],{"xmlns":32,"display":33},[35,5272,5273,5286],{},[38,5274,5275],{},[41,5276,5277],{"notation":43},[45,5278,5279],{"scriptlevel":47,"displaystyle":48},[45,5280,5281],{"scriptlevel":47,"displaystyle":48},[45,5282,5283],{"scriptlevel":47,"displaystyle":53},[55,5284,5285],{},"任意无向图中，奇顶点个数为偶数",[59,5287,5288],{"encoding":61},"\\boxed{\\text{任意无向图中，奇顶点个数为偶数}}",[17,5290,5292],{"className":5291,"ariaHidden":53},[66],[17,5293,5295,5298],{"className":5294},[70],[17,5296],{"className":5297,"style":75},[74],[17,5299,5301],{"className":5300},[79],[17,5302,5304,5341],{"className":5303},[83,84],[17,5305,5307,5338],{"className":5306},[88],[17,5308,5310,5330],{"className":5309,"style":93},[92],[17,5311,5312,5315],{"style":96},[17,5313],{"className":5314,"style":101},[100],[17,5316,5318],{"className":5317},[105],[17,5319,5321],{"className":5320},[79],[17,5322,5324],{"className":5323},[79],[17,5325,5327],{"className":5326},[79,115],[17,5328,5285],{"className":5329},[79,119],[17,5331,5332,5335],{"style":122},[17,5333],{"className":5334,"style":101},[100],[17,5336],{"className":5337,"style":131},[129,130],[17,5339,136],{"className":5340},[135],[17,5342,5344],{"className":5343},[88],[17,5345,5347],{"className":5346,"style":143},[92],[17,5348],{},[13,5350,5351],{},"这条非常常考。",[506,5353],{},[10,5355,5357],{"id":5356},"七子图","七、子图",[13,5359,5360],{},"设：",[17,5362,5364],{"className":5363},[20],[17,5365,5367,5425],{"className":5366},[24],[17,5368,5370],{"className":5369},[28],[30,5371,5372],{"xmlns":32,"display":33},[35,5373,5374,5422],{},[38,5375,5376,5378,5380,5382,5384,5386,5388,5390,5392,5394,5402,5404,5406,5412,5414,5420],{},[187,5377,189],{},[191,5379,193],{},[191,5381,196],{"stretchy":48},[187,5383,199],{},[191,5385,202],{"separator":53},[187,5387,205],{},[191,5389,213],{"stretchy":48},[191,5391,202],{"separator":53},[234,5393],{"width":2053},[4143,5395,5396,5398],{},[187,5397,189],{},[191,5399,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},"0em","′",[191,5403,193],{},[191,5405,196],{"stretchy":48},[4143,5407,5408,5410],{},[187,5409,199],{},[191,5411,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,5413,202],{"separator":53},[4143,5415,5416,5418],{},[187,5417,205],{},[191,5419,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,5421,213],{"stretchy":48},[59,5423,5424],{"encoding":61},"G=\\langle V,E\\rangle,\\quad G'=\\langle V',E'\\rangle",[17,5426,5428,5446,5522],{"className":5427,"ariaHidden":53},[66],[17,5429,5431,5434,5437,5440,5443],{"className":5430},[70],[17,5432],{"className":5433,"style":226},[74],[17,5435,189],{"className":5436},[79,230],[17,5438],{"className":5439,"style":235},[234],[17,5441,193],{"className":5442},[239],[17,5444],{"className":5445,"style":235},[234],[17,5447,5449,5453,5456,5459,5462,5465,5468,5471,5474,5477,5480,5513,5516,5519],{"className":5448},[70],[17,5450],{"className":5451,"style":5452},[74],"height:1.0519em;vertical-align:-0.25em;",[17,5454,196],{"className":5455},[253],[17,5457,199],{"className":5458,"style":257},[79,230],[17,5460,202],{"className":5461},[261],[17,5463],{"className":5464,"style":265},[234],[17,5466,205],{"className":5467,"style":269},[79,230],[17,5469,213],{"className":5470},[282],[17,5472,202],{"className":5473},[261],[17,5475],{"className":5476,"style":2166},[234],[17,5478],{"className":5479,"style":265},[234],[17,5481,5483,5486],{"className":5482},[79],[17,5484,189],{"className":5485},[79,230],[17,5487,5489],{"className":5488},[1453],[17,5490,5492],{"className":5491},[83],[17,5493,5495],{"className":5494},[88],[17,5496,5499],{"className":5497,"style":5498},[92],"height:0.8019em;",[17,5500,5501,5504],{"style":3601},[17,5502],{"className":5503,"style":1470},[100],[17,5505,5507],{"className":5506},[1474,1475,1476,1477],[17,5508,5510],{"className":5509},[79,1477],[17,5511,5401],{"className":5512},[79,1477],[17,5514],{"className":5515,"style":235},[234],[17,5517,193],{"className":5518},[239],[17,5520],{"className":5521,"style":235},[234],[17,5523,5525,5528,5531,5563,5566,5569,5601],{"className":5524},[70],[17,5526],{"className":5527,"style":5452},[74],[17,5529,196],{"className":5530},[253],[17,5532,5534,5537],{"className":5533},[79],[17,5535,199],{"className":5536,"style":257},[79,230],[17,5538,5540],{"className":5539},[1453],[17,5541,5543],{"className":5542},[83],[17,5544,5546],{"className":5545},[88],[17,5547,5549],{"className":5548,"style":5498},[92],[17,5550,5551,5554],{"style":3601},[17,5552],{"className":5553,"style":1470},[100],[17,5555,5557],{"className":5556},[1474,1475,1476,1477],[17,5558,5560],{"className":5559},[79,1477],[17,5561,5401],{"className":5562},[79,1477],[17,5564,202],{"className":5565},[261],[17,5567],{"className":5568,"style":265},[234],[17,5570,5572,5575],{"className":5571},[79],[17,5573,205],{"className":5574,"style":269},[79,230],[17,5576,5578],{"className":5577},[1453],[17,5579,5581],{"className":5580},[83],[17,5582,5584],{"className":5583},[88],[17,5585,5587],{"className":5586,"style":5498},[92],[17,5588,5589,5592],{"style":3601},[17,5590],{"className":5591,"style":1470},[100],[17,5593,5595],{"className":5594},[1474,1475,1476,1477],[17,5596,5598],{"className":5597},[79,1477],[17,5599,5401],{"className":5600},[79,1477],[17,5602,213],{"className":5603},[282],[13,5605,4512],{},[17,5607,5609],{"className":5608},[20],[17,5610,5612,5649],{"className":5611},[24],[17,5613,5615],{"className":5614},[28],[30,5616,5617],{"xmlns":32,"display":33},[35,5618,5619,5646],{},[38,5620,5621,5627,5630,5632,5634,5636,5642,5644],{},[4143,5622,5623,5625],{},[187,5624,199],{},[191,5626,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,5628,5629],{},"⊆",[187,5631,199],{},[191,5633,202],{"separator":53},[234,5635],{"width":2053},[4143,5637,5638,5640],{},[187,5639,205],{},[191,5641,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,5643,5629],{},[187,5645,205],{},[59,5647,5648],{"encoding":61},"V'\\subseteq V,\\quad E'\\subseteq E",[17,5650,5652,5700,5760],{"className":5651,"ariaHidden":53},[66],[17,5653,5655,5659,5691,5694,5697],{"className":5654},[70],[17,5656],{"className":5657,"style":5658},[74],"height:0.9379em;vertical-align:-0.136em;",[17,5660,5662,5665],{"className":5661},[79],[17,5663,199],{"className":5664,"style":257},[79,230],[17,5666,5668],{"className":5667},[1453],[17,5669,5671],{"className":5670},[83],[17,5672,5674],{"className":5673},[88],[17,5675,5677],{"className":5676,"style":5498},[92],[17,5678,5679,5682],{"style":3601},[17,5680],{"className":5681,"style":1470},[100],[17,5683,5685],{"className":5684},[1474,1475,1476,1477],[17,5686,5688],{"className":5687},[79,1477],[17,5689,5401],{"className":5690},[79,1477],[17,5692],{"className":5693,"style":235},[234],[17,5695,5629],{"className":5696},[239],[17,5698],{"className":5699,"style":235},[234],[17,5701,5703,5707,5710,5713,5716,5719,5751,5754,5757],{"className":5702},[70],[17,5704],{"className":5705,"style":5706},[74],"height:0.9963em;vertical-align:-0.1944em;",[17,5708,199],{"className":5709,"style":257},[79,230],[17,5711,202],{"className":5712},[261],[17,5714],{"className":5715,"style":2166},[234],[17,5717],{"className":5718,"style":265},[234],[17,5720,5722,5725],{"className":5721},[79],[17,5723,205],{"className":5724,"style":269},[79,230],[17,5726,5728],{"className":5727},[1453],[17,5729,5731],{"className":5730},[83],[17,5732,5734],{"className":5733},[88],[17,5735,5737],{"className":5736,"style":5498},[92],[17,5738,5739,5742],{"style":3601},[17,5740],{"className":5741,"style":1470},[100],[17,5743,5745],{"className":5744},[1474,1475,1476,1477],[17,5746,5748],{"className":5747},[79,1477],[17,5749,5401],{"className":5750},[79,1477],[17,5752],{"className":5753,"style":235},[234],[17,5755,5629],{"className":5756},[239],[17,5758],{"className":5759,"style":235},[234],[17,5761,5763,5766],{"className":5762},[70],[17,5764],{"className":5765,"style":226},[74],[17,5767,205],{"className":5768,"style":269},[79,230],[13,5770,1944,5771,5835,5836,3891,5864,720],{},[17,5772,5774,5792],{"className":5773},[24],[17,5775,5777],{"className":5776},[28],[30,5778,5779],{"xmlns":32},[35,5780,5781,5789],{},[38,5782,5783],{},[4143,5784,5785,5787],{},[187,5786,189],{},[191,5788,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,5790,5791],{"encoding":61},"G'",[17,5793,5795],{"className":5794,"ariaHidden":53},[66],[17,5796,5798,5802],{"className":5797},[70],[17,5799],{"className":5800,"style":5801},[74],"height:0.7519em;",[17,5803,5805,5808],{"className":5804},[79],[17,5806,189],{"className":5807},[79,230],[17,5809,5811],{"className":5810},[1453],[17,5812,5814],{"className":5813},[83],[17,5815,5817],{"className":5816},[88],[17,5818,5820],{"className":5819,"style":5801},[92],[17,5821,5823,5826],{"style":5822},"top:-3.063em;margin-right:0.05em;",[17,5824],{"className":5825,"style":1470},[100],[17,5827,5829],{"className":5828},[1474,1475,1476,1477],[17,5830,5832],{"className":5831},[79,1477],[17,5833,5401],{"className":5834},[79,1477]," 是 ",[17,5837,5839,5852],{"className":5838},[24],[17,5840,5842],{"className":5841},[28],[30,5843,5844],{"xmlns":32},[35,5845,5846,5850],{},[38,5847,5848],{},[187,5849,189],{},[59,5851,189],{"encoding":61},[17,5853,5855],{"className":5854,"ariaHidden":53},[66],[17,5856,5858,5861],{"className":5857},[70],[17,5859],{"className":5860,"style":226},[74],[17,5862,189],{"className":5863},[79,230],[645,5865,5866],{},"子图",[506,5868],{},[513,5870,5872],{"id":5871},"_1-真子图","1. 真子图",[13,5874,5875,5876,5835,5937,5965],{},"如果 ",[17,5877,5879,5896],{"className":5878},[24],[17,5880,5882],{"className":5881},[28],[30,5883,5884],{"xmlns":32},[35,5885,5886,5894],{},[38,5887,5888],{},[4143,5889,5890,5892],{},[187,5891,189],{},[191,5893,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,5895,5791],{"encoding":61},[17,5897,5899],{"className":5898,"ariaHidden":53},[66],[17,5900,5902,5905],{"className":5901},[70],[17,5903],{"className":5904,"style":5801},[74],[17,5906,5908,5911],{"className":5907},[79],[17,5909,189],{"className":5910},[79,230],[17,5912,5914],{"className":5913},[1453],[17,5915,5917],{"className":5916},[83],[17,5918,5920],{"className":5919},[88],[17,5921,5923],{"className":5922,"style":5801},[92],[17,5924,5925,5928],{"style":5822},[17,5926],{"className":5927,"style":1470},[100],[17,5929,5931],{"className":5930},[1474,1475,1476,1477],[17,5932,5934],{"className":5933},[79,1477],[17,5935,5401],{"className":5936},[79,1477],[17,5938,5940,5953],{"className":5939},[24],[17,5941,5943],{"className":5942},[28],[30,5944,5945],{"xmlns":32},[35,5946,5947,5951],{},[38,5948,5949],{},[187,5950,189],{},[59,5952,189],{"encoding":61},[17,5954,5956],{"className":5955,"ariaHidden":53},[66],[17,5957,5959,5962],{"className":5958},[70],[17,5960],{"className":5961,"style":226},[74],[17,5963,189],{"className":5964},[79,230]," 的子图，但：",[17,5967,5969],{"className":5968},[20],[17,5970,5972,5994],{"className":5971},[24],[17,5973,5975],{"className":5974},[28],[30,5976,5977],{"xmlns":32,"display":33},[35,5978,5979,5991],{},[38,5980,5981,5987,5989],{},[4143,5982,5983,5985],{},[187,5984,199],{},[191,5986,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,5988,2755],{"mathvariant":2754},[187,5990,199],{},[59,5992,5993],{"encoding":61},"V'\\neq V",[17,5995,5997,6077],{"className":5996,"ariaHidden":53},[66],[17,5998,6000,6003,6035,6038,6074],{"className":5999},[70],[17,6001],{"className":6002,"style":5706},[74],[17,6004,6006,6009],{"className":6005},[79],[17,6007,199],{"className":6008,"style":257},[79,230],[17,6010,6012],{"className":6011},[1453],[17,6013,6015],{"className":6014},[83],[17,6016,6018],{"className":6017},[88],[17,6019,6021],{"className":6020,"style":5498},[92],[17,6022,6023,6026],{"style":3601},[17,6024],{"className":6025,"style":1470},[100],[17,6027,6029],{"className":6028},[1474,1475,1476,1477],[17,6030,6032],{"className":6031},[79,1477],[17,6033,5401],{"className":6034},[79,1477],[17,6036],{"className":6037,"style":235},[234],[17,6039,6041,6068,6071],{"className":6040},[239],[17,6042,6044],{"className":6043},[239],[17,6045,6047],{"className":6046},[79,2827],[17,6048,6050],{"className":6049},[2831],[17,6051,6053,6056,6065],{"className":6052},[2835],[17,6054],{"className":6055,"style":2774},[74],[17,6057,6059],{"className":6058},[2842],[17,6060,6062],{"className":6061},[79],[17,6063,2849],{"className":6064},[239],[17,6066],{"className":6067},[2853],[17,6069],{"className":6070},[234,2857],[17,6072,193],{"className":6073},[239],[17,6075],{"className":6076,"style":235},[234],[17,6078,6080,6083],{"className":6079},[70],[17,6081],{"className":6082,"style":226},[74],[17,6084,199],{"className":6085,"style":257},[79,230],[13,6087,6088],{},"或：",[17,6090,6092],{"className":6091},[20],[17,6093,6095,6117],{"className":6094},[24],[17,6096,6098],{"className":6097},[28],[30,6099,6100],{"xmlns":32,"display":33},[35,6101,6102,6114],{},[38,6103,6104,6110,6112],{},[4143,6105,6106,6108],{},[187,6107,205],{},[191,6109,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,6111,2755],{"mathvariant":2754},[187,6113,205],{},[59,6115,6116],{"encoding":61},"E'\\neq E",[17,6118,6120,6200],{"className":6119,"ariaHidden":53},[66],[17,6121,6123,6126,6158,6161,6197],{"className":6122},[70],[17,6124],{"className":6125,"style":5706},[74],[17,6127,6129,6132],{"className":6128},[79],[17,6130,205],{"className":6131,"style":269},[79,230],[17,6133,6135],{"className":6134},[1453],[17,6136,6138],{"className":6137},[83],[17,6139,6141],{"className":6140},[88],[17,6142,6144],{"className":6143,"style":5498},[92],[17,6145,6146,6149],{"style":3601},[17,6147],{"className":6148,"style":1470},[100],[17,6150,6152],{"className":6151},[1474,1475,1476,1477],[17,6153,6155],{"className":6154},[79,1477],[17,6156,5401],{"className":6157},[79,1477],[17,6159],{"className":6160,"style":235},[234],[17,6162,6164,6191,6194],{"className":6163},[239],[17,6165,6167],{"className":6166},[239],[17,6168,6170],{"className":6169},[79,2827],[17,6171,6173],{"className":6172},[2831],[17,6174,6176,6179,6188],{"className":6175},[2835],[17,6177],{"className":6178,"style":2774},[74],[17,6180,6182],{"className":6181},[2842],[17,6183,6185],{"className":6184},[79],[17,6186,2849],{"className":6187},[239],[17,6189],{"className":6190},[2853],[17,6192],{"className":6193},[234,2857],[17,6195,193],{"className":6196},[239],[17,6198],{"className":6199,"style":235},[234],[17,6201,6203,6206],{"className":6202},[70],[17,6204],{"className":6205,"style":226},[74],[17,6207,205],{"className":6208,"style":269},[79,230],[13,6210,6211,6212,5835,6273,3891,6301,720],{},"则称 ",[17,6213,6215,6232],{"className":6214},[24],[17,6216,6218],{"className":6217},[28],[30,6219,6220],{"xmlns":32},[35,6221,6222,6230],{},[38,6223,6224],{},[4143,6225,6226,6228],{},[187,6227,189],{},[191,6229,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,6231,5791],{"encoding":61},[17,6233,6235],{"className":6234,"ariaHidden":53},[66],[17,6236,6238,6241],{"className":6237},[70],[17,6239],{"className":6240,"style":5801},[74],[17,6242,6244,6247],{"className":6243},[79],[17,6245,189],{"className":6246},[79,230],[17,6248,6250],{"className":6249},[1453],[17,6251,6253],{"className":6252},[83],[17,6254,6256],{"className":6255},[88],[17,6257,6259],{"className":6258,"style":5801},[92],[17,6260,6261,6264],{"style":5822},[17,6262],{"className":6263,"style":1470},[100],[17,6265,6267],{"className":6266},[1474,1475,1476,1477],[17,6268,6270],{"className":6269},[79,1477],[17,6271,5401],{"className":6272},[79,1477],[17,6274,6276,6289],{"className":6275},[24],[17,6277,6279],{"className":6278},[28],[30,6280,6281],{"xmlns":32},[35,6282,6283,6287],{},[38,6284,6285],{},[187,6286,189],{},[59,6288,189],{"encoding":61},[17,6290,6292],{"className":6291,"ariaHidden":53},[66],[17,6293,6295,6298],{"className":6294},[70],[17,6296],{"className":6297,"style":226},[74],[17,6299,189],{"className":6300},[79,230],[645,6302,6303],{},"真子图",[506,6305],{},[513,6307,6309],{"id":6308},"_2-生成子图-支撑子图","2. 生成子图 \u002F 支撑子图",[13,6311,4512],{},[17,6313,6315],{"className":6314},[20],[17,6316,6318,6340],{"className":6317},[24],[17,6319,6321],{"className":6320},[28],[30,6322,6323],{"xmlns":32,"display":33},[35,6324,6325,6337],{},[38,6326,6327,6333,6335],{},[4143,6328,6329,6331],{},[187,6330,199],{},[191,6332,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,6334,193],{},[187,6336,199],{},[59,6338,6339],{"encoding":61},"V'=V",[17,6341,6343,6390],{"className":6342,"ariaHidden":53},[66],[17,6344,6346,6349,6381,6384,6387],{"className":6345},[70],[17,6347],{"className":6348,"style":5498},[74],[17,6350,6352,6355],{"className":6351},[79],[17,6353,199],{"className":6354,"style":257},[79,230],[17,6356,6358],{"className":6357},[1453],[17,6359,6361],{"className":6360},[83],[17,6362,6364],{"className":6363},[88],[17,6365,6367],{"className":6366,"style":5498},[92],[17,6368,6369,6372],{"style":3601},[17,6370],{"className":6371,"style":1470},[100],[17,6373,6375],{"className":6374},[1474,1475,1476,1477],[17,6376,6378],{"className":6377},[79,1477],[17,6379,5401],{"className":6380},[79,1477],[17,6382],{"className":6383,"style":235},[234],[17,6385,193],{"className":6386},[239],[17,6388],{"className":6389,"style":235},[234],[17,6391,6393,6396],{"className":6392},[70],[17,6394],{"className":6395,"style":226},[74],[17,6397,199],{"className":6398,"style":257},[79,230],[13,6400,6401],{},"但：",[17,6403,6405],{"className":6404},[20],[17,6406,6408,6430],{"className":6407},[24],[17,6409,6411],{"className":6410},[28],[30,6412,6413],{"xmlns":32,"display":33},[35,6414,6415,6427],{},[38,6416,6417,6423,6425],{},[4143,6418,6419,6421],{},[187,6420,205],{},[191,6422,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,6424,5629],{},[187,6426,205],{},[59,6428,6429],{"encoding":61},"E'\\subseteq E",[17,6431,6433,6480],{"className":6432,"ariaHidden":53},[66],[17,6434,6436,6439,6471,6474,6477],{"className":6435},[70],[17,6437],{"className":6438,"style":5658},[74],[17,6440,6442,6445],{"className":6441},[79],[17,6443,205],{"className":6444,"style":269},[79,230],[17,6446,6448],{"className":6447},[1453],[17,6449,6451],{"className":6450},[83],[17,6452,6454],{"className":6453},[88],[17,6455,6457],{"className":6456,"style":5498},[92],[17,6458,6459,6462],{"style":3601},[17,6460],{"className":6461,"style":1470},[100],[17,6463,6465],{"className":6464},[1474,1475,1476,1477],[17,6466,6468],{"className":6467},[79,1477],[17,6469,5401],{"className":6470},[79,1477],[17,6472],{"className":6473,"style":235},[234],[17,6475,5629],{"className":6476},[239],[17,6478],{"className":6479,"style":235},[234],[17,6481,6483,6486],{"className":6482},[70],[17,6484],{"className":6485,"style":226},[74],[17,6487,205],{"className":6488,"style":269},[79,230],[13,6490,6211,6491,5835,6552,3891,6580,1357,6583,720],{},[17,6492,6494,6511],{"className":6493},[24],[17,6495,6497],{"className":6496},[28],[30,6498,6499],{"xmlns":32},[35,6500,6501,6509],{},[38,6502,6503],{},[4143,6504,6505,6507],{},[187,6506,189],{},[191,6508,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,6510,5791],{"encoding":61},[17,6512,6514],{"className":6513,"ariaHidden":53},[66],[17,6515,6517,6520],{"className":6516},[70],[17,6518],{"className":6519,"style":5801},[74],[17,6521,6523,6526],{"className":6522},[79],[17,6524,189],{"className":6525},[79,230],[17,6527,6529],{"className":6528},[1453],[17,6530,6532],{"className":6531},[83],[17,6533,6535],{"className":6534},[88],[17,6536,6538],{"className":6537,"style":5801},[92],[17,6539,6540,6543],{"style":5822},[17,6541],{"className":6542,"style":1470},[100],[17,6544,6546],{"className":6545},[1474,1475,1476,1477],[17,6547,6549],{"className":6548},[79,1477],[17,6550,5401],{"className":6551},[79,1477],[17,6553,6555,6568],{"className":6554},[24],[17,6556,6558],{"className":6557},[28],[30,6559,6560],{"xmlns":32},[35,6561,6562,6566],{},[38,6563,6564],{},[187,6565,189],{},[59,6567,189],{"encoding":61},[17,6569,6571],{"className":6570,"ariaHidden":53},[66],[17,6572,6574,6577],{"className":6573},[70],[17,6575],{"className":6576,"style":226},[74],[17,6578,189],{"className":6579},[79,230],[645,6581,6582],{},"生成子图",[645,6584,6585],{},"支撑子图",[13,6587,5086],{},[1700,6589,6590],{},[13,6591,6592],{},"顶点全保留，只删一些边。",[506,6594],{},[513,6596,6598],{"id":6597},"_3-顶点导出子图","3. 顶点导出子图",[13,6600,6601],{},"如果取：",[17,6603,6605],{"className":6604},[20],[17,6606,6608,6630],{"className":6607},[24],[17,6609,6611],{"className":6610},[28],[30,6612,6613],{"xmlns":32,"display":33},[35,6614,6615,6627],{},[38,6616,6617,6623,6625],{},[4143,6618,6619,6621],{},[187,6620,199],{},[191,6622,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,6624,5629],{},[187,6626,199],{},[59,6628,6629],{"encoding":61},"V'\\subseteq V",[17,6631,6633,6680],{"className":6632,"ariaHidden":53},[66],[17,6634,6636,6639,6671,6674,6677],{"className":6635},[70],[17,6637],{"className":6638,"style":5658},[74],[17,6640,6642,6645],{"className":6641},[79],[17,6643,199],{"className":6644,"style":257},[79,230],[17,6646,6648],{"className":6647},[1453],[17,6649,6651],{"className":6650},[83],[17,6652,6654],{"className":6653},[88],[17,6655,6657],{"className":6656,"style":5498},[92],[17,6658,6659,6662],{"style":3601},[17,6660],{"className":6661,"style":1470},[100],[17,6663,6665],{"className":6664},[1474,1475,1476,1477],[17,6666,6668],{"className":6667},[79,1477],[17,6669,5401],{"className":6670},[79,1477],[17,6672],{"className":6673,"style":235},[234],[17,6675,5629],{"className":6676},[239],[17,6678],{"className":6679,"style":235},[234],[17,6681,6683,6686],{"className":6682},[70],[17,6684],{"className":6685,"style":226},[74],[17,6687,199],{"className":6688,"style":257},[79,230],[13,6690,6691,6692,6754,6755,1140],{},"并保留 ",[17,6693,6695,6713],{"className":6694},[24],[17,6696,6698],{"className":6697},[28],[30,6699,6700],{"xmlns":32},[35,6701,6702,6710],{},[38,6703,6704],{},[4143,6705,6706,6708],{},[187,6707,199],{},[191,6709,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,6711,6712],{"encoding":61},"V'",[17,6714,6716],{"className":6715,"ariaHidden":53},[66],[17,6717,6719,6722],{"className":6718},[70],[17,6720],{"className":6721,"style":5801},[74],[17,6723,6725,6728],{"className":6724},[79],[17,6726,199],{"className":6727,"style":257},[79,230],[17,6729,6731],{"className":6730},[1453],[17,6732,6734],{"className":6733},[83],[17,6735,6737],{"className":6736},[88],[17,6738,6740],{"className":6739,"style":5801},[92],[17,6741,6742,6745],{"style":5822},[17,6743],{"className":6744,"style":1470},[100],[17,6746,6748],{"className":6747},[1474,1475,1476,1477],[17,6749,6751],{"className":6750},[79,1477],[17,6752,5401],{"className":6753},[79,1477]," 中顶点之间在原图中所有的边，则得到的子图叫",[645,6756,6757],{},"顶点导出子图",[17,6759,6761],{"className":6760},[20],[17,6762,6764,6790],{"className":6763},[24],[17,6765,6767],{"className":6766},[28],[30,6768,6769],{"xmlns":32,"display":33},[35,6770,6771,6787],{},[38,6772,6773,6775,6778,6784],{},[187,6774,189],{},[191,6776,6777],{"stretchy":48},"[",[4143,6779,6780,6782],{},[187,6781,199],{},[191,6783,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,6785,6786],{"stretchy":48},"]",[59,6788,6789],{"encoding":61},"G[V']",[17,6791,6793],{"className":6792,"ariaHidden":53},[66],[17,6794,6796,6799,6802,6805,6837],{"className":6795},[70],[17,6797],{"className":6798,"style":5452},[74],[17,6800,189],{"className":6801},[79,230],[17,6803,6777],{"className":6804},[253],[17,6806,6808,6811],{"className":6807},[79],[17,6809,199],{"className":6810,"style":257},[79,230],[17,6812,6814],{"className":6813},[1453],[17,6815,6817],{"className":6816},[83],[17,6818,6820],{"className":6819},[88],[17,6821,6823],{"className":6822,"style":5498},[92],[17,6824,6825,6828],{"style":3601},[17,6826],{"className":6827,"style":1470},[100],[17,6829,6831],{"className":6830},[1474,1475,1476,1477],[17,6832,6834],{"className":6833},[79,1477],[17,6835,5401],{"className":6836},[79,1477],[17,6838,6786],{"className":6839},[282],[13,6841,6842],{},"通俗说：",[1700,6844,6845],{},[13,6846,6847],{},"选一些顶点，把这些顶点之间原来有的边全部保留。",[506,6849],{},[513,6851,6853],{"id":6852},"_4-边导出子图","4. 边导出子图",[13,6855,6601],{},[17,6857,6859],{"className":6858},[20],[17,6860,6862,6883],{"className":6861},[24],[17,6863,6865],{"className":6864},[28],[30,6866,6867],{"xmlns":32,"display":33},[35,6868,6869,6881],{},[38,6870,6871,6877,6879],{},[4143,6872,6873,6875],{},[187,6874,205],{},[191,6876,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,6878,5629],{},[187,6880,205],{},[59,6882,6429],{"encoding":61},[17,6884,6886,6933],{"className":6885,"ariaHidden":53},[66],[17,6887,6889,6892,6924,6927,6930],{"className":6888},[70],[17,6890],{"className":6891,"style":5658},[74],[17,6893,6895,6898],{"className":6894},[79],[17,6896,205],{"className":6897,"style":269},[79,230],[17,6899,6901],{"className":6900},[1453],[17,6902,6904],{"className":6903},[83],[17,6905,6907],{"className":6906},[88],[17,6908,6910],{"className":6909,"style":5498},[92],[17,6911,6912,6915],{"style":3601},[17,6913],{"className":6914,"style":1470},[100],[17,6916,6918],{"className":6917},[1474,1475,1476,1477],[17,6919,6921],{"className":6920},[79,1477],[17,6922,5401],{"className":6923},[79,1477],[17,6925],{"className":6926,"style":235},[234],[17,6928,5629],{"className":6929},[239],[17,6931],{"className":6932,"style":235},[234],[17,6934,6936,6939],{"className":6935},[70],[17,6937],{"className":6938,"style":226},[74],[17,6940,205],{"className":6941,"style":269},[79,230],[13,6943,6944,6945,1140],{},"并把这些边及其端点组成子图，则叫",[645,6946,6947],{},"边导出子图",[17,6949,6951],{"className":6950},[20],[17,6952,6954,6978],{"className":6953},[24],[17,6955,6957],{"className":6956},[28],[30,6958,6959],{"xmlns":32,"display":33},[35,6960,6961,6975],{},[38,6962,6963,6965,6967,6973],{},[187,6964,189],{},[191,6966,6777],{"stretchy":48},[4143,6968,6969,6971],{},[187,6970,205],{},[191,6972,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,6974,6786],{"stretchy":48},[59,6976,6977],{"encoding":61},"G[E']",[17,6979,6981],{"className":6980,"ariaHidden":53},[66],[17,6982,6984,6987,6990,6993,7025],{"className":6983},[70],[17,6985],{"className":6986,"style":5452},[74],[17,6988,189],{"className":6989},[79,230],[17,6991,6777],{"className":6992},[253],[17,6994,6996,6999],{"className":6995},[79],[17,6997,205],{"className":6998,"style":269},[79,230],[17,7000,7002],{"className":7001},[1453],[17,7003,7005],{"className":7004},[83],[17,7006,7008],{"className":7007},[88],[17,7009,7011],{"className":7010,"style":5498},[92],[17,7012,7013,7016],{"style":3601},[17,7014],{"className":7015,"style":1470},[100],[17,7017,7019],{"className":7018},[1474,1475,1476,1477],[17,7020,7022],{"className":7021},[79,1477],[17,7023,5401],{"className":7024},[79,1477],[17,7026,6786],{"className":7027},[282],[506,7029],{},[513,7031,7033],{"id":7032},"_5-删除顶点","5. 删除顶点",[13,7035,7036,7037,7065,7066,7094,7095,7123],{},"从图 ",[17,7038,7040,7053],{"className":7039},[24],[17,7041,7043],{"className":7042},[28],[30,7044,7045],{"xmlns":32},[35,7046,7047,7051],{},[38,7048,7049],{},[187,7050,189],{},[59,7052,189],{"encoding":61},[17,7054,7056],{"className":7055,"ariaHidden":53},[66],[17,7057,7059,7062],{"className":7058},[70],[17,7060],{"className":7061,"style":226},[74],[17,7063,189],{"className":7064},[79,230]," 中删去顶点 ",[17,7067,7069,7082],{"className":7068},[24],[17,7070,7072],{"className":7071},[28],[30,7073,7074],{"xmlns":32},[35,7075,7076,7080],{},[38,7077,7078],{},[187,7079,793],{},[59,7081,793],{"encoding":61},[17,7083,7085],{"className":7084,"ariaHidden":53},[66],[17,7086,7088,7091],{"className":7087},[70],[17,7089],{"className":7090,"style":769},[74],[17,7092,793],{"className":7093,"style":818},[79,230],"，同时删去与 ",[17,7096,7098,7111],{"className":7097},[24],[17,7099,7101],{"className":7100},[28],[30,7102,7103],{"xmlns":32},[35,7104,7105,7109],{},[38,7106,7107],{},[187,7108,793],{},[59,7110,793],{"encoding":61},[17,7112,7114],{"className":7113,"ariaHidden":53},[66],[17,7115,7117,7120],{"className":7116},[70],[17,7118],{"className":7119,"style":769},[74],[17,7121,793],{"className":7122,"style":818},[79,230]," 关联的所有边，记作：",[17,7125,7127],{"className":7126},[20],[17,7128,7130,7148],{"className":7129},[24],[17,7131,7133],{"className":7132},[28],[30,7134,7135],{"xmlns":32,"display":33},[35,7136,7137,7145],{},[38,7138,7139,7141,7143],{},[187,7140,189],{},[191,7142,972],{},[187,7144,793],{},[59,7146,7147],{"encoding":61},"G-v",[17,7149,7151,7170],{"className":7150,"ariaHidden":53},[66],[17,7152,7154,7158,7161,7164,7167],{"className":7153},[70],[17,7155],{"className":7156,"style":7157},[74],"height:0.7667em;vertical-align:-0.0833em;",[17,7159,189],{"className":7160},[79,230],[17,7162],{"className":7163,"style":257},[234],[17,7165,972],{"className":7166},[997],[17,7168],{"className":7169,"style":257},[234],[17,7171,7173,7176],{"className":7172},[70],[17,7174],{"className":7175,"style":769},[74],[17,7177,793],{"className":7178,"style":818},[79,230],[13,7180,7181,7182,1140],{},"如果删去顶点集合 ",[17,7183,7185,7202],{"className":7184},[24],[17,7186,7188],{"className":7187},[28],[30,7189,7190],{"xmlns":32},[35,7191,7192,7200],{},[38,7193,7194],{},[4143,7195,7196,7198],{},[187,7197,199],{},[191,7199,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,7201,6712],{"encoding":61},[17,7203,7205],{"className":7204,"ariaHidden":53},[66],[17,7206,7208,7211],{"className":7207},[70],[17,7209],{"className":7210,"style":5801},[74],[17,7212,7214,7217],{"className":7213},[79],[17,7215,199],{"className":7216,"style":257},[79,230],[17,7218,7220],{"className":7219},[1453],[17,7221,7223],{"className":7222},[83],[17,7224,7226],{"className":7225},[88],[17,7227,7229],{"className":7228,"style":5801},[92],[17,7230,7231,7234],{"style":5822},[17,7232],{"className":7233,"style":1470},[100],[17,7235,7237],{"className":7236},[1474,1475,1476,1477],[17,7238,7240],{"className":7239},[79,1477],[17,7241,5401],{"className":7242},[79,1477],[17,7244,7246],{"className":7245},[20],[17,7247,7249,7271],{"className":7248},[24],[17,7250,7252],{"className":7251},[28],[30,7253,7254],{"xmlns":32,"display":33},[35,7255,7256,7268],{},[38,7257,7258,7260,7262],{},[187,7259,189],{},[191,7261,972],{},[4143,7263,7264,7266],{},[187,7265,199],{},[191,7267,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,7269,7270],{"encoding":61},"G-V'",[17,7272,7274,7292],{"className":7273,"ariaHidden":53},[66],[17,7275,7277,7280,7283,7286,7289],{"className":7276},[70],[17,7278],{"className":7279,"style":7157},[74],[17,7281,189],{"className":7282},[79,230],[17,7284],{"className":7285,"style":257},[234],[17,7287,972],{"className":7288},[997],[17,7290],{"className":7291,"style":257},[234],[17,7293,7295,7298],{"className":7294},[70],[17,7296],{"className":7297,"style":5498},[74],[17,7299,7301,7304],{"className":7300},[79],[17,7302,199],{"className":7303,"style":257},[79,230],[17,7305,7307],{"className":7306},[1453],[17,7308,7310],{"className":7309},[83],[17,7311,7313],{"className":7312},[88],[17,7314,7316],{"className":7315,"style":5498},[92],[17,7317,7318,7321],{"style":3601},[17,7319],{"className":7320,"style":1470},[100],[17,7322,7324],{"className":7323},[1474,1475,1476,1477],[17,7325,7327],{"className":7326},[79,1477],[17,7328,5401],{"className":7329},[79,1477],[506,7331],{},[513,7333,7335],{"id":7334},"_6-删除边","6. 删除边",[13,7337,7338,7339,1140],{},"从图中删去边 ",[17,7340,7342,7355],{"className":7341},[24],[17,7343,7345],{"className":7344},[28],[30,7346,7347],{"xmlns":32},[35,7348,7349,7353],{},[38,7350,7351],{},[187,7352,757],{},[59,7354,757],{"encoding":61},[17,7356,7358],{"className":7357,"ariaHidden":53},[66],[17,7359,7361,7364],{"className":7360},[70],[17,7362],{"className":7363,"style":769},[74],[17,7365,757],{"className":7366},[79,230],[17,7368,7370],{"className":7369},[20],[17,7371,7373,7391],{"className":7372},[24],[17,7374,7376],{"className":7375},[28],[30,7377,7378],{"xmlns":32,"display":33},[35,7379,7380,7388],{},[38,7381,7382,7384,7386],{},[187,7383,189],{},[191,7385,972],{},[187,7387,757],{},[59,7389,7390],{"encoding":61},"G-e",[17,7392,7394,7412],{"className":7393,"ariaHidden":53},[66],[17,7395,7397,7400,7403,7406,7409],{"className":7396},[70],[17,7398],{"className":7399,"style":7157},[74],[17,7401,189],{"className":7402},[79,230],[17,7404],{"className":7405,"style":257},[234],[17,7407,972],{"className":7408},[997],[17,7410],{"className":7411,"style":257},[234],[17,7413,7415,7418],{"className":7414},[70],[17,7416],{"className":7417,"style":769},[74],[17,7419,757],{"className":7420},[79,230],[13,7422,7423,7424,1140],{},"从图中删去边集 ",[17,7425,7427,7445],{"className":7426},[24],[17,7428,7430],{"className":7429},[28],[30,7431,7432],{"xmlns":32},[35,7433,7434,7442],{},[38,7435,7436],{},[4143,7437,7438,7440],{},[187,7439,205],{},[191,7441,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,7443,7444],{"encoding":61},"E'",[17,7446,7448],{"className":7447,"ariaHidden":53},[66],[17,7449,7451,7454],{"className":7450},[70],[17,7452],{"className":7453,"style":5801},[74],[17,7455,7457,7460],{"className":7456},[79],[17,7458,205],{"className":7459,"style":269},[79,230],[17,7461,7463],{"className":7462},[1453],[17,7464,7466],{"className":7465},[83],[17,7467,7469],{"className":7468},[88],[17,7470,7472],{"className":7471,"style":5801},[92],[17,7473,7474,7477],{"style":5822},[17,7475],{"className":7476,"style":1470},[100],[17,7478,7480],{"className":7479},[1474,1475,1476,1477],[17,7481,7483],{"className":7482},[79,1477],[17,7484,5401],{"className":7485},[79,1477],[17,7487,7489],{"className":7488},[20],[17,7490,7492,7514],{"className":7491},[24],[17,7493,7495],{"className":7494},[28],[30,7496,7497],{"xmlns":32,"display":33},[35,7498,7499,7511],{},[38,7500,7501,7503,7505],{},[187,7502,189],{},[191,7504,972],{},[4143,7506,7507,7509],{},[187,7508,205],{},[191,7510,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,7512,7513],{"encoding":61},"G-E'",[17,7515,7517,7535],{"className":7516,"ariaHidden":53},[66],[17,7518,7520,7523,7526,7529,7532],{"className":7519},[70],[17,7521],{"className":7522,"style":7157},[74],[17,7524,189],{"className":7525},[79,230],[17,7527],{"className":7528,"style":257},[234],[17,7530,972],{"className":7531},[997],[17,7533],{"className":7534,"style":257},[234],[17,7536,7538,7541],{"className":7537},[70],[17,7539],{"className":7540,"style":5498},[74],[17,7542,7544,7547],{"className":7543},[79],[17,7545,205],{"className":7546,"style":269},[79,230],[17,7548,7550],{"className":7549},[1453],[17,7551,7553],{"className":7552},[83],[17,7554,7556],{"className":7555},[88],[17,7557,7559],{"className":7558,"style":5498},[92],[17,7560,7561,7564],{"style":3601},[17,7562],{"className":7563,"style":1470},[100],[17,7565,7567],{"className":7566},[1474,1475,1476,1477],[17,7568,7570],{"className":7569},[79,1477],[17,7571,5401],{"className":7572},[79,1477],[506,7574],{},[513,7576,7578],{"id":7577},"_7-加边","7. 加边",[13,7580,7581,7582,1140],{},"如果在图中加入边 ",[17,7583,7585,7598],{"className":7584},[24],[17,7586,7588],{"className":7587},[28],[30,7589,7590],{"xmlns":32},[35,7591,7592,7596],{},[38,7593,7594],{},[187,7595,757],{},[59,7597,757],{"encoding":61},[17,7599,7601],{"className":7600,"ariaHidden":53},[66],[17,7602,7604,7607],{"className":7603},[70],[17,7605],{"className":7606,"style":769},[74],[17,7608,757],{"className":7609},[79,230],[17,7611,7613],{"className":7612},[20],[17,7614,7616,7634],{"className":7615},[24],[17,7617,7619],{"className":7618},[28],[30,7620,7621],{"xmlns":32,"display":33},[35,7622,7623,7631],{},[38,7624,7625,7627,7629],{},[187,7626,189],{},[191,7628,4149],{},[187,7630,757],{},[59,7632,7633],{"encoding":61},"G+e",[17,7635,7637,7655],{"className":7636,"ariaHidden":53},[66],[17,7638,7640,7643,7646,7649,7652],{"className":7639},[70],[17,7641],{"className":7642,"style":7157},[74],[17,7644,189],{"className":7645},[79,230],[17,7647],{"className":7648,"style":257},[234],[17,7650,4149],{"className":7651},[997],[17,7653],{"className":7654,"style":257},[234],[17,7656,7658,7661],{"className":7657},[70],[17,7659],{"className":7660,"style":769},[74],[17,7662,757],{"className":7663},[79,230],[506,7665],{},[10,7667,7669],{"id":7668},"八补图","八、补图",[513,7671,7673],{"id":7672},"_1-一般补图思想","1. 一般补图思想",[13,7675,7676],{},"补图的意思是：",[1700,7678,7679],{},[13,7680,7681],{},"原图没有的边，在补图里有；原图有的边，在补图里没有。",[506,7683],{},[513,7685,7687],{"id":7686},"_2-简单图的补图","2. 简单图的补图",[13,7689,7690,7691,7719,7720,7748,7749,7777],{},"设 ",[17,7692,7694,7707],{"className":7693},[24],[17,7695,7697],{"className":7696},[28],[30,7698,7699],{"xmlns":32},[35,7700,7701,7705],{},[38,7702,7703],{},[187,7704,189],{},[59,7706,189],{"encoding":61},[17,7708,7710],{"className":7709,"ariaHidden":53},[66],[17,7711,7713,7716],{"className":7712},[70],[17,7714],{"className":7715,"style":226},[74],[17,7717,189],{"className":7718},[79,230]," 是含 ",[17,7721,7723,7736],{"className":7722},[24],[17,7724,7726],{"className":7725},[28],[30,7727,7728],{"xmlns":32},[35,7729,7730,7734],{},[38,7731,7732],{},[187,7733,3183],{},[59,7735,3183],{"encoding":61},[17,7737,7739],{"className":7738,"ariaHidden":53},[66],[17,7740,7742,7745],{"className":7741},[70],[17,7743],{"className":7744,"style":769},[74],[17,7746,3183],{"className":7747},[79,230]," 个顶点的简单图，则 ",[17,7750,7752,7765],{"className":7751},[24],[17,7753,7755],{"className":7754},[28],[30,7756,7757],{"xmlns":32},[35,7758,7759,7763],{},[38,7760,7761],{},[187,7762,189],{},[59,7764,189],{"encoding":61},[17,7766,7768],{"className":7767,"ariaHidden":53},[66],[17,7769,7771,7774],{"className":7770},[70],[17,7772],{"className":7773,"style":226},[74],[17,7775,189],{"className":7776},[79,230]," 的补图记作：",[17,7779,7781],{"className":7780},[20],[17,7782,7784,7804],{"className":7783},[24],[17,7785,7787],{"className":7786},[28],[30,7788,7789],{"xmlns":32,"display":33},[35,7790,7791,7801],{},[38,7792,7793],{},[7794,7795,7796,7798],"mover",{"accent":53},[187,7797,189],{},[191,7799,7800],{"stretchy":53},"‾",[59,7802,7803],{"encoding":61},"\\overline G",[17,7805,7807],{"className":7806,"ariaHidden":53},[66],[17,7808,7810,7814],{"className":7809},[70],[17,7811],{"className":7812,"style":7813},[74],"height:0.8833em;",[17,7815,7818],{"className":7816},[79,7817],"overline",[17,7819,7821],{"className":7820},[83],[17,7822,7824],{"className":7823},[88],[17,7825,7827,7839],{"className":7826,"style":7813},[92],[17,7828,7830,7833],{"style":7829},"top:-3em;",[17,7831],{"className":7832,"style":3390},[100],[17,7834,7836],{"className":7835},[79],[17,7837,189],{"className":7838},[79,230],[17,7840,7842,7845],{"style":7841},"top:-3.8033em;",[17,7843],{"className":7844,"style":3390},[100],[17,7846],{"className":7847,"style":3407},[7848],"overline-line",[13,7850,7851,7852,7880],{},"它的顶点集和 ",[17,7853,7855,7868],{"className":7854},[24],[17,7856,7858],{"className":7857},[28],[30,7859,7860],{"xmlns":32},[35,7861,7862,7866],{},[38,7863,7864],{},[187,7865,189],{},[59,7867,189],{"encoding":61},[17,7869,7871],{"className":7870,"ariaHidden":53},[66],[17,7872,7874,7877],{"className":7873},[70],[17,7875],{"className":7876,"style":226},[74],[17,7878,189],{"className":7879},[79,230]," 相同。",[13,7882,7883],{},"并且：",[17,7885,7887],{"className":7886},[20],[17,7888,7890,7920],{"className":7889},[24],[17,7891,7893],{"className":7892},[28],[30,7894,7895],{"xmlns":32,"display":33},[35,7896,7897,7917],{},[38,7898,7899,7901,7903,7905,7907,7909,7915],{},[187,7900,788],{},[187,7902,793],{},[191,7904,1891],{},[187,7906,205],{},[191,7908,841],{"stretchy":48},[7794,7910,7911,7913],{"accent":53},[187,7912,189],{},[191,7914,7800],{"stretchy":53},[191,7916,850],{"stretchy":48},[59,7918,7919],{"encoding":61},"uv\\in E(\\overline G)",[17,7921,7923,7943],{"className":7922,"ariaHidden":53},[66],[17,7924,7926,7930,7934,7937,7940],{"className":7925},[70],[17,7927],{"className":7928,"style":7929},[74],"height:0.5782em;vertical-align:-0.0391em;",[17,7931,7933],{"className":7932,"style":818},[79,230],"uv",[17,7935],{"className":7936,"style":235},[234],[17,7938,1891],{"className":7939},[239],[17,7941],{"className":7942,"style":235},[234],[17,7944,7946,7950,7953,7956,7987],{"className":7945},[70],[17,7947],{"className":7948,"style":7949},[74],"height:1.1333em;vertical-align:-0.25em;",[17,7951,205],{"className":7952,"style":269},[79,230],[17,7954,841],{"className":7955},[253],[17,7957,7959],{"className":7958},[79,7817],[17,7960,7962],{"className":7961},[83],[17,7963,7965],{"className":7964},[88],[17,7966,7968,7979],{"className":7967,"style":7813},[92],[17,7969,7970,7973],{"style":7829},[17,7971],{"className":7972,"style":3390},[100],[17,7974,7976],{"className":7975},[79],[17,7977,189],{"className":7978},[79,230],[17,7980,7981,7984],{"style":7841},[17,7982],{"className":7983,"style":3390},[100],[17,7985],{"className":7986,"style":3407},[7848],[17,7988,850],{"className":7989},[282],[13,7991,7992],{},"当且仅当：",[17,7994,7996],{"className":7995},[20],[17,7997,7999,8026],{"className":7998},[24],[17,8000,8002],{"className":8001},[28],[30,8003,8004],{"xmlns":32,"display":33},[35,8005,8006,8023],{},[38,8007,8008,8010,8012,8015,8017,8019,8021],{},[187,8009,788],{},[187,8011,793],{},[191,8013,8014],{"mathvariant":2754},"∉",[187,8016,205],{},[191,8018,841],{"stretchy":48},[187,8020,189],{},[191,8022,850],{"stretchy":48},[59,8024,8025],{"encoding":61},"uv\\notin E(G)",[17,8027,8029,8083],{"className":8028,"ariaHidden":53},[66],[17,8030,8032,8035,8038,8041,8080],{"className":8031},[70],[17,8033],{"className":8034,"style":249},[74],[17,8036,7933],{"className":8037,"style":818},[79,230],[17,8039],{"className":8040,"style":235},[234],[17,8042,8044,8050],{"className":8043},[239],[17,8045,8047],{"className":8046},[79],[17,8048,1891],{"className":8049},[239],[17,8051,8053],{"className":8052},[79,2827],[17,8054,8056],{"className":8055},[2831],[17,8057,8060,8063,8077],{"className":8058},[8059],"llap",[17,8061],{"className":8062,"style":249},[74],[17,8064,8066],{"className":8065},[2842],[17,8067,8069,8073],{"className":8068},[79],[17,8070,8072],{"className":8071},[79],"\u002F",[17,8074],{"className":8075,"style":8076},[234],"margin-right:0.0556em;",[17,8078],{"className":8079},[2853],[17,8081],{"className":8082,"style":235},[234],[17,8084,8086,8089,8092,8095,8098],{"className":8085},[70],[17,8087],{"className":8088,"style":249},[74],[17,8090,205],{"className":8091,"style":269},[79,230],[17,8093,841],{"className":8094},[253],[17,8096,189],{"className":8097},[79,230],[17,8099,850],{"className":8100},[282],[13,8102,8103],{},"也就是说：",[17,8105,8107],{"className":8106},[20],[17,8108,8110,8140],{"className":8109},[24],[17,8111,8113],{"className":8112},[28],[30,8114,8115],{"xmlns":32,"display":33},[35,8116,8117,8137],{},[38,8118,8119,8121,8123,8129,8131],{},[187,8120,189],{},[191,8122,4149],{},[7794,8124,8125,8127],{"accent":53},[187,8126,189],{},[191,8128,7800],{"stretchy":53},[191,8130,193],{},[1385,8132,8133,8135],{},[187,8134,3218],{},[187,8136,3183],{},[59,8138,8139],{"encoding":61},"G+\\overline G=K_n",[17,8141,8143,8161,8207],{"className":8142,"ariaHidden":53},[66],[17,8144,8146,8149,8152,8155,8158],{"className":8145},[70],[17,8147],{"className":8148,"style":7157},[74],[17,8150,189],{"className":8151},[79,230],[17,8153],{"className":8154,"style":257},[234],[17,8156,4149],{"className":8157},[997],[17,8159],{"className":8160,"style":257},[234],[17,8162,8164,8167,8198,8201,8204],{"className":8163},[70],[17,8165],{"className":8166,"style":7813},[74],[17,8168,8170],{"className":8169},[79,7817],[17,8171,8173],{"className":8172},[83],[17,8174,8176],{"className":8175},[88],[17,8177,8179,8190],{"className":8178,"style":7813},[92],[17,8180,8181,8184],{"style":7829},[17,8182],{"className":8183,"style":3390},[100],[17,8185,8187],{"className":8186},[79],[17,8188,189],{"className":8189},[79,230],[17,8191,8192,8195],{"style":7841},[17,8193],{"className":8194,"style":3390},[100],[17,8196],{"className":8197,"style":3407},[7848],[17,8199],{"className":8200,"style":235},[234],[17,8202,193],{"className":8203},[239],[17,8205],{"className":8206,"style":235},[234],[17,8208,8210,8213],{"className":8209},[70],[17,8211],{"className":8212,"style":3233},[74],[17,8214,8216,8219],{"className":8215},[79],[17,8217,3218],{"className":8218,"style":3240},[79,230],[17,8220,8222],{"className":8221},[1453],[17,8223,8225,8245],{"className":8224},[83,84],[17,8226,8228,8242],{"className":8227},[88],[17,8229,8231],{"className":8230,"style":3253},[92],[17,8232,8233,8236],{"style":3256},[17,8234],{"className":8235,"style":1470},[100],[17,8237,8239],{"className":8238},[1474,1475,1476,1477],[17,8240,3183],{"className":8241},[79,230,1477],[17,8243,136],{"className":8244},[135],[17,8246,8248],{"className":8247},[88],[17,8249,8251],{"className":8250,"style":1490},[92],[17,8252],{},[506,8254],{},[10,8256,8258],{"id":8257},"九图的同构","九、图的同构",[513,8260,8262],{"id":8261},"_1-定义","1. 定义",[13,8264,8265,8266,1041,8294,8355,8356,720],{},"两个图 ",[17,8267,8269,8282],{"className":8268},[24],[17,8270,8272],{"className":8271},[28],[30,8273,8274],{"xmlns":32},[35,8275,8276,8280],{},[38,8277,8278],{},[187,8279,189],{},[59,8281,189],{"encoding":61},[17,8283,8285],{"className":8284,"ariaHidden":53},[66],[17,8286,8288,8291],{"className":8287},[70],[17,8289],{"className":8290,"style":226},[74],[17,8292,189],{"className":8293},[79,230],[17,8295,8297,8314],{"className":8296},[24],[17,8298,8300],{"className":8299},[28],[30,8301,8302],{"xmlns":32},[35,8303,8304,8312],{},[38,8305,8306],{},[4143,8307,8308,8310],{},[187,8309,189],{},[191,8311,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,8313,5791],{"encoding":61},[17,8315,8317],{"className":8316,"ariaHidden":53},[66],[17,8318,8320,8323],{"className":8319},[70],[17,8321],{"className":8322,"style":5801},[74],[17,8324,8326,8329],{"className":8325},[79],[17,8327,189],{"className":8328},[79,230],[17,8330,8332],{"className":8331},[1453],[17,8333,8335],{"className":8334},[83],[17,8336,8338],{"className":8337},[88],[17,8339,8341],{"className":8340,"style":5801},[92],[17,8342,8343,8346],{"style":5822},[17,8344],{"className":8345,"style":1470},[100],[17,8347,8349],{"className":8348},[1474,1475,1476,1477],[17,8350,8352],{"className":8351},[79,1477],[17,8353,5401],{"className":8354},[79,1477]," 如果只是“画法不同”，但结构完全一样，就叫",[645,8357,8358],{},"同构",[13,8360,8361],{},"严格说，如果存在一个顶点双射：",[17,8363,8365],{"className":8364},[20],[17,8366,8368,8408],{"className":8367},[24],[17,8369,8371],{"className":8370},[28],[30,8372,8373],{"xmlns":32,"display":33},[35,8374,8375,8405],{},[38,8376,8377,8380,8383,8385,8387,8389,8391,8393,8395,8397,8403],{},[187,8378,8379],{},"f",[191,8381,8382],{},":",[187,8384,199],{},[191,8386,841],{"stretchy":48},[187,8388,189],{},[191,8390,850],{"stretchy":48},[191,8392,1306],{},[187,8394,199],{},[191,8396,841],{"stretchy":48},[4143,8398,8399,8401],{},[187,8400,189],{},[191,8402,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,8404,850],{"stretchy":48},[59,8406,8407],{"encoding":61},"f:V(G)\\to V(G')",[17,8409,8411,8430,8457],{"className":8410,"ariaHidden":53},[66],[17,8412,8414,8417,8421,8424,8427],{"className":8413},[70],[17,8415],{"className":8416,"style":2774},[74],[17,8418,8379],{"className":8419,"style":8420},[79,230],"margin-right:0.1076em;",[17,8422],{"className":8423,"style":235},[234],[17,8425,8382],{"className":8426},[239],[17,8428],{"className":8429,"style":235},[234],[17,8431,8433,8436,8439,8442,8445,8448,8451,8454],{"className":8432},[70],[17,8434],{"className":8435,"style":249},[74],[17,8437,199],{"className":8438,"style":257},[79,230],[17,8440,841],{"className":8441},[253],[17,8443,189],{"className":8444},[79,230],[17,8446,850],{"className":8447},[282],[17,8449],{"className":8450,"style":235},[234],[17,8452,1306],{"className":8453},[239],[17,8455],{"className":8456,"style":235},[234],[17,8458,8460,8463,8466,8469,8501],{"className":8459},[70],[17,8461],{"className":8462,"style":5452},[74],[17,8464,199],{"className":8465,"style":257},[79,230],[17,8467,841],{"className":8468},[253],[17,8470,8472,8475],{"className":8471},[79],[17,8473,189],{"className":8474},[79,230],[17,8476,8478],{"className":8477},[1453],[17,8479,8481],{"className":8480},[83],[17,8482,8484],{"className":8483},[88],[17,8485,8487],{"className":8486,"style":5498},[92],[17,8488,8489,8492],{"style":3601},[17,8490],{"className":8491,"style":1470},[100],[17,8493,8495],{"className":8494},[1474,1475,1476,1477],[17,8496,8498],{"className":8497},[79,1477],[17,8499,5401],{"className":8500},[79,1477],[17,8502,850],{"className":8503},[282],[13,8505,8506,8507,8535,8536,8597],{},"并且保持邻接关系，则称 ",[17,8508,8510,8523],{"className":8509},[24],[17,8511,8513],{"className":8512},[28],[30,8514,8515],{"xmlns":32},[35,8516,8517,8521],{},[38,8518,8519],{},[187,8520,189],{},[59,8522,189],{"encoding":61},[17,8524,8526],{"className":8525,"ariaHidden":53},[66],[17,8527,8529,8532],{"className":8528},[70],[17,8530],{"className":8531,"style":226},[74],[17,8533,189],{"className":8534},[79,230]," 与 ",[17,8537,8539,8556],{"className":8538},[24],[17,8540,8542],{"className":8541},[28],[30,8543,8544],{"xmlns":32},[35,8545,8546,8554],{},[38,8547,8548],{},[4143,8549,8550,8552],{},[187,8551,189],{},[191,8553,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,8555,5791],{"encoding":61},[17,8557,8559],{"className":8558,"ariaHidden":53},[66],[17,8560,8562,8565],{"className":8561},[70],[17,8563],{"className":8564,"style":5801},[74],[17,8566,8568,8571],{"className":8567},[79],[17,8569,189],{"className":8570},[79,230],[17,8572,8574],{"className":8573},[1453],[17,8575,8577],{"className":8576},[83],[17,8578,8580],{"className":8579},[88],[17,8581,8583],{"className":8582,"style":5801},[92],[17,8584,8585,8588],{"style":5822},[17,8586],{"className":8587,"style":1470},[100],[17,8589,8591],{"className":8590},[1474,1475,1476,1477],[17,8592,8594],{"className":8593},[79,1477],[17,8595,5401],{"className":8596},[79,1477]," 同构，记作：",[17,8599,8601],{"className":8600},[20],[17,8602,8604,8627],{"className":8603},[24],[17,8605,8607],{"className":8606},[28],[30,8608,8609],{"xmlns":32,"display":33},[35,8610,8611,8624],{},[38,8612,8613,8615,8618],{},[187,8614,189],{},[191,8616,8617],{},"≅",[4143,8619,8620,8622],{},[187,8621,189],{},[191,8623,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[59,8625,8626],{"encoding":61},"G\\cong G'",[17,8628,8630,8648],{"className":8629,"ariaHidden":53},[66],[17,8631,8633,8636,8639,8642,8645],{"className":8632},[70],[17,8634],{"className":8635,"style":226},[74],[17,8637,189],{"className":8638},[79,230],[17,8640],{"className":8641,"style":235},[234],[17,8643,8617],{"className":8644},[239],[17,8646],{"className":8647,"style":235},[234],[17,8649,8651,8654],{"className":8650},[70],[17,8652],{"className":8653,"style":5498},[74],[17,8655,8657,8660],{"className":8656},[79],[17,8658,189],{"className":8659},[79,230],[17,8661,8663],{"className":8662},[1453],[17,8664,8666],{"className":8665},[83],[17,8667,8669],{"className":8668},[88],[17,8670,8672],{"className":8671,"style":5498},[92],[17,8673,8674,8677],{"style":3601},[17,8675],{"className":8676,"style":1470},[100],[17,8678,8680],{"className":8679},[1474,1475,1476,1477],[17,8681,8683],{"className":8682},[79,1477],[17,8684,5401],{"className":8685},[79,1477],[506,8687],{},[513,8689,8691],{"id":8690},"_2-图同构要保持什么","2. 图同构要保持什么",[13,8693,8694],{},"如果两个图同构，必须保持：",[8696,8697,8698,8701,8704,8707,8710,8713],"ol",{},[153,8699,8700],{},"顶点数相同；",[153,8702,8703],{},"边数相同；",[153,8705,8706],{},"度数序列相同；",[153,8708,8709],{},"邻接关系相同；",[153,8711,8712],{},"有向图还要保持方向；",[153,8714,8715],{},"自环、重边数量也要对应。",[506,8717],{},[513,8719,8721],{"id":8720},"_3-注意这些只是必要条件不一定充分","3. 注意：这些只是必要条件，不一定充分",[13,8723,8103],{},[17,8725,8727],{"className":8726},[20],[17,8728,8730,8745],{"className":8729},[24],[17,8731,8733],{"className":8732},[28],[30,8734,8735],{"xmlns":32,"display":33},[35,8736,8737,8742],{},[38,8738,8739],{},[55,8740,8741],{},"顶点数相同、边数相同、度数序列相同",[59,8743,8744],{"encoding":61},"\\text{顶点数相同、边数相同、度数序列相同}",[17,8746,8748],{"className":8747,"ariaHidden":53},[66],[17,8749,8751,8754],{"className":8750},[70],[17,8752],{"className":8753,"style":226},[74],[17,8755,8757],{"className":8756},[79,115],[17,8758,8741],{"className":8759},[79,119],[13,8761,8762,8763,8766],{},"只能说明它们",[645,8764,8765],{},"可能同构","，不能保证一定同构。",[13,8768,8769],{},"判断不同构时，常用方法是找不变量不同。",[13,8771,952],{},[150,8773,8774,8777,8780,8783],{},[153,8775,8776],{},"一个有孤立点，另一个没有；",[153,8778,8779],{},"一个有三角形，另一个没有；",[153,8781,8782],{},"一个有自环，另一个没有；",[153,8784,8785],{},"一个连通，另一个不连通。",[506,8787],{},[10,8789,8791],{"id":8790},"_122-路径与循环","12.2 路径与循环",[13,8793,8794],{},"这一节研究“能不能从一个顶点走到另一个顶点”。",[506,8796],{},[10,8798,8800],{"id":8799},"一路径","一、路径",[13,8802,5360],{},[17,8804,8806],{"className":8805},[20],[17,8807,8809,8834],{"className":8808},[24],[17,8810,8812],{"className":8811},[28],[30,8813,8814],{"xmlns":32,"display":33},[35,8815,8816,8832],{},[38,8817,8818,8820,8822,8824,8826,8828,8830],{},[187,8819,189],{},[191,8821,193],{},[191,8823,196],{"stretchy":48},[187,8825,199],{},[191,8827,202],{"separator":53},[187,8829,205],{},[191,8831,213],{"stretchy":48},[59,8833,4798],{"encoding":61},[17,8835,8837,8855],{"className":8836,"ariaHidden":53},[66],[17,8838,8840,8843,8846,8849,8852],{"className":8839},[70],[17,8841],{"className":8842,"style":226},[74],[17,8844,189],{"className":8845},[79,230],[17,8847],{"className":8848,"style":235},[234],[17,8850,193],{"className":8851},[239],[17,8853],{"className":8854,"style":235},[234],[17,8856,8858,8861,8864,8867,8870,8873,8876],{"className":8857},[70],[17,8859],{"className":8860,"style":249},[74],[17,8862,196],{"className":8863},[253],[17,8865,199],{"className":8866,"style":257},[79,230],[17,8868,202],{"className":8869},[261],[17,8871],{"className":8872,"style":265},[234],[17,8874,205],{"className":8875,"style":269},[79,230],[17,8877,213],{"className":8878},[282],[13,8880,8881],{},"一个路径可以写成：",[17,8883,8885],{"className":8884},[20],[17,8886,8888,8950],{"className":8887},[24],[17,8889,8891],{"className":8890},[28],[30,8892,8893],{"xmlns":32,"display":33},[35,8894,8895,8947],{},[38,8896,8897,8900,8902,8908,8914,8920,8926,8932,8935,8941],{},[187,8898,8899],{},"μ",[191,8901,193],{},[1385,8903,8904,8906],{},[187,8905,793],{},[1390,8907,47],{},[1385,8909,8910,8912],{},[187,8911,757],{},[1390,8913,1392],{},[1385,8915,8916,8918],{},[187,8917,793],{},[1390,8919,1392],{},[1385,8921,8922,8924],{},[187,8923,757],{},[1390,8925,1401],{},[1385,8927,8928,8930],{},[187,8929,793],{},[1390,8931,1401],{},[191,8933,8934],{},"⋯",[1385,8936,8937,8939],{},[187,8938,757],{},[187,8940,4699],{},[1385,8942,8943,8945],{},[187,8944,793],{},[187,8946,4699],{},[59,8948,8949],{"encoding":61},"\\mu=v_0e_1v_1e_2v_2\\cdots e_kv_k",[17,8951,8953,8971],{"className":8952,"ariaHidden":53},[66],[17,8954,8956,8959,8962,8965,8968],{"className":8955},[70],[17,8957],{"className":8958,"style":406},[74],[17,8960,8899],{"className":8961},[79,230],[17,8963],{"className":8964,"style":235},[234],[17,8966,193],{"className":8967},[239],[17,8969],{"className":8970,"style":235},[234],[17,8972,8974,8977,9017,9057,9097,9137,9177,9180,9184,9187,9228],{"className":8973},[70],[17,8975],{"className":8976,"style":2085},[74],[17,8978,8980,8983],{"className":8979},[79],[17,8981,793],{"className":8982,"style":818},[79,230],[17,8984,8986],{"className":8985},[1453],[17,8987,8989,9009],{"className":8988},[83,84],[17,8990,8992,9006],{"className":8991},[88],[17,8993,8995],{"className":8994,"style":1463},[92],[17,8996,8997,9000],{"style":1466},[17,8998],{"className":8999,"style":1470},[100],[17,9001,9003],{"className":9002},[1474,1475,1476,1477],[17,9004,47],{"className":9005},[79,1477],[17,9007,136],{"className":9008},[135],[17,9010,9012],{"className":9011},[88],[17,9013,9015],{"className":9014,"style":1490},[92],[17,9016],{},[17,9018,9020,9023],{"className":9019},[79],[17,9021,757],{"className":9022},[79,230],[17,9024,9026],{"className":9025},[1453],[17,9027,9029,9049],{"className":9028},[83,84],[17,9030,9032,9046],{"className":9031},[88],[17,9033,9035],{"className":9034,"style":1463},[92],[17,9036,9037,9040],{"style":2106},[17,9038],{"className":9039,"style":1470},[100],[17,9041,9043],{"className":9042},[1474,1475,1476,1477],[17,9044,1392],{"className":9045},[79,1477],[17,9047,136],{"className":9048},[135],[17,9050,9052],{"className":9051},[88],[17,9053,9055],{"className":9054,"style":1490},[92],[17,9056],{},[17,9058,9060,9063],{"className":9059},[79],[17,9061,793],{"className":9062,"style":818},[79,230],[17,9064,9066],{"className":9065},[1453],[17,9067,9069,9089],{"className":9068},[83,84],[17,9070,9072,9086],{"className":9071},[88],[17,9073,9075],{"className":9074,"style":1463},[92],[17,9076,9077,9080],{"style":1466},[17,9078],{"className":9079,"style":1470},[100],[17,9081,9083],{"className":9082},[1474,1475,1476,1477],[17,9084,1392],{"className":9085},[79,1477],[17,9087,136],{"className":9088},[135],[17,9090,9092],{"className":9091},[88],[17,9093,9095],{"className":9094,"style":1490},[92],[17,9096],{},[17,9098,9100,9103],{"className":9099},[79],[17,9101,757],{"className":9102},[79,230],[17,9104,9106],{"className":9105},[1453],[17,9107,9109,9129],{"className":9108},[83,84],[17,9110,9112,9126],{"className":9111},[88],[17,9113,9115],{"className":9114,"style":1463},[92],[17,9116,9117,9120],{"style":2106},[17,9118],{"className":9119,"style":1470},[100],[17,9121,9123],{"className":9122},[1474,1475,1476,1477],[17,9124,1401],{"className":9125},[79,1477],[17,9127,136],{"className":9128},[135],[17,9130,9132],{"className":9131},[88],[17,9133,9135],{"className":9134,"style":1490},[92],[17,9136],{},[17,9138,9140,9143],{"className":9139},[79],[17,9141,793],{"className":9142,"style":818},[79,230],[17,9144,9146],{"className":9145},[1453],[17,9147,9149,9169],{"className":9148},[83,84],[17,9150,9152,9166],{"className":9151},[88],[17,9153,9155],{"className":9154,"style":1463},[92],[17,9156,9157,9160],{"style":1466},[17,9158],{"className":9159,"style":1470},[100],[17,9161,9163],{"className":9162},[1474,1475,1476,1477],[17,9164,1401],{"className":9165},[79,1477],[17,9167,136],{"className":9168},[135],[17,9170,9172],{"className":9171},[88],[17,9173,9175],{"className":9174,"style":1490},[92],[17,9176],{},[17,9178],{"className":9179,"style":265},[234],[17,9181,8934],{"className":9182},[9183],"minner",[17,9185],{"className":9186,"style":265},[234],[17,9188,9190,9193],{"className":9189},[79],[17,9191,757],{"className":9192},[79,230],[17,9194,9196],{"className":9195},[1453],[17,9197,9199,9220],{"className":9198},[83,84],[17,9200,9202,9217],{"className":9201},[88],[17,9203,9206],{"className":9204,"style":9205},[92],"height:0.3361em;",[17,9207,9208,9211],{"style":2106},[17,9209],{"className":9210,"style":1470},[100],[17,9212,9214],{"className":9213},[1474,1475,1476,1477],[17,9215,4699],{"className":9216,"style":4715},[79,230,1477],[17,9218,136],{"className":9219},[135],[17,9221,9223],{"className":9222},[88],[17,9224,9226],{"className":9225,"style":1490},[92],[17,9227],{},[17,9229,9231,9234],{"className":9230},[79],[17,9232,793],{"className":9233,"style":818},[79,230],[17,9235,9237],{"className":9236},[1453],[17,9238,9240,9260],{"className":9239},[83,84],[17,9241,9243,9257],{"className":9242},[88],[17,9244,9246],{"className":9245,"style":9205},[92],[17,9247,9248,9251],{"style":1466},[17,9249],{"className":9250,"style":1470},[100],[17,9252,9254],{"className":9253},[1474,1475,1476,1477],[17,9255,4699],{"className":9256,"style":4715},[79,230,1477],[17,9258,136],{"className":9259},[135],[17,9261,9263],{"className":9262},[88],[17,9264,9266],{"className":9265,"style":1490},[92],[17,9267],{},[13,9269,5086],{},[13,9271,9272,9273,9343,9344,9539,9540,720],{},"从 ",[17,9274,9276,9294],{"className":9275},[24],[17,9277,9279],{"className":9278},[28],[30,9280,9281],{"xmlns":32},[35,9282,9283,9291],{},[38,9284,9285],{},[1385,9286,9287,9289],{},[187,9288,793],{},[1390,9290,47],{},[59,9292,9293],{"encoding":61},"v_0",[17,9295,9297],{"className":9296,"ariaHidden":53},[66],[17,9298,9300,9303],{"className":9299},[70],[17,9301],{"className":9302,"style":2085},[74],[17,9304,9306,9309],{"className":9305},[79],[17,9307,793],{"className":9308,"style":818},[79,230],[17,9310,9312],{"className":9311},[1453],[17,9313,9315,9335],{"className":9314},[83,84],[17,9316,9318,9332],{"className":9317},[88],[17,9319,9321],{"className":9320,"style":1463},[92],[17,9322,9323,9326],{"style":1466},[17,9324],{"className":9325,"style":1470},[100],[17,9327,9329],{"className":9328},[1474,1475,1476,1477],[17,9330,47],{"className":9331},[79,1477],[17,9333,136],{"className":9334},[135],[17,9336,9338],{"className":9337},[88],[17,9339,9341],{"className":9340,"style":1490},[92],[17,9342],{}," 出发，经过边 ",[17,9345,9347,9386],{"className":9346},[24],[17,9348,9350],{"className":9349},[28],[30,9351,9352],{"xmlns":32},[35,9353,9354,9383],{},[38,9355,9356,9362,9364,9370,9372,9375,9377],{},[1385,9357,9358,9360],{},[187,9359,757],{},[1390,9361,1392],{},[191,9363,202],{"separator":53},[1385,9365,9366,9368],{},[187,9367,757],{},[1390,9369,1401],{},[191,9371,202],{"separator":53},[191,9373,9374],{},"…",[191,9376,202],{"separator":53},[1385,9378,9379,9381],{},[187,9380,757],{},[187,9382,4699],{},[59,9384,9385],{"encoding":61},"e_1,e_2,\\dots,e_k",[17,9387,9389],{"className":9388,"ariaHidden":53},[66],[17,9390,9392,9395,9435,9438,9441,9481,9484,9487,9490,9493,9496,9499],{"className":9391},[70],[17,9393],{"className":9394,"style":406},[74],[17,9396,9398,9401],{"className":9397},[79],[17,9399,757],{"className":9400},[79,230],[17,9402,9404],{"className":9403},[1453],[17,9405,9407,9427],{"className":9406},[83,84],[17,9408,9410,9424],{"className":9409},[88],[17,9411,9413],{"className":9412,"style":1463},[92],[17,9414,9415,9418],{"style":2106},[17,9416],{"className":9417,"style":1470},[100],[17,9419,9421],{"className":9420},[1474,1475,1476,1477],[17,9422,1392],{"className":9423},[79,1477],[17,9425,136],{"className":9426},[135],[17,9428,9430],{"className":9429},[88],[17,9431,9433],{"className":9432,"style":1490},[92],[17,9434],{},[17,9436,202],{"className":9437},[261],[17,9439],{"className":9440,"style":265},[234],[17,9442,9444,9447],{"className":9443},[79],[17,9445,757],{"className":9446},[79,230],[17,9448,9450],{"className":9449},[1453],[17,9451,9453,9473],{"className":9452},[83,84],[17,9454,9456,9470],{"className":9455},[88],[17,9457,9459],{"className":9458,"style":1463},[92],[17,9460,9461,9464],{"style":2106},[17,9462],{"className":9463,"style":1470},[100],[17,9465,9467],{"className":9466},[1474,1475,1476,1477],[17,9468,1401],{"className":9469},[79,1477],[17,9471,136],{"className":9472},[135],[17,9474,9476],{"className":9475},[88],[17,9477,9479],{"className":9478,"style":1490},[92],[17,9480],{},[17,9482,202],{"className":9483},[261],[17,9485],{"className":9486,"style":265},[234],[17,9488,9374],{"className":9489},[9183],[17,9491],{"className":9492,"style":265},[234],[17,9494,202],{"className":9495},[261],[17,9497],{"className":9498,"style":265},[234],[17,9500,9502,9505],{"className":9501},[79],[17,9503,757],{"className":9504},[79,230],[17,9506,9508],{"className":9507},[1453],[17,9509,9511,9531],{"className":9510},[83,84],[17,9512,9514,9528],{"className":9513},[88],[17,9515,9517],{"className":9516,"style":9205},[92],[17,9518,9519,9522],{"style":2106},[17,9520],{"className":9521,"style":1470},[100],[17,9523,9525],{"className":9524},[1474,1475,1476,1477],[17,9526,4699],{"className":9527,"style":4715},[79,230,1477],[17,9529,136],{"className":9530},[135],[17,9532,9534],{"className":9533},[88],[17,9535,9537],{"className":9536,"style":1490},[92],[17,9538],{},"，最后到达 ",[17,9541,9543,9561],{"className":9542},[24],[17,9544,9546],{"className":9545},[28],[30,9547,9548],{"xmlns":32},[35,9549,9550,9558],{},[38,9551,9552],{},[1385,9553,9554,9556],{},[187,9555,793],{},[187,9557,4699],{},[59,9559,9560],{"encoding":61},"v_k",[17,9562,9564],{"className":9563,"ariaHidden":53},[66],[17,9565,9567,9570],{"className":9566},[70],[17,9568],{"className":9569,"style":2085},[74],[17,9571,9573,9576],{"className":9572},[79],[17,9574,793],{"className":9575,"style":818},[79,230],[17,9577,9579],{"className":9578},[1453],[17,9580,9582,9602],{"className":9581},[83,84],[17,9583,9585,9599],{"className":9584},[88],[17,9586,9588],{"className":9587,"style":9205},[92],[17,9589,9590,9593],{"style":1466},[17,9591],{"className":9592,"style":1470},[100],[17,9594,9596],{"className":9595},[1474,1475,1476,1477],[17,9597,4699],{"className":9598,"style":4715},[79,230,1477],[17,9600,136],{"className":9601},[135],[17,9603,9605],{"className":9604},[88],[17,9606,9608],{"className":9607,"style":1490},[92],[17,9609],{},[13,9611,9612],{},"路径长度是边数：",[17,9614,9616],{"className":9615},[20],[17,9617,9619,9641],{"className":9618},[24],[17,9620,9622],{"className":9621},[28],[30,9623,9624],{"xmlns":32,"display":33},[35,9625,9626,9638],{},[38,9627,9628],{},[41,9629,9630],{"notation":43},[45,9631,9632],{"scriptlevel":47,"displaystyle":48},[45,9633,9634],{"scriptlevel":47,"displaystyle":48},[45,9635,9636],{"scriptlevel":47,"displaystyle":53},[187,9637,4699],{},[59,9639,9640],{"encoding":61},"\\boxed{k}",[17,9642,9644],{"className":9643,"ariaHidden":53},[66],[17,9645,9647,9651],{"className":9646},[70],[17,9648],{"className":9649,"style":9650},[74],"height:1.3744em;vertical-align:-0.34em;",[17,9652,9654],{"className":9653},[79],[17,9655,9657,9696],{"className":9656},[83,84],[17,9658,9660,9693],{"className":9659},[88],[17,9661,9664,9683],{"className":9662,"style":9663},[92],"height:1.0344em;",[17,9665,9667,9671],{"style":9666},"top:-3.3744em;",[17,9668],{"className":9669,"style":9670},[100],"height:3.3744em;",[17,9672,9674],{"className":9673},[105],[17,9675,9677],{"className":9676},[79],[17,9678,9680],{"className":9679},[79],[17,9681,4699],{"className":9682,"style":4715},[79,230],[17,9684,9686,9689],{"style":9685},"top:-3.0344em;",[17,9687],{"className":9688,"style":9670},[100],[17,9690],{"className":9691,"style":9692},[129,130],"height:1.3744em;border-style:solid;border-width:0.04em;",[17,9694,136],{"className":9695},[135],[17,9697,9699],{"className":9698},[88],[17,9700,9702],{"className":9701,"style":143},[92],[17,9703],{},[506,9705],{},[513,9707,9709],{"id":9708},"_1-路径的起点和终点","1. 路径的起点和终点",[13,9711,9712],{},"在：",[17,9714,9716],{"className":9715},[20],[17,9717,9719,9767],{"className":9718},[24],[17,9720,9722],{"className":9721},[28],[30,9723,9724],{"xmlns":32,"display":33},[35,9725,9726,9764],{},[38,9727,9728,9730,9732,9738,9744,9750,9752,9758],{},[187,9729,8899],{},[191,9731,193],{},[1385,9733,9734,9736],{},[187,9735,793],{},[1390,9737,47],{},[1385,9739,9740,9742],{},[187,9741,757],{},[1390,9743,1392],{},[1385,9745,9746,9748],{},[187,9747,793],{},[1390,9749,1392],{},[191,9751,8934],{},[1385,9753,9754,9756],{},[187,9755,757],{},[187,9757,4699],{},[1385,9759,9760,9762],{},[187,9761,793],{},[187,9763,4699],{},[59,9765,9766],{"encoding":61},"\\mu=v_0e_1v_1\\cdots e_kv_k",[17,9768,9770,9788],{"className":9769,"ariaHidden":53},[66],[17,9771,9773,9776,9779,9782,9785],{"className":9772},[70],[17,9774],{"className":9775,"style":406},[74],[17,9777,8899],{"className":9778},[79,230],[17,9780],{"className":9781,"style":235},[234],[17,9783,193],{"className":9784},[239],[17,9786],{"className":9787,"style":235},[234],[17,9789,9791,9794,9834,9874,9914,9917,9920,9923,9963],{"className":9790},[70],[17,9792],{"className":9793,"style":2085},[74],[17,9795,9797,9800],{"className":9796},[79],[17,9798,793],{"className":9799,"style":818},[79,230],[17,9801,9803],{"className":9802},[1453],[17,9804,9806,9826],{"className":9805},[83,84],[17,9807,9809,9823],{"className":9808},[88],[17,9810,9812],{"className":9811,"style":1463},[92],[17,9813,9814,9817],{"style":1466},[17,9815],{"className":9816,"style":1470},[100],[17,9818,9820],{"className":9819},[1474,1475,1476,1477],[17,9821,47],{"className":9822},[79,1477],[17,9824,136],{"className":9825},[135],[17,9827,9829],{"className":9828},[88],[17,9830,9832],{"className":9831,"style":1490},[92],[17,9833],{},[17,9835,9837,9840],{"className":9836},[79],[17,9838,757],{"className":9839},[79,230],[17,9841,9843],{"className":9842},[1453],[17,9844,9846,9866],{"className":9845},[83,84],[17,9847,9849,9863],{"className":9848},[88],[17,9850,9852],{"className":9851,"style":1463},[92],[17,9853,9854,9857],{"style":2106},[17,9855],{"className":9856,"style":1470},[100],[17,9858,9860],{"className":9859},[1474,1475,1476,1477],[17,9861,1392],{"className":9862},[79,1477],[17,9864,136],{"className":9865},[135],[17,9867,9869],{"className":9868},[88],[17,9870,9872],{"className":9871,"style":1490},[92],[17,9873],{},[17,9875,9877,9880],{"className":9876},[79],[17,9878,793],{"className":9879,"style":818},[79,230],[17,9881,9883],{"className":9882},[1453],[17,9884,9886,9906],{"className":9885},[83,84],[17,9887,9889,9903],{"className":9888},[88],[17,9890,9892],{"className":9891,"style":1463},[92],[17,9893,9894,9897],{"style":1466},[17,9895],{"className":9896,"style":1470},[100],[17,9898,9900],{"className":9899},[1474,1475,1476,1477],[17,9901,1392],{"className":9902},[79,1477],[17,9904,136],{"className":9905},[135],[17,9907,9909],{"className":9908},[88],[17,9910,9912],{"className":9911,"style":1490},[92],[17,9913],{},[17,9915],{"className":9916,"style":265},[234],[17,9918,8934],{"className":9919},[9183],[17,9921],{"className":9922,"style":265},[234],[17,9924,9926,9929],{"className":9925},[79],[17,9927,757],{"className":9928},[79,230],[17,9930,9932],{"className":9931},[1453],[17,9933,9935,9955],{"className":9934},[83,84],[17,9936,9938,9952],{"className":9937},[88],[17,9939,9941],{"className":9940,"style":9205},[92],[17,9942,9943,9946],{"style":2106},[17,9944],{"className":9945,"style":1470},[100],[17,9947,9949],{"className":9948},[1474,1475,1476,1477],[17,9950,4699],{"className":9951,"style":4715},[79,230,1477],[17,9953,136],{"className":9954},[135],[17,9956,9958],{"className":9957},[88],[17,9959,9961],{"className":9960,"style":1490},[92],[17,9962],{},[17,9964,9966,9969],{"className":9965},[79],[17,9967,793],{"className":9968,"style":818},[79,230],[17,9970,9972],{"className":9971},[1453],[17,9973,9975,9995],{"className":9974},[83,84],[17,9976,9978,9992],{"className":9977},[88],[17,9979,9981],{"className":9980,"style":9205},[92],[17,9982,9983,9986],{"style":1466},[17,9984],{"className":9985,"style":1470},[100],[17,9987,9989],{"className":9988},[1474,1475,1476,1477],[17,9990,4699],{"className":9991,"style":4715},[79,230,1477],[17,9993,136],{"className":9994},[135],[17,9996,9998],{"className":9997},[88],[17,9999,10001],{"className":10000,"style":1490},[92],[17,10002],{},[13,10004,10005],{},"中：",[150,10007,10008,10079,10151],{},[153,10009,10010,1252],{},[17,10011,10013,10030],{"className":10012},[24],[17,10014,10016],{"className":10015},[28],[30,10017,10018],{"xmlns":32},[35,10019,10020,10028],{},[38,10021,10022],{},[1385,10023,10024,10026],{},[187,10025,793],{},[1390,10027,47],{},[59,10029,9293],{"encoding":61},[17,10031,10033],{"className":10032,"ariaHidden":53},[66],[17,10034,10036,10039],{"className":10035},[70],[17,10037],{"className":10038,"style":2085},[74],[17,10040,10042,10045],{"className":10041},[79],[17,10043,793],{"className":10044,"style":818},[79,230],[17,10046,10048],{"className":10047},[1453],[17,10049,10051,10071],{"className":10050},[83,84],[17,10052,10054,10068],{"className":10053},[88],[17,10055,10057],{"className":10056,"style":1463},[92],[17,10058,10059,10062],{"style":1466},[17,10060],{"className":10061,"style":1470},[100],[17,10063,10065],{"className":10064},[1474,1475,1476,1477],[17,10066,47],{"className":10067},[79,1477],[17,10069,136],{"className":10070},[135],[17,10072,10074],{"className":10073},[88],[17,10075,10077],{"className":10076,"style":1490},[92],[17,10078],{},[153,10080,10081,10150],{},[17,10082,10084,10101],{"className":10083},[24],[17,10085,10087],{"className":10086},[28],[30,10088,10089],{"xmlns":32},[35,10090,10091,10099],{},[38,10092,10093],{},[1385,10094,10095,10097],{},[187,10096,793],{},[187,10098,4699],{},[59,10100,9560],{"encoding":61},[17,10102,10104],{"className":10103,"ariaHidden":53},[66],[17,10105,10107,10110],{"className":10106},[70],[17,10108],{"className":10109,"style":2085},[74],[17,10111,10113,10116],{"className":10112},[79],[17,10114,793],{"className":10115,"style":818},[79,230],[17,10117,10119],{"className":10118},[1453],[17,10120,10122,10142],{"className":10121},[83,84],[17,10123,10125,10139],{"className":10124},[88],[17,10126,10128],{"className":10127,"style":9205},[92],[17,10129,10130,10133],{"style":1466},[17,10131],{"className":10132,"style":1470},[100],[17,10134,10136],{"className":10135},[1474,1475,1476,1477],[17,10137,4699],{"className":10138,"style":4715},[79,230,1477],[17,10140,136],{"className":10141},[135],[17,10143,10145],{"className":10144},[88],[17,10146,10148],{"className":10147,"style":1490},[92],[17,10149],{},"：终点；",[153,10152,10153,10181],{},[17,10154,10156,10169],{"className":10155},[24],[17,10157,10159],{"className":10158},[28],[30,10160,10161],{"xmlns":32},[35,10162,10163,10167],{},[38,10164,10165],{},[187,10166,4699],{},[59,10168,4699],{"encoding":61},[17,10170,10172],{"className":10171,"ariaHidden":53},[66],[17,10173,10175,10178],{"className":10174},[70],[17,10176],{"className":10177,"style":4711},[74],[17,10179,4699],{"className":10180,"style":4715},[79,230],"：路径长度。",[506,10183],{},[513,10185,10187],{"id":10186},"_2-简单路径","2. 简单路径",[13,10189,10190,10191,720],{},"如果路径中的边互不相同，则称为",[645,10192,10193],{},"简单路径",[13,10195,10196],{},"教材中“简单路径”重点看边不重复。",[506,10198],{},[513,10200,10202],{"id":10201},"_3-基本路径-通路","3. 基本路径 \u002F 通路",[13,10204,10205,10206,10209,10210,720],{},"如果路径中的顶点互不相同，则称为",[645,10207,10208],{},"基本路径","，也常叫",[645,10211,10212],{},"通路",[13,10214,10215],{},"顶点不重复自然边也不会重复，所以：",[17,10217,10219],{"className":10218},[20],[17,10220,10222,10245],{"className":10221},[24],[17,10223,10225],{"className":10224},[28],[30,10226,10227],{"xmlns":32,"display":33},[35,10228,10229,10242],{},[38,10230,10231],{},[41,10232,10233],{"notation":43},[45,10234,10235],{"scriptlevel":47,"displaystyle":48},[45,10236,10237],{"scriptlevel":47,"displaystyle":48},[45,10238,10239],{"scriptlevel":47,"displaystyle":53},[55,10240,10241],{},"基本路径一定是简单路径",[59,10243,10244],{"encoding":61},"\\boxed{\\text{基本路径一定是简单路径}}",[17,10246,10248],{"className":10247,"ariaHidden":53},[66],[17,10249,10251,10254],{"className":10250},[70],[17,10252],{"className":10253,"style":75},[74],[17,10255,10257],{"className":10256},[79],[17,10258,10260,10297],{"className":10259},[83,84],[17,10261,10263,10294],{"className":10262},[88],[17,10264,10266,10286],{"className":10265,"style":93},[92],[17,10267,10268,10271],{"style":96},[17,10269],{"className":10270,"style":101},[100],[17,10272,10274],{"className":10273},[105],[17,10275,10277],{"className":10276},[79],[17,10278,10280],{"className":10279},[79],[17,10281,10283],{"className":10282},[79,115],[17,10284,10241],{"className":10285},[79,119],[17,10287,10288,10291],{"style":122},[17,10289],{"className":10290,"style":101},[100],[17,10292],{"className":10293,"style":131},[129,130],[17,10295,136],{"className":10296},[135],[17,10298,10300],{"className":10299},[88],[17,10301,10303],{"className":10302,"style":143},[92],[17,10304],{},[13,10306,10307],{},"但简单路径不一定是基本路径。",[506,10309],{},[10,10311,10313],{"id":10312},"二循环-回路","二、循环 \u002F 回路",[13,10315,10316],{},"如果路径的起点和终点相同：",[17,10318,10320],{"className":10319},[20],[17,10321,10323,10349],{"className":10322},[24],[17,10324,10326],{"className":10325},[28],[30,10327,10328],{"xmlns":32,"display":33},[35,10329,10330,10346],{},[38,10331,10332,10338,10340],{},[1385,10333,10334,10336],{},[187,10335,793],{},[1390,10337,47],{},[191,10339,193],{},[1385,10341,10342,10344],{},[187,10343,793],{},[187,10345,4699],{},[59,10347,10348],{"encoding":61},"v_0=v_k",[17,10350,10352,10407],{"className":10351,"ariaHidden":53},[66],[17,10353,10355,10358,10398,10401,10404],{"className":10354},[70],[17,10356],{"className":10357,"style":2085},[74],[17,10359,10361,10364],{"className":10360},[79],[17,10362,793],{"className":10363,"style":818},[79,230],[17,10365,10367],{"className":10366},[1453],[17,10368,10370,10390],{"className":10369},[83,84],[17,10371,10373,10387],{"className":10372},[88],[17,10374,10376],{"className":10375,"style":1463},[92],[17,10377,10378,10381],{"style":1466},[17,10379],{"className":10380,"style":1470},[100],[17,10382,10384],{"className":10383},[1474,1475,1476,1477],[17,10385,47],{"className":10386},[79,1477],[17,10388,136],{"className":10389},[135],[17,10391,10393],{"className":10392},[88],[17,10394,10396],{"className":10395,"style":1490},[92],[17,10397],{},[17,10399],{"className":10400,"style":235},[234],[17,10402,193],{"className":10403},[239],[17,10405],{"className":10406,"style":235},[234],[17,10408,10410,10413],{"className":10409},[70],[17,10411],{"className":10412,"style":2085},[74],[17,10414,10416,10419],{"className":10415},[79],[17,10417,793],{"className":10418,"style":818},[79,230],[17,10420,10422],{"className":10421},[1453],[17,10423,10425,10445],{"className":10424},[83,84],[17,10426,10428,10442],{"className":10427},[88],[17,10429,10431],{"className":10430,"style":9205},[92],[17,10432,10433,10436],{"style":1466},[17,10434],{"className":10435,"style":1470},[100],[17,10437,10439],{"className":10438},[1474,1475,1476,1477],[17,10440,4699],{"className":10441,"style":4715},[79,230,1477],[17,10443,136],{"className":10444},[135],[17,10446,10448],{"className":10447},[88],[17,10449,10451],{"className":10450,"style":1490},[92],[17,10452],{},[13,10454,10455,10456,10209,10459,720],{},"则称为",[645,10457,10458],{},"循环",[645,10460,10461],{},"回路",[506,10463],{},[513,10465,10467],{"id":10466},"_1-简单循环","1. 简单循环",[13,10469,10470,10471,720],{},"如果循环中的边互不相同，则称为",[645,10472,10473],{},"简单循环",[506,10475],{},[513,10477,10479],{"id":10478},"_2-基本循环","2. 基本循环",[13,10481,10482,10483,720],{},"如果除了起点和终点相同之外，其余顶点互不相同，则称为",[645,10484,10485],{},"基本循环",[506,10487],{},[513,10489,10491],{"id":10490},"_3-基本循环与简单循环关系","3. 基本循环与简单循环关系",[17,10493,10495],{"className":10494},[20],[17,10496,10498,10521],{"className":10497},[24],[17,10499,10501],{"className":10500},[28],[30,10502,10503],{"xmlns":32,"display":33},[35,10504,10505,10518],{},[38,10506,10507],{},[41,10508,10509],{"notation":43},[45,10510,10511],{"scriptlevel":47,"displaystyle":48},[45,10512,10513],{"scriptlevel":47,"displaystyle":48},[45,10514,10515],{"scriptlevel":47,"displaystyle":53},[55,10516,10517],{},"基本循环一定是简单循环",[59,10519,10520],{"encoding":61},"\\boxed{\\text{基本循环一定是简单循环}}",[17,10522,10524],{"className":10523,"ariaHidden":53},[66],[17,10525,10527,10530],{"className":10526},[70],[17,10528],{"className":10529,"style":75},[74],[17,10531,10533],{"className":10532},[79],[17,10534,10536,10573],{"className":10535},[83,84],[17,10537,10539,10570],{"className":10538},[88],[17,10540,10542,10562],{"className":10541,"style":93},[92],[17,10543,10544,10547],{"style":96},[17,10545],{"className":10546,"style":101},[100],[17,10548,10550],{"className":10549},[105],[17,10551,10553],{"className":10552},[79],[17,10554,10556],{"className":10555},[79],[17,10557,10559],{"className":10558},[79,115],[17,10560,10517],{"className":10561},[79,119],[17,10563,10564,10567],{"style":122},[17,10565],{"className":10566,"style":101},[100],[17,10568],{"className":10569,"style":131},[129,130],[17,10571,136],{"className":10572},[135],[17,10574,10576],{"className":10575},[88],[17,10577,10579],{"className":10578,"style":143},[92],[17,10580],{},[13,10582,10583],{},"但简单循环不一定是基本循环。",[506,10585],{},[10,10587,10589],{"id":10588},"三路径长度定理","三、路径长度定理",[13,10591,7690,10592,7719,10620,10648],{},[17,10593,10595,10608],{"className":10594},[24],[17,10596,10598],{"className":10597},[28],[30,10599,10600],{"xmlns":32},[35,10601,10602,10606],{},[38,10603,10604],{},[187,10605,189],{},[59,10607,189],{"encoding":61},[17,10609,10611],{"className":10610,"ariaHidden":53},[66],[17,10612,10614,10617],{"className":10613},[70],[17,10615],{"className":10616,"style":226},[74],[17,10618,189],{"className":10619},[79,230],[17,10621,10623,10636],{"className":10622},[24],[17,10624,10626],{"className":10625},[28],[30,10627,10628],{"xmlns":32},[35,10629,10630,10634],{},[38,10631,10632],{},[187,10633,3183],{},[59,10635,3183],{"encoding":61},[17,10637,10639],{"className":10638,"ariaHidden":53},[66],[17,10640,10642,10645],{"className":10641},[70],[17,10643],{"className":10644,"style":769},[74],[17,10646,3183],{"className":10647},[79,230]," 个顶点的有向图。",[513,10650,10652],{"id":10651},"_1-基本路径长度","1. 基本路径长度",[13,10654,10655],{},"任意基本路径的长度最多为：",[17,10657,10659],{"className":10658},[20],[17,10660,10662,10690],{"className":10661},[24],[17,10663,10665],{"className":10664},[28],[30,10666,10667],{"xmlns":32,"display":33},[35,10668,10669,10687],{},[38,10670,10671],{},[41,10672,10673],{"notation":43},[45,10674,10675],{"scriptlevel":47,"displaystyle":48},[45,10676,10677],{"scriptlevel":47,"displaystyle":48},[45,10678,10679],{"scriptlevel":47,"displaystyle":53},[38,10680,10681,10683,10685],{},[187,10682,3183],{},[191,10684,972],{},[1390,10686,1392],{},[59,10688,10689],{"encoding":61},"\\boxed{n-1}",[17,10691,10693],{"className":10692,"ariaHidden":53},[66],[17,10694,10696,10700],{"className":10695},[70],[17,10697],{"className":10698,"style":10699},[74],"height:1.4078em;vertical-align:-0.4233em;",[17,10701,10703],{"className":10702},[79],[17,10704,10706,10757],{"className":10705},[83,84],[17,10707,10709,10754],{"className":10708},[88],[17,10710,10713,10744],{"className":10711,"style":10712},[92],"height:0.9844em;",[17,10714,10716,10720],{"style":10715},"top:-3.4078em;",[17,10717],{"className":10718,"style":10719},[100],"height:3.4078em;",[17,10721,10723],{"className":10722},[105],[17,10724,10726],{"className":10725},[79],[17,10727,10729,10732,10735,10738,10741],{"className":10728},[79],[17,10730,3183],{"className":10731},[79,230],[17,10733],{"className":10734,"style":257},[234],[17,10736,972],{"className":10737},[997],[17,10739],{"className":10740,"style":257},[234],[17,10742,1392],{"className":10743},[79],[17,10745,10747,10750],{"style":10746},"top:-2.9844em;",[17,10748],{"className":10749,"style":10719},[100],[17,10751],{"className":10752,"style":10753},[129,130],"height:1.4078em;border-style:solid;border-width:0.04em;",[17,10755,136],{"className":10756},[135],[17,10758,10760],{"className":10759},[88],[17,10761,10763],{"className":10762,"style":3148},[92],[17,10764],{},[13,10766,10767],{},"因为基本路径不能重复顶点。",[13,10769,10770,10771,10799,10800,10828,10829,10880],{},"如果有 ",[17,10772,10774,10787],{"className":10773},[24],[17,10775,10777],{"className":10776},[28],[30,10778,10779],{"xmlns":32},[35,10780,10781,10785],{},[38,10782,10783],{},[187,10784,3183],{},[59,10786,3183],{"encoding":61},[17,10788,10790],{"className":10789,"ariaHidden":53},[66],[17,10791,10793,10796],{"className":10792},[70],[17,10794],{"className":10795,"style":769},[74],[17,10797,3183],{"className":10798},[79,230]," 个顶点，最多经过 ",[17,10801,10803,10816],{"className":10802},[24],[17,10804,10806],{"className":10805},[28],[30,10807,10808],{"xmlns":32},[35,10809,10810,10814],{},[38,10811,10812],{},[187,10813,3183],{},[59,10815,3183],{"encoding":61},[17,10817,10819],{"className":10818,"ariaHidden":53},[66],[17,10820,10822,10825],{"className":10821},[70],[17,10823],{"className":10824,"style":769},[74],[17,10826,3183],{"className":10827},[79,230]," 个顶点，因此最多有 ",[17,10830,10832,10850],{"className":10831},[24],[17,10833,10835],{"className":10834},[28],[30,10836,10837],{"xmlns":32},[35,10838,10839,10847],{},[38,10840,10841,10843,10845],{},[187,10842,3183],{},[191,10844,972],{},[1390,10846,1392],{},[59,10848,10849],{"encoding":61},"n-1",[17,10851,10853,10871],{"className":10852,"ariaHidden":53},[66],[17,10854,10856,10859,10862,10865,10868],{"className":10855},[70],[17,10857],{"className":10858,"style":987},[74],[17,10860,3183],{"className":10861},[79,230],[17,10863],{"className":10864,"style":257},[234],[17,10866,972],{"className":10867},[997],[17,10869],{"className":10870,"style":257},[234],[17,10872,10874,10877],{"className":10873},[70],[17,10875],{"className":10876,"style":5244},[74],[17,10878,1392],{"className":10879},[79]," 条边。",[506,10882],{},[513,10884,10886],{"id":10885},"_2-基本循环长度","2. 基本循环长度",[13,10888,10889],{},"任意基本循环的长度最多为：",[17,10891,10893],{"className":10892},[20],[17,10894,10896,10918],{"className":10895},[24],[17,10897,10899],{"className":10898},[28],[30,10900,10901],{"xmlns":32,"display":33},[35,10902,10903,10915],{},[38,10904,10905],{},[41,10906,10907],{"notation":43},[45,10908,10909],{"scriptlevel":47,"displaystyle":48},[45,10910,10911],{"scriptlevel":47,"displaystyle":48},[45,10912,10913],{"scriptlevel":47,"displaystyle":53},[187,10914,3183],{},[59,10916,10917],{"encoding":61},"\\boxed{n}",[17,10919,10921],{"className":10920,"ariaHidden":53},[66],[17,10922,10924,10928],{"className":10923},[70],[17,10925],{"className":10926,"style":10927},[74],"height:1.1106em;vertical-align:-0.34em;",[17,10929,10931],{"className":10930},[79],[17,10932,10934,10973],{"className":10933},[83,84],[17,10935,10937,10970],{"className":10936},[88],[17,10938,10941,10960],{"className":10939,"style":10940},[92],"height:0.7706em;",[17,10942,10944,10948],{"style":10943},"top:-3.1106em;",[17,10945],{"className":10946,"style":10947},[100],"height:3.1106em;",[17,10949,10951],{"className":10950},[105],[17,10952,10954],{"className":10953},[79],[17,10955,10957],{"className":10956},[79],[17,10958,3183],{"className":10959},[79,230],[17,10961,10963,10966],{"style":10962},"top:-2.7706em;",[17,10964],{"className":10965,"style":10947},[100],[17,10967],{"className":10968,"style":10969},[129,130],"height:1.1106em;border-style:solid;border-width:0.04em;",[17,10971,136],{"className":10972},[135],[17,10974,10976],{"className":10975},[88],[17,10977,10979],{"className":10978,"style":143},[92],[17,10980],{},[13,10982,10983],{},"因为基本循环除了起点终点相同外，其他顶点不重复。",[506,10985],{},[10,10987,10989],{"id":10988},"四可达性","四、可达性",[513,10991,10993],{"id":10992},"_1-可达","1. 可达",[13,10995,10996,10997,11025,11026,11054],{},"在有向图中，如果从顶点 ",[17,10998,11000,11013],{"className":10999},[24],[17,11001,11003],{"className":11002},[28],[30,11004,11005],{"xmlns":32},[35,11006,11007,11011],{},[38,11008,11009],{},[187,11010,788],{},[59,11012,788],{"encoding":61},[17,11014,11016],{"className":11015,"ariaHidden":53},[66],[17,11017,11019,11022],{"className":11018},[70],[17,11020],{"className":11021,"style":769},[74],[17,11023,788],{"className":11024},[79,230]," 到顶点 ",[17,11027,11029,11042],{"className":11028},[24],[17,11030,11032],{"className":11031},[28],[30,11033,11034],{"xmlns":32},[35,11035,11036,11040],{},[38,11037,11038],{},[187,11039,793],{},[59,11041,793],{"encoding":61},[17,11043,11045],{"className":11044,"ariaHidden":53},[66],[17,11046,11048,11051],{"className":11047},[70],[17,11049],{"className":11050,"style":769},[74],[17,11052,793],{"className":11053,"style":818},[79,230]," 存在路径，则称：",[17,11056,11058],{"className":11057},[20],[17,11059,11061,11074],{"className":11060},[24],[17,11062,11064],{"className":11063},[28],[30,11065,11066],{"xmlns":32,"display":33},[35,11067,11068,11072],{},[38,11069,11070],{},[187,11071,793],{},[59,11073,793],{"encoding":61},[17,11075,11077],{"className":11076,"ariaHidden":53},[66],[17,11078,11080,11083],{"className":11079},[70],[17,11081],{"className":11082,"style":769},[74],[17,11084,793],{"className":11085,"style":818},[79,230],[13,11087,11088],{},"从：",[17,11090,11092],{"className":11091},[20],[17,11093,11095,11108],{"className":11094},[24],[17,11096,11098],{"className":11097},[28],[30,11099,11100],{"xmlns":32,"display":33},[35,11101,11102,11106],{},[38,11103,11104],{},[187,11105,788],{},[59,11107,788],{"encoding":61},[17,11109,11111],{"className":11110,"ariaHidden":53},[66],[17,11112,11114,11117],{"className":11113},[70],[17,11115],{"className":11116,"style":769},[74],[17,11118,788],{"className":11119},[79,230],[13,11121,11122],{},"可达。",[13,11124,11125],{},"也可以说：",[17,11127,11129],{"className":11128},[20],[17,11130,11132,11149],{"className":11131},[24],[17,11133,11135],{"className":11134},[28],[30,11136,11137],{"xmlns":32,"display":33},[35,11138,11139,11147],{},[38,11140,11141,11143,11145],{},[187,11142,788],{},[191,11144,1306],{},[187,11146,793],{},[59,11148,1311],{"encoding":61},[17,11150,11152,11170],{"className":11151,"ariaHidden":53},[66],[17,11153,11155,11158,11161,11164,11167],{"className":11154},[70],[17,11156],{"className":11157,"style":769},[74],[17,11159,788],{"className":11160},[79,230],[17,11162],{"className":11163,"style":235},[234],[17,11165,1306],{"className":11166},[239],[17,11168],{"className":11169,"style":235},[234],[17,11171,11173,11176],{"className":11172},[70],[17,11174],{"className":11175,"style":769},[74],[17,11177,793],{"className":11178,"style":818},[79,230],[13,11180,11122],{},[506,11182],{},[513,11184,11186],{"id":11185},"_2-顶点到自身可达","2. 顶点到自身可达",[13,11188,11189],{},"规定任意顶点到自己都是可达的。",[13,11191,11192],{},"所以可达关系具有自反性。",[506,11194],{},[513,11196,11198],{"id":11197},"_3-可达关系具有传递性","3. 可达关系具有传递性",[13,11200,4512],{},[17,11202,11204],{"className":11203},[20],[17,11205,11207,11220],{"className":11206},[24],[17,11208,11210],{"className":11209},[28],[30,11211,11212],{"xmlns":32,"display":33},[35,11213,11214,11218],{},[38,11215,11216],{},[187,11217,788],{},[59,11219,788],{"encoding":61},[17,11221,11223],{"className":11222,"ariaHidden":53},[66],[17,11224,11226,11229],{"className":11225},[70],[17,11227],{"className":11228,"style":769},[74],[17,11230,788],{"className":11231},[79,230],[13,11233,11234],{},"可达：",[17,11236,11238],{"className":11237},[20],[17,11239,11241,11254],{"className":11240},[24],[17,11242,11244],{"className":11243},[28],[30,11245,11246],{"xmlns":32,"display":33},[35,11247,11248,11252],{},[38,11249,11250],{},[187,11251,793],{},[59,11253,793],{"encoding":61},[17,11255,11257],{"className":11256,"ariaHidden":53},[66],[17,11258,11260,11263],{"className":11259},[70],[17,11261],{"className":11262,"style":769},[74],[17,11264,793],{"className":11265,"style":818},[79,230],[13,11267,7883],{},[17,11269,11271],{"className":11270},[20],[17,11272,11274,11287],{"className":11273},[24],[17,11275,11277],{"className":11276},[28],[30,11278,11279],{"xmlns":32,"display":33},[35,11280,11281,11285],{},[38,11282,11283],{},[187,11284,793],{},[59,11286,793],{"encoding":61},[17,11288,11290],{"className":11289,"ariaHidden":53},[66],[17,11291,11293,11296],{"className":11292},[70],[17,11294],{"className":11295,"style":769},[74],[17,11297,793],{"className":11298,"style":818},[79,230],[13,11300,11234],{},[17,11302,11304],{"className":11303},[20],[17,11305,11307,11320],{"className":11306},[24],[17,11308,11310],{"className":11309},[28],[30,11311,11312],{"xmlns":32,"display":33},[35,11313,11314,11318],{},[38,11315,11316],{},[187,11317,2070],{},[59,11319,2070],{"encoding":61},[17,11321,11323],{"className":11322,"ariaHidden":53},[66],[17,11324,11326,11329],{"className":11325},[70],[17,11327],{"className":11328,"style":769},[74],[17,11330,2070],{"className":11331,"style":2240},[79,230],[13,11333,11334],{},"则：",[17,11336,11338],{"className":11337},[20],[17,11339,11341,11354],{"className":11340},[24],[17,11342,11344],{"className":11343},[28],[30,11345,11346],{"xmlns":32,"display":33},[35,11347,11348,11352],{},[38,11349,11350],{},[187,11351,788],{},[59,11353,788],{"encoding":61},[17,11355,11357],{"className":11356,"ariaHidden":53},[66],[17,11358,11360,11363],{"className":11359},[70],[17,11361],{"className":11362,"style":769},[74],[17,11364,788],{"className":11365},[79,230],[13,11367,11234],{},[17,11369,11371],{"className":11370},[20],[17,11372,11374,11387],{"className":11373},[24],[17,11375,11377],{"className":11376},[28],[30,11378,11379],{"xmlns":32,"display":33},[35,11380,11381,11385],{},[38,11382,11383],{},[187,11384,2070],{},[59,11386,2070],{"encoding":61},[17,11388,11390],{"className":11389,"ariaHidden":53},[66],[17,11391,11393,11396],{"className":11392},[70],[17,11394],{"className":11395,"style":769},[74],[17,11397,2070],{"className":11398,"style":2240},[79,230],[13,11400,11401],{},"所以可达关系是自反、传递的。",[506,11403],{},[10,11405,11407],{"id":11406},"五距离","五、距离",[13,11409,11410,11411,11541],{},"在有向图中，两个顶点 ",[17,11412,11414,11442],{"className":11413},[24],[17,11415,11417],{"className":11416},[28],[30,11418,11419],{"xmlns":32},[35,11420,11421,11439],{},[38,11422,11423,11430,11432],{},[1385,11424,11425,11427],{},[187,11426,793],{},[187,11428,11429],{},"i",[191,11431,202],{"separator":53},[1385,11433,11434,11436],{},[187,11435,793],{},[187,11437,11438],{},"j",[59,11440,11441],{"encoding":61},"v_i,v_j",[17,11443,11445],{"className":11444,"ariaHidden":53},[66],[17,11446,11448,11452,11493,11496,11499],{"className":11447},[70],[17,11449],{"className":11450,"style":11451},[74],"height:0.7167em;vertical-align:-0.2861em;",[17,11453,11455,11458],{"className":11454},[79],[17,11456,793],{"className":11457,"style":818},[79,230],[17,11459,11461],{"className":11460},[1453],[17,11462,11464,11485],{"className":11463},[83,84],[17,11465,11467,11482],{"className":11466},[88],[17,11468,11471],{"className":11469,"style":11470},[92],"height:0.3117em;",[17,11472,11473,11476],{"style":1466},[17,11474],{"className":11475,"style":1470},[100],[17,11477,11479],{"className":11478},[1474,1475,1476,1477],[17,11480,11429],{"className":11481},[79,230,1477],[17,11483,136],{"className":11484},[135],[17,11486,11488],{"className":11487},[88],[17,11489,11491],{"className":11490,"style":1490},[92],[17,11492],{},[17,11494,202],{"className":11495},[261],[17,11497],{"className":11498,"style":265},[234],[17,11500,11502,11505],{"className":11501},[79],[17,11503,793],{"className":11504,"style":818},[79,230],[17,11506,11508],{"className":11507},[1453],[17,11509,11511,11532],{"className":11510},[83,84],[17,11512,11514,11529],{"className":11513},[88],[17,11515,11517],{"className":11516,"style":11470},[92],[17,11518,11519,11522],{"style":1466},[17,11520],{"className":11521,"style":1470},[100],[17,11523,11525],{"className":11524},[1474,1475,1476,1477],[17,11526,11438],{"className":11527,"style":11528},[79,230,1477],"margin-right:0.0572em;",[17,11530,136],{"className":11531},[135],[17,11533,11535],{"className":11534},[88],[17,11536,11539],{"className":11537,"style":11538},[92],"height:0.2861em;",[17,11540],{}," 的距离记作：",[17,11543,11545],{"className":11544},[20],[17,11546,11548,11580],{"className":11547},[24],[17,11549,11551],{"className":11550},[28],[30,11552,11553],{"xmlns":32,"display":33},[35,11554,11555,11577],{},[38,11556,11557,11559,11561,11567,11569,11575],{},[187,11558,3912],{},[191,11560,6777],{"stretchy":48},[1385,11562,11563,11565],{},[187,11564,793],{},[187,11566,11429],{},[191,11568,202],{"separator":53},[1385,11570,11571,11573],{},[187,11572,793],{},[187,11574,11438],{},[191,11576,6786],{"stretchy":48},[59,11578,11579],{"encoding":61},"d[v_i,v_j]",[17,11581,11583],{"className":11582,"ariaHidden":53},[66],[17,11584,11586,11590,11593,11596,11636,11639,11642,11682],{"className":11585},[70],[17,11587],{"className":11588,"style":11589},[74],"height:1.0361em;vertical-align:-0.2861em;",[17,11591,3912],{"className":11592},[79,230],[17,11594,6777],{"className":11595},[253],[17,11597,11599,11602],{"className":11598},[79],[17,11600,793],{"className":11601,"style":818},[79,230],[17,11603,11605],{"className":11604},[1453],[17,11606,11608,11628],{"className":11607},[83,84],[17,11609,11611,11625],{"className":11610},[88],[17,11612,11614],{"className":11613,"style":11470},[92],[17,11615,11616,11619],{"style":1466},[17,11617],{"className":11618,"style":1470},[100],[17,11620,11622],{"className":11621},[1474,1475,1476,1477],[17,11623,11429],{"className":11624},[79,230,1477],[17,11626,136],{"className":11627},[135],[17,11629,11631],{"className":11630},[88],[17,11632,11634],{"className":11633,"style":1490},[92],[17,11635],{},[17,11637,202],{"className":11638},[261],[17,11640],{"className":11641,"style":265},[234],[17,11643,11645,11648],{"className":11644},[79],[17,11646,793],{"className":11647,"style":818},[79,230],[17,11649,11651],{"className":11650},[1453],[17,11652,11654,11674],{"className":11653},[83,84],[17,11655,11657,11671],{"className":11656},[88],[17,11658,11660],{"className":11659,"style":11470},[92],[17,11661,11662,11665],{"style":1466},[17,11663],{"className":11664,"style":1470},[100],[17,11666,11668],{"className":11667},[1474,1475,1476,1477],[17,11669,11438],{"className":11670,"style":11528},[79,230,1477],[17,11672,136],{"className":11673},[135],[17,11675,11677],{"className":11676},[88],[17,11678,11680],{"className":11679,"style":11538},[92],[17,11681],{},[17,11683,6786],{"className":11684},[282],[13,11686,11687],{},"定义如下：",[8696,11689,11690],{},[153,11691,5875,11692,4874],{},[17,11693,11695,11713],{"className":11694},[24],[17,11696,11698],{"className":11697},[28],[30,11699,11700],{"xmlns":32},[35,11701,11702,11710],{},[38,11703,11704,11706,11708],{},[187,11705,11429],{},[191,11707,193],{},[187,11709,11438],{},[59,11711,11712],{"encoding":61},"i=j",[17,11714,11716,11735],{"className":11715,"ariaHidden":53},[66],[17,11717,11719,11723,11726,11729,11732],{"className":11718},[70],[17,11720],{"className":11721,"style":11722},[74],"height:0.6595em;",[17,11724,11429],{"className":11725},[79,230],[17,11727],{"className":11728,"style":235},[234],[17,11730,193],{"className":11731},[239],[17,11733],{"className":11734,"style":235},[234],[17,11736,11738,11742],{"className":11737},[70],[17,11739],{"className":11740,"style":11741},[74],"height:0.854em;vertical-align:-0.1944em;",[17,11743,11438],{"className":11744,"style":11528},[79,230],[17,11746,11748],{"className":11747},[20],[17,11749,11751,11787],{"className":11750},[24],[17,11752,11754],{"className":11753},[28],[30,11755,11756],{"xmlns":32,"display":33},[35,11757,11758,11784],{},[38,11759,11760,11762,11764,11770,11772,11778,11780,11782],{},[187,11761,3912],{},[191,11763,6777],{"stretchy":48},[1385,11765,11766,11768],{},[187,11767,793],{},[187,11769,11429],{},[191,11771,202],{"separator":53},[1385,11773,11774,11776],{},[187,11775,793],{},[187,11777,11438],{},[191,11779,6786],{"stretchy":48},[191,11781,193],{},[1390,11783,47],{},[59,11785,11786],{"encoding":61},"d[v_i,v_j]=0",[17,11788,11790,11900],{"className":11789,"ariaHidden":53},[66],[17,11791,11793,11796,11799,11802,11842,11845,11848,11888,11891,11894,11897],{"className":11792},[70],[17,11794],{"className":11795,"style":11589},[74],[17,11797,3912],{"className":11798},[79,230],[17,11800,6777],{"className":11801},[253],[17,11803,11805,11808],{"className":11804},[79],[17,11806,793],{"className":11807,"style":818},[79,230],[17,11809,11811],{"className":11810},[1453],[17,11812,11814,11834],{"className":11813},[83,84],[17,11815,11817,11831],{"className":11816},[88],[17,11818,11820],{"className":11819,"style":11470},[92],[17,11821,11822,11825],{"style":1466},[17,11823],{"className":11824,"style":1470},[100],[17,11826,11828],{"className":11827},[1474,1475,1476,1477],[17,11829,11429],{"className":11830},[79,230,1477],[17,11832,136],{"className":11833},[135],[17,11835,11837],{"className":11836},[88],[17,11838,11840],{"className":11839,"style":1490},[92],[17,11841],{},[17,11843,202],{"className":11844},[261],[17,11846],{"className":11847,"style":265},[234],[17,11849,11851,11854],{"className":11850},[79],[17,11852,793],{"className":11853,"style":818},[79,230],[17,11855,11857],{"className":11856},[1453],[17,11858,11860,11880],{"className":11859},[83,84],[17,11861,11863,11877],{"className":11862},[88],[17,11864,11866],{"className":11865,"style":11470},[92],[17,11867,11868,11871],{"style":1466},[17,11869],{"className":11870,"style":1470},[100],[17,11872,11874],{"className":11873},[1474,1475,1476,1477],[17,11875,11438],{"className":11876,"style":11528},[79,230,1477],[17,11878,136],{"className":11879},[135],[17,11881,11883],{"className":11882},[88],[17,11884,11886],{"className":11885,"style":11538},[92],[17,11887],{},[17,11889,6786],{"className":11890},[282],[17,11892],{"className":11893,"style":235},[234],[17,11895,193],{"className":11896},[239],[17,11898],{"className":11899,"style":235},[234],[17,11901,11903,11906],{"className":11902},[70],[17,11904],{"className":11905,"style":5244},[74],[17,11907,47],{"className":11908},[79],[8696,11910,11912],{"start":11911},2,[153,11913,5875,11914,11984,11985,12055],{},[17,11915,11917,11935],{"className":11916},[24],[17,11918,11920],{"className":11919},[28],[30,11921,11922],{"xmlns":32},[35,11923,11924,11932],{},[38,11925,11926],{},[1385,11927,11928,11930],{},[187,11929,793],{},[187,11931,11438],{},[59,11933,11934],{"encoding":61},"v_j",[17,11936,11938],{"className":11937,"ariaHidden":53},[66],[17,11939,11941,11944],{"className":11940},[70],[17,11942],{"className":11943,"style":11451},[74],[17,11945,11947,11950],{"className":11946},[79],[17,11948,793],{"className":11949,"style":818},[79,230],[17,11951,11953],{"className":11952},[1453],[17,11954,11956,11976],{"className":11955},[83,84],[17,11957,11959,11973],{"className":11958},[88],[17,11960,11962],{"className":11961,"style":11470},[92],[17,11963,11964,11967],{"style":1466},[17,11965],{"className":11966,"style":1470},[100],[17,11968,11970],{"className":11969},[1474,1475,1476,1477],[17,11971,11438],{"className":11972,"style":11528},[79,230,1477],[17,11974,136],{"className":11975},[135],[17,11977,11979],{"className":11978},[88],[17,11980,11982],{"className":11981,"style":11538},[92],[17,11983],{}," 从 ",[17,11986,11988,12006],{"className":11987},[24],[17,11989,11991],{"className":11990},[28],[30,11992,11993],{"xmlns":32},[35,11994,11995,12003],{},[38,11996,11997],{},[1385,11998,11999,12001],{},[187,12000,793],{},[187,12002,11429],{},[59,12004,12005],{"encoding":61},"v_i",[17,12007,12009],{"className":12008,"ariaHidden":53},[66],[17,12010,12012,12015],{"className":12011},[70],[17,12013],{"className":12014,"style":2085},[74],[17,12016,12018,12021],{"className":12017},[79],[17,12019,793],{"className":12020,"style":818},[79,230],[17,12022,12024],{"className":12023},[1453],[17,12025,12027,12047],{"className":12026},[83,84],[17,12028,12030,12044],{"className":12029},[88],[17,12031,12033],{"className":12032,"style":11470},[92],[17,12034,12035,12038],{"style":1466},[17,12036],{"className":12037,"style":1470},[100],[17,12039,12041],{"className":12040},[1474,1475,1476,1477],[17,12042,11429],{"className":12043},[79,230,1477],[17,12045,136],{"className":12046},[135],[17,12048,12050],{"className":12049},[88],[17,12051,12053],{"className":12052,"style":1490},[92],[17,12054],{}," 不可达，则：",[17,12057,12059],{"className":12058},[20],[17,12060,12062,12099],{"className":12061},[24],[17,12063,12065],{"className":12064},[28],[30,12066,12067],{"xmlns":32,"display":33},[35,12068,12069,12096],{},[38,12070,12071,12073,12075,12081,12083,12089,12091,12093],{},[187,12072,3912],{},[191,12074,6777],{"stretchy":48},[1385,12076,12077,12079],{},[187,12078,793],{},[187,12080,11429],{},[191,12082,202],{"separator":53},[1385,12084,12085,12087],{},[187,12086,793],{},[187,12088,11438],{},[191,12090,6786],{"stretchy":48},[191,12092,193],{},[187,12094,12095],{"mathvariant":2754},"∞",[59,12097,12098],{"encoding":61},"d[v_i,v_j]=\\infty",[17,12100,12102,12212],{"className":12101,"ariaHidden":53},[66],[17,12103,12105,12108,12111,12114,12154,12157,12160,12200,12203,12206,12209],{"className":12104},[70],[17,12106],{"className":12107,"style":11589},[74],[17,12109,3912],{"className":12110},[79,230],[17,12112,6777],{"className":12113},[253],[17,12115,12117,12120],{"className":12116},[79],[17,12118,793],{"className":12119,"style":818},[79,230],[17,12121,12123],{"className":12122},[1453],[17,12124,12126,12146],{"className":12125},[83,84],[17,12127,12129,12143],{"className":12128},[88],[17,12130,12132],{"className":12131,"style":11470},[92],[17,12133,12134,12137],{"style":1466},[17,12135],{"className":12136,"style":1470},[100],[17,12138,12140],{"className":12139},[1474,1475,1476,1477],[17,12141,11429],{"className":12142},[79,230,1477],[17,12144,136],{"className":12145},[135],[17,12147,12149],{"className":12148},[88],[17,12150,12152],{"className":12151,"style":1490},[92],[17,12153],{},[17,12155,202],{"className":12156},[261],[17,12158],{"className":12159,"style":265},[234],[17,12161,12163,12166],{"className":12162},[79],[17,12164,793],{"className":12165,"style":818},[79,230],[17,12167,12169],{"className":12168},[1453],[17,12170,12172,12192],{"className":12171},[83,84],[17,12173,12175,12189],{"className":12174},[88],[17,12176,12178],{"className":12177,"style":11470},[92],[17,12179,12180,12183],{"style":1466},[17,12181],{"className":12182,"style":1470},[100],[17,12184,12186],{"className":12185},[1474,1475,1476,1477],[17,12187,11438],{"className":12188,"style":11528},[79,230,1477],[17,12190,136],{"className":12191},[135],[17,12193,12195],{"className":12194},[88],[17,12196,12198],{"className":12197,"style":11538},[92],[17,12199],{},[17,12201,6786],{"className":12202},[282],[17,12204],{"className":12205,"style":235},[234],[17,12207,193],{"className":12208},[239],[17,12210],{"className":12211,"style":235},[234],[17,12213,12215,12218],{"className":12214},[70],[17,12216],{"className":12217,"style":769},[74],[17,12219,12095],{"className":12220},[79],[8696,12222,12224],{"start":12223},3,[153,12225,5875,12226,11984,12295,12364],{},[17,12227,12229,12246],{"className":12228},[24],[17,12230,12232],{"className":12231},[28],[30,12233,12234],{"xmlns":32},[35,12235,12236,12244],{},[38,12237,12238],{},[1385,12239,12240,12242],{},[187,12241,793],{},[187,12243,11438],{},[59,12245,11934],{"encoding":61},[17,12247,12249],{"className":12248,"ariaHidden":53},[66],[17,12250,12252,12255],{"className":12251},[70],[17,12253],{"className":12254,"style":11451},[74],[17,12256,12258,12261],{"className":12257},[79],[17,12259,793],{"className":12260,"style":818},[79,230],[17,12262,12264],{"className":12263},[1453],[17,12265,12267,12287],{"className":12266},[83,84],[17,12268,12270,12284],{"className":12269},[88],[17,12271,12273],{"className":12272,"style":11470},[92],[17,12274,12275,12278],{"style":1466},[17,12276],{"className":12277,"style":1470},[100],[17,12279,12281],{"className":12280},[1474,1475,1476,1477],[17,12282,11438],{"className":12283,"style":11528},[79,230,1477],[17,12285,136],{"className":12286},[135],[17,12288,12290],{"className":12289},[88],[17,12291,12293],{"className":12292,"style":11538},[92],[17,12294],{},[17,12296,12298,12315],{"className":12297},[24],[17,12299,12301],{"className":12300},[28],[30,12302,12303],{"xmlns":32},[35,12304,12305,12313],{},[38,12306,12307],{},[1385,12308,12309,12311],{},[187,12310,793],{},[187,12312,11429],{},[59,12314,12005],{"encoding":61},[17,12316,12318],{"className":12317,"ariaHidden":53},[66],[17,12319,12321,12324],{"className":12320},[70],[17,12322],{"className":12323,"style":2085},[74],[17,12325,12327,12330],{"className":12326},[79],[17,12328,793],{"className":12329,"style":818},[79,230],[17,12331,12333],{"className":12332},[1453],[17,12334,12336,12356],{"className":12335},[83,84],[17,12337,12339,12353],{"className":12338},[88],[17,12340,12342],{"className":12341,"style":11470},[92],[17,12343,12344,12347],{"style":1466},[17,12345],{"className":12346,"style":1470},[100],[17,12348,12350],{"className":12349},[1474,1475,1476,1477],[17,12351,11429],{"className":12352},[79,230,1477],[17,12354,136],{"className":12355},[135],[17,12357,12359],{"className":12358},[88],[17,12360,12362],{"className":12361,"style":1490},[92],[17,12363],{}," 可达，则：",[17,12366,12368],{"className":12367},[20],[17,12369,12371,12402],{"className":12370},[24],[17,12372,12374],{"className":12373},[28],[30,12375,12376],{"xmlns":32,"display":33},[35,12377,12378,12400],{},[38,12379,12380,12382,12384,12390,12392,12398],{},[187,12381,3912],{},[191,12383,6777],{"stretchy":48},[1385,12385,12386,12388],{},[187,12387,793],{},[187,12389,11429],{},[191,12391,202],{"separator":53},[1385,12393,12394,12396],{},[187,12395,793],{},[187,12397,11438],{},[191,12399,6786],{"stretchy":48},[59,12401,11579],{"encoding":61},[17,12403,12405],{"className":12404,"ariaHidden":53},[66],[17,12406,12408,12411,12414,12417,12457,12460,12463,12503],{"className":12407},[70],[17,12409],{"className":12410,"style":11589},[74],[17,12412,3912],{"className":12413},[79,230],[17,12415,6777],{"className":12416},[253],[17,12418,12420,12423],{"className":12419},[79],[17,12421,793],{"className":12422,"style":818},[79,230],[17,12424,12426],{"className":12425},[1453],[17,12427,12429,12449],{"className":12428},[83,84],[17,12430,12432,12446],{"className":12431},[88],[17,12433,12435],{"className":12434,"style":11470},[92],[17,12436,12437,12440],{"style":1466},[17,12438],{"className":12439,"style":1470},[100],[17,12441,12443],{"className":12442},[1474,1475,1476,1477],[17,12444,11429],{"className":12445},[79,230,1477],[17,12447,136],{"className":12448},[135],[17,12450,12452],{"className":12451},[88],[17,12453,12455],{"className":12454,"style":1490},[92],[17,12456],{},[17,12458,202],{"className":12459},[261],[17,12461],{"className":12462,"style":265},[234],[17,12464,12466,12469],{"className":12465},[79],[17,12467,793],{"className":12468,"style":818},[79,230],[17,12470,12472],{"className":12471},[1453],[17,12473,12475,12495],{"className":12474},[83,84],[17,12476,12478,12492],{"className":12477},[88],[17,12479,12481],{"className":12480,"style":11470},[92],[17,12482,12483,12486],{"style":1466},[17,12484],{"className":12485,"style":1470},[100],[17,12487,12489],{"className":12488},[1474,1475,1476,1477],[17,12490,11438],{"className":12491,"style":11528},[79,230,1477],[17,12493,136],{"className":12494},[135],[17,12496,12498],{"className":12497},[88],[17,12499,12501],{"className":12500,"style":11538},[92],[17,12502],{},[17,12504,6786],{"className":12505},[282],[13,12507,12508,12509,12578,12579,12648],{},"等于从 ",[17,12510,12512,12529],{"className":12511},[24],[17,12513,12515],{"className":12514},[28],[30,12516,12517],{"xmlns":32},[35,12518,12519,12527],{},[38,12520,12521],{},[1385,12522,12523,12525],{},[187,12524,793],{},[187,12526,11429],{},[59,12528,12005],{"encoding":61},[17,12530,12532],{"className":12531,"ariaHidden":53},[66],[17,12533,12535,12538],{"className":12534},[70],[17,12536],{"className":12537,"style":2085},[74],[17,12539,12541,12544],{"className":12540},[79],[17,12542,793],{"className":12543,"style":818},[79,230],[17,12545,12547],{"className":12546},[1453],[17,12548,12550,12570],{"className":12549},[83,84],[17,12551,12553,12567],{"className":12552},[88],[17,12554,12556],{"className":12555,"style":11470},[92],[17,12557,12558,12561],{"style":1466},[17,12559],{"className":12560,"style":1470},[100],[17,12562,12564],{"className":12563},[1474,1475,1476,1477],[17,12565,11429],{"className":12566},[79,230,1477],[17,12568,136],{"className":12569},[135],[17,12571,12573],{"className":12572},[88],[17,12574,12576],{"className":12575,"style":1490},[92],[17,12577],{}," 到 ",[17,12580,12582,12599],{"className":12581},[24],[17,12583,12585],{"className":12584},[28],[30,12586,12587],{"xmlns":32},[35,12588,12589,12597],{},[38,12590,12591],{},[1385,12592,12593,12595],{},[187,12594,793],{},[187,12596,11438],{},[59,12598,11934],{"encoding":61},[17,12600,12602],{"className":12601,"ariaHidden":53},[66],[17,12603,12605,12608],{"className":12604},[70],[17,12606],{"className":12607,"style":11451},[74],[17,12609,12611,12614],{"className":12610},[79],[17,12612,793],{"className":12613,"style":818},[79,230],[17,12615,12617],{"className":12616},[1453],[17,12618,12620,12640],{"className":12619},[83,84],[17,12621,12623,12637],{"className":12622},[88],[17,12624,12626],{"className":12625,"style":11470},[92],[17,12627,12628,12631],{"style":1466},[17,12629],{"className":12630,"style":1470},[100],[17,12632,12634],{"className":12633},[1474,1475,1476,1477],[17,12635,11438],{"className":12636,"style":11528},[79,230,1477],[17,12638,136],{"className":12639},[135],[17,12641,12643],{"className":12642},[88],[17,12644,12646],{"className":12645,"style":11538},[92],[17,12647],{}," 的最短路径长度。",[506,12650],{},[513,12652,12654],{"id":12653},"注意有向图距离不一定对称","注意：有向图距离不一定对称",[13,12656,12657],{},"一般：",[17,12659,12661],{"className":12660},[20],[17,12662,12664,12718],{"className":12663},[24],[17,12665,12667],{"className":12666},[28],[30,12668,12669],{"xmlns":32,"display":33},[35,12670,12671,12715],{},[38,12672,12673,12675,12677,12683,12685,12691,12693,12695,12697,12699,12705,12707,12713],{},[187,12674,3912],{},[191,12676,6777],{"stretchy":48},[1385,12678,12679,12681],{},[187,12680,793],{},[187,12682,11429],{},[191,12684,202],{"separator":53},[1385,12686,12687,12689],{},[187,12688,793],{},[187,12690,11438],{},[191,12692,6786],{"stretchy":48},[191,12694,2755],{"mathvariant":2754},[187,12696,3912],{},[191,12698,6777],{"stretchy":48},[1385,12700,12701,12703],{},[187,12702,793],{},[187,12704,11438],{},[191,12706,202],{"separator":53},[1385,12708,12709,12711],{},[187,12710,793],{},[187,12712,11429],{},[191,12714,6786],{"stretchy":48},[59,12716,12717],{"encoding":61},"d[v_i,v_j]\\neq d[v_j,v_i]",[17,12719,12721,12864],{"className":12720,"ariaHidden":53},[66],[17,12722,12724,12727,12730,12733,12773,12776,12779,12819,12822,12825,12861],{"className":12723},[70],[17,12725],{"className":12726,"style":11589},[74],[17,12728,3912],{"className":12729},[79,230],[17,12731,6777],{"className":12732},[253],[17,12734,12736,12739],{"className":12735},[79],[17,12737,793],{"className":12738,"style":818},[79,230],[17,12740,12742],{"className":12741},[1453],[17,12743,12745,12765],{"className":12744},[83,84],[17,12746,12748,12762],{"className":12747},[88],[17,12749,12751],{"className":12750,"style":11470},[92],[17,12752,12753,12756],{"style":1466},[17,12754],{"className":12755,"style":1470},[100],[17,12757,12759],{"className":12758},[1474,1475,1476,1477],[17,12760,11429],{"className":12761},[79,230,1477],[17,12763,136],{"className":12764},[135],[17,12766,12768],{"className":12767},[88],[17,12769,12771],{"className":12770,"style":1490},[92],[17,12772],{},[17,12774,202],{"className":12775},[261],[17,12777],{"className":12778,"style":265},[234],[17,12780,12782,12785],{"className":12781},[79],[17,12783,793],{"className":12784,"style":818},[79,230],[17,12786,12788],{"className":12787},[1453],[17,12789,12791,12811],{"className":12790},[83,84],[17,12792,12794,12808],{"className":12793},[88],[17,12795,12797],{"className":12796,"style":11470},[92],[17,12798,12799,12802],{"style":1466},[17,12800],{"className":12801,"style":1470},[100],[17,12803,12805],{"className":12804},[1474,1475,1476,1477],[17,12806,11438],{"className":12807,"style":11528},[79,230,1477],[17,12809,136],{"className":12810},[135],[17,12812,12814],{"className":12813},[88],[17,12815,12817],{"className":12816,"style":11538},[92],[17,12818],{},[17,12820,6786],{"className":12821},[282],[17,12823],{"className":12824,"style":235},[234],[17,12826,12828,12855,12858],{"className":12827},[239],[17,12829,12831],{"className":12830},[239],[17,12832,12834],{"className":12833},[79,2827],[17,12835,12837],{"className":12836},[2831],[17,12838,12840,12843,12852],{"className":12839},[2835],[17,12841],{"className":12842,"style":2774},[74],[17,12844,12846],{"className":12845},[2842],[17,12847,12849],{"className":12848},[79],[17,12850,2849],{"className":12851},[239],[17,12853],{"className":12854},[2853],[17,12856],{"className":12857},[234,2857],[17,12859,193],{"className":12860},[239],[17,12862],{"className":12863,"style":235},[234],[17,12865,12867,12870,12873,12876,12916,12919,12922,12962],{"className":12866},[70],[17,12868],{"className":12869,"style":11589},[74],[17,12871,3912],{"className":12872},[79,230],[17,12874,6777],{"className":12875},[253],[17,12877,12879,12882],{"className":12878},[79],[17,12880,793],{"className":12881,"style":818},[79,230],[17,12883,12885],{"className":12884},[1453],[17,12886,12888,12908],{"className":12887},[83,84],[17,12889,12891,12905],{"className":12890},[88],[17,12892,12894],{"className":12893,"style":11470},[92],[17,12895,12896,12899],{"style":1466},[17,12897],{"className":12898,"style":1470},[100],[17,12900,12902],{"className":12901},[1474,1475,1476,1477],[17,12903,11438],{"className":12904,"style":11528},[79,230,1477],[17,12906,136],{"className":12907},[135],[17,12909,12911],{"className":12910},[88],[17,12912,12914],{"className":12913,"style":11538},[92],[17,12915],{},[17,12917,202],{"className":12918},[261],[17,12920],{"className":12921,"style":265},[234],[17,12923,12925,12928],{"className":12924},[79],[17,12926,793],{"className":12927,"style":818},[79,230],[17,12929,12931],{"className":12930},[1453],[17,12932,12934,12954],{"className":12933},[83,84],[17,12935,12937,12951],{"className":12936},[88],[17,12938,12940],{"className":12939,"style":11470},[92],[17,12941,12942,12945],{"style":1466},[17,12943],{"className":12944,"style":1470},[100],[17,12946,12948],{"className":12947},[1474,1475,1476,1477],[17,12949,11429],{"className":12950},[79,230,1477],[17,12952,136],{"className":12953},[135],[17,12955,12957],{"className":12956},[88],[17,12958,12960],{"className":12959,"style":1490},[92],[17,12961],{},[17,12963,6786],{"className":12964},[282],[13,12966,12967],{},"因为有向边有方向。",[506,12969],{},[10,12971,12973],{"id":12972},"六无向图的连通性","六、无向图的连通性",[513,12975,12977],{"id":12976},"_1-连通图","1. 连通图",[13,12979,7690,12980,13008],{},[17,12981,12983,12996],{"className":12982},[24],[17,12984,12986],{"className":12985},[28],[30,12987,12988],{"xmlns":32},[35,12989,12990,12994],{},[38,12991,12992],{},[187,12993,189],{},[59,12995,189],{"encoding":61},[17,12997,12999],{"className":12998,"ariaHidden":53},[66],[17,13000,13002,13005],{"className":13001},[70],[17,13003],{"className":13004,"style":226},[74],[17,13006,189],{"className":13007},[79,230]," 是无向图。",[13,13010,13011,13012,4590,13040,720],{},"如果任意两个顶点之间都有路径相连，则称 ",[17,13013,13015,13028],{"className":13014},[24],[17,13016,13018],{"className":13017},[28],[30,13019,13020],{"xmlns":32},[35,13021,13022,13026],{},[38,13023,13024],{},[187,13025,189],{},[59,13027,189],{"encoding":61},[17,13029,13031],{"className":13030,"ariaHidden":53},[66],[17,13032,13034,13037],{"className":13033},[70],[17,13035],{"className":13036,"style":226},[74],[17,13038,189],{"className":13039},[79,230],[645,13041,13042],{},"连通图",[506,13044],{},[513,13046,13048],{"id":13047},"_2-连通分支","2. 连通分支",[13,13050,13051],{},"如果无向图不连通，可以分成若干个极大连通子图。",[13,13053,13054,13055,720],{},"这些极大连通子图叫",[645,13056,13057],{},"连通分支",[13,13059,13060],{},"连通分支个数记作：",[17,13062,13064],{"className":13063},[20],[17,13065,13067,13088],{"className":13066},[24],[17,13068,13070],{"className":13069},[28],[30,13071,13072],{"xmlns":32,"display":33},[35,13073,13074,13085],{},[38,13075,13076,13079,13081,13083],{},[187,13077,13078],{},"ω",[191,13080,841],{"stretchy":48},[187,13082,189],{},[191,13084,850],{"stretchy":48},[59,13086,13087],{"encoding":61},"\\omega(G)",[17,13089,13091],{"className":13090,"ariaHidden":53},[66],[17,13092,13094,13097,13100,13103,13106],{"className":13093},[70],[17,13095],{"className":13096,"style":249},[74],[17,13098,13078],{"className":13099,"style":818},[79,230],[17,13101,841],{"className":13102},[253],[17,13104,189],{"className":13105},[79,230],[17,13107,850],{"className":13108},[282],[13,13110,5875,13111,13139],{},[17,13112,13114,13127],{"className":13113},[24],[17,13115,13117],{"className":13116},[28],[30,13118,13119],{"xmlns":32},[35,13120,13121,13125],{},[38,13122,13123],{},[187,13124,189],{},[59,13126,189],{"encoding":61},[17,13128,13130],{"className":13129,"ariaHidden":53},[66],[17,13131,13133,13136],{"className":13132},[70],[17,13134],{"className":13135,"style":226},[74],[17,13137,189],{"className":13138},[79,230]," 是连通图，则：",[17,13141,13143],{"className":13142},[20],[17,13144,13146,13170],{"className":13145},[24],[17,13147,13149],{"className":13148},[28],[30,13150,13151],{"xmlns":32,"display":33},[35,13152,13153,13167],{},[38,13154,13155,13157,13159,13161,13163,13165],{},[187,13156,13078],{},[191,13158,841],{"stretchy":48},[187,13160,189],{},[191,13162,850],{"stretchy":48},[191,13164,193],{},[1390,13166,1392],{},[59,13168,13169],{"encoding":61},"\\omega(G)=1",[17,13171,13173,13200],{"className":13172,"ariaHidden":53},[66],[17,13174,13176,13179,13182,13185,13188,13191,13194,13197],{"className":13175},[70],[17,13177],{"className":13178,"style":249},[74],[17,13180,13078],{"className":13181,"style":818},[79,230],[17,13183,841],{"className":13184},[253],[17,13186,189],{"className":13187},[79,230],[17,13189,850],{"className":13190},[282],[17,13192],{"className":13193,"style":235},[234],[17,13195,193],{"className":13196},[239],[17,13198],{"className":13199,"style":235},[234],[17,13201,13203,13206],{"className":13202},[70],[17,13204],{"className":13205,"style":5244},[74],[17,13207,1392],{"className":13208},[79],[506,13210],{},[513,13212,13214],{"id":13213},"_3-割边-桥","3. 割边 \u002F 桥",[13,13216,13217,13218,1357,13221,720],{},"如果删去某条边后，图的连通分支数增加，则这条边叫",[645,13219,13220],{},"割边",[645,13222,13223],{},"桥",[13,13225,13226],{},"即：",[17,13228,13230],{"className":13229},[20],[17,13231,13233,13268],{"className":13232},[24],[17,13234,13236],{"className":13235},[28],[30,13237,13238],{"xmlns":32,"display":33},[35,13239,13240,13265],{},[38,13241,13242,13244,13246,13248,13250,13252,13254,13257,13259,13261,13263],{},[187,13243,13078],{},[191,13245,841],{"stretchy":48},[187,13247,189],{},[191,13249,972],{},[187,13251,757],{},[191,13253,850],{"stretchy":48},[191,13255,13256],{},">",[187,13258,13078],{},[191,13260,841],{"stretchy":48},[187,13262,189],{},[191,13264,850],{"stretchy":48},[59,13266,13267],{"encoding":61},"\\omega(G-e)>\\omega(G)",[17,13269,13271,13295,13316],{"className":13270,"ariaHidden":53},[66],[17,13272,13274,13277,13280,13283,13286,13289,13292],{"className":13273},[70],[17,13275],{"className":13276,"style":249},[74],[17,13278,13078],{"className":13279,"style":818},[79,230],[17,13281,841],{"className":13282},[253],[17,13284,189],{"className":13285},[79,230],[17,13287],{"className":13288,"style":257},[234],[17,13290,972],{"className":13291},[997],[17,13293],{"className":13294,"style":257},[234],[17,13296,13298,13301,13304,13307,13310,13313],{"className":13297},[70],[17,13299],{"className":13300,"style":249},[74],[17,13302,757],{"className":13303},[79,230],[17,13305,850],{"className":13306},[282],[17,13308],{"className":13309,"style":235},[234],[17,13311,13256],{"className":13312},[239],[17,13314],{"className":13315,"style":235},[234],[17,13317,13319,13322,13325,13328,13331],{"className":13318},[70],[17,13320],{"className":13321,"style":249},[74],[17,13323,13078],{"className":13324,"style":818},[79,230],[17,13326,841],{"className":13327},[253],[17,13329,189],{"className":13330},[79,230],[17,13332,850],{"className":13333},[282],[13,13335,1944,13336,13364],{},[17,13337,13339,13352],{"className":13338},[24],[17,13340,13342],{"className":13341},[28],[30,13343,13344],{"xmlns":32},[35,13345,13346,13350],{},[38,13347,13348],{},[187,13349,757],{},[59,13351,757],{"encoding":61},[17,13353,13355],{"className":13354,"ariaHidden":53},[66],[17,13356,13358,13361],{"className":13357},[70],[17,13359],{"className":13360,"style":769},[74],[17,13362,757],{"className":13363},[79,230]," 是割边。",[13,13366,13367],{},"直观理解：",[1700,13369,13370],{},[13,13371,13372],{},"一删这条边，图就更散了。",[506,13374],{},[513,13376,13378],{"id":13377},"_4-割点","4. 割点",[13,13380,13381,13382,720],{},"如果删去某个顶点以及与它关联的边后，图的连通分支数增加，则这个顶点叫",[645,13383,13384],{},"割点",[13,13386,13226],{},[17,13388,13390],{"className":13389},[20],[17,13391,13393,13427],{"className":13392},[24],[17,13394,13396],{"className":13395},[28],[30,13397,13398],{"xmlns":32,"display":33},[35,13399,13400,13424],{},[38,13401,13402,13404,13406,13408,13410,13412,13414,13416,13418,13420,13422],{},[187,13403,13078],{},[191,13405,841],{"stretchy":48},[187,13407,189],{},[191,13409,972],{},[187,13411,793],{},[191,13413,850],{"stretchy":48},[191,13415,13256],{},[187,13417,13078],{},[191,13419,841],{"stretchy":48},[187,13421,189],{},[191,13423,850],{"stretchy":48},[59,13425,13426],{"encoding":61},"\\omega(G-v)>\\omega(G)",[17,13428,13430,13454,13475],{"className":13429,"ariaHidden":53},[66],[17,13431,13433,13436,13439,13442,13445,13448,13451],{"className":13432},[70],[17,13434],{"className":13435,"style":249},[74],[17,13437,13078],{"className":13438,"style":818},[79,230],[17,13440,841],{"className":13441},[253],[17,13443,189],{"className":13444},[79,230],[17,13446],{"className":13447,"style":257},[234],[17,13449,972],{"className":13450},[997],[17,13452],{"className":13453,"style":257},[234],[17,13455,13457,13460,13463,13466,13469,13472],{"className":13456},[70],[17,13458],{"className":13459,"style":249},[74],[17,13461,793],{"className":13462,"style":818},[79,230],[17,13464,850],{"className":13465},[282],[17,13467],{"className":13468,"style":235},[234],[17,13470,13256],{"className":13471},[239],[17,13473],{"className":13474,"style":235},[234],[17,13476,13478,13481,13484,13487,13490],{"className":13477},[70],[17,13479],{"className":13480,"style":249},[74],[17,13482,13078],{"className":13483,"style":818},[79,230],[17,13485,841],{"className":13486},[253],[17,13488,189],{"className":13489},[79,230],[17,13491,850],{"className":13492},[282],[13,13494,1944,13495,13523],{},[17,13496,13498,13511],{"className":13497},[24],[17,13499,13501],{"className":13500},[28],[30,13502,13503],{"xmlns":32},[35,13504,13505,13509],{},[38,13506,13507],{},[187,13508,793],{},[59,13510,793],{"encoding":61},[17,13512,13514],{"className":13513,"ariaHidden":53},[66],[17,13515,13517,13520],{"className":13516},[70],[17,13518],{"className":13519,"style":769},[74],[17,13521,793],{"className":13522,"style":818},[79,230]," 是割点。",[506,13525],{},[10,13527,13529],{"id":13528},"七有向图的连通性","七、有向图的连通性",[13,13531,13532],{},"有向图比无向图复杂，教材分三种：",[513,13534,13536],{"id":13535},"_1-强连通","1. 强连通",[13,13538,13539,13540,13581],{},"如果任意两个顶点 ",[17,13541,13543,13560],{"className":13542},[24],[17,13544,13546],{"className":13545},[28],[30,13547,13548],{"xmlns":32},[35,13549,13550,13558],{},[38,13551,13552,13554,13556],{},[187,13553,788],{},[191,13555,202],{"separator":53},[187,13557,793],{},[59,13559,796],{"encoding":61},[17,13561,13563],{"className":13562,"ariaHidden":53},[66],[17,13564,13566,13569,13572,13575,13578],{"className":13565},[70],[17,13567],{"className":13568,"style":406},[74],[17,13570,788],{"className":13571},[79,230],[17,13573,202],{"className":13574},[261],[17,13576],{"className":13577,"style":265},[234],[17,13579,793],{"className":13580,"style":818},[79,230],"，都有：",[17,13583,13585],{"className":13584},[20],[17,13586,13588,13607],{"className":13587},[24],[17,13589,13591],{"className":13590},[28],[30,13592,13593],{"xmlns":32,"display":33},[35,13594,13595,13604],{},[38,13596,13597,13599,13602],{},[187,13598,788],{},[55,13600,13601],{}," 可达 ",[187,13603,793],{},[59,13605,13606],{"encoding":61},"u\\text{ 可达 }v",[17,13608,13610],{"className":13609,"ariaHidden":53},[66],[17,13611,13613,13616,13619,13632],{"className":13612},[70],[17,13614],{"className":13615,"style":226},[74],[17,13617,788],{"className":13618},[79,230],[17,13620,13622,13625,13629],{"className":13621},[79,115],[17,13623,4056],{"className":13624},[79],[17,13626,13628],{"className":13627},[79,119],"可达",[17,13630,4056],{"className":13631},[79],[17,13633,793],{"className":13634,"style":818},[79,230],[13,13636,7883],{},[17,13638,13640],{"className":13639},[20],[17,13641,13643,13661],{"className":13642},[24],[17,13644,13646],{"className":13645},[28],[30,13647,13648],{"xmlns":32,"display":33},[35,13649,13650,13658],{},[38,13651,13652,13654,13656],{},[187,13653,793],{},[55,13655,13601],{},[187,13657,788],{},[59,13659,13660],{"encoding":61},"v\\text{ 可达 }u",[17,13662,13664],{"className":13663,"ariaHidden":53},[66],[17,13665,13667,13670,13673,13685],{"className":13666},[70],[17,13668],{"className":13669,"style":226},[74],[17,13671,793],{"className":13672,"style":818},[79,230],[17,13674,13676,13679,13682],{"className":13675},[79,115],[17,13677,4056],{"className":13678},[79],[17,13680,13628],{"className":13681},[79,119],[17,13683,4056],{"className":13684},[79],[17,13686,788],{"className":13687},[79,230],[13,13689,13690,13691,720],{},"则称有向图是",[645,13692,13693],{},"强连通图",[13,13695,6842],{},[1700,13697,13698],{},[13,13699,13700],{},"任意两个点之间都能双向到达。",[506,13702],{},[513,13704,13706],{"id":13705},"_2-单向连通","2. 单向连通",[13,13708,13539,13709,13750],{},[17,13710,13712,13729],{"className":13711},[24],[17,13713,13715],{"className":13714},[28],[30,13716,13717],{"xmlns":32},[35,13718,13719,13727],{},[38,13720,13721,13723,13725],{},[187,13722,788],{},[191,13724,202],{"separator":53},[187,13726,793],{},[59,13728,796],{"encoding":61},[17,13730,13732],{"className":13731,"ariaHidden":53},[66],[17,13733,13735,13738,13741,13744,13747],{"className":13734},[70],[17,13736],{"className":13737,"style":406},[74],[17,13739,788],{"className":13740},[79,230],[17,13742,202],{"className":13743},[261],[17,13745],{"className":13746,"style":265},[234],[17,13748,793],{"className":13749,"style":818},[79,230],"，至少有一个方向可达：",[17,13752,13754],{"className":13753},[20],[17,13755,13757,13774],{"className":13756},[24],[17,13758,13760],{"className":13759},[28],[30,13761,13762],{"xmlns":32,"display":33},[35,13763,13764,13772],{},[38,13765,13766,13768,13770],{},[187,13767,788],{},[55,13769,13601],{},[187,13771,793],{},[59,13773,13606],{"encoding":61},[17,13775,13777],{"className":13776,"ariaHidden":53},[66],[17,13778,13780,13783,13786,13798],{"className":13779},[70],[17,13781],{"className":13782,"style":226},[74],[17,13784,788],{"className":13785},[79,230],[17,13787,13789,13792,13795],{"className":13788},[79,115],[17,13790,4056],{"className":13791},[79],[17,13793,13628],{"className":13794},[79,119],[17,13796,4056],{"className":13797},[79],[17,13799,793],{"className":13800,"style":818},[79,230],[13,13802,6088],{},[17,13804,13806],{"className":13805},[20],[17,13807,13809,13826],{"className":13808},[24],[17,13810,13812],{"className":13811},[28],[30,13813,13814],{"xmlns":32,"display":33},[35,13815,13816,13824],{},[38,13817,13818,13820,13822],{},[187,13819,793],{},[55,13821,13601],{},[187,13823,788],{},[59,13825,13660],{"encoding":61},[17,13827,13829],{"className":13828,"ariaHidden":53},[66],[17,13830,13832,13835,13838,13850],{"className":13831},[70],[17,13833],{"className":13834,"style":226},[74],[17,13836,793],{"className":13837,"style":818},[79,230],[17,13839,13841,13844,13847],{"className":13840},[79,115],[17,13842,4056],{"className":13843},[79],[17,13845,13628],{"className":13846},[79,119],[17,13848,4056],{"className":13849},[79],[17,13851,788],{"className":13852},[79,230],[13,13854,10455,13855,720],{},[645,13856,13857],{},"单向连通图",[506,13859],{},[513,13861,13863],{"id":13862},"_3-弱连通","3. 弱连通",[13,13865,13866,13867,720],{},"如果把有向图中所有边的方向去掉后，得到的无向图是连通图，则称原有向图是",[645,13868,13869],{},"弱连通图",[506,13871],{},[513,13873,13875],{"id":13874},"_4-三者关系","4. 三者关系",[17,13877,13879],{"className":13878},[20],[17,13880,13882,13918],{"className":13881},[24],[17,13883,13885],{"className":13884},[28],[30,13886,13887],{"xmlns":32,"display":33},[35,13888,13889,13915],{},[38,13890,13891],{},[41,13892,13893],{"notation":43},[45,13894,13895],{"scriptlevel":47,"displaystyle":48},[45,13896,13897],{"scriptlevel":47,"displaystyle":48},[45,13898,13899],{"scriptlevel":47,"displaystyle":53},[38,13900,13901,13904,13907,13910,13912],{},[55,13902,13903],{},"强连通",[191,13905,13906],{},"⇒",[55,13908,13909],{},"单向连通",[191,13911,13906],{},[55,13913,13914],{},"弱连通",[59,13916,13917],{"encoding":61},"\\boxed{\\text{强连通} \\Rightarrow \\text{单向连通} \\Rightarrow \\text{弱连通}}",[17,13919,13921],{"className":13920,"ariaHidden":53},[66],[17,13922,13924,13927],{"className":13923},[70],[17,13925],{"className":13926,"style":75},[74],[17,13928,13930],{"className":13929},[79],[17,13931,13933,14000],{"className":13932},[83,84],[17,13934,13936,13997],{"className":13935},[88],[17,13937,13939,13989],{"className":13938,"style":93},[92],[17,13940,13941,13944],{"style":96},[17,13942],{"className":13943,"style":101},[100],[17,13945,13947],{"className":13946},[105],[17,13948,13950],{"className":13949},[79],[17,13951,13953,13959,13962,13965,13968,13974,13977,13980,13983],{"className":13952},[79],[17,13954,13956],{"className":13955},[79,115],[17,13957,13903],{"className":13958},[79,119],[17,13960],{"className":13961,"style":235},[234],[17,13963,13906],{"className":13964},[239],[17,13966],{"className":13967,"style":235},[234],[17,13969,13971],{"className":13970},[79,115],[17,13972,13909],{"className":13973},[79,119],[17,13975],{"className":13976,"style":235},[234],[17,13978,13906],{"className":13979},[239],[17,13981],{"className":13982,"style":235},[234],[17,13984,13986],{"className":13985},[79,115],[17,13987,13914],{"className":13988},[79,119],[17,13990,13991,13994],{"style":122},[17,13992],{"className":13993,"style":101},[100],[17,13995],{"className":13996,"style":131},[129,130],[17,13998,136],{"className":13999},[135],[17,14001,14003],{"className":14002},[88],[17,14004,14006],{"className":14005,"style":143},[92],[17,14007],{},[13,14009,14010],{},"反过来一般不成立。",[13,14012,8103],{},[150,14014,14015,14018,14021],{},[153,14016,14017],{},"强连通最强；",[153,14019,14020],{},"单向连通居中；",[153,14022,14023],{},"弱连通最弱。",[506,14025],{},[10,14027,14029],{"id":14028},"八极大连通子图","八、极大连通子图",[513,14031,14033],{"id":14032},"_1-强分图","1. 强分图",[13,14035,14036,14037,720],{},"有向图中的极大强连通子图叫",[645,14038,14039],{},"强分图",[506,14041],{},[513,14043,14045],{"id":14044},"_2-单向分图","2. 单向分图",[13,14047,14048,14049,720],{},"有向图中的极大单向连通子图叫",[645,14050,14051],{},"单向分图",[506,14053],{},[513,14055,14057],{"id":14056},"_3-弱分图","3. 弱分图",[13,14059,14060,14061,720],{},"有向图中的极大弱连通子图叫",[645,14062,14063],{},"弱分图",[506,14065],{},[513,14067,14069],{"id":14068},"_4-常见性质","4. 常见性质",[13,14071,14072],{},"对于有向图：",[150,14074,14075,14078,14081],{},[153,14076,14077],{},"每个顶点恰好属于一个强分图；",[153,14079,14080],{},"每个顶点和每条边至少属于一个单向分图；",[153,14082,14083],{},"每个顶点和每条边恰好属于一个弱分图。",[506,14085],{},[10,14087,14089],{"id":14088},"_123-图的矩阵表示","12.3 图的矩阵表示",[13,14091,14092],{},"这一节很重要，因为它把图变成矩阵，方便计算机处理。",[13,14094,14095],{},"主要有：",[8696,14097,14098,14101,14104,14107],{},[153,14099,14100],{},"关联矩阵；",[153,14102,14103],{},"邻接矩阵；",[153,14105,14106],{},"可达矩阵；",[153,14108,14109],{},"距离矩阵。",[506,14111],{},[10,14113,14115],{"id":14114},"一关联矩阵","一、关联矩阵",[13,14117,14118],{},"关联矩阵描述的是：",[17,14120,14122],{"className":14121},[20],[17,14123,14125,14148],{"className":14124},[24],[17,14126,14128],{"className":14127},[28],[30,14129,14130],{"xmlns":32,"display":33},[35,14131,14132,14145],{},[38,14133,14134],{},[41,14135,14136],{"notation":43},[45,14137,14138],{"scriptlevel":47,"displaystyle":48},[45,14139,14140],{"scriptlevel":47,"displaystyle":48},[45,14141,14142],{"scriptlevel":47,"displaystyle":53},[55,14143,14144],{},"顶点和边之间的关系",[59,14146,14147],{"encoding":61},"\\boxed{\\text{顶点和边之间的关系}}",[17,14149,14151],{"className":14150,"ariaHidden":53},[66],[17,14152,14154,14157],{"className":14153},[70],[17,14155],{"className":14156,"style":75},[74],[17,14158,14160],{"className":14159},[79],[17,14161,14163,14200],{"className":14162},[83,84],[17,14164,14166,14197],{"className":14165},[88],[17,14167,14169,14189],{"className":14168,"style":93},[92],[17,14170,14171,14174],{"style":96},[17,14172],{"className":14173,"style":101},[100],[17,14175,14177],{"className":14176},[105],[17,14178,14180],{"className":14179},[79],[17,14181,14183],{"className":14182},[79],[17,14184,14186],{"className":14185},[79,115],[17,14187,14144],{"className":14188},[79,119],[17,14190,14191,14194],{"style":122},[17,14192],{"className":14193,"style":101},[100],[17,14195],{"className":14196,"style":131},[129,130],[17,14198,136],{"className":14199},[135],[17,14201,14203],{"className":14202},[88],[17,14204,14206],{"className":14205,"style":143},[92],[17,14207],{},[13,14209,5360],{},[17,14211,14213],{"className":14212},[20],[17,14214,14216,14260],{"className":14215},[24],[17,14217,14219],{"className":14218},[28],[30,14220,14221],{"xmlns":32,"display":33},[35,14222,14223,14257],{},[38,14224,14225,14227,14229],{},[187,14226,199],{},[191,14228,193],{},[38,14230,14231,14237,14239,14245,14247,14249,14251],{},[1385,14232,14233,14235],{},[187,14234,793],{},[1390,14236,1392],{},[191,14238,202],{"separator":53},[1385,14240,14241,14243],{},[187,14242,793],{},[1390,14244,1401],{},[191,14246,202],{"separator":53},[191,14248,9374],{},[191,14250,202],{"separator":53},[1385,14252,14253,14255],{},[187,14254,793],{},[187,14256,3183],{},[59,14258,14259],{"encoding":61},"V={v_1,v_2,\\dots,v_n}",[17,14261,14263,14281],{"className":14262,"ariaHidden":53},[66],[17,14264,14266,14269,14272,14275,14278],{"className":14265},[70],[17,14267],{"className":14268,"style":226},[74],[17,14270,199],{"className":14271,"style":257},[79,230],[17,14273],{"className":14274,"style":235},[234],[17,14276,193],{"className":14277},[239],[17,14279],{"className":14280,"style":235},[234],[17,14282,14284,14287],{"className":14283},[70],[17,14285],{"className":14286,"style":406},[74],[17,14288,14290,14330,14333,14336,14376,14379,14382,14385,14388,14391,14394],{"className":14289},[79],[17,14291,14293,14296],{"className":14292},[79],[17,14294,793],{"className":14295,"style":818},[79,230],[17,14297,14299],{"className":14298},[1453],[17,14300,14302,14322],{"className":14301},[83,84],[17,14303,14305,14319],{"className":14304},[88],[17,14306,14308],{"className":14307,"style":1463},[92],[17,14309,14310,14313],{"style":1466},[17,14311],{"className":14312,"style":1470},[100],[17,14314,14316],{"className":14315},[1474,1475,1476,1477],[17,14317,1392],{"className":14318},[79,1477],[17,14320,136],{"className":14321},[135],[17,14323,14325],{"className":14324},[88],[17,14326,14328],{"className":14327,"style":1490},[92],[17,14329],{},[17,14331,202],{"className":14332},[261],[17,14334],{"className":14335,"style":265},[234],[17,14337,14339,14342],{"className":14338},[79],[17,14340,793],{"className":14341,"style":818},[79,230],[17,14343,14345],{"className":14344},[1453],[17,14346,14348,14368],{"className":14347},[83,84],[17,14349,14351,14365],{"className":14350},[88],[17,14352,14354],{"className":14353,"style":1463},[92],[17,14355,14356,14359],{"style":1466},[17,14357],{"className":14358,"style":1470},[100],[17,14360,14362],{"className":14361},[1474,1475,1476,1477],[17,14363,1401],{"className":14364},[79,1477],[17,14366,136],{"className":14367},[135],[17,14369,14371],{"className":14370},[88],[17,14372,14374],{"className":14373,"style":1490},[92],[17,14375],{},[17,14377,202],{"className":14378},[261],[17,14380],{"className":14381,"style":265},[234],[17,14383,9374],{"className":14384},[9183],[17,14386],{"className":14387,"style":265},[234],[17,14389,202],{"className":14390},[261],[17,14392],{"className":14393,"style":265},[234],[17,14395,14397,14400],{"className":14396},[79],[17,14398,793],{"className":14399,"style":818},[79,230],[17,14401,14403],{"className":14402},[1453],[17,14404,14406,14426],{"className":14405},[83,84],[17,14407,14409,14423],{"className":14408},[88],[17,14410,14412],{"className":14411,"style":3253},[92],[17,14413,14414,14417],{"style":1466},[17,14415],{"className":14416,"style":1470},[100],[17,14418,14420],{"className":14419},[1474,1475,1476,1477],[17,14421,3183],{"className":14422},[79,230,1477],[17,14424,136],{"className":14425},[135],[17,14427,14429],{"className":14428},[88],[17,14430,14432],{"className":14431,"style":1490},[92],[17,14433],{},[17,14435,14437],{"className":14436},[20],[17,14438,14440,14484],{"className":14439},[24],[17,14441,14443],{"className":14442},[28],[30,14444,14445],{"xmlns":32,"display":33},[35,14446,14447,14481],{},[38,14448,14449,14451,14453],{},[187,14450,205],{},[191,14452,193],{},[38,14454,14455,14461,14463,14469,14471,14473,14475],{},[1385,14456,14457,14459],{},[187,14458,757],{},[1390,14460,1392],{},[191,14462,202],{"separator":53},[1385,14464,14465,14467],{},[187,14466,757],{},[1390,14468,1401],{},[191,14470,202],{"separator":53},[191,14472,9374],{},[191,14474,202],{"separator":53},[1385,14476,14477,14479],{},[187,14478,757],{},[187,14480,4859],{},[59,14482,14483],{"encoding":61},"E={e_1,e_2,\\dots,e_m}",[17,14485,14487,14505],{"className":14486,"ariaHidden":53},[66],[17,14488,14490,14493,14496,14499,14502],{"className":14489},[70],[17,14491],{"className":14492,"style":226},[74],[17,14494,205],{"className":14495,"style":269},[79,230],[17,14497],{"className":14498,"style":235},[234],[17,14500,193],{"className":14501},[239],[17,14503],{"className":14504,"style":235},[234],[17,14506,14508,14511],{"className":14507},[70],[17,14509],{"className":14510,"style":406},[74],[17,14512,14514,14554,14557,14560,14600,14603,14606,14609,14612,14615,14618],{"className":14513},[79],[17,14515,14517,14520],{"className":14516},[79],[17,14518,757],{"className":14519},[79,230],[17,14521,14523],{"className":14522},[1453],[17,14524,14526,14546],{"className":14525},[83,84],[17,14527,14529,14543],{"className":14528},[88],[17,14530,14532],{"className":14531,"style":1463},[92],[17,14533,14534,14537],{"style":2106},[17,14535],{"className":14536,"style":1470},[100],[17,14538,14540],{"className":14539},[1474,1475,1476,1477],[17,14541,1392],{"className":14542},[79,1477],[17,14544,136],{"className":14545},[135],[17,14547,14549],{"className":14548},[88],[17,14550,14552],{"className":14551,"style":1490},[92],[17,14553],{},[17,14555,202],{"className":14556},[261],[17,14558],{"className":14559,"style":265},[234],[17,14561,14563,14566],{"className":14562},[79],[17,14564,757],{"className":14565},[79,230],[17,14567,14569],{"className":14568},[1453],[17,14570,14572,14592],{"className":14571},[83,84],[17,14573,14575,14589],{"className":14574},[88],[17,14576,14578],{"className":14577,"style":1463},[92],[17,14579,14580,14583],{"style":2106},[17,14581],{"className":14582,"style":1470},[100],[17,14584,14586],{"className":14585},[1474,1475,1476,1477],[17,14587,1401],{"className":14588},[79,1477],[17,14590,136],{"className":14591},[135],[17,14593,14595],{"className":14594},[88],[17,14596,14598],{"className":14597,"style":1490},[92],[17,14599],{},[17,14601,202],{"className":14602},[261],[17,14604],{"className":14605,"style":265},[234],[17,14607,9374],{"className":14608},[9183],[17,14610],{"className":14611,"style":265},[234],[17,14613,202],{"className":14614},[261],[17,14616],{"className":14617,"style":265},[234],[17,14619,14621,14624],{"className":14620},[79],[17,14622,757],{"className":14623},[79,230],[17,14625,14627],{"className":14626},[1453],[17,14628,14630,14650],{"className":14629},[83,84],[17,14631,14633,14647],{"className":14632},[88],[17,14634,14636],{"className":14635,"style":3253},[92],[17,14637,14638,14641],{"style":2106},[17,14639],{"className":14640,"style":1470},[100],[17,14642,14644],{"className":14643},[1474,1475,1476,1477],[17,14645,4859],{"className":14646},[79,230,1477],[17,14648,136],{"className":14649},[135],[17,14651,14653],{"className":14652},[88],[17,14654,14656],{"className":14655,"style":1490},[92],[17,14657],{},[13,14659,14660],{},"关联矩阵是一个：",[17,14662,14664],{"className":14663},[20],[17,14665,14667,14686],{"className":14666},[24],[17,14668,14670],{"className":14669},[28],[30,14671,14672],{"xmlns":32,"display":33},[35,14673,14674,14683],{},[38,14675,14676,14678,14681],{},[187,14677,3183],{},[191,14679,14680],{},"×",[187,14682,4859],{},[59,14684,14685],{"encoding":61},"n\\times m",[17,14687,14689,14707],{"className":14688,"ariaHidden":53},[66],[17,14690,14692,14695,14698,14701,14704],{"className":14691},[70],[17,14693],{"className":14694,"style":987},[74],[17,14696,3183],{"className":14697},[79,230],[17,14699],{"className":14700,"style":257},[234],[17,14702,14680],{"className":14703},[997],[17,14705],{"className":14706,"style":257},[234],[17,14708,14710,14713],{"className":14709},[70],[17,14711],{"className":14712,"style":769},[74],[17,14714,4859],{"className":14715},[79,230],[13,14717,14718],{},"矩阵。",[13,14720,14721],{},"行对应顶点，列对应边。",[506,14723],{},[513,14725,14727],{"id":14726},"_1-无向图关联矩阵","1. 无向图关联矩阵",[13,14729,14730],{},"无向图中：",[17,14732,14734],{"className":14733},[20],[17,14735,14737,14778],{"className":14736},[24],[17,14738,14740],{"className":14739},[28],[30,14741,14742],{"xmlns":32,"display":33},[35,14743,14744,14775],{},[38,14745,14746,14749,14751,14753,14763],{},[187,14747,14748],{},"F",[191,14750,193],{},[191,14752,841],{"stretchy":48},[1385,14754,14755,14757],{},[187,14756,8379],{},[38,14758,14759,14761],{},[187,14760,11429],{},[187,14762,11438],{},[1385,14764,14765,14767],{},[191,14766,850],{"stretchy":48},[38,14768,14769,14771,14773],{},[187,14770,3183],{},[191,14772,14680],{},[187,14774,4859],{},[59,14776,14777],{"encoding":61},"F=(f_{ij})_{n\\times m}",[17,14779,14781,14800],{"className":14780,"ariaHidden":53},[66],[17,14782,14784,14787,14791,14794,14797],{"className":14783},[70],[17,14785],{"className":14786,"style":226},[74],[17,14788,14748],{"className":14789,"style":14790},[79,230],"margin-right:0.1389em;",[17,14792],{"className":14793,"style":235},[234],[17,14795,193],{"className":14796},[239],[17,14798],{"className":14799,"style":235},[234],[17,14801,14803,14806,14809,14854],{"className":14802},[70],[17,14804],{"className":14805,"style":11589},[74],[17,14807,841],{"className":14808},[253],[17,14810,14812,14815],{"className":14811},[79],[17,14813,8379],{"className":14814,"style":8420},[79,230],[17,14816,14818],{"className":14817},[1453],[17,14819,14821,14846],{"className":14820},[83,84],[17,14822,14824,14843],{"className":14823},[88],[17,14825,14827],{"className":14826,"style":11470},[92],[17,14828,14830,14833],{"style":14829},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[17,14831],{"className":14832,"style":1470},[100],[17,14834,14836],{"className":14835},[1474,1475,1476,1477],[17,14837,14839],{"className":14838},[79,1477],[17,14840,14842],{"className":14841,"style":11528},[79,230,1477],"ij",[17,14844,136],{"className":14845},[135],[17,14847,14849],{"className":14848},[88],[17,14850,14852],{"className":14851,"style":11538},[92],[17,14853],{},[17,14855,14857,14860],{"className":14856},[282],[17,14858,850],{"className":14859},[282],[17,14861,14863],{"className":14862},[1453],[17,14864,14866,14896],{"className":14865},[83,84],[17,14867,14869,14893],{"className":14868},[88],[17,14870,14873],{"className":14871,"style":14872},[92],"height:0.2583em;",[17,14874,14875,14878],{"style":2106},[17,14876],{"className":14877,"style":1470},[100],[17,14879,14881],{"className":14880},[1474,1475,1476,1477],[17,14882,14884,14887,14890],{"className":14883},[79,1477],[17,14885,3183],{"className":14886},[79,230,1477],[17,14888,14680],{"className":14889},[997,1477],[17,14891,4859],{"className":14892},[79,230,1477],[17,14894,136],{"className":14895},[135],[17,14897,14899],{"className":14898},[88],[17,14900,14903],{"className":14901,"style":14902},[92],"height:0.2083em;",[17,14904],{},[13,14906,285],{},[17,14908,14910],{"className":14909},[20],[17,14911,14913,15036],{"className":14912},[24],[17,14914,14916],{"className":14915},[28],[30,14917,14918],{"xmlns":32,"display":33},[35,14919,14920,15033],{},[38,14921,14922,14932,14934],{},[1385,14923,14924,14926],{},[187,14925,8379],{},[38,14927,14928,14930],{},[187,14929,11429],{},[187,14931,11438],{},[191,14933,193],{},[38,14935,14936,14939],{},[191,14937,14938],{"fence":53},"{",[14940,14941,14944],"mtable",{"rowspacing":14942,"columnalign":14943,"columnspacing":2053},"0.36em","left left",[14945,14946,14947,14958,14985,15012],"mtr",{},[14948,14949,14950],"mtd",{},[45,14951,14952],{"scriptlevel":47,"displaystyle":48},[38,14953,14954,14956],{},[1390,14955,47],{},[191,14957,202],{"separator":53},[14948,14959,14960],{},[45,14961,14962],{"scriptlevel":47,"displaystyle":48},[38,14963,14964,14970,14973,14979,14981,14983],{},[1385,14965,14966,14968],{},[187,14967,757],{},[187,14969,11438],{},[55,14971,14972],{}," 不关联 ",[1385,14974,14975,14977],{},[187,14976,793],{},[187,14978,11429],{},[55,14980,4056],{},[1390,14982,1392],{},[191,14984,202],{"separator":53},[14948,14986,14987],{},[45,14988,14989],{"scriptlevel":47,"displaystyle":48},[38,14990,14991,14997,15000,15006,15008,15010],{},[1385,14992,14993,14995],{},[187,14994,757],{},[187,14996,11438],{},[55,14998,14999],{}," 是非自环且关联 ",[1385,15001,15002,15004],{},[187,15003,793],{},[187,15005,11429],{},[55,15007,4056],{},[1390,15009,1401],{},[191,15011,202],{"separator":53},[14948,15013,15014],{},[45,15015,15016],{"scriptlevel":47,"displaystyle":48},[38,15017,15018,15024,15027],{},[1385,15019,15020,15022],{},[187,15021,757],{},[187,15023,11438],{},[55,15025,15026],{}," 是自环且关联 ",[1385,15028,15029,15031],{},[187,15030,793],{},[187,15032,11429],{},[59,15034,15035],{"encoding":61},"f_{ij}=\n\\begin{cases}\n0,& e_j\\text{ 不关联 }v_i\\\n1,& e_j\\text{ 是非自环且关联 }v_i\\\n2,& e_j\\text{ 是自环且关联 }v_i\n\\end{cases}",[17,15037,15039,15098],{"className":15038,"ariaHidden":53},[66],[17,15040,15042,15046,15089,15092,15095],{"className":15041},[70],[17,15043],{"className":15044,"style":15045},[74],"height:0.9805em;vertical-align:-0.2861em;",[17,15047,15049,15052],{"className":15048},[79],[17,15050,8379],{"className":15051,"style":8420},[79,230],[17,15053,15055],{"className":15054},[1453],[17,15056,15058,15081],{"className":15057},[83,84],[17,15059,15061,15078],{"className":15060},[88],[17,15062,15064],{"className":15063,"style":11470},[92],[17,15065,15066,15069],{"style":14829},[17,15067],{"className":15068,"style":1470},[100],[17,15070,15072],{"className":15071},[1474,1475,1476,1477],[17,15073,15075],{"className":15074},[79,1477],[17,15076,14842],{"className":15077,"style":11528},[79,230,1477],[17,15079,136],{"className":15080},[135],[17,15082,15084],{"className":15083},[88],[17,15085,15087],{"className":15086,"style":11538},[92],[17,15088],{},[17,15090],{"className":15091,"style":235},[234],[17,15093,193],{"className":15094},[239],[17,15096],{"className":15097,"style":235},[234],[17,15099,15101,15105],{"className":15100},[70],[17,15102],{"className":15103,"style":15104},[74],"height:1.8em;vertical-align:-0.65em;",[17,15106,15108,15118,15572],{"className":15107},[9183],[17,15109,15113],{"className":15110,"style":15112},[253,15111],"delimcenter","top:0em;",[17,15114,14938],{"className":15115},[15116,15117],"delimsizing","size2",[17,15119,15121],{"className":15120},[79],[17,15122,15124,15166,15171,15304,15308,15442,15445,15448],{"className":15123},[14940],[17,15125,15128],{"className":15126},[15127],"col-align-l",[17,15129,15131,15157],{"className":15130},[83,84],[17,15132,15134,15154],{"className":15133},[88],[17,15135,15138],{"className":15136,"style":15137},[92],"height:0.97em;",[17,15139,15141,15145],{"style":15140},"top:-2.97em;",[17,15142],{"className":15143,"style":15144},[100],"height:3.008em;",[17,15146,15148,15151],{"className":15147},[79],[17,15149,47],{"className":15150},[79],[17,15152,202],{"className":15153},[261],[17,15155,136],{"className":15156},[135],[17,15158,15160],{"className":15159},[88],[17,15161,15164],{"className":15162,"style":15163},[92],"height:0.47em;",[17,15165],{},[17,15167],{"className":15168,"style":15170},[15169],"arraycolsep","width:1em;",[17,15172,15174],{"className":15173},[15127],[17,15175,15177,15296],{"className":15176},[83,84],[17,15178,15180,15293],{"className":15179},[88],[17,15181,15183],{"className":15182,"style":15137},[92],[17,15184,15185,15188],{"style":15140},[17,15186],{"className":15187,"style":15144},[100],[17,15189,15191,15231,15244,15284,15287,15290],{"className":15190},[79],[17,15192,15194,15197],{"className":15193},[79],[17,15195,757],{"className":15196},[79,230],[17,15198,15200],{"className":15199},[1453],[17,15201,15203,15223],{"className":15202},[83,84],[17,15204,15206,15220],{"className":15205},[88],[17,15207,15209],{"className":15208,"style":11470},[92],[17,15210,15211,15214],{"style":2106},[17,15212],{"className":15213,"style":1470},[100],[17,15215,15217],{"className":15216},[1474,1475,1476,1477],[17,15218,11438],{"className":15219,"style":11528},[79,230,1477],[17,15221,136],{"className":15222},[135],[17,15224,15226],{"className":15225},[88],[17,15227,15229],{"className":15228,"style":11538},[92],[17,15230],{},[17,15232,15234,15237,15241],{"className":15233},[79,115],[17,15235,4056],{"className":15236},[79],[17,15238,15240],{"className":15239},[79,119],"不关联",[17,15242,4056],{"className":15243},[79],[17,15245,15247,15250],{"className":15246},[79],[17,15248,793],{"className":15249,"style":818},[79,230],[17,15251,15253],{"className":15252},[1453],[17,15254,15256,15276],{"className":15255},[83,84],[17,15257,15259,15273],{"className":15258},[88],[17,15260,15262],{"className":15261,"style":11470},[92],[17,15263,15264,15267],{"style":1466},[17,15265],{"className":15266,"style":1470},[100],[17,15268,15270],{"className":15269},[1474,1475,1476,1477],[17,15271,11429],{"className":15272},[79,230,1477],[17,15274,136],{"className":15275},[135],[17,15277,15279],{"className":15278},[88],[17,15280,15282],{"className":15281,"style":1490},[92],[17,15283],{},[17,15285,4056],{"className":15286},[234],[17,15288,1392],{"className":15289},[79],[17,15291,202],{"className":15292},[261],[17,15294,136],{"className":15295},[135],[17,15297,15299],{"className":15298},[88],[17,15300,15302],{"className":15301,"style":15163},[92],[17,15303],{},[17,15305],{"className":15306,"style":15307},[15169],"width:0.5em;",[17,15309,15312],{"className":15310},[15311],"col-align-c",[17,15313,15315,15434],{"className":15314},[83,84],[17,15316,15318,15431],{"className":15317},[88],[17,15319,15321],{"className":15320,"style":15137},[92],[17,15322,15323,15326],{"style":15140},[17,15324],{"className":15325,"style":15144},[100],[17,15327,15329,15369,15382,15422,15425,15428],{"className":15328},[79],[17,15330,15332,15335],{"className":15331},[79],[17,15333,757],{"className":15334},[79,230],[17,15336,15338],{"className":15337},[1453],[17,15339,15341,15361],{"className":15340},[83,84],[17,15342,15344,15358],{"className":15343},[88],[17,15345,15347],{"className":15346,"style":11470},[92],[17,15348,15349,15352],{"style":2106},[17,15350],{"className":15351,"style":1470},[100],[17,15353,15355],{"className":15354},[1474,1475,1476,1477],[17,15356,11438],{"className":15357,"style":11528},[79,230,1477],[17,15359,136],{"className":15360},[135],[17,15362,15364],{"className":15363},[88],[17,15365,15367],{"className":15366,"style":11538},[92],[17,15368],{},[17,15370,15372,15375,15379],{"className":15371},[79,115],[17,15373,4056],{"className":15374},[79],[17,15376,15378],{"className":15377},[79,119],"是非自环且关联",[17,15380,4056],{"className":15381},[79],[17,15383,15385,15388],{"className":15384},[79],[17,15386,793],{"className":15387,"style":818},[79,230],[17,15389,15391],{"className":15390},[1453],[17,15392,15394,15414],{"className":15393},[83,84],[17,15395,15397,15411],{"className":15396},[88],[17,15398,15400],{"className":15399,"style":11470},[92],[17,15401,15402,15405],{"style":1466},[17,15403],{"className":15404,"style":1470},[100],[17,15406,15408],{"className":15407},[1474,1475,1476,1477],[17,15409,11429],{"className":15410},[79,230,1477],[17,15412,136],{"className":15413},[135],[17,15415,15417],{"className":15416},[88],[17,15418,15420],{"className":15419,"style":1490},[92],[17,15421],{},[17,15423,4056],{"className":15424},[234],[17,15426,1401],{"className":15427},[79],[17,15429,202],{"className":15430},[261],[17,15432,136],{"className":15433},[135],[17,15435,15437],{"className":15436},[88],[17,15438,15440],{"className":15439,"style":15163},[92],[17,15441],{},[17,15443],{"className":15444,"style":15307},[15169],[17,15446],{"className":15447,"style":15307},[15169],[17,15449,15451],{"className":15450},[15311],[17,15452,15454,15564],{"className":15453},[83,84],[17,15455,15457,15561],{"className":15456},[88],[17,15458,15460],{"className":15459,"style":15137},[92],[17,15461,15462,15465],{"style":15140},[17,15463],{"className":15464,"style":15144},[100],[17,15466,15468,15508,15521],{"className":15467},[79],[17,15469,15471,15474],{"className":15470},[79],[17,15472,757],{"className":15473},[79,230],[17,15475,15477],{"className":15476},[1453],[17,15478,15480,15500],{"className":15479},[83,84],[17,15481,15483,15497],{"className":15482},[88],[17,15484,15486],{"className":15485,"style":11470},[92],[17,15487,15488,15491],{"style":2106},[17,15489],{"className":15490,"style":1470},[100],[17,15492,15494],{"className":15493},[1474,1475,1476,1477],[17,15495,11438],{"className":15496,"style":11528},[79,230,1477],[17,15498,136],{"className":15499},[135],[17,15501,15503],{"className":15502},[88],[17,15504,15506],{"className":15505,"style":11538},[92],[17,15507],{},[17,15509,15511,15514,15518],{"className":15510},[79,115],[17,15512,4056],{"className":15513},[79],[17,15515,15517],{"className":15516},[79,119],"是自环且关联",[17,15519,4056],{"className":15520},[79],[17,15522,15524,15527],{"className":15523},[79],[17,15525,793],{"className":15526,"style":818},[79,230],[17,15528,15530],{"className":15529},[1453],[17,15531,15533,15553],{"className":15532},[83,84],[17,15534,15536,15550],{"className":15535},[88],[17,15537,15539],{"className":15538,"style":11470},[92],[17,15540,15541,15544],{"style":1466},[17,15542],{"className":15543,"style":1470},[100],[17,15545,15547],{"className":15546},[1474,1475,1476,1477],[17,15548,11429],{"className":15549},[79,230,1477],[17,15551,136],{"className":15552},[135],[17,15554,15556],{"className":15555},[88],[17,15557,15559],{"className":15558,"style":1490},[92],[17,15560],{},[17,15562,136],{"className":15563},[135],[17,15565,15567],{"className":15566},[88],[17,15568,15570],{"className":15569,"style":15163},[92],[17,15571],{},[17,15573],{"className":15574},[282,3370],[13,15576,15577],{},"解释：",[150,15579,15580,15583],{},[153,15581,15582],{},"普通边连接两个顶点，所以对应两行各有一个 1；",[153,15584,15585],{},"自环在一个顶点上贡献 2。",[506,15587],{},[513,15589,15591],{"id":15590},"_2-无向图关联矩阵性质","2. 无向图关联矩阵性质",[8696,15593,15594,15597,15600,15603],{},[153,15595,15596],{},"每一列元素和为 2；",[153,15598,15599],{},"每一行元素和等于对应顶点的度；",[153,15601,15602],{},"全 0 行对应孤立点；",[153,15604,15605],{},"重边对应相同的列。",[506,15607],{},[513,15609,15611],{"id":15610},"_3-有向图关联矩阵","3. 有向图关联矩阵",[13,15613,15614],{},"有向图中，关联矩阵要体现方向。",[13,15616,15617],{},"一般按教材定义：",[17,15619,15621],{"className":15620},[20],[17,15622,15624,15775],{"className":15623},[24],[17,15625,15627],{"className":15626},[28],[30,15628,15629],{"xmlns":32,"display":33},[35,15630,15631,15772],{},[38,15632,15633,15643,15645],{},[1385,15634,15635,15637],{},[187,15636,8379],{},[38,15638,15639,15641],{},[187,15640,11429],{},[187,15642,11438],{},[191,15644,193],{},[38,15646,15647,15649],{},[191,15648,14938],{"fence":53},[14940,15650,15651],{"rowspacing":14942,"columnalign":14943,"columnspacing":2053},[14945,15652,15653,15663,15689,15719,15748],{},[14948,15654,15655],{},[45,15656,15657],{"scriptlevel":47,"displaystyle":48},[38,15658,15659,15661],{},[1390,15660,47],{},[191,15662,202],{"separator":53},[14948,15664,15665],{},[45,15666,15667],{"scriptlevel":47,"displaystyle":48},[38,15668,15669,15675,15677,15683,15685,15687],{},[1385,15670,15671,15673],{},[187,15672,757],{},[187,15674,11438],{},[55,15676,14972],{},[1385,15678,15679,15681],{},[187,15680,793],{},[187,15682,11429],{},[55,15684,4056],{},[1390,15686,1392],{},[191,15688,202],{"separator":53},[14948,15690,15691],{},[45,15692,15693],{"scriptlevel":47,"displaystyle":48},[38,15694,15695,15701,15704,15710,15713,15715,15717],{},[1385,15696,15697,15699],{},[187,15698,757],{},[187,15700,11438],{},[55,15702,15703],{}," 以 ",[1385,15705,15706,15708],{},[187,15707,793],{},[187,15709,11429],{},[55,15711,15712],{}," 为起点 ",[191,15714,972],{},[1390,15716,1392],{},[191,15718,202],{"separator":53},[14948,15720,15721],{},[45,15722,15723],{"scriptlevel":47,"displaystyle":48},[38,15724,15725,15731,15733,15739,15742,15744,15746],{},[1385,15726,15727,15729],{},[187,15728,757],{},[187,15730,11438],{},[55,15732,15703],{},[1385,15734,15735,15737],{},[187,15736,793],{},[187,15738,11429],{},[55,15740,15741],{}," 为终点 ",[191,15743,972],{},[1390,15745,1401],{},[191,15747,202],{"separator":53},[14948,15749,15750],{},[45,15751,15752],{"scriptlevel":47,"displaystyle":48},[38,15753,15754,15760,15763,15769],{},[1385,15755,15756,15758],{},[187,15757,757],{},[187,15759,11438],{},[55,15761,15762],{}," 是关联 ",[1385,15764,15765,15767],{},[187,15766,793],{},[187,15768,11429],{},[55,15770,15771],{}," 的自环",[59,15773,15774],{"encoding":61},"f_{ij}=\n\\begin{cases}\n0,& e_j\\text{ 不关联 }v_i\\\n1,& e_j\\text{ 以 }v_i\\text{ 为起点}\\\n-1,& e_j\\text{ 以 }v_i\\text{ 为终点}\\\n-2,& e_j\\text{ 是关联 }v_i\\text{ 的自环}\n\\end{cases}",[17,15776,15778,15836],{"className":15777,"ariaHidden":53},[66],[17,15779,15781,15784,15827,15830,15833],{"className":15780},[70],[17,15782],{"className":15783,"style":15045},[74],[17,15785,15787,15790],{"className":15786},[79],[17,15788,8379],{"className":15789,"style":8420},[79,230],[17,15791,15793],{"className":15792},[1453],[17,15794,15796,15819],{"className":15795},[83,84],[17,15797,15799,15816],{"className":15798},[88],[17,15800,15802],{"className":15801,"style":11470},[92],[17,15803,15804,15807],{"style":14829},[17,15805],{"className":15806,"style":1470},[100],[17,15808,15810],{"className":15809},[1474,1475,1476,1477],[17,15811,15813],{"className":15812},[79,1477],[17,15814,14842],{"className":15815,"style":11528},[79,230,1477],[17,15817,136],{"className":15818},[135],[17,15820,15822],{"className":15821},[88],[17,15823,15825],{"className":15824,"style":11538},[92],[17,15826],{},[17,15828],{"className":15829,"style":235},[234],[17,15831,193],{"className":15832},[239],[17,15834],{"className":15835,"style":235},[234],[17,15837,15839,15842],{"className":15838},[70],[17,15840],{"className":15841,"style":15104},[74],[17,15843,15845,15851,16481],{"className":15844},[9183],[17,15846,15848],{"className":15847,"style":15112},[253,15111],[17,15849,14938],{"className":15850},[15116,15117],[17,15852,15854],{"className":15853},[79],[17,15855,15857,15894,15897,16029,16032,16184,16187,16190,16341,16344,16347],{"className":15856},[14940],[17,15858,15860],{"className":15859},[15127],[17,15861,15863,15886],{"className":15862},[83,84],[17,15864,15866,15883],{"className":15865},[88],[17,15867,15869],{"className":15868,"style":15137},[92],[17,15870,15871,15874],{"style":15140},[17,15872],{"className":15873,"style":15144},[100],[17,15875,15877,15880],{"className":15876},[79],[17,15878,47],{"className":15879},[79],[17,15881,202],{"className":15882},[261],[17,15884,136],{"className":15885},[135],[17,15887,15889],{"className":15888},[88],[17,15890,15892],{"className":15891,"style":15163},[92],[17,15893],{},[17,15895],{"className":15896,"style":15170},[15169],[17,15898,15900],{"className":15899},[15127],[17,15901,15903,16021],{"className":15902},[83,84],[17,15904,15906,16018],{"className":15905},[88],[17,15907,15909],{"className":15908,"style":15137},[92],[17,15910,15911,15914],{"style":15140},[17,15912],{"className":15913,"style":15144},[100],[17,15915,15917,15957,15969,16009,16012,16015],{"className":15916},[79],[17,15918,15920,15923],{"className":15919},[79],[17,15921,757],{"className":15922},[79,230],[17,15924,15926],{"className":15925},[1453],[17,15927,15929,15949],{"className":15928},[83,84],[17,15930,15932,15946],{"className":15931},[88],[17,15933,15935],{"className":15934,"style":11470},[92],[17,15936,15937,15940],{"style":2106},[17,15938],{"className":15939,"style":1470},[100],[17,15941,15943],{"className":15942},[1474,1475,1476,1477],[17,15944,11438],{"className":15945,"style":11528},[79,230,1477],[17,15947,136],{"className":15948},[135],[17,15950,15952],{"className":15951},[88],[17,15953,15955],{"className":15954,"style":11538},[92],[17,15956],{},[17,15958,15960,15963,15966],{"className":15959},[79,115],[17,15961,4056],{"className":15962},[79],[17,15964,15240],{"className":15965},[79,119],[17,15967,4056],{"className":15968},[79],[17,15970,15972,15975],{"className":15971},[79],[17,15973,793],{"className":15974,"style":818},[79,230],[17,15976,15978],{"className":15977},[1453],[17,15979,15981,16001],{"className":15980},[83,84],[17,15982,15984,15998],{"className":15983},[88],[17,15985,15987],{"className":15986,"style":11470},[92],[17,15988,15989,15992],{"style":1466},[17,15990],{"className":15991,"style":1470},[100],[17,15993,15995],{"className":15994},[1474,1475,1476,1477],[17,15996,11429],{"className":15997},[79,230,1477],[17,15999,136],{"className":16000},[135],[17,16002,16004],{"className":16003},[88],[17,16005,16007],{"className":16006,"style":1490},[92],[17,16008],{},[17,16010,4056],{"className":16011},[234],[17,16013,1392],{"className":16014},[79],[17,16016,202],{"className":16017},[261],[17,16019,136],{"className":16020},[135],[17,16022,16024],{"className":16023},[88],[17,16025,16027],{"className":16026,"style":15163},[92],[17,16028],{},[17,16030],{"className":16031,"style":15307},[15169],[17,16033,16035],{"className":16034},[15311],[17,16036,16038,16176],{"className":16037},[83,84],[17,16039,16041,16173],{"className":16040},[88],[17,16042,16044],{"className":16043,"style":15137},[92],[17,16045,16046,16049],{"style":15140},[17,16047],{"className":16048,"style":15144},[100],[17,16050,16052,16092,16105,16145,16155,16158,16161,16164,16167,16170],{"className":16051},[79],[17,16053,16055,16058],{"className":16054},[79],[17,16056,757],{"className":16057},[79,230],[17,16059,16061],{"className":16060},[1453],[17,16062,16064,16084],{"className":16063},[83,84],[17,16065,16067,16081],{"className":16066},[88],[17,16068,16070],{"className":16069,"style":11470},[92],[17,16071,16072,16075],{"style":2106},[17,16073],{"className":16074,"style":1470},[100],[17,16076,16078],{"className":16077},[1474,1475,1476,1477],[17,16079,11438],{"className":16080,"style":11528},[79,230,1477],[17,16082,136],{"className":16083},[135],[17,16085,16087],{"className":16086},[88],[17,16088,16090],{"className":16089,"style":11538},[92],[17,16091],{},[17,16093,16095,16098,16102],{"className":16094},[79,115],[17,16096,4056],{"className":16097},[79],[17,16099,16101],{"className":16100},[79,119],"以",[17,16103,4056],{"className":16104},[79],[17,16106,16108,16111],{"className":16107},[79],[17,16109,793],{"className":16110,"style":818},[79,230],[17,16112,16114],{"className":16113},[1453],[17,16115,16117,16137],{"className":16116},[83,84],[17,16118,16120,16134],{"className":16119},[88],[17,16121,16123],{"className":16122,"style":11470},[92],[17,16124,16125,16128],{"style":1466},[17,16126],{"className":16127,"style":1470},[100],[17,16129,16131],{"className":16130},[1474,1475,1476,1477],[17,16132,11429],{"className":16133},[79,230,1477],[17,16135,136],{"className":16136},[135],[17,16138,16140],{"className":16139},[88],[17,16141,16143],{"className":16142,"style":1490},[92],[17,16144],{},[17,16146,16148,16151],{"className":16147},[79,115],[17,16149,4056],{"className":16150},[79],[17,16152,16154],{"className":16153},[79,119],"为起点",[17,16156,4056],{"className":16157},[234],[17,16159],{"className":16160,"style":257},[234],[17,16162,972],{"className":16163},[997],[17,16165],{"className":16166,"style":257},[234],[17,16168,1392],{"className":16169},[79],[17,16171,202],{"className":16172},[261],[17,16174,136],{"className":16175},[135],[17,16177,16179],{"className":16178},[88],[17,16180,16182],{"className":16181,"style":15163},[92],[17,16183],{},[17,16185],{"className":16186,"style":15307},[15169],[17,16188],{"className":16189,"style":15307},[15169],[17,16191,16193],{"className":16192},[15311],[17,16194,16196,16333],{"className":16195},[83,84],[17,16197,16199,16330],{"className":16198},[88],[17,16200,16202],{"className":16201,"style":15137},[92],[17,16203,16204,16207],{"style":15140},[17,16205],{"className":16206,"style":15144},[100],[17,16208,16210,16250,16262,16302,16312,16315,16318,16321,16324,16327],{"className":16209},[79],[17,16211,16213,16216],{"className":16212},[79],[17,16214,757],{"className":16215},[79,230],[17,16217,16219],{"className":16218},[1453],[17,16220,16222,16242],{"className":16221},[83,84],[17,16223,16225,16239],{"className":16224},[88],[17,16226,16228],{"className":16227,"style":11470},[92],[17,16229,16230,16233],{"style":2106},[17,16231],{"className":16232,"style":1470},[100],[17,16234,16236],{"className":16235},[1474,1475,1476,1477],[17,16237,11438],{"className":16238,"style":11528},[79,230,1477],[17,16240,136],{"className":16241},[135],[17,16243,16245],{"className":16244},[88],[17,16246,16248],{"className":16247,"style":11538},[92],[17,16249],{},[17,16251,16253,16256,16259],{"className":16252},[79,115],[17,16254,4056],{"className":16255},[79],[17,16257,16101],{"className":16258},[79,119],[17,16260,4056],{"className":16261},[79],[17,16263,16265,16268],{"className":16264},[79],[17,16266,793],{"className":16267,"style":818},[79,230],[17,16269,16271],{"className":16270},[1453],[17,16272,16274,16294],{"className":16273},[83,84],[17,16275,16277,16291],{"className":16276},[88],[17,16278,16280],{"className":16279,"style":11470},[92],[17,16281,16282,16285],{"style":1466},[17,16283],{"className":16284,"style":1470},[100],[17,16286,16288],{"className":16287},[1474,1475,1476,1477],[17,16289,11429],{"className":16290},[79,230,1477],[17,16292,136],{"className":16293},[135],[17,16295,16297],{"className":16296},[88],[17,16298,16300],{"className":16299,"style":1490},[92],[17,16301],{},[17,16303,16305,16308],{"className":16304},[79,115],[17,16306,4056],{"className":16307},[79],[17,16309,16311],{"className":16310},[79,119],"为终点",[17,16313,4056],{"className":16314},[234],[17,16316],{"className":16317,"style":257},[234],[17,16319,972],{"className":16320},[997],[17,16322],{"className":16323,"style":257},[234],[17,16325,1401],{"className":16326},[79],[17,16328,202],{"className":16329},[261],[17,16331,136],{"className":16332},[135],[17,16334,16336],{"className":16335},[88],[17,16337,16339],{"className":16338,"style":15163},[92],[17,16340],{},[17,16342],{"className":16343,"style":15307},[15169],[17,16345],{"className":16346,"style":15307},[15169],[17,16348,16350],{"className":16349},[15311],[17,16351,16353,16473],{"className":16352},[83,84],[17,16354,16356,16470],{"className":16355},[88],[17,16357,16359],{"className":16358,"style":15137},[92],[17,16360,16361,16364],{"style":15140},[17,16362],{"className":16363,"style":15144},[100],[17,16365,16367,16407,16420,16460],{"className":16366},[79],[17,16368,16370,16373],{"className":16369},[79],[17,16371,757],{"className":16372},[79,230],[17,16374,16376],{"className":16375},[1453],[17,16377,16379,16399],{"className":16378},[83,84],[17,16380,16382,16396],{"className":16381},[88],[17,16383,16385],{"className":16384,"style":11470},[92],[17,16386,16387,16390],{"style":2106},[17,16388],{"className":16389,"style":1470},[100],[17,16391,16393],{"className":16392},[1474,1475,1476,1477],[17,16394,11438],{"className":16395,"style":11528},[79,230,1477],[17,16397,136],{"className":16398},[135],[17,16400,16402],{"className":16401},[88],[17,16403,16405],{"className":16404,"style":11538},[92],[17,16406],{},[17,16408,16410,16413,16417],{"className":16409},[79,115],[17,16411,4056],{"className":16412},[79],[17,16414,16416],{"className":16415},[79,119],"是关联",[17,16418,4056],{"className":16419},[79],[17,16421,16423,16426],{"className":16422},[79],[17,16424,793],{"className":16425,"style":818},[79,230],[17,16427,16429],{"className":16428},[1453],[17,16430,16432,16452],{"className":16431},[83,84],[17,16433,16435,16449],{"className":16434},[88],[17,16436,16438],{"className":16437,"style":11470},[92],[17,16439,16440,16443],{"style":1466},[17,16441],{"className":16442,"style":1470},[100],[17,16444,16446],{"className":16445},[1474,1475,1476,1477],[17,16447,11429],{"className":16448},[79,230,1477],[17,16450,136],{"className":16451},[135],[17,16453,16455],{"className":16454},[88],[17,16456,16458],{"className":16457,"style":1490},[92],[17,16459],{},[17,16461,16463,16466],{"className":16462},[79,115],[17,16464,4056],{"className":16465},[79],[17,16467,16469],{"className":16468},[79,119],"的自环",[17,16471,136],{"className":16472},[135],[17,16474,16476],{"className":16475},[88],[17,16477,16479],{"className":16478,"style":15163},[92],[17,16480],{},[17,16482],{"className":16483},[282,3370],[13,16485,16486],{},"不同教材对有向自环的矩阵记法可能略有差异，但普通有向边最重要的是：",[17,16488,16490],{"className":16489},[20],[17,16491,16493,16529],{"className":16492},[24],[17,16494,16496],{"className":16495},[28],[30,16497,16498],{"xmlns":32,"display":33},[35,16499,16500,16526],{},[38,16501,16502],{},[41,16503,16504],{"notation":43},[45,16505,16506],{"scriptlevel":47,"displaystyle":48},[45,16507,16508],{"scriptlevel":47,"displaystyle":48},[45,16509,16510],{"scriptlevel":47,"displaystyle":53},[38,16511,16512,16515,16517,16519,16522,16524],{},[55,16513,16514],{},"起点记 ",[1390,16516,1392],{},[191,16518,202],{"separator":53},[55,16520,16521],{}," 终点记 ",[191,16523,972],{},[1390,16525,1392],{},[59,16527,16528],{"encoding":61},"\\boxed{\\text{起点记 }1,\\text{ 终点记 }-1}",[17,16530,16532],{"className":16531,"ariaHidden":53},[66],[17,16533,16535,16539],{"className":16534},[70],[17,16536],{"className":16537,"style":16538},[74],"height:1.5578em;vertical-align:-0.5344em;",[17,16540,16542],{"className":16541},[79],[17,16543,16545,16623],{"className":16544},[83,84],[17,16546,16548,16620],{"className":16547},[88],[17,16549,16551,16611],{"className":16550,"style":93},[92],[17,16552,16554,16558],{"style":16553},"top:-3.5578em;",[17,16555],{"className":16556,"style":16557},[100],"height:3.5578em;",[17,16559,16561],{"className":16560},[105],[17,16562,16564],{"className":16563},[79],[17,16565,16567,16577,16580,16583,16586,16599,16602,16605,16608],{"className":16566},[79],[17,16568,16570,16574],{"className":16569},[79,115],[17,16571,16573],{"className":16572},[79,119],"起点记",[17,16575,4056],{"className":16576},[79],[17,16578,1392],{"className":16579},[79],[17,16581,202],{"className":16582},[261],[17,16584],{"className":16585,"style":265},[234],[17,16587,16589,16592,16596],{"className":16588},[79,115],[17,16590,4056],{"className":16591},[79],[17,16593,16595],{"className":16594},[79,119],"终点记",[17,16597,4056],{"className":16598},[79],[17,16600],{"className":16601,"style":257},[234],[17,16603,972],{"className":16604},[997],[17,16606],{"className":16607,"style":257},[234],[17,16609,1392],{"className":16610},[79],[17,16612,16613,16616],{"style":122},[17,16614],{"className":16615,"style":16557},[100],[17,16617],{"className":16618,"style":16619},[129,130],"height:1.5578em;border-style:solid;border-width:0.04em;",[17,16621,136],{"className":16622},[135],[17,16624,16626],{"className":16625},[88],[17,16627,16630],{"className":16628,"style":16629},[92],"height:0.5344em;",[17,16631],{},[506,16633],{},[10,16635,16637],{"id":16636},"二邻接矩阵","二、邻接矩阵",[13,16639,16640],{},"邻接矩阵描述的是：",[17,16642,16644],{"className":16643},[20],[17,16645,16647,16670],{"className":16646},[24],[17,16648,16650],{"className":16649},[28],[30,16651,16652],{"xmlns":32,"display":33},[35,16653,16654,16667],{},[38,16655,16656],{},[41,16657,16658],{"notation":43},[45,16659,16660],{"scriptlevel":47,"displaystyle":48},[45,16661,16662],{"scriptlevel":47,"displaystyle":48},[45,16663,16664],{"scriptlevel":47,"displaystyle":53},[55,16665,16666],{},"顶点和顶点之间的连接关系",[59,16668,16669],{"encoding":61},"\\boxed{\\text{顶点和顶点之间的连接关系}}",[17,16671,16673],{"className":16672,"ariaHidden":53},[66],[17,16674,16676,16679],{"className":16675},[70],[17,16677],{"className":16678,"style":75},[74],[17,16680,16682],{"className":16681},[79],[17,16683,16685,16722],{"className":16684},[83,84],[17,16686,16688,16719],{"className":16687},[88],[17,16689,16691,16711],{"className":16690,"style":93},[92],[17,16692,16693,16696],{"style":96},[17,16694],{"className":16695,"style":101},[100],[17,16697,16699],{"className":16698},[105],[17,16700,16702],{"className":16701},[79],[17,16703,16705],{"className":16704},[79],[17,16706,16708],{"className":16707},[79,115],[17,16709,16666],{"className":16710},[79,119],[17,16712,16713,16716],{"style":122},[17,16714],{"className":16715,"style":101},[100],[17,16717],{"className":16718,"style":131},[129,130],[17,16720,136],{"className":16721},[135],[17,16723,16725],{"className":16724},[88],[17,16726,16728],{"className":16727,"style":143},[92],[17,16729],{},[13,16731,5360],{},[17,16733,16735],{"className":16734},[20],[17,16736,16738,16781],{"className":16737},[24],[17,16739,16741],{"className":16740},[28],[30,16742,16743],{"xmlns":32,"display":33},[35,16744,16745,16779],{},[38,16746,16747,16749,16751],{},[187,16748,199],{},[191,16750,193],{},[38,16752,16753,16759,16761,16767,16769,16771,16773],{},[1385,16754,16755,16757],{},[187,16756,793],{},[1390,16758,1392],{},[191,16760,202],{"separator":53},[1385,16762,16763,16765],{},[187,16764,793],{},[1390,16766,1401],{},[191,16768,202],{"separator":53},[191,16770,9374],{},[191,16772,202],{"separator":53},[1385,16774,16775,16777],{},[187,16776,793],{},[187,16778,3183],{},[59,16780,14259],{"encoding":61},[17,16782,16784,16802],{"className":16783,"ariaHidden":53},[66],[17,16785,16787,16790,16793,16796,16799],{"className":16786},[70],[17,16788],{"className":16789,"style":226},[74],[17,16791,199],{"className":16792,"style":257},[79,230],[17,16794],{"className":16795,"style":235},[234],[17,16797,193],{"className":16798},[239],[17,16800],{"className":16801,"style":235},[234],[17,16803,16805,16808],{"className":16804},[70],[17,16806],{"className":16807,"style":406},[74],[17,16809,16811,16851,16854,16857,16897,16900,16903,16906,16909,16912,16915],{"className":16810},[79],[17,16812,16814,16817],{"className":16813},[79],[17,16815,793],{"className":16816,"style":818},[79,230],[17,16818,16820],{"className":16819},[1453],[17,16821,16823,16843],{"className":16822},[83,84],[17,16824,16826,16840],{"className":16825},[88],[17,16827,16829],{"className":16828,"style":1463},[92],[17,16830,16831,16834],{"style":1466},[17,16832],{"className":16833,"style":1470},[100],[17,16835,16837],{"className":16836},[1474,1475,1476,1477],[17,16838,1392],{"className":16839},[79,1477],[17,16841,136],{"className":16842},[135],[17,16844,16846],{"className":16845},[88],[17,16847,16849],{"className":16848,"style":1490},[92],[17,16850],{},[17,16852,202],{"className":16853},[261],[17,16855],{"className":16856,"style":265},[234],[17,16858,16860,16863],{"className":16859},[79],[17,16861,793],{"className":16862,"style":818},[79,230],[17,16864,16866],{"className":16865},[1453],[17,16867,16869,16889],{"className":16868},[83,84],[17,16870,16872,16886],{"className":16871},[88],[17,16873,16875],{"className":16874,"style":1463},[92],[17,16876,16877,16880],{"style":1466},[17,16878],{"className":16879,"style":1470},[100],[17,16881,16883],{"className":16882},[1474,1475,1476,1477],[17,16884,1401],{"className":16885},[79,1477],[17,16887,136],{"className":16888},[135],[17,16890,16892],{"className":16891},[88],[17,16893,16895],{"className":16894,"style":1490},[92],[17,16896],{},[17,16898,202],{"className":16899},[261],[17,16901],{"className":16902,"style":265},[234],[17,16904,9374],{"className":16905},[9183],[17,16907],{"className":16908,"style":265},[234],[17,16910,202],{"className":16911},[261],[17,16913],{"className":16914,"style":265},[234],[17,16916,16918,16921],{"className":16917},[79],[17,16919,793],{"className":16920,"style":818},[79,230],[17,16922,16924],{"className":16923},[1453],[17,16925,16927,16947],{"className":16926},[83,84],[17,16928,16930,16944],{"className":16929},[88],[17,16931,16933],{"className":16932,"style":3253},[92],[17,16934,16935,16938],{"style":1466},[17,16936],{"className":16937,"style":1470},[100],[17,16939,16941],{"className":16940},[1474,1475,1476,1477],[17,16942,3183],{"className":16943},[79,230,1477],[17,16945,136],{"className":16946},[135],[17,16948,16950],{"className":16949},[88],[17,16951,16953],{"className":16952,"style":1490},[92],[17,16954],{},[13,16956,16957],{},"邻接矩阵是：",[17,16959,16961],{"className":16960},[20],[17,16962,16964,16982],{"className":16963},[24],[17,16965,16967],{"className":16966},[28],[30,16968,16969],{"xmlns":32,"display":33},[35,16970,16971,16979],{},[38,16972,16973,16975,16977],{},[187,16974,3183],{},[191,16976,14680],{},[187,16978,3183],{},[59,16980,16981],{"encoding":61},"n\\times n",[17,16983,16985,17003],{"className":16984,"ariaHidden":53},[66],[17,16986,16988,16991,16994,16997,17000],{"className":16987},[70],[17,16989],{"className":16990,"style":987},[74],[17,16992,3183],{"className":16993},[79,230],[17,16995],{"className":16996,"style":257},[234],[17,16998,14680],{"className":16999},[997],[17,17001],{"className":17002,"style":257},[234],[17,17004,17006,17009],{"className":17005},[70],[17,17007],{"className":17008,"style":769},[74],[17,17010,3183],{"className":17011},[79,230],[13,17013,14718],{},[506,17015],{},[513,17017,17019],{"id":17018},"_1-有向图邻接矩阵","1. 有向图邻接矩阵",[13,17021,17022],{},"有向图中：",[17,17024,17026],{"className":17025},[20],[17,17027,17029,17071],{"className":17028},[24],[17,17030,17032],{"className":17031},[28],[30,17033,17034],{"xmlns":32,"display":33},[35,17035,17036,17068],{},[38,17037,17038,17041,17043,17045,17056],{},[187,17039,17040],{},"A",[191,17042,193],{},[191,17044,841],{"stretchy":48},[1385,17046,17047,17050],{},[187,17048,17049],{},"a",[38,17051,17052,17054],{},[187,17053,11429],{},[187,17055,11438],{},[1385,17057,17058,17060],{},[191,17059,850],{"stretchy":48},[38,17061,17062,17064,17066],{},[187,17063,3183],{},[191,17065,14680],{},[187,17067,3183],{},[59,17069,17070],{"encoding":61},"A=(a_{ij})_{n\\times n}",[17,17072,17074,17092],{"className":17073,"ariaHidden":53},[66],[17,17075,17077,17080,17083,17086,17089],{"className":17076},[70],[17,17078],{"className":17079,"style":226},[74],[17,17081,17040],{"className":17082},[79,230],[17,17084],{"className":17085,"style":235},[234],[17,17087,193],{"className":17088},[239],[17,17090],{"className":17091,"style":235},[234],[17,17093,17095,17098,17101,17144],{"className":17094},[70],[17,17096],{"className":17097,"style":11589},[74],[17,17099,841],{"className":17100},[253],[17,17102,17104,17107],{"className":17103},[79],[17,17105,17049],{"className":17106},[79,230],[17,17108,17110],{"className":17109},[1453],[17,17111,17113,17136],{"className":17112},[83,84],[17,17114,17116,17133],{"className":17115},[88],[17,17117,17119],{"className":17118,"style":11470},[92],[17,17120,17121,17124],{"style":2106},[17,17122],{"className":17123,"style":1470},[100],[17,17125,17127],{"className":17126},[1474,1475,1476,1477],[17,17128,17130],{"className":17129},[79,1477],[17,17131,14842],{"className":17132,"style":11528},[79,230,1477],[17,17134,136],{"className":17135},[135],[17,17137,17139],{"className":17138},[88],[17,17140,17142],{"className":17141,"style":11538},[92],[17,17143],{},[17,17145,17147,17150],{"className":17146},[282],[17,17148,850],{"className":17149},[282],[17,17151,17153],{"className":17152},[1453],[17,17154,17156,17185],{"className":17155},[83,84],[17,17157,17159,17182],{"className":17158},[88],[17,17160,17162],{"className":17161,"style":14872},[92],[17,17163,17164,17167],{"style":2106},[17,17165],{"className":17166,"style":1470},[100],[17,17168,17170],{"className":17169},[1474,1475,1476,1477],[17,17171,17173,17176,17179],{"className":17172},[79,1477],[17,17174,3183],{"className":17175},[79,230,1477],[17,17177,14680],{"className":17178},[997,1477],[17,17180,3183],{"className":17181},[79,230,1477],[17,17183,136],{"className":17184},[135],[17,17186,17188],{"className":17187},[88],[17,17189,17191],{"className":17190,"style":14902},[92],[17,17192],{},[13,17194,285],{},[17,17196,17198],{"className":17197},[20],[17,17199,17201,17227],{"className":17200},[24],[17,17202,17204],{"className":17203},[28],[30,17205,17206],{"xmlns":32,"display":33},[35,17207,17208,17224],{},[38,17209,17210,17220,17222],{},[1385,17211,17212,17214],{},[187,17213,17049],{},[38,17215,17216,17218],{},[187,17217,11429],{},[187,17219,11438],{},[191,17221,193],{},[187,17223,4699],{},[59,17225,17226],{"encoding":61},"a_{ij}=k",[17,17228,17230,17288],{"className":17229,"ariaHidden":53},[66],[17,17231,17233,17236,17279,17282,17285],{"className":17232},[70],[17,17234],{"className":17235,"style":11451},[74],[17,17237,17239,17242],{"className":17238},[79],[17,17240,17049],{"className":17241},[79,230],[17,17243,17245],{"className":17244},[1453],[17,17246,17248,17271],{"className":17247},[83,84],[17,17249,17251,17268],{"className":17250},[88],[17,17252,17254],{"className":17253,"style":11470},[92],[17,17255,17256,17259],{"style":2106},[17,17257],{"className":17258,"style":1470},[100],[17,17260,17262],{"className":17261},[1474,1475,1476,1477],[17,17263,17265],{"className":17264},[79,1477],[17,17266,14842],{"className":17267,"style":11528},[79,230,1477],[17,17269,136],{"className":17270},[135],[17,17272,17274],{"className":17273},[88],[17,17275,17277],{"className":17276,"style":11538},[92],[17,17278],{},[17,17280],{"className":17281,"style":235},[234],[17,17283,193],{"className":17284},[239],[17,17286],{"className":17287,"style":235},[234],[17,17289,17291,17294],{"className":17290},[70],[17,17292],{"className":17293,"style":4711},[74],[17,17295,4699],{"className":17296,"style":4715},[79,230],[13,17298,17299,17300,12578,17369,17438,17439,17467],{},"表示从 ",[17,17301,17303,17320],{"className":17302},[24],[17,17304,17306],{"className":17305},[28],[30,17307,17308],{"xmlns":32},[35,17309,17310,17318],{},[38,17311,17312],{},[1385,17313,17314,17316],{},[187,17315,793],{},[187,17317,11429],{},[59,17319,12005],{"encoding":61},[17,17321,17323],{"className":17322,"ariaHidden":53},[66],[17,17324,17326,17329],{"className":17325},[70],[17,17327],{"className":17328,"style":2085},[74],[17,17330,17332,17335],{"className":17331},[79],[17,17333,793],{"className":17334,"style":818},[79,230],[17,17336,17338],{"className":17337},[1453],[17,17339,17341,17361],{"className":17340},[83,84],[17,17342,17344,17358],{"className":17343},[88],[17,17345,17347],{"className":17346,"style":11470},[92],[17,17348,17349,17352],{"style":1466},[17,17350],{"className":17351,"style":1470},[100],[17,17353,17355],{"className":17354},[1474,1475,1476,1477],[17,17356,11429],{"className":17357},[79,230,1477],[17,17359,136],{"className":17360},[135],[17,17362,17364],{"className":17363},[88],[17,17365,17367],{"className":17366,"style":1490},[92],[17,17368],{},[17,17370,17372,17389],{"className":17371},[24],[17,17373,17375],{"className":17374},[28],[30,17376,17377],{"xmlns":32},[35,17378,17379,17387],{},[38,17380,17381],{},[1385,17382,17383,17385],{},[187,17384,793],{},[187,17386,11438],{},[59,17388,11934],{"encoding":61},[17,17390,17392],{"className":17391,"ariaHidden":53},[66],[17,17393,17395,17398],{"className":17394},[70],[17,17396],{"className":17397,"style":11451},[74],[17,17399,17401,17404],{"className":17400},[79],[17,17402,793],{"className":17403,"style":818},[79,230],[17,17405,17407],{"className":17406},[1453],[17,17408,17410,17430],{"className":17409},[83,84],[17,17411,17413,17427],{"className":17412},[88],[17,17414,17416],{"className":17415,"style":11470},[92],[17,17417,17418,17421],{"style":1466},[17,17419],{"className":17420,"style":1470},[100],[17,17422,17424],{"className":17423},[1474,1475,1476,1477],[17,17425,11438],{"className":17426,"style":11528},[79,230,1477],[17,17428,136],{"className":17429},[135],[17,17431,17433],{"className":17432},[88],[17,17434,17436],{"className":17435,"style":11538},[92],[17,17437],{}," 的有向边有 ",[17,17440,17442,17455],{"className":17441},[24],[17,17443,17445],{"className":17444},[28],[30,17446,17447],{"xmlns":32},[35,17448,17449,17453],{},[38,17450,17451],{},[187,17452,4699],{},[59,17454,4699],{"encoding":61},[17,17456,17458],{"className":17457,"ariaHidden":53},[66],[17,17459,17461,17464],{"className":17460},[70],[17,17462],{"className":17463,"style":4711},[74],[17,17465,4699],{"className":17466,"style":4715},[79,230]," 条。",[13,17469,17470],{},"如果没有边，则：",[17,17472,17474],{"className":17473},[20],[17,17475,17477,17503],{"className":17476},[24],[17,17478,17480],{"className":17479},[28],[30,17481,17482],{"xmlns":32,"display":33},[35,17483,17484,17500],{},[38,17485,17486,17496,17498],{},[1385,17487,17488,17490],{},[187,17489,17049],{},[38,17491,17492,17494],{},[187,17493,11429],{},[187,17495,11438],{},[191,17497,193],{},[1390,17499,47],{},[59,17501,17502],{"encoding":61},"a_{ij}=0",[17,17504,17506,17564],{"className":17505,"ariaHidden":53},[66],[17,17507,17509,17512,17555,17558,17561],{"className":17508},[70],[17,17510],{"className":17511,"style":11451},[74],[17,17513,17515,17518],{"className":17514},[79],[17,17516,17049],{"className":17517},[79,230],[17,17519,17521],{"className":17520},[1453],[17,17522,17524,17547],{"className":17523},[83,84],[17,17525,17527,17544],{"className":17526},[88],[17,17528,17530],{"className":17529,"style":11470},[92],[17,17531,17532,17535],{"style":2106},[17,17533],{"className":17534,"style":1470},[100],[17,17536,17538],{"className":17537},[1474,1475,1476,1477],[17,17539,17541],{"className":17540},[79,1477],[17,17542,14842],{"className":17543,"style":11528},[79,230,1477],[17,17545,136],{"className":17546},[135],[17,17548,17550],{"className":17549},[88],[17,17551,17553],{"className":17552,"style":11538},[92],[17,17554],{},[17,17556],{"className":17557,"style":235},[234],[17,17559,193],{"className":17560},[239],[17,17562],{"className":17563,"style":235},[234],[17,17565,17567,17570],{"className":17566},[70],[17,17568],{"className":17569,"style":5244},[74],[17,17571,47],{"className":17572},[79],[506,17574],{},[513,17576,17578],{"id":17577},"_2-无向图邻接矩阵","2. 无向图邻接矩阵",[13,17580,14730],{},[17,17582,17584],{"className":17583},[20],[17,17585,17587,17612],{"className":17586},[24],[17,17588,17590],{"className":17589},[28],[30,17591,17592],{"xmlns":32,"display":33},[35,17593,17594,17610],{},[38,17595,17596,17606,17608],{},[1385,17597,17598,17600],{},[187,17599,17049],{},[38,17601,17602,17604],{},[187,17603,11429],{},[187,17605,11438],{},[191,17607,193],{},[187,17609,4699],{},[59,17611,17226],{"encoding":61},[17,17613,17615,17673],{"className":17614,"ariaHidden":53},[66],[17,17616,17618,17621,17664,17667,17670],{"className":17617},[70],[17,17619],{"className":17620,"style":11451},[74],[17,17622,17624,17627],{"className":17623},[79],[17,17625,17049],{"className":17626},[79,230],[17,17628,17630],{"className":17629},[1453],[17,17631,17633,17656],{"className":17632},[83,84],[17,17634,17636,17653],{"className":17635},[88],[17,17637,17639],{"className":17638,"style":11470},[92],[17,17640,17641,17644],{"style":2106},[17,17642],{"className":17643,"style":1470},[100],[17,17645,17647],{"className":17646},[1474,1475,1476,1477],[17,17648,17650],{"className":17649},[79,1477],[17,17651,14842],{"className":17652,"style":11528},[79,230,1477],[17,17654,136],{"className":17655},[135],[17,17657,17659],{"className":17658},[88],[17,17660,17662],{"className":17661,"style":11538},[92],[17,17663],{},[17,17665],{"className":17666,"style":235},[234],[17,17668,193],{"className":17669},[239],[17,17671],{"className":17672,"style":235},[234],[17,17674,17676,17679],{"className":17675},[70],[17,17677],{"className":17678,"style":4711},[74],[17,17680,4699],{"className":17681,"style":4715},[79,230],[13,17683,1012,17684,1041,17753,17822,17823,10880],{},[17,17685,17687,17704],{"className":17686},[24],[17,17688,17690],{"className":17689},[28],[30,17691,17692],{"xmlns":32},[35,17693,17694,17702],{},[38,17695,17696],{},[1385,17697,17698,17700],{},[187,17699,793],{},[187,17701,11429],{},[59,17703,12005],{"encoding":61},[17,17705,17707],{"className":17706,"ariaHidden":53},[66],[17,17708,17710,17713],{"className":17709},[70],[17,17711],{"className":17712,"style":2085},[74],[17,17714,17716,17719],{"className":17715},[79],[17,17717,793],{"className":17718,"style":818},[79,230],[17,17720,17722],{"className":17721},[1453],[17,17723,17725,17745],{"className":17724},[83,84],[17,17726,17728,17742],{"className":17727},[88],[17,17729,17731],{"className":17730,"style":11470},[92],[17,17732,17733,17736],{"style":1466},[17,17734],{"className":17735,"style":1470},[100],[17,17737,17739],{"className":17738},[1474,1475,1476,1477],[17,17740,11429],{"className":17741},[79,230,1477],[17,17743,136],{"className":17744},[135],[17,17746,17748],{"className":17747},[88],[17,17749,17751],{"className":17750,"style":1490},[92],[17,17752],{},[17,17754,17756,17773],{"className":17755},[24],[17,17757,17759],{"className":17758},[28],[30,17760,17761],{"xmlns":32},[35,17762,17763,17771],{},[38,17764,17765],{},[1385,17766,17767,17769],{},[187,17768,793],{},[187,17770,11438],{},[59,17772,11934],{"encoding":61},[17,17774,17776],{"className":17775,"ariaHidden":53},[66],[17,17777,17779,17782],{"className":17778},[70],[17,17780],{"className":17781,"style":11451},[74],[17,17783,17785,17788],{"className":17784},[79],[17,17786,793],{"className":17787,"style":818},[79,230],[17,17789,17791],{"className":17790},[1453],[17,17792,17794,17814],{"className":17793},[83,84],[17,17795,17797,17811],{"className":17796},[88],[17,17798,17800],{"className":17799,"style":11470},[92],[17,17801,17802,17805],{"style":1466},[17,17803],{"className":17804,"style":1470},[100],[17,17806,17808],{"className":17807},[1474,1475,1476,1477],[17,17809,11438],{"className":17810,"style":11528},[79,230,1477],[17,17812,136],{"className":17813},[135],[17,17815,17817],{"className":17816},[88],[17,17818,17820],{"className":17819,"style":11538},[92],[17,17821],{}," 之间有 ",[17,17824,17826,17839],{"className":17825},[24],[17,17827,17829],{"className":17828},[28],[30,17830,17831],{"xmlns":32},[35,17832,17833,17837],{},[38,17834,17835],{},[187,17836,4699],{},[59,17838,4699],{"encoding":61},[17,17840,17842],{"className":17841,"ariaHidden":53},[66],[17,17843,17845,17848],{"className":17844},[70],[17,17846],{"className":17847,"style":4711},[74],[17,17849,4699],{"className":17850,"style":4715},[79,230],[506,17852],{},[513,17854,17856],{"id":17855},"_3-简单图邻接矩阵特点","3. 简单图邻接矩阵特点",[13,17858,5875,17859,17887],{},[17,17860,17862,17875],{"className":17861},[24],[17,17863,17865],{"className":17864},[28],[30,17866,17867],{"xmlns":32},[35,17868,17869,17873],{},[38,17870,17871],{},[187,17872,189],{},[59,17874,189],{"encoding":61},[17,17876,17878],{"className":17877,"ariaHidden":53},[66],[17,17879,17881,17884],{"className":17880},[70],[17,17882],{"className":17883,"style":226},[74],[17,17885,189],{"className":17886},[79,230]," 是简单图，则：",[8696,17889,17890,17893,17896],{},[153,17891,17892],{},"主对角线元素全为 0；",[153,17894,17895],{},"每个元素只能是 0 或 1；",[153,17897,17898],{},"无向简单图的邻接矩阵是对称矩阵。",[13,17900,13226],{},[17,17902,17904],{"className":17903},[20],[17,17905,17907,17930],{"className":17906},[24],[17,17908,17910],{"className":17909},[28],[30,17911,17912],{"xmlns":32,"display":33},[35,17913,17914,17927],{},[38,17915,17916,17918,17920],{},[187,17917,17040],{},[191,17919,193],{},[4143,17921,17922,17924],{},[187,17923,17040],{},[187,17925,17926],{},"T",[59,17928,17929],{"encoding":61},"A=A^T",[17,17931,17933,17951],{"className":17932,"ariaHidden":53},[66],[17,17934,17936,17939,17942,17945,17948],{"className":17935},[70],[17,17937],{"className":17938,"style":226},[74],[17,17940,17040],{"className":17941},[79,230],[17,17943],{"className":17944,"style":235},[234],[17,17946,193],{"className":17947},[239],[17,17949],{"className":17950,"style":235},[234],[17,17952,17954,17958],{"className":17953},[70],[17,17955],{"className":17956,"style":17957},[74],"height:0.8913em;",[17,17959,17961,17964],{"className":17960},[79],[17,17962,17040],{"className":17963},[79,230],[17,17965,17967],{"className":17966},[1453],[17,17968,17970],{"className":17969},[83],[17,17971,17973],{"className":17972},[88],[17,17974,17976],{"className":17975,"style":17957},[92],[17,17977,17978,17981],{"style":3601},[17,17979],{"className":17980,"style":1470},[100],[17,17982,17984],{"className":17983},[1474,1475,1476,1477],[17,17985,17926],{"className":17986,"style":14790},[79,230,1477],[506,17988],{},[513,17990,17992],{"id":17991},"_4-用邻接矩阵求度","4. 用邻接矩阵求度",[13,17994,14072],{},[4092,17996,4094],{"id":17997},"出度-1",[17,17999,18001],{"className":18000},[20],[17,18002,18004,18059],{"className":18003},[24],[17,18005,18007],{"className":18006},[28],[30,18008,18009],{"xmlns":32,"display":33},[35,18010,18011,18056],{},[38,18012,18013,18019,18021,18027,18029,18031,18046],{},[4143,18014,18015,18017],{},[187,18016,3912],{},[191,18018,4149],{},[191,18020,841],{"stretchy":48},[1385,18022,18023,18025],{},[187,18024,793],{},[187,18026,11429],{},[191,18028,850],{"stretchy":48},[191,18030,193],{},[18032,18033,18034,18036,18044],"munderover",{},[191,18035,4905],{},[38,18037,18038,18040,18042],{},[187,18039,11438],{},[191,18041,193],{},[1390,18043,1392],{},[187,18045,3183],{},[1385,18047,18048,18050],{},[187,18049,17049],{},[38,18051,18052,18054],{},[187,18053,11429],{},[187,18055,11438],{},[59,18057,18058],{"encoding":61},"d^+(v_i)=\\sum_{j=1}^{n}a_{ij}",[17,18060,18062,18152],{"className":18061,"ariaHidden":53},[66],[17,18063,18065,18068,18097,18100,18140,18143,18146,18149],{"className":18064},[70],[17,18066],{"className":18067,"style":4168},[74],[17,18069,18071,18074],{"className":18070},[79],[17,18072,3912],{"className":18073},[79,230],[17,18075,18077],{"className":18076},[1453],[17,18078,18080],{"className":18079},[83],[17,18081,18083],{"className":18082},[88],[17,18084,18086],{"className":18085,"style":4187},[92],[17,18087,18088,18091],{"style":3601},[17,18089],{"className":18090,"style":1470},[100],[17,18092,18094],{"className":18093},[1474,1475,1476,1477],[17,18095,4149],{"className":18096},[997,1477],[17,18098,841],{"className":18099},[253],[17,18101,18103,18106],{"className":18102},[79],[17,18104,793],{"className":18105,"style":818},[79,230],[17,18107,18109],{"className":18108},[1453],[17,18110,18112,18132],{"className":18111},[83,84],[17,18113,18115,18129],{"className":18114},[88],[17,18116,18118],{"className":18117,"style":11470},[92],[17,18119,18120,18123],{"style":1466},[17,18121],{"className":18122,"style":1470},[100],[17,18124,18126],{"className":18125},[1474,1475,1476,1477],[17,18127,11429],{"className":18128},[79,230,1477],[17,18130,136],{"className":18131},[135],[17,18133,18135],{"className":18134},[88],[17,18136,18138],{"className":18137,"style":1490},[92],[17,18139],{},[17,18141,850],{"className":18142},[282],[17,18144],{"className":18145,"style":235},[234],[17,18147,193],{"className":18148},[239],[17,18150],{"className":18151,"style":235},[234],[17,18153,18155,18159,18230,18233],{"className":18154},[70],[17,18156],{"className":18157,"style":18158},[74],"height:3.0652em;vertical-align:-1.4138em;",[17,18160,18162],{"className":18161},[4973,4974],[17,18163,18165,18221],{"className":18164},[83,84],[17,18166,18168,18218],{"className":18167},[88],[17,18169,18172,18193,18203],{"className":18170,"style":18171},[92],"height:1.6514em;",[17,18173,18175,18178],{"style":18174},"top:-1.8723em;margin-left:0em;",[17,18176],{"className":18177,"style":4991},[100],[17,18179,18181],{"className":18180},[1474,1475,1476,1477],[17,18182,18184,18187,18190],{"className":18183},[79,1477],[17,18185,11438],{"className":18186,"style":11528},[79,230,1477],[17,18188,193],{"className":18189},[239,1477],[17,18191,1392],{"className":18192},[79,1477],[17,18194,18195,18198],{"style":5009},[17,18196],{"className":18197,"style":4991},[100],[17,18199,18200],{},[17,18201,4905],{"className":18202},[4973,5018,5019],[17,18204,18206,18209],{"style":18205},"top:-4.3em;margin-left:0em;",[17,18207],{"className":18208,"style":4991},[100],[17,18210,18212],{"className":18211},[1474,1475,1476,1477],[17,18213,18215],{"className":18214},[79,1477],[17,18216,3183],{"className":18217},[79,230,1477],[17,18219,136],{"className":18220},[135],[17,18222,18224],{"className":18223},[88],[17,18225,18228],{"className":18226,"style":18227},[92],"height:1.4138em;",[17,18229],{},[17,18231],{"className":18232,"style":265},[234],[17,18234,18236,18239],{"className":18235},[79],[17,18237,17049],{"className":18238},[79,230],[17,18240,18242],{"className":18241},[1453],[17,18243,18245,18268],{"className":18244},[83,84],[17,18246,18248,18265],{"className":18247},[88],[17,18249,18251],{"className":18250,"style":11470},[92],[17,18252,18253,18256],{"style":2106},[17,18254],{"className":18255,"style":1470},[100],[17,18257,18259],{"className":18258},[1474,1475,1476,1477],[17,18260,18262],{"className":18261},[79,1477],[17,18263,14842],{"className":18264,"style":11528},[79,230,1477],[17,18266,136],{"className":18267},[135],[17,18269,18271],{"className":18270},[88],[17,18272,18274],{"className":18273,"style":11538},[92],[17,18275],{},[13,18277,18278,18279,18307],{},"也就是第 ",[17,18280,18282,18295],{"className":18281},[24],[17,18283,18285],{"className":18284},[28],[30,18286,18287],{"xmlns":32},[35,18288,18289,18293],{},[38,18290,18291],{},[187,18292,11429],{},[59,18294,11429],{"encoding":61},[17,18296,18298],{"className":18297,"ariaHidden":53},[66],[17,18299,18301,18304],{"className":18300},[70],[17,18302],{"className":18303,"style":11722},[74],[17,18305,11429],{"className":18306},[79,230]," 行元素之和。",[4092,18309,4210],{"id":18310},"入度-1",[17,18312,18314],{"className":18313},[20],[17,18315,18317,18371],{"className":18316},[24],[17,18318,18320],{"className":18319},[28],[30,18321,18322],{"xmlns":32,"display":33},[35,18323,18324,18368],{},[38,18325,18326,18332,18334,18340,18342,18344,18358],{},[4143,18327,18328,18330],{},[187,18329,3912],{},[191,18331,972],{},[191,18333,841],{"stretchy":48},[1385,18335,18336,18338],{},[187,18337,793],{},[187,18339,11429],{},[191,18341,850],{"stretchy":48},[191,18343,193],{},[18032,18345,18346,18348,18356],{},[191,18347,4905],{},[38,18349,18350,18352,18354],{},[187,18351,11438],{},[191,18353,193],{},[1390,18355,1392],{},[187,18357,3183],{},[1385,18359,18360,18362],{},[187,18361,17049],{},[38,18363,18364,18366],{},[187,18365,11438],{},[187,18367,11429],{},[59,18369,18370],{"encoding":61},"d^-(v_i)=\\sum_{j=1}^{n}a_{ji}",[17,18372,18374,18464],{"className":18373,"ariaHidden":53},[66],[17,18375,18377,18380,18409,18412,18452,18455,18458,18461],{"className":18376},[70],[17,18378],{"className":18379,"style":4168},[74],[17,18381,18383,18386],{"className":18382},[79],[17,18384,3912],{"className":18385},[79,230],[17,18387,18389],{"className":18388},[1453],[17,18390,18392],{"className":18391},[83],[17,18393,18395],{"className":18394},[88],[17,18396,18398],{"className":18397,"style":4187},[92],[17,18399,18400,18403],{"style":3601},[17,18401],{"className":18402,"style":1470},[100],[17,18404,18406],{"className":18405},[1474,1475,1476,1477],[17,18407,972],{"className":18408},[997,1477],[17,18410,841],{"className":18411},[253],[17,18413,18415,18418],{"className":18414},[79],[17,18416,793],{"className":18417,"style":818},[79,230],[17,18419,18421],{"className":18420},[1453],[17,18422,18424,18444],{"className":18423},[83,84],[17,18425,18427,18441],{"className":18426},[88],[17,18428,18430],{"className":18429,"style":11470},[92],[17,18431,18432,18435],{"style":1466},[17,18433],{"className":18434,"style":1470},[100],[17,18436,18438],{"className":18437},[1474,1475,1476,1477],[17,18439,11429],{"className":18440},[79,230,1477],[17,18442,136],{"className":18443},[135],[17,18445,18447],{"className":18446},[88],[17,18448,18450],{"className":18449,"style":1490},[92],[17,18451],{},[17,18453,850],{"className":18454},[282],[17,18456],{"className":18457,"style":235},[234],[17,18459,193],{"className":18460},[239],[17,18462],{"className":18463,"style":235},[234],[17,18465,18467,18470,18537,18540],{"className":18466},[70],[17,18468],{"className":18469,"style":18158},[74],[17,18471,18473],{"className":18472},[4973,4974],[17,18474,18476,18529],{"className":18475},[83,84],[17,18477,18479,18526],{"className":18478},[88],[17,18480,18482,18502,18512],{"className":18481,"style":18171},[92],[17,18483,18484,18487],{"style":18174},[17,18485],{"className":18486,"style":4991},[100],[17,18488,18490],{"className":18489},[1474,1475,1476,1477],[17,18491,18493,18496,18499],{"className":18492},[79,1477],[17,18494,11438],{"className":18495,"style":11528},[79,230,1477],[17,18497,193],{"className":18498},[239,1477],[17,18500,1392],{"className":18501},[79,1477],[17,18503,18504,18507],{"style":5009},[17,18505],{"className":18506,"style":4991},[100],[17,18508,18509],{},[17,18510,4905],{"className":18511},[4973,5018,5019],[17,18513,18514,18517],{"style":18205},[17,18515],{"className":18516,"style":4991},[100],[17,18518,18520],{"className":18519},[1474,1475,1476,1477],[17,18521,18523],{"className":18522},[79,1477],[17,18524,3183],{"className":18525},[79,230,1477],[17,18527,136],{"className":18528},[135],[17,18530,18532],{"className":18531},[88],[17,18533,18535],{"className":18534,"style":18227},[92],[17,18536],{},[17,18538],{"className":18539,"style":265},[234],[17,18541,18543,18546],{"className":18542},[79],[17,18544,17049],{"className":18545},[79,230],[17,18547,18549],{"className":18548},[1453],[17,18550,18552,18578],{"className":18551},[83,84],[17,18553,18555,18575],{"className":18554},[88],[17,18556,18558],{"className":18557,"style":11470},[92],[17,18559,18560,18563],{"style":2106},[17,18561],{"className":18562,"style":1470},[100],[17,18564,18566],{"className":18565},[1474,1475,1476,1477],[17,18567,18569,18572],{"className":18568},[79,1477],[17,18570,11438],{"className":18571,"style":11528},[79,230,1477],[17,18573,11429],{"className":18574},[79,230,1477],[17,18576,136],{"className":18577},[135],[17,18579,18581],{"className":18580},[88],[17,18582,18584],{"className":18583,"style":11538},[92],[17,18585],{},[13,18587,18278,18588,18616],{},[17,18589,18591,18604],{"className":18590},[24],[17,18592,18594],{"className":18593},[28],[30,18595,18596],{"xmlns":32},[35,18597,18598,18602],{},[38,18599,18600],{},[187,18601,11429],{},[59,18603,11429],{"encoding":61},[17,18605,18607],{"className":18606,"ariaHidden":53},[66],[17,18608,18610,18613],{"className":18609},[70],[17,18611],{"className":18612,"style":11722},[74],[17,18614,11429],{"className":18615},[79,230]," 列元素之和。",[4092,18618,4322],{"id":18619},"总度-1",[17,18621,18623],{"className":18622},[20],[17,18624,18626,18686],{"className":18625},[24],[17,18627,18629],{"className":18628},[28],[30,18630,18631],{"xmlns":32,"display":33},[35,18632,18633,18683],{},[38,18634,18635,18637,18639,18645,18647,18649,18655,18657,18663,18665,18667,18673,18675,18681],{},[187,18636,3912],{},[191,18638,841],{"stretchy":48},[1385,18640,18641,18643],{},[187,18642,793],{},[187,18644,11429],{},[191,18646,850],{"stretchy":48},[191,18648,193],{},[4143,18650,18651,18653],{},[187,18652,3912],{},[191,18654,4149],{},[191,18656,841],{"stretchy":48},[1385,18658,18659,18661],{},[187,18660,793],{},[187,18662,11429],{},[191,18664,850],{"stretchy":48},[191,18666,4149],{},[4143,18668,18669,18671],{},[187,18670,3912],{},[191,18672,972],{},[191,18674,841],{"stretchy":48},[1385,18676,18677,18679],{},[187,18678,793],{},[187,18680,11429],{},[191,18682,850],{"stretchy":48},[59,18684,18685],{"encoding":61},"d(v_i)=d^+(v_i)+d^-(v_i)",[17,18687,18689,18753,18843],{"className":18688,"ariaHidden":53},[66],[17,18690,18692,18695,18698,18701,18741,18744,18747,18750],{"className":18691},[70],[17,18693],{"className":18694,"style":249},[74],[17,18696,3912],{"className":18697},[79,230],[17,18699,841],{"className":18700},[253],[17,18702,18704,18707],{"className":18703},[79],[17,18705,793],{"className":18706,"style":818},[79,230],[17,18708,18710],{"className":18709},[1453],[17,18711,18713,18733],{"className":18712},[83,84],[17,18714,18716,18730],{"className":18715},[88],[17,18717,18719],{"className":18718,"style":11470},[92],[17,18720,18721,18724],{"style":1466},[17,18722],{"className":18723,"style":1470},[100],[17,18725,18727],{"className":18726},[1474,1475,1476,1477],[17,18728,11429],{"className":18729},[79,230,1477],[17,18731,136],{"className":18732},[135],[17,18734,18736],{"className":18735},[88],[17,18737,18739],{"className":18738,"style":1490},[92],[17,18740],{},[17,18742,850],{"className":18743},[282],[17,18745],{"className":18746,"style":235},[234],[17,18748,193],{"className":18749},[239],[17,18751],{"className":18752,"style":235},[234],[17,18754,18756,18759,18788,18791,18831,18834,18837,18840],{"className":18755},[70],[17,18757],{"className":18758,"style":4168},[74],[17,18760,18762,18765],{"className":18761},[79],[17,18763,3912],{"className":18764},[79,230],[17,18766,18768],{"className":18767},[1453],[17,18769,18771],{"className":18770},[83],[17,18772,18774],{"className":18773},[88],[17,18775,18777],{"className":18776,"style":4187},[92],[17,18778,18779,18782],{"style":3601},[17,18780],{"className":18781,"style":1470},[100],[17,18783,18785],{"className":18784},[1474,1475,1476,1477],[17,18786,4149],{"className":18787},[997,1477],[17,18789,841],{"className":18790},[253],[17,18792,18794,18797],{"className":18793},[79],[17,18795,793],{"className":18796,"style":818},[79,230],[17,18798,18800],{"className":18799},[1453],[17,18801,18803,18823],{"className":18802},[83,84],[17,18804,18806,18820],{"className":18805},[88],[17,18807,18809],{"className":18808,"style":11470},[92],[17,18810,18811,18814],{"style":1466},[17,18812],{"className":18813,"style":1470},[100],[17,18815,18817],{"className":18816},[1474,1475,1476,1477],[17,18818,11429],{"className":18819},[79,230,1477],[17,18821,136],{"className":18822},[135],[17,18824,18826],{"className":18825},[88],[17,18827,18829],{"className":18828,"style":1490},[92],[17,18830],{},[17,18832,850],{"className":18833},[282],[17,18835],{"className":18836,"style":257},[234],[17,18838,4149],{"className":18839},[997],[17,18841],{"className":18842,"style":257},[234],[17,18844,18846,18849,18878,18881,18921],{"className":18845},[70],[17,18847],{"className":18848,"style":4168},[74],[17,18850,18852,18855],{"className":18851},[79],[17,18853,3912],{"className":18854},[79,230],[17,18856,18858],{"className":18857},[1453],[17,18859,18861],{"className":18860},[83],[17,18862,18864],{"className":18863},[88],[17,18865,18867],{"className":18866,"style":4187},[92],[17,18868,18869,18872],{"style":3601},[17,18870],{"className":18871,"style":1470},[100],[17,18873,18875],{"className":18874},[1474,1475,1476,1477],[17,18876,972],{"className":18877},[997,1477],[17,18879,841],{"className":18880},[253],[17,18882,18884,18887],{"className":18883},[79],[17,18885,793],{"className":18886,"style":818},[79,230],[17,18888,18890],{"className":18889},[1453],[17,18891,18893,18913],{"className":18892},[83,84],[17,18894,18896,18910],{"className":18895},[88],[17,18897,18899],{"className":18898,"style":11470},[92],[17,18900,18901,18904],{"style":1466},[17,18902],{"className":18903,"style":1470},[100],[17,18905,18907],{"className":18906},[1474,1475,1476,1477],[17,18908,11429],{"className":18909},[79,230,1477],[17,18911,136],{"className":18912},[135],[17,18914,18916],{"className":18915},[88],[17,18917,18919],{"className":18918,"style":1490},[92],[17,18920],{},[17,18922,850],{"className":18923},[282],[506,18925],{},[10,18927,18929],{"id":18928},"三邻接矩阵的幂","三、邻接矩阵的幂",[13,18931,18932],{},"这是很重要的计算结论。",[13,18934,7690,18935,18963],{},[17,18936,18938,18951],{"className":18937},[24],[17,18939,18941],{"className":18940},[28],[30,18942,18943],{"xmlns":32},[35,18944,18945,18949],{},[38,18946,18947],{},[187,18948,17040],{},[59,18950,17040],{"encoding":61},[17,18952,18954],{"className":18953,"ariaHidden":53},[66],[17,18955,18957,18960],{"className":18956},[70],[17,18958],{"className":18959,"style":226},[74],[17,18961,17040],{"className":18962},[79,230]," 是无重边有向图的邻接矩阵。",[13,18965,18966],{},"那么：",[17,18968,18970],{"className":18969},[20],[17,18971,18973,18991],{"className":18972},[24],[17,18974,18976],{"className":18975},[28],[30,18977,18978],{"xmlns":32,"display":33},[35,18979,18980,18988],{},[38,18981,18982],{},[4143,18983,18984,18986],{},[187,18985,17040],{},[187,18987,4859],{},[59,18989,18990],{"encoding":61},"A^m",[17,18992,18994],{"className":18993,"ariaHidden":53},[66],[17,18995,18997,19001],{"className":18996},[70],[17,18998],{"className":18999,"style":19000},[74],"height:0.7144em;",[17,19002,19004,19007],{"className":19003},[79],[17,19005,17040],{"className":19006},[79,230],[17,19008,19010],{"className":19009},[1453],[17,19011,19013],{"className":19012},[83],[17,19014,19016],{"className":19015},[88],[17,19017,19019],{"className":19018,"style":19000},[92],[17,19020,19021,19024],{"style":3601},[17,19022],{"className":19023,"style":1470},[100],[17,19025,19027],{"className":19026},[1474,1475,1476,1477],[17,19028,4859],{"className":19029},[79,230,1477],[13,19031,19032,19033,19075],{},"中第 ",[17,19034,19036,19054],{"className":19035},[24],[17,19037,19039],{"className":19038},[28],[30,19040,19041],{"xmlns":32},[35,19042,19043,19051],{},[38,19044,19045,19047,19049],{},[187,19046,11429],{},[191,19048,202],{"separator":53},[187,19050,11438],{},[59,19052,19053],{"encoding":61},"i,j",[17,19055,19057],{"className":19056,"ariaHidden":53},[66],[17,19058,19060,19063,19066,19069,19072],{"className":19059},[70],[17,19061],{"className":19062,"style":11741},[74],[17,19064,11429],{"className":19065},[79,230],[17,19067,202],{"className":19068},[261],[17,19070],{"className":19071,"style":265},[234],[17,19073,11438],{"className":19074,"style":11528},[79,230]," 个元素表示：",[17,19077,19079],{"className":19078},[20],[17,19080,19082,19130],{"className":19081},[24],[17,19083,19085],{"className":19084},[28],[30,19086,19087],{"xmlns":32,"display":33},[35,19088,19089,19127],{},[38,19090,19091],{},[41,19092,19093],{"notation":43},[45,19094,19095],{"scriptlevel":47,"displaystyle":48},[45,19096,19097],{"scriptlevel":47,"displaystyle":48},[45,19098,19099],{"scriptlevel":47,"displaystyle":53},[38,19100,19101,19104,19110,19113,19119,19122,19124],{},[55,19102,19103],{},"从 ",[1385,19105,19106,19108],{},[187,19107,793],{},[187,19109,11429],{},[55,19111,19112],{}," 到 ",[1385,19114,19115,19117],{},[187,19116,793],{},[187,19118,11438],{},[55,19120,19121],{}," 的长度为 ",[187,19123,4859],{},[55,19125,19126],{}," 的路径条数",[59,19128,19129],{"encoding":61},"\\boxed{\\text{从 }v_i\\text{ 到 }v_j\\text{ 的长度为 }m\\text{ 的路径条数}}",[17,19131,19133],{"className":19132,"ariaHidden":53},[66],[17,19134,19136,19140],{"className":19135},[70],[17,19137],{"className":19138,"style":19139},[74],"height:1.6494em;vertical-align:-0.6261em;",[17,19141,19143],{"className":19142},[79],[17,19144,19146,19309],{"className":19145},[83,84],[17,19147,19149,19306],{"className":19148},[88],[17,19150,19152,19297],{"className":19151,"style":93},[92],[17,19153,19155,19159],{"style":19154},"top:-3.6494em;",[17,19156],{"className":19157,"style":19158},[100],"height:3.6494em;",[17,19160,19162],{"className":19161},[105],[17,19163,19165],{"className":19164},[79],[17,19166,19168,19178,19218,19231,19271,19284,19287],{"className":19167},[79],[17,19169,19171,19175],{"className":19170},[79,115],[17,19172,19174],{"className":19173},[79,119],"从",[17,19176,4056],{"className":19177},[79],[17,19179,19181,19184],{"className":19180},[79],[17,19182,793],{"className":19183,"style":818},[79,230],[17,19185,19187],{"className":19186},[1453],[17,19188,19190,19210],{"className":19189},[83,84],[17,19191,19193,19207],{"className":19192},[88],[17,19194,19196],{"className":19195,"style":11470},[92],[17,19197,19198,19201],{"style":1466},[17,19199],{"className":19200,"style":1470},[100],[17,19202,19204],{"className":19203},[1474,1475,1476,1477],[17,19205,11429],{"className":19206},[79,230,1477],[17,19208,136],{"className":19209},[135],[17,19211,19213],{"className":19212},[88],[17,19214,19216],{"className":19215,"style":1490},[92],[17,19217],{},[17,19219,19221,19224,19228],{"className":19220},[79,115],[17,19222,4056],{"className":19223},[79],[17,19225,19227],{"className":19226},[79,119],"到",[17,19229,4056],{"className":19230},[79],[17,19232,19234,19237],{"className":19233},[79],[17,19235,793],{"className":19236,"style":818},[79,230],[17,19238,19240],{"className":19239},[1453],[17,19241,19243,19263],{"className":19242},[83,84],[17,19244,19246,19260],{"className":19245},[88],[17,19247,19249],{"className":19248,"style":11470},[92],[17,19250,19251,19254],{"style":1466},[17,19252],{"className":19253,"style":1470},[100],[17,19255,19257],{"className":19256},[1474,1475,1476,1477],[17,19258,11438],{"className":19259,"style":11528},[79,230,1477],[17,19261,136],{"className":19262},[135],[17,19264,19266],{"className":19265},[88],[17,19267,19269],{"className":19268,"style":11538},[92],[17,19270],{},[17,19272,19274,19277,19281],{"className":19273},[79,115],[17,19275,4056],{"className":19276},[79],[17,19278,19280],{"className":19279},[79,119],"的长度为",[17,19282,4056],{"className":19283},[79],[17,19285,4859],{"className":19286},[79,230],[17,19288,19290,19293],{"className":19289},[79,115],[17,19291,4056],{"className":19292},[79],[17,19294,19296],{"className":19295},[79,119],"的路径条数",[17,19298,19299,19302],{"style":122},[17,19300],{"className":19301,"style":19158},[100],[17,19303],{"className":19304,"style":19305},[129,130],"height:1.6494em;border-style:solid;border-width:0.04em;",[17,19307,136],{"className":19308},[135],[17,19310,19312],{"className":19311},[88],[17,19313,19316],{"className":19314,"style":19315},[92],"height:0.6261em;",[17,19317],{},[13,19319,4512],{},[17,19321,19323],{"className":19322},[20],[17,19324,19326,19343],{"className":19325},[24],[17,19327,19329],{"className":19328},[28],[30,19330,19331],{"xmlns":32,"display":33},[35,19332,19333,19341],{},[38,19334,19335,19337,19339],{},[187,19336,11429],{},[191,19338,193],{},[187,19340,11438],{},[59,19342,11712],{"encoding":61},[17,19344,19346,19364],{"className":19345,"ariaHidden":53},[66],[17,19347,19349,19352,19355,19358,19361],{"className":19348},[70],[17,19350],{"className":19351,"style":11722},[74],[17,19353,11429],{"className":19354},[79,230],[17,19356],{"className":19357,"style":235},[234],[17,19359,193],{"className":19360},[239],[17,19362],{"className":19363,"style":235},[234],[17,19365,19367,19370],{"className":19366},[70],[17,19368],{"className":19369,"style":11741},[74],[17,19371,11438],{"className":19372,"style":11528},[79,230],[13,19374,19375,19376,19445,19446,19515,19516,19544],{},"则表示从 ",[17,19377,19379,19396],{"className":19378},[24],[17,19380,19382],{"className":19381},[28],[30,19383,19384],{"xmlns":32},[35,19385,19386,19394],{},[38,19387,19388],{},[1385,19389,19390,19392],{},[187,19391,793],{},[187,19393,11429],{},[59,19395,12005],{"encoding":61},[17,19397,19399],{"className":19398,"ariaHidden":53},[66],[17,19400,19402,19405],{"className":19401},[70],[17,19403],{"className":19404,"style":2085},[74],[17,19406,19408,19411],{"className":19407},[79],[17,19409,793],{"className":19410,"style":818},[79,230],[17,19412,19414],{"className":19413},[1453],[17,19415,19417,19437],{"className":19416},[83,84],[17,19418,19420,19434],{"className":19419},[88],[17,19421,19423],{"className":19422,"style":11470},[92],[17,19424,19425,19428],{"style":1466},[17,19426],{"className":19427,"style":1470},[100],[17,19429,19431],{"className":19430},[1474,1475,1476,1477],[17,19432,11429],{"className":19433},[79,230,1477],[17,19435,136],{"className":19436},[135],[17,19438,19440],{"className":19439},[88],[17,19441,19443],{"className":19442,"style":1490},[92],[17,19444],{}," 出发又回到 ",[17,19447,19449,19466],{"className":19448},[24],[17,19450,19452],{"className":19451},[28],[30,19453,19454],{"xmlns":32},[35,19455,19456,19464],{},[38,19457,19458],{},[1385,19459,19460,19462],{},[187,19461,793],{},[187,19463,11429],{},[59,19465,12005],{"encoding":61},[17,19467,19469],{"className":19468,"ariaHidden":53},[66],[17,19470,19472,19475],{"className":19471},[70],[17,19473],{"className":19474,"style":2085},[74],[17,19476,19478,19481],{"className":19477},[79],[17,19479,793],{"className":19480,"style":818},[79,230],[17,19482,19484],{"className":19483},[1453],[17,19485,19487,19507],{"className":19486},[83,84],[17,19488,19490,19504],{"className":19489},[88],[17,19491,19493],{"className":19492,"style":11470},[92],[17,19494,19495,19498],{"style":1466},[17,19496],{"className":19497,"style":1470},[100],[17,19499,19501],{"className":19500},[1474,1475,1476,1477],[17,19502,11429],{"className":19503},[79,230,1477],[17,19505,136],{"className":19506},[135],[17,19508,19510],{"className":19509},[88],[17,19511,19513],{"className":19512,"style":1490},[92],[17,19514],{}," 的长度为 ",[17,19517,19519,19532],{"className":19518},[24],[17,19520,19522],{"className":19521},[28],[30,19523,19524],{"xmlns":32},[35,19525,19526,19530],{},[38,19527,19528],{},[187,19529,4859],{},[59,19531,4859],{"encoding":61},[17,19533,19535],{"className":19534,"ariaHidden":53},[66],[17,19536,19538,19541],{"className":19537},[70],[17,19539],{"className":19540,"style":769},[74],[17,19542,4859],{"className":19543},[79,230]," 的循环条数。",[506,19546],{},[513,19548,19549],{"id":19549},"例子理解",[13,19551,4512],{},[17,19553,19555],{"className":19554},[20],[17,19556,19558,19590],{"className":19557},[24],[17,19559,19561],{"className":19560},[28],[30,19562,19563],{"xmlns":32,"display":33},[35,19564,19565,19587],{},[38,19566,19567,19569,19575,19582,19584],{},[191,19568,841],{"stretchy":48},[4143,19570,19571,19573],{},[187,19572,17040],{},[1390,19574,1410],{},[1385,19576,19577,19579],{},[191,19578,850],{"stretchy":48},[1390,19580,19581],{},"24",[191,19583,193],{},[1390,19585,19586],{},"5",[59,19588,19589],{"encoding":61},"(A^3)_{24}=5",[17,19591,19593,19684],{"className":19592,"ariaHidden":53},[66],[17,19594,19596,19600,19603,19632,19675,19678,19681],{"className":19595},[70],[17,19597],{"className":19598,"style":19599},[74],"height:1.1141em;vertical-align:-0.25em;",[17,19601,841],{"className":19602},[253],[17,19604,19606,19609],{"className":19605},[79],[17,19607,17040],{"className":19608},[79,230],[17,19610,19612],{"className":19611},[1453],[17,19613,19615],{"className":19614},[83],[17,19616,19618],{"className":19617},[88],[17,19619,19621],{"className":19620,"style":3586},[92],[17,19622,19623,19626],{"style":3601},[17,19624],{"className":19625,"style":1470},[100],[17,19627,19629],{"className":19628},[1474,1475,1476,1477],[17,19630,1410],{"className":19631},[79,1477],[17,19633,19635,19638],{"className":19634},[282],[17,19636,850],{"className":19637},[282],[17,19639,19641],{"className":19640},[1453],[17,19642,19644,19667],{"className":19643},[83,84],[17,19645,19647,19664],{"className":19646},[88],[17,19648,19650],{"className":19649,"style":1463},[92],[17,19651,19652,19655],{"style":2106},[17,19653],{"className":19654,"style":1470},[100],[17,19656,19658],{"className":19657},[1474,1475,1476,1477],[17,19659,19661],{"className":19660},[79,1477],[17,19662,19581],{"className":19663},[79,1477],[17,19665,136],{"className":19666},[135],[17,19668,19670],{"className":19669},[88],[17,19671,19673],{"className":19672,"style":1490},[92],[17,19674],{},[17,19676],{"className":19677,"style":235},[234],[17,19679,193],{"className":19680},[239],[17,19682],{"className":19683,"style":235},[234],[17,19685,19687,19690],{"className":19686},[70],[17,19688],{"className":19689,"style":5244},[74],[17,19691,19586],{"className":19692},[79],[13,19694,19695],{},"表示：",[1700,19697,19698],{},[13,19699,9272,19700,12578,19770,19841],{},[17,19701,19703,19721],{"className":19702},[24],[17,19704,19706],{"className":19705},[28],[30,19707,19708],{"xmlns":32},[35,19709,19710,19718],{},[38,19711,19712],{},[1385,19713,19714,19716],{},[187,19715,793],{},[1390,19717,1401],{},[59,19719,19720],{"encoding":61},"v_2",[17,19722,19724],{"className":19723,"ariaHidden":53},[66],[17,19725,19727,19730],{"className":19726},[70],[17,19728],{"className":19729,"style":2085},[74],[17,19731,19733,19736],{"className":19732},[79],[17,19734,793],{"className":19735,"style":818},[79,230],[17,19737,19739],{"className":19738},[1453],[17,19740,19742,19762],{"className":19741},[83,84],[17,19743,19745,19759],{"className":19744},[88],[17,19746,19748],{"className":19747,"style":1463},[92],[17,19749,19750,19753],{"style":1466},[17,19751],{"className":19752,"style":1470},[100],[17,19754,19756],{"className":19755},[1474,1475,1476,1477],[17,19757,1401],{"className":19758},[79,1477],[17,19760,136],{"className":19761},[135],[17,19763,19765],{"className":19764},[88],[17,19766,19768],{"className":19767,"style":1490},[92],[17,19769],{},[17,19771,19773,19792],{"className":19772},[24],[17,19774,19776],{"className":19775},[28],[30,19777,19778],{"xmlns":32},[35,19779,19780,19789],{},[38,19781,19782],{},[1385,19783,19784,19786],{},[187,19785,793],{},[1390,19787,19788],{},"4",[59,19790,19791],{"encoding":61},"v_4",[17,19793,19795],{"className":19794,"ariaHidden":53},[66],[17,19796,19798,19801],{"className":19797},[70],[17,19799],{"className":19800,"style":2085},[74],[17,19802,19804,19807],{"className":19803},[79],[17,19805,793],{"className":19806,"style":818},[79,230],[17,19808,19810],{"className":19809},[1453],[17,19811,19813,19833],{"className":19812},[83,84],[17,19814,19816,19830],{"className":19815},[88],[17,19817,19819],{"className":19818,"style":1463},[92],[17,19820,19821,19824],{"style":1466},[17,19822],{"className":19823,"style":1470},[100],[17,19825,19827],{"className":19826},[1474,1475,1476,1477],[17,19828,19788],{"className":19829},[79,1477],[17,19831,136],{"className":19832},[135],[17,19834,19836],{"className":19835},[88],[17,19837,19839],{"className":19838,"style":1490},[92],[17,19840],{}," 的长度为 3 的路径有 5 条。",[506,19843],{},[10,19845,19847],{"id":19846},"四可达矩阵","四、可达矩阵",[13,19849,19850],{},"可达矩阵只关心：",[1700,19852,19853],{},[13,19854,19855],{},"能不能到达。",[13,19857,19858],{},"不关心有几条路径，也不关心路径长度。",[13,19860,19861,19862,19890],{},"设有向图 ",[17,19863,19865,19878],{"className":19864},[24],[17,19866,19868],{"className":19867},[28],[30,19869,19870],{"xmlns":32},[35,19871,19872,19876],{},[38,19873,19874],{},[187,19875,189],{},[59,19877,189],{"encoding":61},[17,19879,19881],{"className":19880,"ariaHidden":53},[66],[17,19882,19884,19887],{"className":19883},[70],[17,19885],{"className":19886,"style":226},[74],[17,19888,189],{"className":19889},[79,230]," 的可达矩阵为：",[17,19892,19894],{"className":19893},[20],[17,19895,19897,19928],{"className":19896},[24],[17,19898,19900],{"className":19899},[28],[30,19901,19902],{"xmlns":32,"display":33},[35,19903,19904,19925],{},[38,19905,19906,19909,19911,19913,19923],{},[187,19907,19908],{},"P",[191,19910,193],{},[191,19912,841],{"stretchy":48},[1385,19914,19915,19917],{},[187,19916,13],{},[38,19918,19919,19921],{},[187,19920,11429],{},[187,19922,11438],{},[191,19924,850],{"stretchy":48},[59,19926,19927],{"encoding":61},"P=(p_{ij})",[17,19929,19931,19949],{"className":19930,"ariaHidden":53},[66],[17,19932,19934,19937,19940,19943,19946],{"className":19933},[70],[17,19935],{"className":19936,"style":226},[74],[17,19938,19908],{"className":19939,"style":14790},[79,230],[17,19941],{"className":19942,"style":235},[234],[17,19944,193],{"className":19945},[239],[17,19947],{"className":19948,"style":235},[234],[17,19950,19952,19955,19958,20001],{"className":19951},[70],[17,19953],{"className":19954,"style":11589},[74],[17,19956,841],{"className":19957},[253],[17,19959,19961,19964],{"className":19960},[79],[17,19962,13],{"className":19963},[79,230],[17,19965,19967],{"className":19966},[1453],[17,19968,19970,19993],{"className":19969},[83,84],[17,19971,19973,19990],{"className":19972},[88],[17,19974,19976],{"className":19975,"style":11470},[92],[17,19977,19978,19981],{"style":2106},[17,19979],{"className":19980,"style":1470},[100],[17,19982,19984],{"className":19983},[1474,1475,1476,1477],[17,19985,19987],{"className":19986},[79,1477],[17,19988,14842],{"className":19989,"style":11528},[79,230,1477],[17,19991,136],{"className":19992},[135],[17,19994,19996],{"className":19995},[88],[17,19997,19999],{"className":19998,"style":11538},[92],[17,20000],{},[17,20002,850],{"className":20003},[282],[13,20005,285],{},[17,20007,20009],{"className":20008},[20],[17,20010,20012,20113],{"className":20011},[24],[17,20013,20015],{"className":20014},[28],[30,20016,20017],{"xmlns":32,"display":33},[35,20018,20019,20110],{},[38,20020,20021,20031,20033],{},[1385,20022,20023,20025],{},[187,20024,13],{},[38,20026,20027,20029],{},[187,20028,11429],{},[187,20030,11438],{},[191,20032,193],{},[38,20034,20035,20037],{},[191,20036,14938],{"fence":53},[14940,20038,20039],{"rowspacing":14942,"columnalign":14943,"columnspacing":2053},[14945,20040,20041,20051,20087],{},[14948,20042,20043],{},[45,20044,20045],{"scriptlevel":47,"displaystyle":48},[38,20046,20047,20049],{},[1390,20048,1392],{},[191,20050,202],{"separator":53},[14948,20052,20053],{},[45,20054,20055],{"scriptlevel":47,"displaystyle":48},[38,20056,20057,20059,20061,20063,20066,20072,20075,20081,20083,20085],{},[187,20058,11429],{},[191,20060,193],{},[187,20062,11438],{},[55,20064,20065],{}," 或 ",[1385,20067,20068,20070],{},[187,20069,793],{},[187,20071,11438],{},[55,20073,20074],{}," 从 ",[1385,20076,20077,20079],{},[187,20078,793],{},[187,20080,11429],{},[55,20082,13601],{},[1390,20084,47],{},[191,20086,202],{"separator":53},[14948,20088,20089],{},[45,20090,20091],{"scriptlevel":47,"displaystyle":48},[38,20092,20093,20099,20101,20107],{},[1385,20094,20095,20097],{},[187,20096,793],{},[187,20098,11438],{},[55,20100,20074],{},[1385,20102,20103,20105],{},[187,20104,793],{},[187,20106,11429],{},[55,20108,20109],{}," 不可达",[59,20111,20112],{"encoding":61},"p_{ij}=\n\\begin{cases}\n1,& i=j\\text{ 或 }v_j\\text{ 从 }v_i\\text{ 可达}\\\n0,& v_j\\text{ 从 }v_i\\text{ 不可达}\n\\end{cases}",[17,20114,20116,20174],{"className":20115,"ariaHidden":53},[66],[17,20117,20119,20122,20165,20168,20171],{"className":20118},[70],[17,20120],{"className":20121,"style":11451},[74],[17,20123,20125,20128],{"className":20124},[79],[17,20126,13],{"className":20127},[79,230],[17,20129,20131],{"className":20130},[1453],[17,20132,20134,20157],{"className":20133},[83,84],[17,20135,20137,20154],{"className":20136},[88],[17,20138,20140],{"className":20139,"style":11470},[92],[17,20141,20142,20145],{"style":2106},[17,20143],{"className":20144,"style":1470},[100],[17,20146,20148],{"className":20147},[1474,1475,1476,1477],[17,20149,20151],{"className":20150},[79,1477],[17,20152,14842],{"className":20153,"style":11528},[79,230,1477],[17,20155,136],{"className":20156},[135],[17,20158,20160],{"className":20159},[88],[17,20161,20163],{"className":20162,"style":11538},[92],[17,20164],{},[17,20166],{"className":20167,"style":235},[234],[17,20169,193],{"className":20170},[239],[17,20172],{"className":20173,"style":235},[234],[17,20175,20177,20180],{"className":20176},[70],[17,20178],{"className":20179,"style":15104},[74],[17,20181,20183,20189,20540],{"className":20182},[9183],[17,20184,20186],{"className":20185,"style":15112},[253,15111],[17,20187,14938],{"className":20188},[15116,15117],[17,20190,20192],{"className":20191},[79],[17,20193,20195,20232,20235,20404,20407],{"className":20194},[14940],[17,20196,20198],{"className":20197},[15127],[17,20199,20201,20224],{"className":20200},[83,84],[17,20202,20204,20221],{"className":20203},[88],[17,20205,20207],{"className":20206,"style":15137},[92],[17,20208,20209,20212],{"style":15140},[17,20210],{"className":20211,"style":15144},[100],[17,20213,20215,20218],{"className":20214},[79],[17,20216,1392],{"className":20217},[79],[17,20219,202],{"className":20220},[261],[17,20222,136],{"className":20223},[135],[17,20225,20227],{"className":20226},[88],[17,20228,20230],{"className":20229,"style":15163},[92],[17,20231],{},[17,20233],{"className":20234,"style":15170},[15169],[17,20236,20238],{"className":20237},[15127],[17,20239,20241,20396],{"className":20240},[83,84],[17,20242,20244,20393],{"className":20243},[88],[17,20245,20247],{"className":20246,"style":15137},[92],[17,20248,20249,20252],{"style":15140},[17,20250],{"className":20251,"style":15144},[100],[17,20253,20255,20258,20261,20264,20267,20270,20283,20323,20335,20375,20384,20387,20390],{"className":20254},[79],[17,20256,11429],{"className":20257},[79,230],[17,20259],{"className":20260,"style":235},[234],[17,20262,193],{"className":20263},[239],[17,20265],{"className":20266,"style":235},[234],[17,20268,11438],{"className":20269,"style":11528},[79,230],[17,20271,20273,20276,20280],{"className":20272},[79,115],[17,20274,4056],{"className":20275},[79],[17,20277,20279],{"className":20278},[79,119],"或",[17,20281,4056],{"className":20282},[79],[17,20284,20286,20289],{"className":20285},[79],[17,20287,793],{"className":20288,"style":818},[79,230],[17,20290,20292],{"className":20291},[1453],[17,20293,20295,20315],{"className":20294},[83,84],[17,20296,20298,20312],{"className":20297},[88],[17,20299,20301],{"className":20300,"style":11470},[92],[17,20302,20303,20306],{"style":1466},[17,20304],{"className":20305,"style":1470},[100],[17,20307,20309],{"className":20308},[1474,1475,1476,1477],[17,20310,11438],{"className":20311,"style":11528},[79,230,1477],[17,20313,136],{"className":20314},[135],[17,20316,20318],{"className":20317},[88],[17,20319,20321],{"className":20320,"style":11538},[92],[17,20322],{},[17,20324,20326,20329,20332],{"className":20325},[79,115],[17,20327,4056],{"className":20328},[79],[17,20330,19174],{"className":20331},[79,119],[17,20333,4056],{"className":20334},[79],[17,20336,20338,20341],{"className":20337},[79],[17,20339,793],{"className":20340,"style":818},[79,230],[17,20342,20344],{"className":20343},[1453],[17,20345,20347,20367],{"className":20346},[83,84],[17,20348,20350,20364],{"className":20349},[88],[17,20351,20353],{"className":20352,"style":11470},[92],[17,20354,20355,20358],{"style":1466},[17,20356],{"className":20357,"style":1470},[100],[17,20359,20361],{"className":20360},[1474,1475,1476,1477],[17,20362,11429],{"className":20363},[79,230,1477],[17,20365,136],{"className":20366},[135],[17,20368,20370],{"className":20369},[88],[17,20371,20373],{"className":20372,"style":1490},[92],[17,20374],{},[17,20376,20378,20381],{"className":20377},[79,115],[17,20379,4056],{"className":20380},[79],[17,20382,13628],{"className":20383},[79,119],[17,20385,4056],{"className":20386},[234],[17,20388,47],{"className":20389},[79],[17,20391,202],{"className":20392},[261],[17,20394,136],{"className":20395},[135],[17,20397,20399],{"className":20398},[88],[17,20400,20402],{"className":20401,"style":15163},[92],[17,20403],{},[17,20405],{"className":20406,"style":15307},[15169],[17,20408,20410],{"className":20409},[15311],[17,20411,20413,20532],{"className":20412},[83,84],[17,20414,20416,20529],{"className":20415},[88],[17,20417,20419],{"className":20418,"style":15137},[92],[17,20420,20421,20424],{"style":15140},[17,20422],{"className":20423,"style":15144},[100],[17,20425,20427,20467,20479,20519],{"className":20426},[79],[17,20428,20430,20433],{"className":20429},[79],[17,20431,793],{"className":20432,"style":818},[79,230],[17,20434,20436],{"className":20435},[1453],[17,20437,20439,20459],{"className":20438},[83,84],[17,20440,20442,20456],{"className":20441},[88],[17,20443,20445],{"className":20444,"style":11470},[92],[17,20446,20447,20450],{"style":1466},[17,20448],{"className":20449,"style":1470},[100],[17,20451,20453],{"className":20452},[1474,1475,1476,1477],[17,20454,11438],{"className":20455,"style":11528},[79,230,1477],[17,20457,136],{"className":20458},[135],[17,20460,20462],{"className":20461},[88],[17,20463,20465],{"className":20464,"style":11538},[92],[17,20466],{},[17,20468,20470,20473,20476],{"className":20469},[79,115],[17,20471,4056],{"className":20472},[79],[17,20474,19174],{"className":20475},[79,119],[17,20477,4056],{"className":20478},[79],[17,20480,20482,20485],{"className":20481},[79],[17,20483,793],{"className":20484,"style":818},[79,230],[17,20486,20488],{"className":20487},[1453],[17,20489,20491,20511],{"className":20490},[83,84],[17,20492,20494,20508],{"className":20493},[88],[17,20495,20497],{"className":20496,"style":11470},[92],[17,20498,20499,20502],{"style":1466},[17,20500],{"className":20501,"style":1470},[100],[17,20503,20505],{"className":20504},[1474,1475,1476,1477],[17,20506,11429],{"className":20507},[79,230,1477],[17,20509,136],{"className":20510},[135],[17,20512,20514],{"className":20513},[88],[17,20515,20517],{"className":20516,"style":1490},[92],[17,20518],{},[17,20520,20522,20525],{"className":20521},[79,115],[17,20523,4056],{"className":20524},[79],[17,20526,20528],{"className":20527},[79,119],"不可达",[17,20530,136],{"className":20531},[135],[17,20533,20535],{"className":20534},[88],[17,20536,20538],{"className":20537,"style":15163},[92],[17,20539],{},[17,20541],{"className":20542},[282,3370],[506,20544],{},[513,20546,20548],{"id":20547},"_1-可达矩阵的含义","1. 可达矩阵的含义",[13,20550,4512],{},[17,20552,20554],{"className":20553},[20],[17,20555,20557,20583],{"className":20556},[24],[17,20558,20560],{"className":20559},[28],[30,20561,20562],{"xmlns":32,"display":33},[35,20563,20564,20580],{},[38,20565,20566,20576,20578],{},[1385,20567,20568,20570],{},[187,20569,13],{},[38,20571,20572,20574],{},[187,20573,11429],{},[187,20575,11438],{},[191,20577,193],{},[1390,20579,1392],{},[59,20581,20582],{"encoding":61},"p_{ij}=1",[17,20584,20586,20644],{"className":20585,"ariaHidden":53},[66],[17,20587,20589,20592,20635,20638,20641],{"className":20588},[70],[17,20590],{"className":20591,"style":11451},[74],[17,20593,20595,20598],{"className":20594},[79],[17,20596,13],{"className":20597},[79,230],[17,20599,20601],{"className":20600},[1453],[17,20602,20604,20627],{"className":20603},[83,84],[17,20605,20607,20624],{"className":20606},[88],[17,20608,20610],{"className":20609,"style":11470},[92],[17,20611,20612,20615],{"style":2106},[17,20613],{"className":20614,"style":1470},[100],[17,20616,20618],{"className":20617},[1474,1475,1476,1477],[17,20619,20621],{"className":20620},[79,1477],[17,20622,14842],{"className":20623,"style":11528},[79,230,1477],[17,20625,136],{"className":20626},[135],[17,20628,20630],{"className":20629},[88],[17,20631,20633],{"className":20632,"style":11538},[92],[17,20634],{},[17,20636],{"className":20637,"style":235},[234],[17,20639,193],{"className":20640},[239],[17,20642],{"className":20643,"style":235},[234],[17,20645,20647,20650],{"className":20646},[70],[17,20648],{"className":20649,"style":5244},[74],[17,20651,1392],{"className":20652},[79],[13,20654,19695],{},[17,20656,20658],{"className":20657},[20],[17,20659,20661,20687],{"className":20660},[24],[17,20662,20664],{"className":20663},[28],[30,20665,20666],{"xmlns":32,"display":33},[35,20667,20668,20684],{},[38,20669,20670,20676,20678],{},[1385,20671,20672,20674],{},[187,20673,793],{},[187,20675,11429],{},[191,20677,1306],{},[1385,20679,20680,20682],{},[187,20681,793],{},[187,20683,11438],{},[59,20685,20686],{"encoding":61},"v_i\\to v_j",[17,20688,20690,20745],{"className":20689,"ariaHidden":53},[66],[17,20691,20693,20696,20736,20739,20742],{"className":20692},[70],[17,20694],{"className":20695,"style":2085},[74],[17,20697,20699,20702],{"className":20698},[79],[17,20700,793],{"className":20701,"style":818},[79,230],[17,20703,20705],{"className":20704},[1453],[17,20706,20708,20728],{"className":20707},[83,84],[17,20709,20711,20725],{"className":20710},[88],[17,20712,20714],{"className":20713,"style":11470},[92],[17,20715,20716,20719],{"style":1466},[17,20717],{"className":20718,"style":1470},[100],[17,20720,20722],{"className":20721},[1474,1475,1476,1477],[17,20723,11429],{"className":20724},[79,230,1477],[17,20726,136],{"className":20727},[135],[17,20729,20731],{"className":20730},[88],[17,20732,20734],{"className":20733,"style":1490},[92],[17,20735],{},[17,20737],{"className":20738,"style":235},[234],[17,20740,1306],{"className":20741},[239],[17,20743],{"className":20744,"style":235},[234],[17,20746,20748,20751],{"className":20747},[70],[17,20749],{"className":20750,"style":11451},[74],[17,20752,20754,20757],{"className":20753},[79],[17,20755,793],{"className":20756,"style":818},[79,230],[17,20758,20760],{"className":20759},[1453],[17,20761,20763,20783],{"className":20762},[83,84],[17,20764,20766,20780],{"className":20765},[88],[17,20767,20769],{"className":20768,"style":11470},[92],[17,20770,20771,20774],{"style":1466},[17,20772],{"className":20773,"style":1470},[100],[17,20775,20777],{"className":20776},[1474,1475,1476,1477],[17,20778,11438],{"className":20779,"style":11528},[79,230,1477],[17,20781,136],{"className":20782},[135],[17,20784,20786],{"className":20785},[88],[17,20787,20789],{"className":20788,"style":11538},[92],[17,20790],{},[13,20792,11122],{},[13,20794,4512],{},[17,20796,20798],{"className":20797},[20],[17,20799,20801,20827],{"className":20800},[24],[17,20802,20804],{"className":20803},[28],[30,20805,20806],{"xmlns":32,"display":33},[35,20807,20808,20824],{},[38,20809,20810,20820,20822],{},[1385,20811,20812,20814],{},[187,20813,13],{},[38,20815,20816,20818],{},[187,20817,11429],{},[187,20819,11438],{},[191,20821,193],{},[1390,20823,47],{},[59,20825,20826],{"encoding":61},"p_{ij}=0",[17,20828,20830,20888],{"className":20829,"ariaHidden":53},[66],[17,20831,20833,20836,20879,20882,20885],{"className":20832},[70],[17,20834],{"className":20835,"style":11451},[74],[17,20837,20839,20842],{"className":20838},[79],[17,20840,13],{"className":20841},[79,230],[17,20843,20845],{"className":20844},[1453],[17,20846,20848,20871],{"className":20847},[83,84],[17,20849,20851,20868],{"className":20850},[88],[17,20852,20854],{"className":20853,"style":11470},[92],[17,20855,20856,20859],{"style":2106},[17,20857],{"className":20858,"style":1470},[100],[17,20860,20862],{"className":20861},[1474,1475,1476,1477],[17,20863,20865],{"className":20864},[79,1477],[17,20866,14842],{"className":20867,"style":11528},[79,230,1477],[17,20869,136],{"className":20870},[135],[17,20872,20874],{"className":20873},[88],[17,20875,20877],{"className":20876,"style":11538},[92],[17,20878],{},[17,20880],{"className":20881,"style":235},[234],[17,20883,193],{"className":20884},[239],[17,20886],{"className":20887,"style":235},[234],[17,20889,20891,20894],{"className":20890},[70],[17,20892],{"className":20893,"style":5244},[74],[17,20895,47],{"className":20896},[79],[13,20898,20899],{},"表示不可达。",[506,20901],{},[513,20903,20905],{"id":20904},"_2-用邻接矩阵求可达矩阵","2. 用邻接矩阵求可达矩阵",[13,20907,10770,20908,20936,20937,20987],{},[17,20909,20911,20924],{"className":20910},[24],[17,20912,20914],{"className":20913},[28],[30,20915,20916],{"xmlns":32},[35,20917,20918,20922],{},[38,20919,20920],{},[187,20921,3183],{},[59,20923,3183],{"encoding":61},[17,20925,20927],{"className":20926,"ariaHidden":53},[66],[17,20928,20930,20933],{"className":20929},[70],[17,20931],{"className":20932,"style":769},[74],[17,20934,3183],{"className":20935},[79,230]," 个顶点，则只需考虑长度不超过 ",[17,20938,20940,20957],{"className":20939},[24],[17,20941,20943],{"className":20942},[28],[30,20944,20945],{"xmlns":32},[35,20946,20947,20955],{},[38,20948,20949,20951,20953],{},[187,20950,3183],{},[191,20952,972],{},[1390,20954,1392],{},[59,20956,10849],{"encoding":61},[17,20958,20960,20978],{"className":20959,"ariaHidden":53},[66],[17,20961,20963,20966,20969,20972,20975],{"className":20962},[70],[17,20964],{"className":20965,"style":987},[74],[17,20967,3183],{"className":20968},[79,230],[17,20970],{"className":20971,"style":257},[234],[17,20973,972],{"className":20974},[997],[17,20976],{"className":20977,"style":257},[234],[17,20979,20981,20984],{"className":20980},[70],[17,20982],{"className":20983,"style":5244},[74],[17,20985,1392],{"className":20986},[79]," 的基本路径。",[13,20989,20990],{},"所以可以用布尔矩阵运算：",[17,20992,20994],{"className":20993},[20],[17,20995,20997,21057],{"className":20996},[24],[17,20998,21000],{"className":20999},[28],[30,21001,21002],{"xmlns":32,"display":33},[35,21003,21004,21054],{},[38,21005,21006,21008,21010,21013,21016,21018,21020,21032,21034,21036,21038],{},[187,21007,19908],{},[191,21009,193],{},[187,21011,21012],{},"I",[191,21014,21015],{},"∨",[187,21017,17040],{},[191,21019,21015],{},[4143,21021,21022,21024],{},[187,21023,17040],{},[38,21025,21026,21028,21030],{},[191,21027,841],{"stretchy":48},[1390,21029,1401],{},[191,21031,850],{"stretchy":48},[191,21033,21015],{},[191,21035,8934],{},[191,21037,21015],{},[4143,21039,21040,21042],{},[187,21041,17040],{},[38,21043,21044,21046,21048,21050,21052],{},[191,21045,841],{"stretchy":48},[187,21047,3183],{},[191,21049,972],{},[1390,21051,1392],{},[191,21053,850],{"stretchy":48},[59,21055,21056],{"encoding":61},"P=I\\lor A\\lor A^{(2)}\\lor\\cdots\\lor A^{(n-1)}",[17,21058,21060,21078,21097,21115,21169,21188],{"className":21059,"ariaHidden":53},[66],[17,21061,21063,21066,21069,21072,21075],{"className":21062},[70],[17,21064],{"className":21065,"style":226},[74],[17,21067,19908],{"className":21068,"style":14790},[79,230],[17,21070],{"className":21071,"style":235},[234],[17,21073,193],{"className":21074},[239],[17,21076],{"className":21077,"style":235},[234],[17,21079,21081,21084,21088,21091,21094],{"className":21080},[70],[17,21082],{"className":21083,"style":226},[74],[17,21085,21012],{"className":21086,"style":21087},[79,230],"margin-right:0.0785em;",[17,21089],{"className":21090,"style":257},[234],[17,21092,21015],{"className":21093},[997],[17,21095],{"className":21096,"style":257},[234],[17,21098,21100,21103,21106,21109,21112],{"className":21099},[70],[17,21101],{"className":21102,"style":226},[74],[17,21104,17040],{"className":21105},[79,230],[17,21107],{"className":21108,"style":257},[234],[17,21110,21015],{"className":21111},[997],[17,21113],{"className":21114,"style":257},[234],[17,21116,21118,21122,21160,21163,21166],{"className":21117},[70],[17,21119],{"className":21120,"style":21121},[74],"height:0.938em;",[17,21123,21125,21128],{"className":21124},[79],[17,21126,17040],{"className":21127},[79,230],[17,21129,21131],{"className":21130},[1453],[17,21132,21134],{"className":21133},[83],[17,21135,21137],{"className":21136},[88],[17,21138,21140],{"className":21139,"style":21121},[92],[17,21141,21142,21145],{"style":3601},[17,21143],{"className":21144,"style":1470},[100],[17,21146,21148],{"className":21147},[1474,1475,1476,1477],[17,21149,21151,21154,21157],{"className":21150},[79,1477],[17,21152,841],{"className":21153},[253,1477],[17,21155,1401],{"className":21156},[79,1477],[17,21158,850],{"className":21159},[282,1477],[17,21161],{"className":21162,"style":257},[234],[17,21164,21015],{"className":21165},[997],[17,21167],{"className":21168,"style":257},[234],[17,21170,21172,21176,21179,21182,21185],{"className":21171},[70],[17,21173],{"className":21174,"style":21175},[74],"height:0.5556em;",[17,21177,8934],{"className":21178},[9183],[17,21180],{"className":21181,"style":257},[234],[17,21183,21015],{"className":21184},[997],[17,21186],{"className":21187,"style":257},[234],[17,21189,21191,21194],{"className":21190},[70],[17,21192],{"className":21193,"style":21121},[74],[17,21195,21197,21200],{"className":21196},[79],[17,21198,17040],{"className":21199},[79,230],[17,21201,21203],{"className":21202},[1453],[17,21204,21206],{"className":21205},[83],[17,21207,21209],{"className":21208},[88],[17,21210,21212],{"className":21211,"style":21121},[92],[17,21213,21214,21217],{"style":3601},[17,21215],{"className":21216,"style":1470},[100],[17,21218,21220],{"className":21219},[1474,1475,1476,1477],[17,21221,21223,21226,21229,21232,21235],{"className":21222},[79,1477],[17,21224,841],{"className":21225},[253,1477],[17,21227,3183],{"className":21228},[79,230,1477],[17,21230,972],{"className":21231},[997,1477],[17,21233,1392],{"className":21234},[79,1477],[17,21236,850],{"className":21237},[282,1477],[13,21239,285],{},[150,21241,21242,21273,21380],{},[153,21243,21244,21272],{},[17,21245,21247,21260],{"className":21246},[24],[17,21248,21250],{"className":21249},[28],[30,21251,21252],{"xmlns":32},[35,21253,21254,21258],{},[38,21255,21256],{},[187,21257,21012],{},[59,21259,21012],{"encoding":61},[17,21261,21263],{"className":21262,"ariaHidden":53},[66],[17,21264,21266,21269],{"className":21265},[70],[17,21267],{"className":21268,"style":226},[74],[17,21270,21012],{"className":21271,"style":21087},[79,230],"：单位矩阵，表示自己到自己可达；",[153,21274,21275,21350,21351,21379],{},[17,21276,21278,21302],{"className":21277},[24],[17,21279,21281],{"className":21280},[28],[30,21282,21283],{"xmlns":32},[35,21284,21285,21299],{},[38,21286,21287],{},[4143,21288,21289,21291],{},[187,21290,17040],{},[38,21292,21293,21295,21297],{},[191,21294,841],{"stretchy":48},[187,21296,4699],{},[191,21298,850],{"stretchy":48},[59,21300,21301],{"encoding":61},"A^{(k)}",[17,21303,21305],{"className":21304,"ariaHidden":53},[66],[17,21306,21308,21312],{"className":21307},[70],[17,21309],{"className":21310,"style":21311},[74],"height:0.888em;",[17,21313,21315,21318],{"className":21314},[79],[17,21316,17040],{"className":21317},[79,230],[17,21319,21321],{"className":21320},[1453],[17,21322,21324],{"className":21323},[83],[17,21325,21327],{"className":21326},[88],[17,21328,21330],{"className":21329,"style":21311},[92],[17,21331,21332,21335],{"style":5822},[17,21333],{"className":21334,"style":1470},[100],[17,21336,21338],{"className":21337},[1474,1475,1476,1477],[17,21339,21341,21344,21347],{"className":21340},[79,1477],[17,21342,841],{"className":21343},[253,1477],[17,21345,4699],{"className":21346,"style":4715},[79,230,1477],[17,21348,850],{"className":21349},[282,1477],"：布尔意义下的 ",[17,21352,21354,21367],{"className":21353},[24],[17,21355,21357],{"className":21356},[28],[30,21358,21359],{"xmlns":32},[35,21360,21361,21365],{},[38,21362,21363],{},[187,21364,4699],{},[59,21366,4699],{"encoding":61},[17,21368,21370],{"className":21369,"ariaHidden":53},[66],[17,21371,21373,21376],{"className":21372},[70],[17,21374],{"className":21375,"style":4711},[74],[17,21377,4699],{"className":21378,"style":4715},[79,230]," 次幂；",[153,21381,21382,21411],{},[17,21383,21385,21399],{"className":21384},[24],[17,21386,21388],{"className":21387},[28],[30,21389,21390],{"xmlns":32},[35,21391,21392,21396],{},[38,21393,21394],{},[191,21395,21015],{},[59,21397,21398],{"encoding":61},"\\lor",[17,21400,21402],{"className":21401,"ariaHidden":53},[66],[17,21403,21405,21408],{"className":21404},[70],[17,21406],{"className":21407,"style":21175},[74],[17,21409,21015],{"className":21410},[79],"：布尔或。",[13,21413,21414],{},"也可以先求普通幂：",[17,21416,21418],{"className":21417},[20],[17,21419,21421,21461],{"className":21420},[24],[17,21422,21424],{"className":21423},[28],[30,21425,21426],{"xmlns":32,"display":33},[35,21427,21428,21458],{},[38,21429,21430,21432,21434,21440,21442,21444,21446],{},[187,21431,17040],{},[191,21433,4149],{},[4143,21435,21436,21438],{},[187,21437,17040],{},[1390,21439,1401],{},[191,21441,4149],{},[191,21443,8934],{},[191,21445,4149],{},[4143,21447,21448,21450],{},[187,21449,17040],{},[38,21451,21452,21454,21456],{},[187,21453,3183],{},[191,21455,972],{},[1390,21457,1392],{},[59,21459,21460],{"encoding":61},"A+A^2+\\cdots+A^{n-1}",[17,21462,21464,21482,21527,21545],{"className":21463,"ariaHidden":53},[66],[17,21465,21467,21470,21473,21476,21479],{"className":21466},[70],[17,21468],{"className":21469,"style":7157},[74],[17,21471,17040],{"className":21472},[79,230],[17,21474],{"className":21475,"style":257},[234],[17,21477,4149],{"className":21478},[997],[17,21480],{"className":21481,"style":257},[234],[17,21483,21485,21489,21518,21521,21524],{"className":21484},[70],[17,21486],{"className":21487,"style":21488},[74],"height:0.9474em;vertical-align:-0.0833em;",[17,21490,21492,21495],{"className":21491},[79],[17,21493,17040],{"className":21494},[79,230],[17,21496,21498],{"className":21497},[1453],[17,21499,21501],{"className":21500},[83],[17,21502,21504],{"className":21503},[88],[17,21505,21507],{"className":21506,"style":3586},[92],[17,21508,21509,21512],{"style":3601},[17,21510],{"className":21511,"style":1470},[100],[17,21513,21515],{"className":21514},[1474,1475,1476,1477],[17,21516,1401],{"className":21517},[79,1477],[17,21519],{"className":21520,"style":257},[234],[17,21522,4149],{"className":21523},[997],[17,21525],{"className":21526,"style":257},[234],[17,21528,21530,21533,21536,21539,21542],{"className":21529},[70],[17,21531],{"className":21532,"style":987},[74],[17,21534,8934],{"className":21535},[9183],[17,21537],{"className":21538,"style":257},[234],[17,21540,4149],{"className":21541},[997],[17,21543],{"className":21544,"style":257},[234],[17,21546,21548,21551],{"className":21547},[70],[17,21549],{"className":21550,"style":3586},[74],[17,21552,21554,21557],{"className":21553},[79],[17,21555,17040],{"className":21556},[79,230],[17,21558,21560],{"className":21559},[1453],[17,21561,21563],{"className":21562},[83],[17,21564,21566],{"className":21565},[88],[17,21567,21569],{"className":21568,"style":3586},[92],[17,21570,21571,21574],{"style":3601},[17,21572],{"className":21573,"style":1470},[100],[17,21575,21577],{"className":21576},[1474,1475,1476,1477],[17,21578,21580,21583,21586],{"className":21579},[79,1477],[17,21581,3183],{"className":21582},[79,230,1477],[17,21584,972],{"className":21585},[997,1477],[17,21587,1392],{"className":21588},[79,1477],[13,21590,21591],{},"再把非零元素改成 1。",[506,21593],{},[513,21595,21597],{"id":21596},"_3-强分图与可达矩阵","3. 强分图与可达矩阵",[13,21599,21600,21601,21629],{},"如果有可达矩阵 ",[17,21602,21604,21617],{"className":21603},[24],[17,21605,21607],{"className":21606},[28],[30,21608,21609],{"xmlns":32},[35,21610,21611,21615],{},[38,21612,21613],{},[187,21614,19908],{},[59,21616,19908],{"encoding":61},[17,21618,21620],{"className":21619,"ariaHidden":53},[66],[17,21621,21623,21626],{"className":21622},[70],[17,21624],{"className":21625,"style":226},[74],[17,21627,19908],{"className":21628,"style":14790},[79,230],"，那么：",[17,21631,21633],{"className":21632},[20],[17,21634,21636,21659],{"className":21635},[24],[17,21637,21639],{"className":21638},[28],[30,21640,21641],{"xmlns":32,"display":33},[35,21642,21643,21656],{},[38,21644,21645,21647,21650],{},[187,21646,19908],{},[191,21648,21649],{},"∧",[4143,21651,21652,21654],{},[187,21653,19908],{},[187,21655,17926],{},[59,21657,21658],{"encoding":61},"P\\land P^T",[17,21660,21662,21680],{"className":21661,"ariaHidden":53},[66],[17,21663,21665,21668,21671,21674,21677],{"className":21664},[70],[17,21666],{"className":21667,"style":226},[74],[17,21669,19908],{"className":21670,"style":14790},[79,230],[17,21672],{"className":21673,"style":257},[234],[17,21675,21649],{"className":21676},[997],[17,21678],{"className":21679,"style":257},[234],[17,21681,21683,21686],{"className":21682},[70],[17,21684],{"className":21685,"style":17957},[74],[17,21687,21689,21692],{"className":21688},[79],[17,21690,19908],{"className":21691,"style":14790},[79,230],[17,21693,21695],{"className":21694},[1453],[17,21696,21698],{"className":21697},[83],[17,21699,21701],{"className":21700},[88],[17,21702,21704],{"className":21703,"style":17957},[92],[17,21705,21706,21709],{"style":3601},[17,21707],{"className":21708,"style":1470},[100],[17,21710,21712],{"className":21711},[1474,1475,1476,1477],[17,21713,17926],{"className":21714,"style":14790},[79,230,1477],[13,21716,21717],{},"可以表示互相可达关系。",[13,21719,4512],{},[17,21721,21723],{"className":21722},[20],[17,21724,21726,21751],{"className":21725},[24],[17,21727,21729],{"className":21728},[28],[30,21730,21731],{"xmlns":32,"display":33},[35,21732,21733,21749],{},[38,21734,21735,21745,21747],{},[1385,21736,21737,21739],{},[187,21738,13],{},[38,21740,21741,21743],{},[187,21742,11429],{},[187,21744,11438],{},[191,21746,193],{},[1390,21748,1392],{},[59,21750,20582],{"encoding":61},[17,21752,21754,21812],{"className":21753,"ariaHidden":53},[66],[17,21755,21757,21760,21803,21806,21809],{"className":21756},[70],[17,21758],{"className":21759,"style":11451},[74],[17,21761,21763,21766],{"className":21762},[79],[17,21764,13],{"className":21765},[79,230],[17,21767,21769],{"className":21768},[1453],[17,21770,21772,21795],{"className":21771},[83,84],[17,21773,21775,21792],{"className":21774},[88],[17,21776,21778],{"className":21777,"style":11470},[92],[17,21779,21780,21783],{"style":2106},[17,21781],{"className":21782,"style":1470},[100],[17,21784,21786],{"className":21785},[1474,1475,1476,1477],[17,21787,21789],{"className":21788},[79,1477],[17,21790,14842],{"className":21791,"style":11528},[79,230,1477],[17,21793,136],{"className":21794},[135],[17,21796,21798],{"className":21797},[88],[17,21799,21801],{"className":21800,"style":11538},[92],[17,21802],{},[17,21804],{"className":21805,"style":235},[234],[17,21807,193],{"className":21808},[239],[17,21810],{"className":21811,"style":235},[234],[17,21813,21815,21818],{"className":21814},[70],[17,21816],{"className":21817,"style":5244},[74],[17,21819,1392],{"className":21820},[79],[13,21822,21823],{},"且：",[17,21825,21827],{"className":21826},[20],[17,21828,21830,21856],{"className":21829},[24],[17,21831,21833],{"className":21832},[28],[30,21834,21835],{"xmlns":32,"display":33},[35,21836,21837,21853],{},[38,21838,21839,21849,21851],{},[1385,21840,21841,21843],{},[187,21842,13],{},[38,21844,21845,21847],{},[187,21846,11438],{},[187,21848,11429],{},[191,21850,193],{},[1390,21852,1392],{},[59,21854,21855],{"encoding":61},"p_{ji}=1",[17,21857,21859,21920],{"className":21858,"ariaHidden":53},[66],[17,21860,21862,21865,21911,21914,21917],{"className":21861},[70],[17,21863],{"className":21864,"style":11451},[74],[17,21866,21868,21871],{"className":21867},[79],[17,21869,13],{"className":21870},[79,230],[17,21872,21874],{"className":21873},[1453],[17,21875,21877,21903],{"className":21876},[83,84],[17,21878,21880,21900],{"className":21879},[88],[17,21881,21883],{"className":21882,"style":11470},[92],[17,21884,21885,21888],{"style":2106},[17,21886],{"className":21887,"style":1470},[100],[17,21889,21891],{"className":21890},[1474,1475,1476,1477],[17,21892,21894,21897],{"className":21893},[79,1477],[17,21895,11438],{"className":21896,"style":11528},[79,230,1477],[17,21898,11429],{"className":21899},[79,230,1477],[17,21901,136],{"className":21902},[135],[17,21904,21906],{"className":21905},[88],[17,21907,21909],{"className":21908,"style":11538},[92],[17,21910],{},[17,21912],{"className":21913,"style":235},[234],[17,21915,193],{"className":21916},[239],[17,21918],{"className":21919,"style":235},[234],[17,21921,21923,21926],{"className":21922},[70],[17,21924],{"className":21925,"style":5244},[74],[17,21927,1392],{"className":21928},[79],[13,21930,21931],{},"说明：",[17,21933,21935],{"className":21934},[20],[17,21936,21938,21955],{"className":21937},[24],[17,21939,21941],{"className":21940},[28],[30,21942,21943],{"xmlns":32,"display":33},[35,21944,21945,21953],{},[38,21946,21947],{},[1385,21948,21949,21951],{},[187,21950,793],{},[187,21952,11429],{},[59,21954,12005],{"encoding":61},[17,21956,21958],{"className":21957,"ariaHidden":53},[66],[17,21959,21961,21964],{"className":21960},[70],[17,21962],{"className":21963,"style":2085},[74],[17,21965,21967,21970],{"className":21966},[79],[17,21968,793],{"className":21969,"style":818},[79,230],[17,21971,21973],{"className":21972},[1453],[17,21974,21976,21996],{"className":21975},[83,84],[17,21977,21979,21993],{"className":21978},[88],[17,21980,21982],{"className":21981,"style":11470},[92],[17,21983,21984,21987],{"style":1466},[17,21985],{"className":21986,"style":1470},[100],[17,21988,21990],{"className":21989},[1474,1475,1476,1477],[17,21991,11429],{"className":21992},[79,230,1477],[17,21994,136],{"className":21995},[135],[17,21997,21999],{"className":21998},[88],[17,22000,22002],{"className":22001,"style":1490},[92],[17,22003],{},[13,22005,22006],{},"和：",[17,22008,22010],{"className":22009},[20],[17,22011,22013,22030],{"className":22012},[24],[17,22014,22016],{"className":22015},[28],[30,22017,22018],{"xmlns":32,"display":33},[35,22019,22020,22028],{},[38,22021,22022],{},[1385,22023,22024,22026],{},[187,22025,793],{},[187,22027,11438],{},[59,22029,11934],{"encoding":61},[17,22031,22033],{"className":22032,"ariaHidden":53},[66],[17,22034,22036,22039],{"className":22035},[70],[17,22037],{"className":22038,"style":11451},[74],[17,22040,22042,22045],{"className":22041},[79],[17,22043,793],{"className":22044,"style":818},[79,230],[17,22046,22048],{"className":22047},[1453],[17,22049,22051,22071],{"className":22050},[83,84],[17,22052,22054,22068],{"className":22053},[88],[17,22055,22057],{"className":22056,"style":11470},[92],[17,22058,22059,22062],{"style":1466},[17,22060],{"className":22061,"style":1470},[100],[17,22063,22065],{"className":22064},[1474,1475,1476,1477],[17,22066,11438],{"className":22067,"style":11528},[79,230,1477],[17,22069,136],{"className":22070},[135],[17,22072,22074],{"className":22073},[88],[17,22075,22077],{"className":22076,"style":11538},[92],[17,22078],{},[13,22080,22081],{},"互相可达，可能属于同一个强分图。",[506,22083],{},[10,22085,22087],{"id":22086},"五距离矩阵","五、距离矩阵",[13,22089,22090],{},"距离矩阵记录的是两个顶点之间最短距离。",[13,22092,5360],{},[17,22094,22096],{"className":22095},[20],[17,22097,22099,22130],{"className":22098},[24],[17,22100,22102],{"className":22101},[28],[30,22103,22104],{"xmlns":32,"display":33},[35,22105,22106,22127],{},[38,22107,22108,22111,22113,22115,22125],{},[187,22109,22110],{},"D",[191,22112,193],{},[191,22114,841],{"stretchy":48},[1385,22116,22117,22119],{},[187,22118,3912],{},[38,22120,22121,22123],{},[187,22122,11429],{},[187,22124,11438],{},[191,22126,850],{"stretchy":48},[59,22128,22129],{"encoding":61},"D=(d_{ij})",[17,22131,22133,22152],{"className":22132,"ariaHidden":53},[66],[17,22134,22136,22139,22143,22146,22149],{"className":22135},[70],[17,22137],{"className":22138,"style":226},[74],[17,22140,22110],{"className":22141,"style":22142},[79,230],"margin-right:0.0278em;",[17,22144],{"className":22145,"style":235},[234],[17,22147,193],{"className":22148},[239],[17,22150],{"className":22151,"style":235},[234],[17,22153,22155,22158,22161,22204],{"className":22154},[70],[17,22156],{"className":22157,"style":11589},[74],[17,22159,841],{"className":22160},[253],[17,22162,22164,22167],{"className":22163},[79],[17,22165,3912],{"className":22166},[79,230],[17,22168,22170],{"className":22169},[1453],[17,22171,22173,22196],{"className":22172},[83,84],[17,22174,22176,22193],{"className":22175},[88],[17,22177,22179],{"className":22178,"style":11470},[92],[17,22180,22181,22184],{"style":2106},[17,22182],{"className":22183,"style":1470},[100],[17,22185,22187],{"className":22186},[1474,1475,1476,1477],[17,22188,22190],{"className":22189},[79,1477],[17,22191,14842],{"className":22192,"style":11528},[79,230,1477],[17,22194,136],{"className":22195},[135],[17,22197,22199],{"className":22198},[88],[17,22200,22202],{"className":22201,"style":11538},[92],[17,22203],{},[17,22205,850],{"className":22206},[282],[13,22208,285],{},[17,22210,22212],{"className":22211},[20],[17,22213,22215,22259],{"className":22214},[24],[17,22216,22218],{"className":22217},[28],[30,22219,22220],{"xmlns":32,"display":33},[35,22221,22222,22256],{},[38,22223,22224,22234,22236,22238,22240,22246,22248,22254],{},[1385,22225,22226,22228],{},[187,22227,3912],{},[38,22229,22230,22232],{},[187,22231,11429],{},[187,22233,11438],{},[191,22235,193],{},[187,22237,3912],{},[191,22239,6777],{"stretchy":48},[1385,22241,22242,22244],{},[187,22243,793],{},[187,22245,11429],{},[191,22247,202],{"separator":53},[1385,22249,22250,22252],{},[187,22251,793],{},[187,22253,11438],{},[191,22255,6786],{"stretchy":48},[59,22257,22258],{"encoding":61},"d_{ij}=d[v_i,v_j]",[17,22260,22262,22320],{"className":22261,"ariaHidden":53},[66],[17,22263,22265,22268,22311,22314,22317],{"className":22264},[70],[17,22266],{"className":22267,"style":15045},[74],[17,22269,22271,22274],{"className":22270},[79],[17,22272,3912],{"className":22273},[79,230],[17,22275,22277],{"className":22276},[1453],[17,22278,22280,22303],{"className":22279},[83,84],[17,22281,22283,22300],{"className":22282},[88],[17,22284,22286],{"className":22285,"style":11470},[92],[17,22287,22288,22291],{"style":2106},[17,22289],{"className":22290,"style":1470},[100],[17,22292,22294],{"className":22293},[1474,1475,1476,1477],[17,22295,22297],{"className":22296},[79,1477],[17,22298,14842],{"className":22299,"style":11528},[79,230,1477],[17,22301,136],{"className":22302},[135],[17,22304,22306],{"className":22305},[88],[17,22307,22309],{"className":22308,"style":11538},[92],[17,22310],{},[17,22312],{"className":22313,"style":235},[234],[17,22315,193],{"className":22316},[239],[17,22318],{"className":22319,"style":235},[234],[17,22321,22323,22326,22329,22332,22372,22375,22378,22418],{"className":22322},[70],[17,22324],{"className":22325,"style":11589},[74],[17,22327,3912],{"className":22328},[79,230],[17,22330,6777],{"className":22331},[253],[17,22333,22335,22338],{"className":22334},[79],[17,22336,793],{"className":22337,"style":818},[79,230],[17,22339,22341],{"className":22340},[1453],[17,22342,22344,22364],{"className":22343},[83,84],[17,22345,22347,22361],{"className":22346},[88],[17,22348,22350],{"className":22349,"style":11470},[92],[17,22351,22352,22355],{"style":1466},[17,22353],{"className":22354,"style":1470},[100],[17,22356,22358],{"className":22357},[1474,1475,1476,1477],[17,22359,11429],{"className":22360},[79,230,1477],[17,22362,136],{"className":22363},[135],[17,22365,22367],{"className":22366},[88],[17,22368,22370],{"className":22369,"style":1490},[92],[17,22371],{},[17,22373,202],{"className":22374},[261],[17,22376],{"className":22377,"style":265},[234],[17,22379,22381,22384],{"className":22380},[79],[17,22382,793],{"className":22383,"style":818},[79,230],[17,22385,22387],{"className":22386},[1453],[17,22388,22390,22410],{"className":22389},[83,84],[17,22391,22393,22407],{"className":22392},[88],[17,22394,22396],{"className":22395,"style":11470},[92],[17,22397,22398,22401],{"style":1466},[17,22399],{"className":22400,"style":1470},[100],[17,22402,22404],{"className":22403},[1474,1475,1476,1477],[17,22405,11438],{"className":22406,"style":11528},[79,230,1477],[17,22408,136],{"className":22409},[135],[17,22411,22413],{"className":22412},[88],[17,22414,22416],{"className":22415,"style":11538},[92],[17,22417],{},[17,22419,6786],{"className":22420},[282],[13,22422,22423],{},"如果不可达，则：",[17,22425,22427],{"className":22426},[20],[17,22428,22430,22456],{"className":22429},[24],[17,22431,22433],{"className":22432},[28],[30,22434,22435],{"xmlns":32,"display":33},[35,22436,22437,22453],{},[38,22438,22439,22449,22451],{},[1385,22440,22441,22443],{},[187,22442,3912],{},[38,22444,22445,22447],{},[187,22446,11429],{},[187,22448,11438],{},[191,22450,193],{},[187,22452,12095],{"mathvariant":2754},[59,22454,22455],{"encoding":61},"d_{ij}=\\infty",[17,22457,22459,22517],{"className":22458,"ariaHidden":53},[66],[17,22460,22462,22465,22508,22511,22514],{"className":22461},[70],[17,22463],{"className":22464,"style":15045},[74],[17,22466,22468,22471],{"className":22467},[79],[17,22469,3912],{"className":22470},[79,230],[17,22472,22474],{"className":22473},[1453],[17,22475,22477,22500],{"className":22476},[83,84],[17,22478,22480,22497],{"className":22479},[88],[17,22481,22483],{"className":22482,"style":11470},[92],[17,22484,22485,22488],{"style":2106},[17,22486],{"className":22487,"style":1470},[100],[17,22489,22491],{"className":22490},[1474,1475,1476,1477],[17,22492,22494],{"className":22493},[79,1477],[17,22495,14842],{"className":22496,"style":11528},[79,230,1477],[17,22498,136],{"className":22499},[135],[17,22501,22503],{"className":22502},[88],[17,22504,22506],{"className":22505,"style":11538},[92],[17,22507],{},[17,22509],{"className":22510,"style":235},[234],[17,22512,193],{"className":22513},[239],[17,22515],{"className":22516,"style":235},[234],[17,22518,22520,22523],{"className":22519},[70],[17,22521],{"className":22522,"style":769},[74],[17,22524,12095],{"className":22525},[79],[13,22527,4512],{},[17,22529,22531],{"className":22530},[20],[17,22532,22534,22551],{"className":22533},[24],[17,22535,22537],{"className":22536},[28],[30,22538,22539],{"xmlns":32,"display":33},[35,22540,22541,22549],{},[38,22542,22543,22545,22547],{},[187,22544,11429],{},[191,22546,193],{},[187,22548,11438],{},[59,22550,11712],{"encoding":61},[17,22552,22554,22572],{"className":22553,"ariaHidden":53},[66],[17,22555,22557,22560,22563,22566,22569],{"className":22556},[70],[17,22558],{"className":22559,"style":11722},[74],[17,22561,11429],{"className":22562},[79,230],[17,22564],{"className":22565,"style":235},[234],[17,22567,193],{"className":22568},[239],[17,22570],{"className":22571,"style":235},[234],[17,22573,22575,22578],{"className":22574},[70],[17,22576],{"className":22577,"style":11741},[74],[17,22579,11438],{"className":22580,"style":11528},[79,230],[13,22582,11334],{},[17,22584,22586],{"className":22585},[20],[17,22587,22589,22615],{"className":22588},[24],[17,22590,22592],{"className":22591},[28],[30,22593,22594],{"xmlns":32,"display":33},[35,22595,22596,22612],{},[38,22597,22598,22608,22610],{},[1385,22599,22600,22602],{},[187,22601,3912],{},[38,22603,22604,22606],{},[187,22605,11429],{},[187,22607,11429],{},[191,22609,193],{},[1390,22611,47],{},[59,22613,22614],{"encoding":61},"d_{ii}=0",[17,22616,22618,22678],{"className":22617,"ariaHidden":53},[66],[17,22619,22621,22625,22669,22672,22675],{"className":22620},[70],[17,22622],{"className":22623,"style":22624},[74],"height:0.8444em;vertical-align:-0.15em;",[17,22626,22628,22631],{"className":22627},[79],[17,22629,3912],{"className":22630},[79,230],[17,22632,22634],{"className":22633},[1453],[17,22635,22637,22661],{"className":22636},[83,84],[17,22638,22640,22658],{"className":22639},[88],[17,22641,22643],{"className":22642,"style":11470},[92],[17,22644,22645,22648],{"style":2106},[17,22646],{"className":22647,"style":1470},[100],[17,22649,22651],{"className":22650},[1474,1475,1476,1477],[17,22652,22654],{"className":22653},[79,1477],[17,22655,22657],{"className":22656},[79,230,1477],"ii",[17,22659,136],{"className":22660},[135],[17,22662,22664],{"className":22663},[88],[17,22665,22667],{"className":22666,"style":1490},[92],[17,22668],{},[17,22670],{"className":22671,"style":235},[234],[17,22673,193],{"className":22674},[239],[17,22676],{"className":22677,"style":235},[234],[17,22679,22681,22684],{"className":22680},[70],[17,22682],{"className":22683,"style":5244},[74],[17,22685,47],{"className":22686},[79],[506,22688],{},[10,22690,22692],{"id":22691},"_124-应用举例","12.4 应用举例",[13,22694,22695],{},"这一节主要讲图论应用。",[13,22697,22698,22699,720],{},"教材里有几类：",[645,22700,22701],{},"均分问题、最短路径问题、最优路径问题、关键路径问题",[506,22703],{},[10,22705,22707],{"id":22706},"一均分问题","一、均分问题",[13,22709,22710],{},"这种题一般把“状态”看成顶点，把“一步操作”看成边。",[13,22712,22713],{},"比如三个容器倒水问题：",[150,22715,22716,22719,22722],{},[153,22717,22718],{},"每一种水量分布是一个状态；",[153,22720,22721],{},"从一种状态倒水到另一种状态，就是一条边；",[153,22723,22724],{},"问能否均分，就是问图中是否存在从初始状态到目标状态的路径。",[13,22726,22727],{},"核心思想：",[17,22729,22731],{"className":22730},[20],[17,22732,22734,22757],{"className":22733},[24],[17,22735,22737],{"className":22736},[28],[30,22738,22739],{"xmlns":32,"display":33},[35,22740,22741,22754],{},[38,22742,22743],{},[41,22744,22745],{"notation":43},[45,22746,22747],{"scriptlevel":47,"displaystyle":48},[45,22748,22749],{"scriptlevel":47,"displaystyle":48},[45,22750,22751],{"scriptlevel":47,"displaystyle":53},[55,22752,22753],{},"状态 = 顶点，操作 = 边，求解 = 找路径",[59,22755,22756],{"encoding":61},"\\boxed{\\text{状态 = 顶点，操作 = 边，求解 = 找路径}}",[17,22758,22760],{"className":22759,"ariaHidden":53},[66],[17,22761,22763,22766],{"className":22762},[70],[17,22764],{"className":22765,"style":75},[74],[17,22767,22769],{"className":22768},[79],[17,22770,22772,22831],{"className":22771},[83,84],[17,22773,22775,22828],{"className":22774},[88],[17,22776,22778,22820],{"className":22777,"style":93},[92],[17,22779,22780,22783],{"style":96},[17,22781],{"className":22782,"style":101},[100],[17,22784,22786],{"className":22785},[105],[17,22787,22789],{"className":22788},[79],[17,22790,22792],{"className":22791},[79],[17,22793,22795,22799,22802,22806,22809,22813,22816],{"className":22794},[79,115],[17,22796,22798],{"className":22797},[79,119],"状态",[17,22800,3117],{"className":22801},[79],[17,22803,22805],{"className":22804},[79,119],"顶点，操作",[17,22807,3117],{"className":22808},[79],[17,22810,22812],{"className":22811},[79,119],"边，求解",[17,22814,3117],{"className":22815},[79],[17,22817,22819],{"className":22818},[79,119],"找路径",[17,22821,22822,22825],{"style":122},[17,22823],{"className":22824,"style":101},[100],[17,22826],{"className":22827,"style":131},[129,130],[17,22829,136],{"className":22830},[135],[17,22832,22834],{"className":22833},[88],[17,22835,22837],{"className":22836,"style":143},[92],[17,22838],{},[506,22840],{},[10,22842,22844],{"id":22843},"二赋权图","二、赋权图",[513,22846,8262],{"id":22847},"_1-定义-1",[13,22849,22850,22851,1357,22854,720],{},"如果图的每条边都赋有一个数值，称为",[645,22852,22853],{},"赋权图",[645,22855,22856],{},"带权图",[13,22858,22859,22860,22888],{},"记边 ",[17,22861,22863,22876],{"className":22862},[24],[17,22864,22866],{"className":22865},[28],[30,22867,22868],{"xmlns":32},[35,22869,22870,22874],{},[38,22871,22872],{},[187,22873,757],{},[59,22875,757],{"encoding":61},[17,22877,22879],{"className":22878,"ariaHidden":53},[66],[17,22880,22882,22885],{"className":22881},[70],[17,22883],{"className":22884,"style":769},[74],[17,22886,757],{"className":22887},[79,230]," 的权为：",[17,22890,22892],{"className":22891},[20],[17,22893,22895,22916],{"className":22894},[24],[17,22896,22898],{"className":22897},[28],[30,22899,22900],{"xmlns":32,"display":33},[35,22901,22902,22913],{},[38,22903,22904,22907,22909,22911],{},[187,22905,22906],{},"W",[191,22908,841],{"stretchy":48},[187,22910,757],{},[191,22912,850],{"stretchy":48},[59,22914,22915],{"encoding":61},"W(e)",[17,22917,22919],{"className":22918,"ariaHidden":53},[66],[17,22920,22922,22925,22928,22931,22934],{"className":22921},[70],[17,22923],{"className":22924,"style":249},[74],[17,22926,22906],{"className":22927,"style":14790},[79,230],[17,22929,841],{"className":22930},[253],[17,22932,757],{"className":22933},[79,230],[17,22935,850],{"className":22936},[282],[13,22938,22939],{},"权可以表示：",[150,22941,22942,22945,22948,22951,22954,22957],{},[153,22943,22944],{},"距离；",[153,22946,22947],{},"时间；",[153,22949,22950],{},"费用；",[153,22952,22953],{},"风险；",[153,22955,22956],{},"容量；",[153,22958,22959],{},"损耗。",[506,22961],{},[513,22963,22965],{"id":22964},"_2-路径长度","2. 路径长度",[13,22967,22968],{},"在赋权图中，一条路径的长度不是边数，而是路径上所有边权之和。",[13,22970,22971],{},"如果路径：",[17,22973,22975],{"className":22974},[20],[17,22976,22978,23014],{"className":22977},[24],[17,22979,22981],{"className":22980},[28],[30,22982,22983],{"xmlns":32,"display":33},[35,22984,22985,23011],{},[38,22986,22987,22989,22991,22997,23003,23005],{},[187,22988,8899],{},[191,22990,193],{},[1385,22992,22993,22995],{},[187,22994,757],{},[1390,22996,1392],{},[1385,22998,22999,23001],{},[187,23000,757],{},[1390,23002,1401],{},[191,23004,8934],{},[1385,23006,23007,23009],{},[187,23008,757],{},[187,23010,4699],{},[59,23012,23013],{"encoding":61},"\\mu=e_1e_2\\cdots e_k",[17,23015,23017,23035],{"className":23016,"ariaHidden":53},[66],[17,23018,23020,23023,23026,23029,23032],{"className":23019},[70],[17,23021],{"className":23022,"style":406},[74],[17,23024,8899],{"className":23025},[79,230],[17,23027],{"className":23028,"style":235},[234],[17,23030,193],{"className":23031},[239],[17,23033],{"className":23034,"style":235},[234],[17,23036,23038,23041,23081,23121,23124,23127,23130],{"className":23037},[70],[17,23039],{"className":23040,"style":2085},[74],[17,23042,23044,23047],{"className":23043},[79],[17,23045,757],{"className":23046},[79,230],[17,23048,23050],{"className":23049},[1453],[17,23051,23053,23073],{"className":23052},[83,84],[17,23054,23056,23070],{"className":23055},[88],[17,23057,23059],{"className":23058,"style":1463},[92],[17,23060,23061,23064],{"style":2106},[17,23062],{"className":23063,"style":1470},[100],[17,23065,23067],{"className":23066},[1474,1475,1476,1477],[17,23068,1392],{"className":23069},[79,1477],[17,23071,136],{"className":23072},[135],[17,23074,23076],{"className":23075},[88],[17,23077,23079],{"className":23078,"style":1490},[92],[17,23080],{},[17,23082,23084,23087],{"className":23083},[79],[17,23085,757],{"className":23086},[79,230],[17,23088,23090],{"className":23089},[1453],[17,23091,23093,23113],{"className":23092},[83,84],[17,23094,23096,23110],{"className":23095},[88],[17,23097,23099],{"className":23098,"style":1463},[92],[17,23100,23101,23104],{"style":2106},[17,23102],{"className":23103,"style":1470},[100],[17,23105,23107],{"className":23106},[1474,1475,1476,1477],[17,23108,1401],{"className":23109},[79,1477],[17,23111,136],{"className":23112},[135],[17,23114,23116],{"className":23115},[88],[17,23117,23119],{"className":23118,"style":1490},[92],[17,23120],{},[17,23122],{"className":23123,"style":265},[234],[17,23125,8934],{"className":23126},[9183],[17,23128],{"className":23129,"style":265},[234],[17,23131,23133,23136],{"className":23132},[79],[17,23134,757],{"className":23135},[79,230],[17,23137,23139],{"className":23138},[1453],[17,23140,23142,23162],{"className":23141},[83,84],[17,23143,23145,23159],{"className":23144},[88],[17,23146,23148],{"className":23147,"style":9205},[92],[17,23149,23150,23153],{"style":2106},[17,23151],{"className":23152,"style":1470},[100],[17,23154,23156],{"className":23155},[1474,1475,1476,1477],[17,23157,4699],{"className":23158,"style":4715},[79,230,1477],[17,23160,136],{"className":23161},[135],[17,23163,23165],{"className":23164},[88],[17,23166,23168],{"className":23167,"style":1490},[92],[17,23169],{},[13,23171,11334],{},[17,23173,23175],{"className":23174},[20],[17,23176,23178,23245],{"className":23177},[24],[17,23179,23181],{"className":23180},[28],[30,23182,23183],{"xmlns":32,"display":33},[35,23184,23185,23242],{},[38,23186,23187,23190,23192,23194,23196,23198,23200,23202,23208,23210,23212,23214,23216,23222,23224,23226,23228,23230,23232,23234,23240],{},[187,23188,23189],{},"l",[191,23191,841],{"stretchy":48},[187,23193,8899],{},[191,23195,850],{"stretchy":48},[191,23197,193],{},[187,23199,22906],{},[191,23201,841],{"stretchy":48},[1385,23203,23204,23206],{},[187,23205,757],{},[1390,23207,1392],{},[191,23209,850],{"stretchy":48},[191,23211,4149],{},[187,23213,22906],{},[191,23215,841],{"stretchy":48},[1385,23217,23218,23220],{},[187,23219,757],{},[1390,23221,1401],{},[191,23223,850],{"stretchy":48},[191,23225,4149],{},[191,23227,8934],{},[191,23229,4149],{},[187,23231,22906],{},[191,23233,841],{"stretchy":48},[1385,23235,23236,23238],{},[187,23237,757],{},[187,23239,4699],{},[191,23241,850],{"stretchy":48},[59,23243,23244],{"encoding":61},"l(\\mu)=W(e_1)+W(e_2)+\\cdots+W(e_k)",[17,23246,23248,23276,23340,23404,23422],{"className":23247,"ariaHidden":53},[66],[17,23249,23251,23254,23258,23261,23264,23267,23270,23273],{"className":23250},[70],[17,23252],{"className":23253,"style":249},[74],[17,23255,23189],{"className":23256,"style":23257},[79,230],"margin-right:0.0197em;",[17,23259,841],{"className":23260},[253],[17,23262,8899],{"className":23263},[79,230],[17,23265,850],{"className":23266},[282],[17,23268],{"className":23269,"style":235},[234],[17,23271,193],{"className":23272},[239],[17,23274],{"className":23275,"style":235},[234],[17,23277,23279,23282,23285,23288,23328,23331,23334,23337],{"className":23278},[70],[17,23280],{"className":23281,"style":249},[74],[17,23283,22906],{"className":23284,"style":14790},[79,230],[17,23286,841],{"className":23287},[253],[17,23289,23291,23294],{"className":23290},[79],[17,23292,757],{"className":23293},[79,230],[17,23295,23297],{"className":23296},[1453],[17,23298,23300,23320],{"className":23299},[83,84],[17,23301,23303,23317],{"className":23302},[88],[17,23304,23306],{"className":23305,"style":1463},[92],[17,23307,23308,23311],{"style":2106},[17,23309],{"className":23310,"style":1470},[100],[17,23312,23314],{"className":23313},[1474,1475,1476,1477],[17,23315,1392],{"className":23316},[79,1477],[17,23318,136],{"className":23319},[135],[17,23321,23323],{"className":23322},[88],[17,23324,23326],{"className":23325,"style":1490},[92],[17,23327],{},[17,23329,850],{"className":23330},[282],[17,23332],{"className":23333,"style":257},[234],[17,23335,4149],{"className":23336},[997],[17,23338],{"className":23339,"style":257},[234],[17,23341,23343,23346,23349,23352,23392,23395,23398,23401],{"className":23342},[70],[17,23344],{"className":23345,"style":249},[74],[17,23347,22906],{"className":23348,"style":14790},[79,230],[17,23350,841],{"className":23351},[253],[17,23353,23355,23358],{"className":23354},[79],[17,23356,757],{"className":23357},[79,230],[17,23359,23361],{"className":23360},[1453],[17,23362,23364,23384],{"className":23363},[83,84],[17,23365,23367,23381],{"className":23366},[88],[17,23368,23370],{"className":23369,"style":1463},[92],[17,23371,23372,23375],{"style":2106},[17,23373],{"className":23374,"style":1470},[100],[17,23376,23378],{"className":23377},[1474,1475,1476,1477],[17,23379,1401],{"className":23380},[79,1477],[17,23382,136],{"className":23383},[135],[17,23385,23387],{"className":23386},[88],[17,23388,23390],{"className":23389,"style":1490},[92],[17,23391],{},[17,23393,850],{"className":23394},[282],[17,23396],{"className":23397,"style":257},[234],[17,23399,4149],{"className":23400},[997],[17,23402],{"className":23403,"style":257},[234],[17,23405,23407,23410,23413,23416,23419],{"className":23406},[70],[17,23408],{"className":23409,"style":987},[74],[17,23411,8934],{"className":23412},[9183],[17,23414],{"className":23415,"style":257},[234],[17,23417,4149],{"className":23418},[997],[17,23420],{"className":23421,"style":257},[234],[17,23423,23425,23428,23431,23434,23474],{"className":23424},[70],[17,23426],{"className":23427,"style":249},[74],[17,23429,22906],{"className":23430,"style":14790},[79,230],[17,23432,841],{"className":23433},[253],[17,23435,23437,23440],{"className":23436},[79],[17,23438,757],{"className":23439},[79,230],[17,23441,23443],{"className":23442},[1453],[17,23444,23446,23466],{"className":23445},[83,84],[17,23447,23449,23463],{"className":23448},[88],[17,23450,23452],{"className":23451,"style":9205},[92],[17,23453,23454,23457],{"style":2106},[17,23455],{"className":23456,"style":1470},[100],[17,23458,23460],{"className":23459},[1474,1475,1476,1477],[17,23461,4699],{"className":23462,"style":4715},[79,230,1477],[17,23464,136],{"className":23465},[135],[17,23467,23469],{"className":23468},[88],[17,23470,23472],{"className":23471,"style":1490},[92],[17,23473],{},[17,23475,850],{"className":23476},[282],[506,23478],{},[10,23480,23482],{"id":23481},"三dijkstra-算法","三、Dijkstra 算法",[13,23484,23485],{},"Dijkstra 算法用于求：",[17,23487,23489],{"className":23488},[20],[17,23490,23492,23515],{"className":23491},[24],[17,23493,23495],{"className":23494},[28],[30,23496,23497],{"xmlns":32,"display":33},[35,23498,23499,23512],{},[38,23500,23501],{},[41,23502,23503],{"notation":43},[45,23504,23505],{"scriptlevel":47,"displaystyle":48},[45,23506,23507],{"scriptlevel":47,"displaystyle":48},[45,23508,23509],{"scriptlevel":47,"displaystyle":53},[55,23510,23511],{},"从一个源点到其他顶点的最短路径",[59,23513,23514],{"encoding":61},"\\boxed{\\text{从一个源点到其他顶点的最短路径}}",[17,23516,23518],{"className":23517,"ariaHidden":53},[66],[17,23519,23521,23524],{"className":23520},[70],[17,23522],{"className":23523,"style":75},[74],[17,23525,23527],{"className":23526},[79],[17,23528,23530,23567],{"className":23529},[83,84],[17,23531,23533,23564],{"className":23532},[88],[17,23534,23536,23556],{"className":23535,"style":93},[92],[17,23537,23538,23541],{"style":96},[17,23539],{"className":23540,"style":101},[100],[17,23542,23544],{"className":23543},[105],[17,23545,23547],{"className":23546},[79],[17,23548,23550],{"className":23549},[79],[17,23551,23553],{"className":23552},[79,115],[17,23554,23511],{"className":23555},[79,119],[17,23557,23558,23561],{"style":122},[17,23559],{"className":23560,"style":101},[100],[17,23562],{"className":23563,"style":131},[129,130],[17,23565,136],{"className":23566},[135],[17,23568,23570],{"className":23569},[88],[17,23571,23573],{"className":23572,"style":143},[92],[17,23574],{},[13,23576,23577],{},"通常要求边权非负。",[506,23579],{},[513,23581,23583],{"id":23582},"_1-算法思想","1. 算法思想",[13,23585,23586],{},"把顶点分成两类：",[287,23588,23589,23598],{},[290,23590,23591],{},[293,23592,23593,23596],{},[296,23594,23595],{},"集合",[296,23597,301],{},[303,23599,23600,23635],{},[293,23601,23602,23632],{},[308,23603,23604],{},[17,23605,23607,23620],{"className":23606},[24],[17,23608,23610],{"className":23609},[28],[30,23611,23612],{"xmlns":32},[35,23613,23614,23618],{},[38,23615,23616],{},[187,23617,19908],{},[59,23619,19908],{"encoding":61},[17,23621,23623],{"className":23622,"ariaHidden":53},[66],[17,23624,23626,23629],{"className":23625},[70],[17,23627],{"className":23628,"style":226},[74],[17,23630,19908],{"className":23631,"style":14790},[79,230],[308,23633,23634],{},"已确定最短路径的顶点",[293,23636,23637,23667],{},[308,23638,23639],{},[17,23640,23642,23655],{"className":23641},[24],[17,23643,23645],{"className":23644},[28],[30,23646,23647],{"xmlns":32},[35,23648,23649,23653],{},[38,23650,23651],{},[187,23652,17926],{},[59,23654,17926],{"encoding":61},[17,23656,23658],{"className":23657,"ariaHidden":53},[66],[17,23659,23661,23664],{"className":23660},[70],[17,23662],{"className":23663,"style":226},[74],[17,23665,17926],{"className":23666,"style":14790},[79,230],[308,23668,23669],{},"暂时未确定的顶点",[13,23671,23672],{},"初始时：",[17,23674,23676],{"className":23675},[20],[17,23677,23679,23701],{"className":23678},[24],[17,23680,23682],{"className":23681},[28],[30,23683,23684],{"xmlns":32,"display":33},[35,23685,23686,23698],{},[38,23687,23688,23690,23692],{},[187,23689,19908],{},[191,23691,193],{},[1385,23693,23694,23696],{},[187,23695,793],{},[1390,23697,47],{},[59,23699,23700],{"encoding":61},"P={v_0}",[17,23702,23704,23722],{"className":23703,"ariaHidden":53},[66],[17,23705,23707,23710,23713,23716,23719],{"className":23706},[70],[17,23708],{"className":23709,"style":226},[74],[17,23711,19908],{"className":23712,"style":14790},[79,230],[17,23714],{"className":23715,"style":235},[234],[17,23717,193],{"className":23718},[239],[17,23720],{"className":23721,"style":235},[234],[17,23723,23725,23728],{"className":23724},[70],[17,23726],{"className":23727,"style":2085},[74],[17,23729,23731],{"className":23730},[79],[17,23732,23734,23737],{"className":23733},[79],[17,23735,793],{"className":23736,"style":818},[79,230],[17,23738,23740],{"className":23739},[1453],[17,23741,23743,23763],{"className":23742},[83,84],[17,23744,23746,23760],{"className":23745},[88],[17,23747,23749],{"className":23748,"style":1463},[92],[17,23750,23751,23754],{"style":1466},[17,23752],{"className":23753,"style":1470},[100],[17,23755,23757],{"className":23756},[1474,1475,1476,1477],[17,23758,47],{"className":23759},[79,1477],[17,23761,136],{"className":23762},[135],[17,23764,23766],{"className":23765},[88],[17,23767,23769],{"className":23768,"style":1490},[92],[17,23770],{},[13,23772,23773,23774,23802,23803,23831],{},"然后不断从 ",[17,23775,23777,23790],{"className":23776},[24],[17,23778,23780],{"className":23779},[28],[30,23781,23782],{"xmlns":32},[35,23783,23784,23788],{},[38,23785,23786],{},[187,23787,17926],{},[59,23789,17926],{"encoding":61},[17,23791,23793],{"className":23792,"ariaHidden":53},[66],[17,23794,23796,23799],{"className":23795},[70],[17,23797],{"className":23798,"style":226},[74],[17,23800,17926],{"className":23801,"style":14790},[79,230]," 中选出当前距离最小的顶点，加入 ",[17,23804,23806,23819],{"className":23805},[24],[17,23807,23809],{"className":23808},[28],[30,23810,23811],{"xmlns":32},[35,23812,23813,23817],{},[38,23814,23815],{},[187,23816,19908],{},[59,23818,19908],{"encoding":61},[17,23820,23822],{"className":23821,"ariaHidden":53},[66],[17,23823,23825,23828],{"className":23824},[70],[17,23826],{"className":23827,"style":226},[74],[17,23829,19908],{"className":23830,"style":14790},[79,230],"，并更新它的邻接点距离。",[506,23833],{},[513,23835,23837],{"id":23836},"_2-算法步骤","2. 算法步骤",[13,23839,23840,23841,720],{},"设源点为 ",[17,23842,23844,23861],{"className":23843},[24],[17,23845,23847],{"className":23846},[28],[30,23848,23849],{"xmlns":32},[35,23850,23851,23859],{},[38,23852,23853],{},[1385,23854,23855,23857],{},[187,23856,793],{},[1390,23858,47],{},[59,23860,9293],{"encoding":61},[17,23862,23864],{"className":23863,"ariaHidden":53},[66],[17,23865,23867,23870],{"className":23866},[70],[17,23868],{"className":23869,"style":2085},[74],[17,23871,23873,23876],{"className":23872},[79],[17,23874,793],{"className":23875,"style":818},[79,230],[17,23877,23879],{"className":23878},[1453],[17,23880,23882,23902],{"className":23881},[83,84],[17,23883,23885,23899],{"className":23884},[88],[17,23886,23888],{"className":23887,"style":1463},[92],[17,23889,23890,23893],{"style":1466},[17,23891],{"className":23892,"style":1470},[100],[17,23894,23896],{"className":23895},[1474,1475,1476,1477],[17,23897,47],{"className":23898},[79,1477],[17,23900,136],{"className":23901},[135],[17,23903,23905],{"className":23904},[88],[17,23906,23908],{"className":23907,"style":1490},[92],[17,23909],{},[4092,23911,23913],{"id":23912},"第一步初始化","第一步：初始化",[17,23915,23917],{"className":23916},[20],[17,23918,23920,23948],{"className":23919},[24],[17,23921,23923],{"className":23922},[28],[30,23924,23925],{"xmlns":32,"display":33},[35,23926,23927,23945],{},[38,23928,23929,23931,23933,23939,23941,23943],{},[187,23930,3912],{},[191,23932,841],{"stretchy":48},[1385,23934,23935,23937],{},[187,23936,793],{},[1390,23938,47],{},[191,23940,850],{"stretchy":48},[191,23942,193],{},[1390,23944,47],{},[59,23946,23947],{"encoding":61},"d(v_0)=0",[17,23949,23951,24015],{"className":23950,"ariaHidden":53},[66],[17,23952,23954,23957,23960,23963,24003,24006,24009,24012],{"className":23953},[70],[17,23955],{"className":23956,"style":249},[74],[17,23958,3912],{"className":23959},[79,230],[17,23961,841],{"className":23962},[253],[17,23964,23966,23969],{"className":23965},[79],[17,23967,793],{"className":23968,"style":818},[79,230],[17,23970,23972],{"className":23971},[1453],[17,23973,23975,23995],{"className":23974},[83,84],[17,23976,23978,23992],{"className":23977},[88],[17,23979,23981],{"className":23980,"style":1463},[92],[17,23982,23983,23986],{"style":1466},[17,23984],{"className":23985,"style":1470},[100],[17,23987,23989],{"className":23988},[1474,1475,1476,1477],[17,23990,47],{"className":23991},[79,1477],[17,23993,136],{"className":23994},[135],[17,23996,23998],{"className":23997},[88],[17,23999,24001],{"className":24000,"style":1490},[92],[17,24002],{},[17,24004,850],{"className":24005},[282],[17,24007],{"className":24008,"style":235},[234],[17,24010,193],{"className":24011},[239],[17,24013],{"className":24014,"style":235},[234],[17,24016,24018,24021],{"className":24017},[70],[17,24019],{"className":24020,"style":5244},[74],[17,24022,47],{"className":24023},[79],[13,24025,24026],{},"对于其他顶点：",[17,24028,24030],{"className":24029},[20],[17,24031,24033,24146],{"className":24032},[24],[17,24034,24036],{"className":24035},[28],[30,24037,24038],{"xmlns":32,"display":33},[35,24039,24040,24143],{},[38,24041,24042,24044,24046,24052,24054,24056],{},[187,24043,3912],{},[191,24045,841],{"stretchy":48},[1385,24047,24048,24050],{},[187,24049,793],{},[187,24051,11429],{},[191,24053,850],{"stretchy":48},[191,24055,193],{},[38,24057,24058,24060],{},[191,24059,14938],{"fence":53},[14940,24061,24062],{"rowspacing":14942,"columnalign":14943,"columnspacing":2053},[14945,24063,24064,24092,24120],{},[14948,24065,24066],{},[45,24067,24068],{"scriptlevel":47,"displaystyle":48},[38,24069,24070,24072,24074,24080,24082,24088,24090],{},[187,24071,22906],{},[191,24073,841],{"stretchy":48},[1385,24075,24076,24078],{},[187,24077,793],{},[1390,24079,47],{},[191,24081,202],{"separator":53},[1385,24083,24084,24086],{},[187,24085,793],{},[187,24087,11429],{},[191,24089,850],{"stretchy":48},[191,24091,202],{"separator":53},[14948,24093,24094],{},[45,24095,24096],{"scriptlevel":47,"displaystyle":48},[38,24097,24098,24104,24107,24113,24116,24118],{},[1385,24099,24100,24102],{},[187,24101,793],{},[1390,24103,47],{},[55,24105,24106],{}," 与 ",[1385,24108,24109,24111],{},[187,24110,793],{},[187,24112,11429],{},[55,24114,24115],{}," 有边 ",[187,24117,12095],{"mathvariant":2754},[191,24119,202],{"separator":53},[14948,24121,24122],{},[45,24123,24124],{"scriptlevel":47,"displaystyle":48},[38,24125,24126,24132,24134,24140],{},[1385,24127,24128,24130],{},[187,24129,793],{},[1390,24131,47],{},[55,24133,24106],{},[1385,24135,24136,24138],{},[187,24137,793],{},[187,24139,11429],{},[55,24141,24142],{}," 无边",[59,24144,24145],{"encoding":61},"d(v_i)=\n\\begin{cases}\nW(v_0,v_i),& v_0\\text{ 与 }v_i\\text{ 有边}\\\n\\infty,& v_0\\text{ 与 }v_i\\text{ 无边}\n\\end{cases}",[17,24147,24149,24213],{"className":24148,"ariaHidden":53},[66],[17,24150,24152,24155,24158,24161,24201,24204,24207,24210],{"className":24151},[70],[17,24153],{"className":24154,"style":249},[74],[17,24156,3912],{"className":24157},[79,230],[17,24159,841],{"className":24160},[253],[17,24162,24164,24167],{"className":24163},[79],[17,24165,793],{"className":24166,"style":818},[79,230],[17,24168,24170],{"className":24169},[1453],[17,24171,24173,24193],{"className":24172},[83,84],[17,24174,24176,24190],{"className":24175},[88],[17,24177,24179],{"className":24178,"style":11470},[92],[17,24180,24181,24184],{"style":1466},[17,24182],{"className":24183,"style":1470},[100],[17,24185,24187],{"className":24186},[1474,1475,1476,1477],[17,24188,11429],{"className":24189},[79,230,1477],[17,24191,136],{"className":24192},[135],[17,24194,24196],{"className":24195},[88],[17,24197,24199],{"className":24198,"style":1490},[92],[17,24200],{},[17,24202,850],{"className":24203},[282],[17,24205],{"className":24206,"style":235},[234],[17,24208,193],{"className":24209},[239],[17,24211],{"className":24212,"style":235},[234],[17,24214,24216,24219],{"className":24215},[70],[17,24217],{"className":24218,"style":15104},[74],[17,24220,24222,24228,24645],{"className":24221},[9183],[17,24223,24225],{"className":24224,"style":15112},[253,15111],[17,24226,14938],{"className":24227},[15116,15117],[17,24229,24231],{"className":24230},[79],[17,24232,24234,24363,24366,24509,24512],{"className":24233},[14940],[17,24235,24237],{"className":24236},[15127],[17,24238,24240,24355],{"className":24239},[83,84],[17,24241,24243,24352],{"className":24242},[88],[17,24244,24246],{"className":24245,"style":15137},[92],[17,24247,24248,24251],{"style":15140},[17,24249],{"className":24250,"style":15144},[100],[17,24252,24254,24257,24260,24300,24303,24306,24346,24349],{"className":24253},[79],[17,24255,22906],{"className":24256,"style":14790},[79,230],[17,24258,841],{"className":24259},[253],[17,24261,24263,24266],{"className":24262},[79],[17,24264,793],{"className":24265,"style":818},[79,230],[17,24267,24269],{"className":24268},[1453],[17,24270,24272,24292],{"className":24271},[83,84],[17,24273,24275,24289],{"className":24274},[88],[17,24276,24278],{"className":24277,"style":1463},[92],[17,24279,24280,24283],{"style":1466},[17,24281],{"className":24282,"style":1470},[100],[17,24284,24286],{"className":24285},[1474,1475,1476,1477],[17,24287,47],{"className":24288},[79,1477],[17,24290,136],{"className":24291},[135],[17,24293,24295],{"className":24294},[88],[17,24296,24298],{"className":24297,"style":1490},[92],[17,24299],{},[17,24301,202],{"className":24302},[261],[17,24304],{"className":24305,"style":265},[234],[17,24307,24309,24312],{"className":24308},[79],[17,24310,793],{"className":24311,"style":818},[79,230],[17,24313,24315],{"className":24314},[1453],[17,24316,24318,24338],{"className":24317},[83,84],[17,24319,24321,24335],{"className":24320},[88],[17,24322,24324],{"className":24323,"style":11470},[92],[17,24325,24326,24329],{"style":1466},[17,24327],{"className":24328,"style":1470},[100],[17,24330,24332],{"className":24331},[1474,1475,1476,1477],[17,24333,11429],{"className":24334},[79,230,1477],[17,24336,136],{"className":24337},[135],[17,24339,24341],{"className":24340},[88],[17,24342,24344],{"className":24343,"style":1490},[92],[17,24345],{},[17,24347,850],{"className":24348},[282],[17,24350,202],{"className":24351},[261],[17,24353,136],{"className":24354},[135],[17,24356,24358],{"className":24357},[88],[17,24359,24361],{"className":24360,"style":15163},[92],[17,24362],{},[17,24364],{"className":24365,"style":15170},[15169],[17,24367,24369],{"className":24368},[15127],[17,24370,24372,24501],{"className":24371},[83,84],[17,24373,24375,24498],{"className":24374},[88],[17,24376,24378],{"className":24377,"style":15137},[92],[17,24379,24380,24383],{"style":15140},[17,24381],{"className":24382,"style":15144},[100],[17,24384,24386,24426,24439,24479,24489,24492,24495],{"className":24385},[79],[17,24387,24389,24392],{"className":24388},[79],[17,24390,793],{"className":24391,"style":818},[79,230],[17,24393,24395],{"className":24394},[1453],[17,24396,24398,24418],{"className":24397},[83,84],[17,24399,24401,24415],{"className":24400},[88],[17,24402,24404],{"className":24403,"style":1463},[92],[17,24405,24406,24409],{"style":1466},[17,24407],{"className":24408,"style":1470},[100],[17,24410,24412],{"className":24411},[1474,1475,1476,1477],[17,24413,47],{"className":24414},[79,1477],[17,24416,136],{"className":24417},[135],[17,24419,24421],{"className":24420},[88],[17,24422,24424],{"className":24423,"style":1490},[92],[17,24425],{},[17,24427,24429,24432,24436],{"className":24428},[79,115],[17,24430,4056],{"className":24431},[79],[17,24433,24435],{"className":24434},[79,119],"与",[17,24437,4056],{"className":24438},[79],[17,24440,24442,24445],{"className":24441},[79],[17,24443,793],{"className":24444,"style":818},[79,230],[17,24446,24448],{"className":24447},[1453],[17,24449,24451,24471],{"className":24450},[83,84],[17,24452,24454,24468],{"className":24453},[88],[17,24455,24457],{"className":24456,"style":11470},[92],[17,24458,24459,24462],{"style":1466},[17,24460],{"className":24461,"style":1470},[100],[17,24463,24465],{"className":24464},[1474,1475,1476,1477],[17,24466,11429],{"className":24467},[79,230,1477],[17,24469,136],{"className":24470},[135],[17,24472,24474],{"className":24473},[88],[17,24475,24477],{"className":24476,"style":1490},[92],[17,24478],{},[17,24480,24482,24485],{"className":24481},[79,115],[17,24483,4056],{"className":24484},[79],[17,24486,24488],{"className":24487},[79,119],"有边",[17,24490,4056],{"className":24491},[234],[17,24493,12095],{"className":24494},[79],[17,24496,202],{"className":24497},[261],[17,24499,136],{"className":24500},[135],[17,24502,24504],{"className":24503},[88],[17,24505,24507],{"className":24506,"style":15163},[92],[17,24508],{},[17,24510],{"className":24511,"style":15307},[15169],[17,24513,24515],{"className":24514},[15311],[17,24516,24518,24637],{"className":24517},[83,84],[17,24519,24521,24634],{"className":24520},[88],[17,24522,24524],{"className":24523,"style":15137},[92],[17,24525,24526,24529],{"style":15140},[17,24527],{"className":24528,"style":15144},[100],[17,24530,24532,24572,24584,24624],{"className":24531},[79],[17,24533,24535,24538],{"className":24534},[79],[17,24536,793],{"className":24537,"style":818},[79,230],[17,24539,24541],{"className":24540},[1453],[17,24542,24544,24564],{"className":24543},[83,84],[17,24545,24547,24561],{"className":24546},[88],[17,24548,24550],{"className":24549,"style":1463},[92],[17,24551,24552,24555],{"style":1466},[17,24553],{"className":24554,"style":1470},[100],[17,24556,24558],{"className":24557},[1474,1475,1476,1477],[17,24559,47],{"className":24560},[79,1477],[17,24562,136],{"className":24563},[135],[17,24565,24567],{"className":24566},[88],[17,24568,24570],{"className":24569,"style":1490},[92],[17,24571],{},[17,24573,24575,24578,24581],{"className":24574},[79,115],[17,24576,4056],{"className":24577},[79],[17,24579,24435],{"className":24580},[79,119],[17,24582,4056],{"className":24583},[79],[17,24585,24587,24590],{"className":24586},[79],[17,24588,793],{"className":24589,"style":818},[79,230],[17,24591,24593],{"className":24592},[1453],[17,24594,24596,24616],{"className":24595},[83,84],[17,24597,24599,24613],{"className":24598},[88],[17,24600,24602],{"className":24601,"style":11470},[92],[17,24603,24604,24607],{"style":1466},[17,24605],{"className":24606,"style":1470},[100],[17,24608,24610],{"className":24609},[1474,1475,1476,1477],[17,24611,11429],{"className":24612},[79,230,1477],[17,24614,136],{"className":24615},[135],[17,24617,24619],{"className":24618},[88],[17,24620,24622],{"className":24621,"style":1490},[92],[17,24623],{},[17,24625,24627,24630],{"className":24626},[79,115],[17,24628,4056],{"className":24629},[79],[17,24631,24633],{"className":24632},[79,119],"无边",[17,24635,136],{"className":24636},[135],[17,24638,24640],{"className":24639},[88],[17,24641,24643],{"className":24642,"style":15163},[92],[17,24644],{},[17,24646],{"className":24647},[282,3370],[506,24649],{},[4092,24651,24653],{"id":24652},"第二步选最小","第二步：选最小",[13,24655,24656,24657,24685,24686,24755,24756,720],{},"从未确定顶点中选 ",[17,24658,24660,24673],{"className":24659},[24],[17,24661,24663],{"className":24662},[28],[30,24664,24665],{"xmlns":32},[35,24666,24667,24671],{},[38,24668,24669],{},[187,24670,3912],{},[59,24672,3912],{"encoding":61},[17,24674,24676],{"className":24675,"ariaHidden":53},[66],[17,24677,24679,24682],{"className":24678},[70],[17,24680],{"className":24681,"style":4711},[74],[17,24683,3912],{"className":24684},[79,230]," 值最小的顶点 ",[17,24687,24689,24706],{"className":24688},[24],[17,24690,24692],{"className":24691},[28],[30,24693,24694],{"xmlns":32},[35,24695,24696,24704],{},[38,24697,24698],{},[1385,24699,24700,24702],{},[187,24701,793],{},[187,24703,4699],{},[59,24705,9560],{"encoding":61},[17,24707,24709],{"className":24708,"ariaHidden":53},[66],[17,24710,24712,24715],{"className":24711},[70],[17,24713],{"className":24714,"style":2085},[74],[17,24716,24718,24721],{"className":24717},[79],[17,24719,793],{"className":24720,"style":818},[79,230],[17,24722,24724],{"className":24723},[1453],[17,24725,24727,24747],{"className":24726},[83,84],[17,24728,24730,24744],{"className":24729},[88],[17,24731,24733],{"className":24732,"style":9205},[92],[17,24734,24735,24738],{"style":1466},[17,24736],{"className":24737,"style":1470},[100],[17,24739,24741],{"className":24740},[1474,1475,1476,1477],[17,24742,4699],{"className":24743,"style":4715},[79,230,1477],[17,24745,136],{"className":24746},[135],[17,24748,24750],{"className":24749},[88],[17,24751,24753],{"className":24752,"style":1490},[92],[17,24754],{},"，加入 ",[17,24757,24759,24772],{"className":24758},[24],[17,24760,24762],{"className":24761},[28],[30,24763,24764],{"xmlns":32},[35,24765,24766,24770],{},[38,24767,24768],{},[187,24769,19908],{},[59,24771,19908],{"encoding":61},[17,24773,24775],{"className":24774,"ariaHidden":53},[66],[17,24776,24778,24781],{"className":24777},[70],[17,24779],{"className":24780,"style":226},[74],[17,24782,19908],{"className":24783,"style":14790},[79,230],[506,24785],{},[4092,24787,24789],{"id":24788},"第三步更新","第三步：更新",[13,24791,24792,24793,24862,24863,24932],{},"对 ",[17,24794,24796,24813],{"className":24795},[24],[17,24797,24799],{"className":24798},[28],[30,24800,24801],{"xmlns":32},[35,24802,24803,24811],{},[38,24804,24805],{},[1385,24806,24807,24809],{},[187,24808,793],{},[187,24810,4699],{},[59,24812,9560],{"encoding":61},[17,24814,24816],{"className":24815,"ariaHidden":53},[66],[17,24817,24819,24822],{"className":24818},[70],[17,24820],{"className":24821,"style":2085},[74],[17,24823,24825,24828],{"className":24824},[79],[17,24826,793],{"className":24827,"style":818},[79,230],[17,24829,24831],{"className":24830},[1453],[17,24832,24834,24854],{"className":24833},[83,84],[17,24835,24837,24851],{"className":24836},[88],[17,24838,24840],{"className":24839,"style":9205},[92],[17,24841,24842,24845],{"style":1466},[17,24843],{"className":24844,"style":1470},[100],[17,24846,24848],{"className":24847},[1474,1475,1476,1477],[17,24849,4699],{"className":24850,"style":4715},[79,230,1477],[17,24852,136],{"className":24853},[135],[17,24855,24857],{"className":24856},[88],[17,24858,24860],{"className":24859,"style":1490},[92],[17,24861],{}," 的邻接顶点 ",[17,24864,24866,24883],{"className":24865},[24],[17,24867,24869],{"className":24868},[28],[30,24870,24871],{"xmlns":32},[35,24872,24873,24881],{},[38,24874,24875],{},[1385,24876,24877,24879],{},[187,24878,793],{},[187,24880,11429],{},[59,24882,12005],{"encoding":61},[17,24884,24886],{"className":24885,"ariaHidden":53},[66],[17,24887,24889,24892],{"className":24888},[70],[17,24890],{"className":24891,"style":2085},[74],[17,24893,24895,24898],{"className":24894},[79],[17,24896,793],{"className":24897,"style":818},[79,230],[17,24899,24901],{"className":24900},[1453],[17,24902,24904,24924],{"className":24903},[83,84],[17,24905,24907,24921],{"className":24906},[88],[17,24908,24910],{"className":24909,"style":11470},[92],[17,24911,24912,24915],{"style":1466},[17,24913],{"className":24914,"style":1470},[100],[17,24916,24918],{"className":24917},[1474,1475,1476,1477],[17,24919,11429],{"className":24920},[79,230,1477],[17,24922,136],{"className":24923},[135],[17,24925,24927],{"className":24926},[88],[17,24928,24930],{"className":24929,"style":1490},[92],[17,24931],{},"，若：",[17,24934,24936],{"className":24935},[20],[17,24937,24939,25000],{"className":24938},[24],[17,24940,24942],{"className":24941},[28],[30,24943,24944],{"xmlns":32,"display":33},[35,24945,24946,24997],{},[38,24947,24948,24950,24952,24958,24960,24962,24964,24966,24972,24974,24980,24982,24985,24987,24989,24995],{},[187,24949,3912],{},[191,24951,841],{"stretchy":48},[1385,24953,24954,24956],{},[187,24955,793],{},[187,24957,4699],{},[191,24959,850],{"stretchy":48},[191,24961,4149],{},[187,24963,22906],{},[191,24965,841],{"stretchy":48},[1385,24967,24968,24970],{},[187,24969,793],{},[187,24971,4699],{},[191,24973,202],{"separator":53},[1385,24975,24976,24978],{},[187,24977,793],{},[187,24979,11429],{},[191,24981,850],{"stretchy":48},[191,24983,24984],{},"\u003C",[187,24986,3912],{},[191,24988,841],{"stretchy":48},[1385,24990,24991,24993],{},[187,24992,793],{},[187,24994,11429],{},[191,24996,850],{"stretchy":48},[59,24998,24999],{"encoding":61},"d(v_k)+W(v_k,v_i)\u003Cd(v_i)",[17,25001,25003,25067,25177],{"className":25002,"ariaHidden":53},[66],[17,25004,25006,25009,25012,25015,25055,25058,25061,25064],{"className":25005},[70],[17,25007],{"className":25008,"style":249},[74],[17,25010,3912],{"className":25011},[79,230],[17,25013,841],{"className":25014},[253],[17,25016,25018,25021],{"className":25017},[79],[17,25019,793],{"className":25020,"style":818},[79,230],[17,25022,25024],{"className":25023},[1453],[17,25025,25027,25047],{"className":25026},[83,84],[17,25028,25030,25044],{"className":25029},[88],[17,25031,25033],{"className":25032,"style":9205},[92],[17,25034,25035,25038],{"style":1466},[17,25036],{"className":25037,"style":1470},[100],[17,25039,25041],{"className":25040},[1474,1475,1476,1477],[17,25042,4699],{"className":25043,"style":4715},[79,230,1477],[17,25045,136],{"className":25046},[135],[17,25048,25050],{"className":25049},[88],[17,25051,25053],{"className":25052,"style":1490},[92],[17,25054],{},[17,25056,850],{"className":25057},[282],[17,25059],{"className":25060,"style":257},[234],[17,25062,4149],{"className":25063},[997],[17,25065],{"className":25066,"style":257},[234],[17,25068,25070,25073,25076,25079,25119,25122,25125,25165,25168,25171,25174],{"className":25069},[70],[17,25071],{"className":25072,"style":249},[74],[17,25074,22906],{"className":25075,"style":14790},[79,230],[17,25077,841],{"className":25078},[253],[17,25080,25082,25085],{"className":25081},[79],[17,25083,793],{"className":25084,"style":818},[79,230],[17,25086,25088],{"className":25087},[1453],[17,25089,25091,25111],{"className":25090},[83,84],[17,25092,25094,25108],{"className":25093},[88],[17,25095,25097],{"className":25096,"style":9205},[92],[17,25098,25099,25102],{"style":1466},[17,25100],{"className":25101,"style":1470},[100],[17,25103,25105],{"className":25104},[1474,1475,1476,1477],[17,25106,4699],{"className":25107,"style":4715},[79,230,1477],[17,25109,136],{"className":25110},[135],[17,25112,25114],{"className":25113},[88],[17,25115,25117],{"className":25116,"style":1490},[92],[17,25118],{},[17,25120,202],{"className":25121},[261],[17,25123],{"className":25124,"style":265},[234],[17,25126,25128,25131],{"className":25127},[79],[17,25129,793],{"className":25130,"style":818},[79,230],[17,25132,25134],{"className":25133},[1453],[17,25135,25137,25157],{"className":25136},[83,84],[17,25138,25140,25154],{"className":25139},[88],[17,25141,25143],{"className":25142,"style":11470},[92],[17,25144,25145,25148],{"style":1466},[17,25146],{"className":25147,"style":1470},[100],[17,25149,25151],{"className":25150},[1474,1475,1476,1477],[17,25152,11429],{"className":25153},[79,230,1477],[17,25155,136],{"className":25156},[135],[17,25158,25160],{"className":25159},[88],[17,25161,25163],{"className":25162,"style":1490},[92],[17,25164],{},[17,25166,850],{"className":25167},[282],[17,25169],{"className":25170,"style":235},[234],[17,25172,24984],{"className":25173},[239],[17,25175],{"className":25176,"style":235},[234],[17,25178,25180,25183,25186,25189,25229],{"className":25179},[70],[17,25181],{"className":25182,"style":249},[74],[17,25184,3912],{"className":25185},[79,230],[17,25187,841],{"className":25188},[253],[17,25190,25192,25195],{"className":25191},[79],[17,25193,793],{"className":25194,"style":818},[79,230],[17,25196,25198],{"className":25197},[1453],[17,25199,25201,25221],{"className":25200},[83,84],[17,25202,25204,25218],{"className":25203},[88],[17,25205,25207],{"className":25206,"style":11470},[92],[17,25208,25209,25212],{"style":1466},[17,25210],{"className":25211,"style":1470},[100],[17,25213,25215],{"className":25214},[1474,1475,1476,1477],[17,25216,11429],{"className":25217},[79,230,1477],[17,25219,136],{"className":25220},[135],[17,25222,25224],{"className":25223},[88],[17,25225,25227],{"className":25226,"style":1490},[92],[17,25228],{},[17,25230,850],{"className":25231},[282],[13,25233,25234],{},"则更新：",[17,25236,25238],{"className":25237},[20],[17,25239,25241,25301],{"className":25240},[24],[17,25242,25244],{"className":25243},[28],[30,25245,25246],{"xmlns":32,"display":33},[35,25247,25248,25298],{},[38,25249,25250,25252,25254,25260,25262,25264,25266,25268,25274,25276,25278,25280,25282,25288,25290,25296],{},[187,25251,3912],{},[191,25253,841],{"stretchy":48},[1385,25255,25256,25258],{},[187,25257,793],{},[187,25259,11429],{},[191,25261,850],{"stretchy":48},[191,25263,193],{},[187,25265,3912],{},[191,25267,841],{"stretchy":48},[1385,25269,25270,25272],{},[187,25271,793],{},[187,25273,4699],{},[191,25275,850],{"stretchy":48},[191,25277,4149],{},[187,25279,22906],{},[191,25281,841],{"stretchy":48},[1385,25283,25284,25286],{},[187,25285,793],{},[187,25287,4699],{},[191,25289,202],{"separator":53},[1385,25291,25292,25294],{},[187,25293,793],{},[187,25295,11429],{},[191,25297,850],{"stretchy":48},[59,25299,25300],{"encoding":61},"d(v_i)=d(v_k)+W(v_k,v_i)",[17,25302,25304,25368,25432],{"className":25303,"ariaHidden":53},[66],[17,25305,25307,25310,25313,25316,25356,25359,25362,25365],{"className":25306},[70],[17,25308],{"className":25309,"style":249},[74],[17,25311,3912],{"className":25312},[79,230],[17,25314,841],{"className":25315},[253],[17,25317,25319,25322],{"className":25318},[79],[17,25320,793],{"className":25321,"style":818},[79,230],[17,25323,25325],{"className":25324},[1453],[17,25326,25328,25348],{"className":25327},[83,84],[17,25329,25331,25345],{"className":25330},[88],[17,25332,25334],{"className":25333,"style":11470},[92],[17,25335,25336,25339],{"style":1466},[17,25337],{"className":25338,"style":1470},[100],[17,25340,25342],{"className":25341},[1474,1475,1476,1477],[17,25343,11429],{"className":25344},[79,230,1477],[17,25346,136],{"className":25347},[135],[17,25349,25351],{"className":25350},[88],[17,25352,25354],{"className":25353,"style":1490},[92],[17,25355],{},[17,25357,850],{"className":25358},[282],[17,25360],{"className":25361,"style":235},[234],[17,25363,193],{"className":25364},[239],[17,25366],{"className":25367,"style":235},[234],[17,25369,25371,25374,25377,25380,25420,25423,25426,25429],{"className":25370},[70],[17,25372],{"className":25373,"style":249},[74],[17,25375,3912],{"className":25376},[79,230],[17,25378,841],{"className":25379},[253],[17,25381,25383,25386],{"className":25382},[79],[17,25384,793],{"className":25385,"style":818},[79,230],[17,25387,25389],{"className":25388},[1453],[17,25390,25392,25412],{"className":25391},[83,84],[17,25393,25395,25409],{"className":25394},[88],[17,25396,25398],{"className":25397,"style":9205},[92],[17,25399,25400,25403],{"style":1466},[17,25401],{"className":25402,"style":1470},[100],[17,25404,25406],{"className":25405},[1474,1475,1476,1477],[17,25407,4699],{"className":25408,"style":4715},[79,230,1477],[17,25410,136],{"className":25411},[135],[17,25413,25415],{"className":25414},[88],[17,25416,25418],{"className":25417,"style":1490},[92],[17,25419],{},[17,25421,850],{"className":25422},[282],[17,25424],{"className":25425,"style":257},[234],[17,25427,4149],{"className":25428},[997],[17,25430],{"className":25431,"style":257},[234],[17,25433,25435,25438,25441,25444,25484,25487,25490,25530],{"className":25434},[70],[17,25436],{"className":25437,"style":249},[74],[17,25439,22906],{"className":25440,"style":14790},[79,230],[17,25442,841],{"className":25443},[253],[17,25445,25447,25450],{"className":25446},[79],[17,25448,793],{"className":25449,"style":818},[79,230],[17,25451,25453],{"className":25452},[1453],[17,25454,25456,25476],{"className":25455},[83,84],[17,25457,25459,25473],{"className":25458},[88],[17,25460,25462],{"className":25461,"style":9205},[92],[17,25463,25464,25467],{"style":1466},[17,25465],{"className":25466,"style":1470},[100],[17,25468,25470],{"className":25469},[1474,1475,1476,1477],[17,25471,4699],{"className":25472,"style":4715},[79,230,1477],[17,25474,136],{"className":25475},[135],[17,25477,25479],{"className":25478},[88],[17,25480,25482],{"className":25481,"style":1490},[92],[17,25483],{},[17,25485,202],{"className":25486},[261],[17,25488],{"className":25489,"style":265},[234],[17,25491,25493,25496],{"className":25492},[79],[17,25494,793],{"className":25495,"style":818},[79,230],[17,25497,25499],{"className":25498},[1453],[17,25500,25502,25522],{"className":25501},[83,84],[17,25503,25505,25519],{"className":25504},[88],[17,25506,25508],{"className":25507,"style":11470},[92],[17,25509,25510,25513],{"style":1466},[17,25511],{"className":25512,"style":1470},[100],[17,25514,25516],{"className":25515},[1474,1475,1476,1477],[17,25517,11429],{"className":25518},[79,230,1477],[17,25520,136],{"className":25521},[135],[17,25523,25525],{"className":25524},[88],[17,25526,25528],{"className":25527,"style":1490},[92],[17,25529],{},[17,25531,850],{"className":25532},[282],[506,25534],{},[4092,25536,25538],{"id":25537},"第四步重复","第四步：重复",[13,25540,25541,25542,25570,25571,720],{},"一直重复，直到目标点被加入 ",[17,25543,25545,25558],{"className":25544},[24],[17,25546,25548],{"className":25547},[28],[30,25549,25550],{"xmlns":32},[35,25551,25552,25556],{},[38,25553,25554],{},[187,25555,19908],{},[59,25557,19908],{"encoding":61},[17,25559,25561],{"className":25560,"ariaHidden":53},[66],[17,25562,25564,25567],{"className":25563},[70],[17,25565],{"className":25566,"style":226},[74],[17,25568,19908],{"className":25569,"style":14790},[79,230],"，或者所有顶点都加入 ",[17,25572,25574,25587],{"className":25573},[24],[17,25575,25577],{"className":25576},[28],[30,25578,25579],{"xmlns":32},[35,25580,25581,25585],{},[38,25582,25583],{},[187,25584,19908],{},[59,25586,19908],{"encoding":61},[17,25588,25590],{"className":25589,"ariaHidden":53},[66],[17,25591,25593,25596],{"className":25592},[70],[17,25594],{"className":25595,"style":226},[74],[17,25597,19908],{"className":25598,"style":14790},[79,230],[506,25600],{},[513,25602,25604],{"id":25603},"_3-适用场景","3. 适用场景",[13,25606,25607],{},"Dijkstra 适合：",[150,25609,25610,25613,25616,25619,25622],{},[153,25611,25612],{},"单源最短路径；",[153,25614,25615],{},"非负权图；",[153,25617,25618],{},"地图导航；",[153,25620,25621],{},"网络路由；",[153,25623,25624],{},"成本最小问题。",[506,25626],{},[10,25628,25630],{"id":25629},"四floyd-算法","四、Floyd 算法",[13,25632,25633],{},"Floyd 算法用于求：",[17,25635,25637],{"className":25636},[20],[17,25638,25640,25663],{"className":25639},[24],[17,25641,25643],{"className":25642},[28],[30,25644,25645],{"xmlns":32,"display":33},[35,25646,25647,25660],{},[38,25648,25649],{},[41,25650,25651],{"notation":43},[45,25652,25653],{"scriptlevel":47,"displaystyle":48},[45,25654,25655],{"scriptlevel":47,"displaystyle":48},[45,25656,25657],{"scriptlevel":47,"displaystyle":53},[55,25658,25659],{},"任意两点之间的最短路径",[59,25661,25662],{"encoding":61},"\\boxed{\\text{任意两点之间的最短路径}}",[17,25664,25666],{"className":25665,"ariaHidden":53},[66],[17,25667,25669,25672],{"className":25668},[70],[17,25670],{"className":25671,"style":75},[74],[17,25673,25675],{"className":25674},[79],[17,25676,25678,25715],{"className":25677},[83,84],[17,25679,25681,25712],{"className":25680},[88],[17,25682,25684,25704],{"className":25683,"style":93},[92],[17,25685,25686,25689],{"style":96},[17,25687],{"className":25688,"style":101},[100],[17,25690,25692],{"className":25691},[105],[17,25693,25695],{"className":25694},[79],[17,25696,25698],{"className":25697},[79],[17,25699,25701],{"className":25700},[79,115],[17,25702,25659],{"className":25703},[79,119],[17,25705,25706,25709],{"style":122},[17,25707],{"className":25708,"style":101},[100],[17,25710],{"className":25711,"style":131},[129,130],[17,25713,136],{"className":25714},[135],[17,25716,25718],{"className":25717},[88],[17,25719,25721],{"className":25720,"style":143},[92],[17,25722],{},[13,25724,25725],{},"也叫全源最短路径算法。",[506,25727],{},[513,25729,25731],{"id":25730},"_1-初始矩阵","1. 初始矩阵",[13,25733,25734],{},"设初始距离矩阵为：",[17,25736,25738],{"className":25737},[20],[17,25739,25741,25789],{"className":25740},[24],[17,25742,25744],{"className":25743},[28],[30,25745,25746],{"xmlns":32,"display":33},[35,25747,25748,25786],{},[38,25749,25750,25762,25764,25766,25784],{},[4143,25751,25752,25754],{},[187,25753,22110],{},[38,25755,25756,25758,25760],{},[191,25757,841],{"stretchy":48},[1390,25759,47],{},[191,25761,850],{"stretchy":48},[191,25763,193],{},[191,25765,841],{"stretchy":48},[3526,25767,25768,25770,25776],{},[187,25769,3912],{},[38,25771,25772,25774],{},[187,25773,11429],{},[187,25775,11438],{},[38,25777,25778,25780,25782],{},[191,25779,841],{"stretchy":48},[1390,25781,47],{},[191,25783,850],{"stretchy":48},[191,25785,850],{"stretchy":48},[59,25787,25788],{"encoding":61},"D^{(0)}=(d_{ij}^{(0)})",[17,25790,25792,25845],{"className":25791,"ariaHidden":53},[66],[17,25793,25795,25798,25836,25839,25842],{"className":25794},[70],[17,25796],{"className":25797,"style":21121},[74],[17,25799,25801,25804],{"className":25800},[79],[17,25802,22110],{"className":25803,"style":22142},[79,230],[17,25805,25807],{"className":25806},[1453],[17,25808,25810],{"className":25809},[83],[17,25811,25813],{"className":25812},[88],[17,25814,25816],{"className":25815,"style":21121},[92],[17,25817,25818,25821],{"style":3601},[17,25819],{"className":25820,"style":1470},[100],[17,25822,25824],{"className":25823},[1474,1475,1476,1477],[17,25825,25827,25830,25833],{"className":25826},[79,1477],[17,25828,841],{"className":25829},[253,1477],[17,25831,47],{"className":25832},[79,1477],[17,25834,850],{"className":25835},[282,1477],[17,25837],{"className":25838,"style":235},[234],[17,25840,193],{"className":25841},[239],[17,25843],{"className":25844,"style":235},[234],[17,25846,25848,25852,25855,25922],{"className":25847},[70],[17,25849],{"className":25850,"style":25851},[74],"height:1.4578em;vertical-align:-0.413em;",[17,25853,841],{"className":25854},[253],[17,25856,25858,25861],{"className":25857},[79],[17,25859,3912],{"className":25860},[79,230],[17,25862,25864],{"className":25863},[1453],[17,25865,25867,25913],{"className":25866},[83,84],[17,25868,25870,25910],{"className":25869},[88],[17,25871,25874,25889],{"className":25872,"style":25873},[92],"height:1.0448em;",[17,25875,25877,25880],{"style":25876},"top:-2.4231em;margin-left:0em;margin-right:0.05em;",[17,25878],{"className":25879,"style":1470},[100],[17,25881,25883],{"className":25882},[1474,1475,1476,1477],[17,25884,25886],{"className":25885},[79,1477],[17,25887,14842],{"className":25888,"style":11528},[79,230,1477],[17,25890,25892,25895],{"style":25891},"top:-3.2198em;margin-right:0.05em;",[17,25893],{"className":25894,"style":1470},[100],[17,25896,25898],{"className":25897},[1474,1475,1476,1477],[17,25899,25901,25904,25907],{"className":25900},[79,1477],[17,25902,841],{"className":25903},[253,1477],[17,25905,47],{"className":25906},[79,1477],[17,25908,850],{"className":25909},[282,1477],[17,25911,136],{"className":25912},[135],[17,25914,25916],{"className":25915},[88],[17,25917,25920],{"className":25918,"style":25919},[92],"height:0.413em;",[17,25921],{},[17,25923,850],{"className":25924},[282],[13,25926,285],{},[17,25928,25930],{"className":25929},[20],[17,25931,25933,25963],{"className":25932},[24],[17,25934,25936],{"className":25935},[28],[30,25937,25938],{"xmlns":32,"display":33},[35,25939,25940,25960],{},[38,25941,25942],{},[3526,25943,25944,25946,25952],{},[187,25945,3912],{},[38,25947,25948,25950],{},[187,25949,11429],{},[187,25951,11438],{},[38,25953,25954,25956,25958],{},[191,25955,841],{"stretchy":48},[1390,25957,47],{},[191,25959,850],{"stretchy":48},[59,25961,25962],{"encoding":61},"d_{ij}^{(0)}",[17,25964,25966],{"className":25965,"ariaHidden":53},[66],[17,25967,25969,25972],{"className":25968},[70],[17,25970],{"className":25971,"style":25851},[74],[17,25973,25975,25978],{"className":25974},[79],[17,25976,3912],{"className":25977},[79,230],[17,25979,25981],{"className":25980},[1453],[17,25982,25984,26027],{"className":25983},[83,84],[17,25985,25987,26024],{"className":25986},[88],[17,25988,25990,26004],{"className":25989,"style":25873},[92],[17,25991,25992,25995],{"style":25876},[17,25993],{"className":25994,"style":1470},[100],[17,25996,25998],{"className":25997},[1474,1475,1476,1477],[17,25999,26001],{"className":26000},[79,1477],[17,26002,14842],{"className":26003,"style":11528},[79,230,1477],[17,26005,26006,26009],{"style":25891},[17,26007],{"className":26008,"style":1470},[100],[17,26010,26012],{"className":26011},[1474,1475,1476,1477],[17,26013,26015,26018,26021],{"className":26014},[79,1477],[17,26016,841],{"className":26017},[253,1477],[17,26019,47],{"className":26020},[79,1477],[17,26022,850],{"className":26023},[282,1477],[17,26025,136],{"className":26026},[135],[17,26028,26030],{"className":26029},[88],[17,26031,26033],{"className":26032,"style":25919},[92],[17,26034],{},[13,26036,26037,26038,26170],{},"表示边 ",[17,26039,26041,26066],{"className":26040},[24],[17,26042,26044],{"className":26043},[28],[30,26045,26046],{"xmlns":32},[35,26047,26048,26064],{},[38,26049,26050,26056,26058],{},[1385,26051,26052,26054],{},[187,26053,793],{},[187,26055,11429],{},[191,26057,1306],{},[1385,26059,26060,26062],{},[187,26061,793],{},[187,26063,11438],{},[59,26065,20686],{"encoding":61},[17,26067,26069,26124],{"className":26068,"ariaHidden":53},[66],[17,26070,26072,26075,26115,26118,26121],{"className":26071},[70],[17,26073],{"className":26074,"style":2085},[74],[17,26076,26078,26081],{"className":26077},[79],[17,26079,793],{"className":26080,"style":818},[79,230],[17,26082,26084],{"className":26083},[1453],[17,26085,26087,26107],{"className":26086},[83,84],[17,26088,26090,26104],{"className":26089},[88],[17,26091,26093],{"className":26092,"style":11470},[92],[17,26094,26095,26098],{"style":1466},[17,26096],{"className":26097,"style":1470},[100],[17,26099,26101],{"className":26100},[1474,1475,1476,1477],[17,26102,11429],{"className":26103},[79,230,1477],[17,26105,136],{"className":26106},[135],[17,26108,26110],{"className":26109},[88],[17,26111,26113],{"className":26112,"style":1490},[92],[17,26114],{},[17,26116],{"className":26117,"style":235},[234],[17,26119,1306],{"className":26120},[239],[17,26122],{"className":26123,"style":235},[234],[17,26125,26127,26130],{"className":26126},[70],[17,26128],{"className":26129,"style":11451},[74],[17,26131,26133,26136],{"className":26132},[79],[17,26134,793],{"className":26135,"style":818},[79,230],[17,26137,26139],{"className":26138},[1453],[17,26140,26142,26162],{"className":26141},[83,84],[17,26143,26145,26159],{"className":26144},[88],[17,26146,26148],{"className":26147,"style":11470},[92],[17,26149,26150,26153],{"style":1466},[17,26151],{"className":26152,"style":1470},[100],[17,26154,26156],{"className":26155},[1474,1475,1476,1477],[17,26157,11438],{"className":26158,"style":11528},[79,230,1477],[17,26160,136],{"className":26161},[135],[17,26163,26165],{"className":26164},[88],[17,26166,26168],{"className":26167,"style":11538},[92],[17,26169],{}," 的权。",[13,26172,26173],{},"如果没有边：",[17,26175,26177],{"className":26176},[20],[17,26178,26180,26214],{"className":26179},[24],[17,26181,26183],{"className":26182},[28],[30,26184,26185],{"xmlns":32,"display":33},[35,26186,26187,26211],{},[38,26188,26189,26207,26209],{},[3526,26190,26191,26193,26199],{},[187,26192,3912],{},[38,26194,26195,26197],{},[187,26196,11429],{},[187,26198,11438],{},[38,26200,26201,26203,26205],{},[191,26202,841],{"stretchy":48},[1390,26204,47],{},[191,26206,850],{"stretchy":48},[191,26208,193],{},[187,26210,12095],{"mathvariant":2754},[59,26212,26213],{"encoding":61},"d_{ij}^{(0)}=\\infty",[17,26215,26217,26295],{"className":26216,"ariaHidden":53},[66],[17,26218,26220,26223,26286,26289,26292],{"className":26219},[70],[17,26221],{"className":26222,"style":25851},[74],[17,26224,26226,26229],{"className":26225},[79],[17,26227,3912],{"className":26228},[79,230],[17,26230,26232],{"className":26231},[1453],[17,26233,26235,26278],{"className":26234},[83,84],[17,26236,26238,26275],{"className":26237},[88],[17,26239,26241,26255],{"className":26240,"style":25873},[92],[17,26242,26243,26246],{"style":25876},[17,26244],{"className":26245,"style":1470},[100],[17,26247,26249],{"className":26248},[1474,1475,1476,1477],[17,26250,26252],{"className":26251},[79,1477],[17,26253,14842],{"className":26254,"style":11528},[79,230,1477],[17,26256,26257,26260],{"style":25891},[17,26258],{"className":26259,"style":1470},[100],[17,26261,26263],{"className":26262},[1474,1475,1476,1477],[17,26264,26266,26269,26272],{"className":26265},[79,1477],[17,26267,841],{"className":26268},[253,1477],[17,26270,47],{"className":26271},[79,1477],[17,26273,850],{"className":26274},[282,1477],[17,26276,136],{"className":26277},[135],[17,26279,26281],{"className":26280},[88],[17,26282,26284],{"className":26283,"style":25919},[92],[17,26285],{},[17,26287],{"className":26288,"style":235},[234],[17,26290,193],{"className":26291},[239],[17,26293],{"className":26294,"style":235},[234],[17,26296,26298,26301],{"className":26297},[70],[17,26299],{"className":26300,"style":769},[74],[17,26302,12095],{"className":26303},[79],[13,26305,4512],{},[17,26307,26309],{"className":26308},[20],[17,26310,26312,26329],{"className":26311},[24],[17,26313,26315],{"className":26314},[28],[30,26316,26317],{"xmlns":32,"display":33},[35,26318,26319,26327],{},[38,26320,26321,26323,26325],{},[187,26322,11429],{},[191,26324,193],{},[187,26326,11438],{},[59,26328,11712],{"encoding":61},[17,26330,26332,26350],{"className":26331,"ariaHidden":53},[66],[17,26333,26335,26338,26341,26344,26347],{"className":26334},[70],[17,26336],{"className":26337,"style":11722},[74],[17,26339,11429],{"className":26340},[79,230],[17,26342],{"className":26343,"style":235},[234],[17,26345,193],{"className":26346},[239],[17,26348],{"className":26349,"style":235},[234],[17,26351,26353,26356],{"className":26352},[70],[17,26354],{"className":26355,"style":11741},[74],[17,26357,11438],{"className":26358,"style":11528},[79,230],[13,26360,11334],{},[17,26362,26364],{"className":26363},[20],[17,26365,26367,26401],{"className":26366},[24],[17,26368,26370],{"className":26369},[28],[30,26371,26372],{"xmlns":32,"display":33},[35,26373,26374,26398],{},[38,26375,26376,26394,26396],{},[3526,26377,26378,26380,26386],{},[187,26379,3912],{},[38,26381,26382,26384],{},[187,26383,11429],{},[187,26385,11429],{},[38,26387,26388,26390,26392],{},[191,26389,841],{"stretchy":48},[1390,26391,47],{},[191,26393,850],{"stretchy":48},[191,26395,193],{},[1390,26397,47],{},[59,26399,26400],{"encoding":61},"d_{ii}^{(0)}=0",[17,26402,26404,26484],{"className":26403,"ariaHidden":53},[66],[17,26405,26407,26411,26475,26478,26481],{"className":26406},[70],[17,26408],{"className":26409,"style":26410},[74],"height:1.3217em;vertical-align:-0.2769em;",[17,26412,26414,26417],{"className":26413},[79],[17,26415,3912],{"className":26416},[79,230],[17,26418,26420],{"className":26419},[1453],[17,26421,26423,26466],{"className":26422},[83,84],[17,26424,26426,26463],{"className":26425},[88],[17,26427,26429,26443],{"className":26428,"style":25873},[92],[17,26430,26431,26434],{"style":25876},[17,26432],{"className":26433,"style":1470},[100],[17,26435,26437],{"className":26436},[1474,1475,1476,1477],[17,26438,26440],{"className":26439},[79,1477],[17,26441,22657],{"className":26442},[79,230,1477],[17,26444,26445,26448],{"style":25891},[17,26446],{"className":26447,"style":1470},[100],[17,26449,26451],{"className":26450},[1474,1475,1476,1477],[17,26452,26454,26457,26460],{"className":26453},[79,1477],[17,26455,841],{"className":26456},[253,1477],[17,26458,47],{"className":26459},[79,1477],[17,26461,850],{"className":26462},[282,1477],[17,26464,136],{"className":26465},[135],[17,26467,26469],{"className":26468},[88],[17,26470,26473],{"className":26471,"style":26472},[92],"height:0.2769em;",[17,26474],{},[17,26476],{"className":26477,"style":235},[234],[17,26479,193],{"className":26480},[239],[17,26482],{"className":26483,"style":235},[234],[17,26485,26487,26490],{"className":26486},[70],[17,26488],{"className":26489,"style":5244},[74],[17,26491,47],{"className":26492},[79],[506,26494],{},[513,26496,26498],{"id":26497},"_2-核心更新公式","2. 核心更新公式",[13,26500,26501],{},"Floyd 算法的核心是：",[17,26503,26505],{"className":26504},[20],[17,26506,26508,26634],{"className":26507},[24],[17,26509,26511],{"className":26510},[28],[30,26512,26513],{"xmlns":32,"display":33},[35,26514,26515,26631],{},[38,26516,26517],{},[41,26518,26519],{"notation":43},[45,26520,26521],{"scriptlevel":47,"displaystyle":48},[45,26522,26523],{"scriptlevel":47,"displaystyle":48},[45,26524,26525],{"scriptlevel":47,"displaystyle":53},[38,26526,26527,26545,26547,26550,26553],{},[3526,26528,26529,26531,26537],{},[187,26530,3912],{},[38,26532,26533,26535],{},[187,26534,11429],{},[187,26536,11438],{},[38,26538,26539,26541,26543],{},[191,26540,841],{"stretchy":48},[187,26542,4699],{},[191,26544,850],{"stretchy":48},[191,26546,193],{},[187,26548,26549],{},"min",[191,26551,26552],{},"⁡",[38,26554,26555,26557,26579,26581,26583,26605,26607,26629],{},[191,26556,841],{"fence":53},[3526,26558,26559,26561,26567],{},[187,26560,3912],{},[38,26562,26563,26565],{},[187,26564,11429],{},[187,26566,11438],{},[38,26568,26569,26571,26573,26575,26577],{},[191,26570,841],{"stretchy":48},[187,26572,4699],{},[191,26574,972],{},[1390,26576,1392],{},[191,26578,850],{"stretchy":48},[191,26580,202],{"separator":53},[55,26582,4056],{},[3526,26584,26585,26587,26593],{},[187,26586,3912],{},[38,26588,26589,26591],{},[187,26590,11429],{},[187,26592,4699],{},[38,26594,26595,26597,26599,26601,26603],{},[191,26596,841],{"stretchy":48},[187,26598,4699],{},[191,26600,972],{},[1390,26602,1392],{},[191,26604,850],{"stretchy":48},[191,26606,4149],{},[3526,26608,26609,26611,26617],{},[187,26610,3912],{},[38,26612,26613,26615],{},[187,26614,4699],{},[187,26616,11438],{},[38,26618,26619,26621,26623,26625,26627],{},[191,26620,841],{"stretchy":48},[187,26622,4699],{},[191,26624,972],{},[1390,26626,1392],{},[191,26628,850],{"stretchy":48},[191,26630,850],{"fence":53},[59,26632,26633],{"encoding":61},"\\boxed{\nd_{ij}^{(k)}\n=\n\\min\\left(d_{ij}^{(k-1)},\\ d_{ik}^{(k-1)}+d_{kj}^{(k-1)}\\right)\n}",[17,26635,26637],{"className":26636,"ariaHidden":53},[66],[17,26638,26640,26644],{"className":26639},[70],[17,26641],{"className":26642,"style":26643},[74],"height:2.48em;vertical-align:-0.99em;",[17,26645,26647],{"className":26646},[79],[17,26648,26650,27011],{"className":26649},[83,84],[17,26651,26653,27008],{"className":26652},[88],[17,26654,26657,26998],{"className":26655,"style":26656},[92],"height:1.49em;",[17,26658,26660,26664],{"style":26659},"top:-4.48em;",[17,26661],{"className":26662,"style":26663},[100],"height:4.48em;",[17,26665,26667],{"className":26666},[105],[17,26668,26670],{"className":26669},[79],[17,26671,26673,26736,26739,26742,26745,26748,26751],{"className":26672},[79],[17,26674,26676,26679],{"className":26675},[79],[17,26677,3912],{"className":26678},[79,230],[17,26680,26682],{"className":26681},[1453],[17,26683,26685,26728],{"className":26684},[83,84],[17,26686,26688,26725],{"className":26687},[88],[17,26689,26691,26705],{"className":26690,"style":25873},[92],[17,26692,26693,26696],{"style":25876},[17,26694],{"className":26695,"style":1470},[100],[17,26697,26699],{"className":26698},[1474,1475,1476,1477],[17,26700,26702],{"className":26701},[79,1477],[17,26703,14842],{"className":26704,"style":11528},[79,230,1477],[17,26706,26707,26710],{"style":25891},[17,26708],{"className":26709,"style":1470},[100],[17,26711,26713],{"className":26712},[1474,1475,1476,1477],[17,26714,26716,26719,26722],{"className":26715},[79,1477],[17,26717,841],{"className":26718},[253,1477],[17,26720,4699],{"className":26721,"style":4715},[79,230,1477],[17,26723,850],{"className":26724},[282,1477],[17,26726,136],{"className":26727},[135],[17,26729,26731],{"className":26730},[88],[17,26732,26734],{"className":26733,"style":25919},[92],[17,26735],{},[17,26737],{"className":26738,"style":235},[234],[17,26740,193],{"className":26741},[239],[17,26743],{"className":26744,"style":235},[234],[17,26746,26549],{"className":26747},[4973],[17,26749],{"className":26750,"style":265},[234],[17,26752,26754,26760,26829,26832,26835,26838,26910,26913,26916,26919,26992],{"className":26753},[9183],[17,26755,26757],{"className":26756,"style":15112},[253,15111],[17,26758,841],{"className":26759},[15116,15117],[17,26761,26763,26766],{"className":26762},[79],[17,26764,3912],{"className":26765},[79,230],[17,26767,26769],{"className":26768},[1453],[17,26770,26772,26821],{"className":26771},[83,84],[17,26773,26775,26818],{"className":26774},[88],[17,26776,26778,26792],{"className":26777,"style":25873},[92],[17,26779,26780,26783],{"style":25876},[17,26781],{"className":26782,"style":1470},[100],[17,26784,26786],{"className":26785},[1474,1475,1476,1477],[17,26787,26789],{"className":26788},[79,1477],[17,26790,14842],{"className":26791,"style":11528},[79,230,1477],[17,26793,26794,26797],{"style":25891},[17,26795],{"className":26796,"style":1470},[100],[17,26798,26800],{"className":26799},[1474,1475,1476,1477],[17,26801,26803,26806,26809,26812,26815],{"className":26802},[79,1477],[17,26804,841],{"className":26805},[253,1477],[17,26807,4699],{"className":26808,"style":4715},[79,230,1477],[17,26810,972],{"className":26811},[997,1477],[17,26813,1392],{"className":26814},[79,1477],[17,26816,850],{"className":26817},[282,1477],[17,26819,136],{"className":26820},[135],[17,26822,26824],{"className":26823},[88],[17,26825,26827],{"className":26826,"style":25919},[92],[17,26828],{},[17,26830,202],{"className":26831},[261],[17,26833,4056],{"className":26834},[234],[17,26836],{"className":26837,"style":265},[234],[17,26839,26841,26844],{"className":26840},[79],[17,26842,3912],{"className":26843},[79,230],[17,26845,26847],{"className":26846},[1453],[17,26848,26850,26901],{"className":26849},[83,84],[17,26851,26853,26898],{"className":26852},[88],[17,26854,26856,26872],{"className":26855,"style":25873},[92],[17,26857,26859,26862],{"style":26858},"top:-2.3987em;margin-left:0em;margin-right:0.05em;",[17,26860],{"className":26861,"style":1470},[100],[17,26863,26865],{"className":26864},[1474,1475,1476,1477],[17,26866,26868],{"className":26867},[79,1477],[17,26869,26871],{"className":26870,"style":4715},[79,230,1477],"ik",[17,26873,26874,26877],{"style":25891},[17,26875],{"className":26876,"style":1470},[100],[17,26878,26880],{"className":26879},[1474,1475,1476,1477],[17,26881,26883,26886,26889,26892,26895],{"className":26882},[79,1477],[17,26884,841],{"className":26885},[253,1477],[17,26887,4699],{"className":26888,"style":4715},[79,230,1477],[17,26890,972],{"className":26891},[997,1477],[17,26893,1392],{"className":26894},[79,1477],[17,26896,850],{"className":26897},[282,1477],[17,26899,136],{"className":26900},[135],[17,26902,26904],{"className":26903},[88],[17,26905,26908],{"className":26906,"style":26907},[92],"height:0.3013em;",[17,26909],{},[17,26911],{"className":26912,"style":257},[234],[17,26914,4149],{"className":26915},[997],[17,26917],{"className":26918,"style":257},[234],[17,26920,26922,26925],{"className":26921},[79],[17,26923,3912],{"className":26924},[79,230],[17,26926,26928],{"className":26927},[1453],[17,26929,26931,26983],{"className":26930},[83,84],[17,26932,26934,26980],{"className":26933},[88],[17,26935,26937,26954],{"className":26936,"style":25873},[92],[17,26938,26939,26942],{"style":26858},[17,26940],{"className":26941,"style":1470},[100],[17,26943,26945],{"className":26944},[1474,1475,1476,1477],[17,26946,26948,26951],{"className":26947},[79,1477],[17,26949,4699],{"className":26950,"style":4715},[79,230,1477],[17,26952,11438],{"className":26953,"style":11528},[79,230,1477],[17,26955,26956,26959],{"style":25891},[17,26957],{"className":26958,"style":1470},[100],[17,26960,26962],{"className":26961},[1474,1475,1476,1477],[17,26963,26965,26968,26971,26974,26977],{"className":26964},[79,1477],[17,26966,841],{"className":26967},[253,1477],[17,26969,4699],{"className":26970,"style":4715},[79,230,1477],[17,26972,972],{"className":26973},[997,1477],[17,26975,1392],{"className":26976},[79,1477],[17,26978,850],{"className":26979},[282,1477],[17,26981,136],{"className":26982},[135],[17,26984,26986],{"className":26985},[88],[17,26987,26990],{"className":26988,"style":26989},[92],"height:0.4374em;",[17,26991],{},[17,26993,26995],{"className":26994,"style":15112},[282,15111],[17,26996,850],{"className":26997},[15116,15117],[17,26999,27001,27004],{"style":27000},"top:-3.49em;",[17,27002],{"className":27003,"style":26663},[100],[17,27005],{"className":27006,"style":27007},[129,130],"height:2.48em;border-style:solid;border-width:0.04em;",[17,27009,136],{"className":27010},[135],[17,27012,27014],{"className":27013},[88],[17,27015,27018],{"className":27016,"style":27017},[92],"height:0.99em;",[17,27019],{},[13,27021,5086],{},[1700,27023,27024],{},[13,27025,9272,27026,12578,27054,27082,27083,27111,27112,720],{},[17,27027,27029,27042],{"className":27028},[24],[17,27030,27032],{"className":27031},[28],[30,27033,27034],{"xmlns":32},[35,27035,27036,27040],{},[38,27037,27038],{},[187,27039,11429],{},[59,27041,11429],{"encoding":61},[17,27043,27045],{"className":27044,"ariaHidden":53},[66],[17,27046,27048,27051],{"className":27047},[70],[17,27049],{"className":27050,"style":11722},[74],[17,27052,11429],{"className":27053},[79,230],[17,27055,27057,27070],{"className":27056},[24],[17,27058,27060],{"className":27059},[28],[30,27061,27062],{"xmlns":32},[35,27063,27064,27068],{},[38,27065,27066],{},[187,27067,11438],{},[59,27069,11438],{"encoding":61},[17,27071,27073],{"className":27072,"ariaHidden":53},[66],[17,27074,27076,27079],{"className":27075},[70],[17,27077],{"className":27078,"style":11741},[74],[17,27080,11438],{"className":27081,"style":11528},[79,230]," 的最短路，要么不经过 ",[17,27084,27086,27099],{"className":27085},[24],[17,27087,27089],{"className":27088},[28],[30,27090,27091],{"xmlns":32},[35,27092,27093,27097],{},[38,27094,27095],{},[187,27096,4699],{},[59,27098,4699],{"encoding":61},[17,27100,27102],{"className":27101,"ariaHidden":53},[66],[17,27103,27105,27108],{"className":27104},[70],[17,27106],{"className":27107,"style":4711},[74],[17,27109,4699],{"className":27110,"style":4715},[79,230],"，要么经过 ",[17,27113,27115,27128],{"className":27114},[24],[17,27116,27118],{"className":27117},[28],[30,27119,27120],{"xmlns":32},[35,27121,27122,27126],{},[38,27123,27124],{},[187,27125,4699],{},[59,27127,4699],{"encoding":61},[17,27129,27131],{"className":27130,"ariaHidden":53},[66],[17,27132,27134,27137],{"className":27133},[70],[17,27135],{"className":27136,"style":4711},[74],[17,27138,4699],{"className":27139,"style":4715},[79,230],[13,27141,27142,27143,27171],{},"如果经过 ",[17,27144,27146,27159],{"className":27145},[24],[17,27147,27149],{"className":27148},[28],[30,27150,27151],{"xmlns":32},[35,27152,27153,27157],{},[38,27154,27155],{},[187,27156,4699],{},[59,27158,4699],{"encoding":61},[17,27160,27162],{"className":27161,"ariaHidden":53},[66],[17,27163,27165,27168],{"className":27164},[70],[17,27166],{"className":27167,"style":4711},[74],[17,27169,4699],{"className":27170,"style":4715},[79,230]," 更短，就更新。",[506,27173],{},[513,27175,27177],{"id":27176},"_3-算法过程","3. 算法过程",[13,27179,27180],{},"依次令：",[17,27182,27184],{"className":27183},[20],[17,27185,27187,27217],{"className":27186},[24],[17,27188,27190],{"className":27189},[28],[30,27191,27192],{"xmlns":32,"display":33},[35,27193,27194,27214],{},[38,27195,27196,27198,27200,27202,27204,27206,27208,27210,27212],{},[187,27197,4699],{},[191,27199,193],{},[1390,27201,1392],{},[191,27203,202],{"separator":53},[1390,27205,1401],{},[191,27207,202],{"separator":53},[191,27209,9374],{},[191,27211,202],{"separator":53},[187,27213,3183],{},[59,27215,27216],{"encoding":61},"k=1,2,\\dots,n",[17,27218,27220,27238],{"className":27219,"ariaHidden":53},[66],[17,27221,27223,27226,27229,27232,27235],{"className":27222},[70],[17,27224],{"className":27225,"style":4711},[74],[17,27227,4699],{"className":27228,"style":4715},[79,230],[17,27230],{"className":27231,"style":235},[234],[17,27233,193],{"className":27234},[239],[17,27236],{"className":27237,"style":235},[234],[17,27239,27241,27245,27248,27251,27254,27257,27260,27263,27266,27269,27272,27275],{"className":27240},[70],[17,27242],{"className":27243,"style":27244},[74],"height:0.8389em;vertical-align:-0.1944em;",[17,27246,1392],{"className":27247},[79],[17,27249,202],{"className":27250},[261],[17,27252],{"className":27253,"style":265},[234],[17,27255,1401],{"className":27256},[79],[17,27258,202],{"className":27259},[261],[17,27261],{"className":27262,"style":265},[234],[17,27264,9374],{"className":27265},[9183],[17,27267],{"className":27268,"style":265},[234],[17,27270,202],{"className":27271},[261],[17,27273],{"className":27274,"style":265},[234],[17,27276,3183],{"className":27277},[79,230],[13,27279,27280],{},"逐步允许路径经过更多中间顶点。",[13,27282,27283],{},"最终：",[17,27285,27287],{"className":27286},[20],[17,27288,27290,27314],{"className":27289},[24],[17,27291,27293],{"className":27292},[28],[30,27294,27295],{"xmlns":32,"display":33},[35,27296,27297,27311],{},[38,27298,27299],{},[4143,27300,27301,27303],{},[187,27302,22110],{},[38,27304,27305,27307,27309],{},[191,27306,841],{"stretchy":48},[187,27308,3183],{},[191,27310,850],{"stretchy":48},[59,27312,27313],{"encoding":61},"D^{(n)}",[17,27315,27317],{"className":27316,"ariaHidden":53},[66],[17,27318,27320,27323],{"className":27319},[70],[17,27321],{"className":27322,"style":21121},[74],[17,27324,27326,27329],{"className":27325},[79],[17,27327,22110],{"className":27328,"style":22142},[79,230],[17,27330,27332],{"className":27331},[1453],[17,27333,27335],{"className":27334},[83],[17,27336,27338],{"className":27337},[88],[17,27339,27341],{"className":27340,"style":21121},[92],[17,27342,27343,27346],{"style":3601},[17,27344],{"className":27345,"style":1470},[100],[17,27347,27349],{"className":27348},[1474,1475,1476,1477],[17,27350,27352,27355,27358],{"className":27351},[79,1477],[17,27353,841],{"className":27354},[253,1477],[17,27356,3183],{"className":27357},[79,230,1477],[17,27359,850],{"className":27360},[282,1477],[13,27362,27363],{},"就是所有顶点对之间的最短距离矩阵。",[506,27365],{},[513,27367,27369],{"id":27368},"_4-dijkstra-与-floyd-区别","4. Dijkstra 与 Floyd 区别",[287,27371,27372,27382],{},[290,27373,27374],{},[293,27375,27376,27379],{},[296,27377,27378],{},"算法",[296,27380,27381],{},"作用",[303,27383,27384,27392],{},[293,27385,27386,27389],{},[308,27387,27388],{},"Dijkstra",[308,27390,27391],{},"求一个源点到其他点的最短路径",[293,27393,27394,27397],{},[308,27395,27396],{},"Floyd",[308,27398,27399],{},"求任意两点之间的最短路径",[13,27401,27402],{},"一句话：",[17,27404,27406],{"className":27405},[20],[17,27407,27409,27432],{"className":27408},[24],[17,27410,27412],{"className":27411},[28],[30,27413,27414],{"xmlns":32,"display":33},[35,27415,27416,27429],{},[38,27417,27418],{},[41,27419,27420],{"notation":43},[45,27421,27422],{"scriptlevel":47,"displaystyle":48},[45,27423,27424],{"scriptlevel":47,"displaystyle":48},[45,27425,27426],{"scriptlevel":47,"displaystyle":53},[55,27427,27428],{},"Dijkstra 是单源，Floyd 是全源",[59,27430,27431],{"encoding":61},"\\boxed{\\text{Dijkstra 是单源，Floyd 是全源}}",[17,27433,27435],{"className":27434,"ariaHidden":53},[66],[17,27436,27438,27442],{"className":27437},[70],[17,27439],{"className":27440,"style":27441},[74],"height:1.5689em;vertical-align:-0.5344em;",[17,27443,27445],{"className":27444},[79],[17,27446,27448,27501],{"className":27447},[83,84],[17,27449,27451,27498],{"className":27450},[88],[17,27452,27454,27489],{"className":27453,"style":9663},[92],[17,27455,27457,27461],{"style":27456},"top:-3.5689em;",[17,27458],{"className":27459,"style":27460},[100],"height:3.5689em;",[17,27462,27464],{"className":27463},[105],[17,27465,27467],{"className":27466},[79],[17,27468,27470],{"className":27469},[79],[17,27471,27473,27477,27481,27485],{"className":27472},[79,115],[17,27474,27476],{"className":27475},[79],"Dijkstra ",[17,27478,27480],{"className":27479},[79,119],"是单源，",[17,27482,27484],{"className":27483},[79],"Floyd ",[17,27486,27488],{"className":27487},[79,119],"是全源",[17,27490,27491,27494],{"style":9685},[17,27492],{"className":27493,"style":27460},[100],[17,27495],{"className":27496,"style":27497},[129,130],"height:1.5689em;border-style:solid;border-width:0.04em;",[17,27499,136],{"className":27500},[135],[17,27502,27504],{"className":27503},[88],[17,27505,27507],{"className":27506,"style":16629},[92],[17,27508],{},[506,27510],{},[10,27512,27514],{"id":27513},"五决策图与最优路径","五、决策图与最优路径",[513,27516,27518],{"id":27517},"_1-决策图","1. 决策图",[13,27520,27521],{},"决策图是一类有向赋权图。",[13,27523,27524],{},"顶点分层：",[17,27526,27528],{"className":27527},[20],[17,27529,27531,27570],{"className":27530},[24],[17,27532,27534],{"className":27533},[28],[30,27535,27536],{"xmlns":32,"display":33},[35,27537,27538,27567],{},[38,27539,27540,27546,27548,27554,27556,27558,27560],{},[1385,27541,27542,27544],{},[187,27543,199],{},[1390,27545,1392],{},[191,27547,202],{"separator":53},[1385,27549,27550,27552],{},[187,27551,199],{},[1390,27553,1401],{},[191,27555,202],{"separator":53},[191,27557,9374],{},[191,27559,202],{"separator":53},[1385,27561,27562,27564],{},[187,27563,199],{},[187,27565,27566],{},"s",[59,27568,27569],{"encoding":61},"V_1,V_2,\\dots,V_s",[17,27571,27573],{"className":27572,"ariaHidden":53},[66],[17,27574,27576,27580,27621,27624,27627,27667,27670,27673,27676,27679,27682,27685],{"className":27575},[70],[17,27577],{"className":27578,"style":27579},[74],"height:0.8778em;vertical-align:-0.1944em;",[17,27581,27583,27586],{"className":27582},[79],[17,27584,199],{"className":27585,"style":257},[79,230],[17,27587,27589],{"className":27588},[1453],[17,27590,27592,27613],{"className":27591},[83,84],[17,27593,27595,27610],{"className":27594},[88],[17,27596,27598],{"className":27597,"style":1463},[92],[17,27599,27601,27604],{"style":27600},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[17,27602],{"className":27603,"style":1470},[100],[17,27605,27607],{"className":27606},[1474,1475,1476,1477],[17,27608,1392],{"className":27609},[79,1477],[17,27611,136],{"className":27612},[135],[17,27614,27616],{"className":27615},[88],[17,27617,27619],{"className":27618,"style":1490},[92],[17,27620],{},[17,27622,202],{"className":27623},[261],[17,27625],{"className":27626,"style":265},[234],[17,27628,27630,27633],{"className":27629},[79],[17,27631,199],{"className":27632,"style":257},[79,230],[17,27634,27636],{"className":27635},[1453],[17,27637,27639,27659],{"className":27638},[83,84],[17,27640,27642,27656],{"className":27641},[88],[17,27643,27645],{"className":27644,"style":1463},[92],[17,27646,27647,27650],{"style":27600},[17,27648],{"className":27649,"style":1470},[100],[17,27651,27653],{"className":27652},[1474,1475,1476,1477],[17,27654,1401],{"className":27655},[79,1477],[17,27657,136],{"className":27658},[135],[17,27660,27662],{"className":27661},[88],[17,27663,27665],{"className":27664,"style":1490},[92],[17,27666],{},[17,27668,202],{"className":27669},[261],[17,27671],{"className":27672,"style":265},[234],[17,27674,9374],{"className":27675},[9183],[17,27677],{"className":27678,"style":265},[234],[17,27680,202],{"className":27681},[261],[17,27683],{"className":27684,"style":265},[234],[17,27686,27688,27691],{"className":27687},[79],[17,27689,199],{"className":27690,"style":257},[79,230],[17,27692,27694],{"className":27693},[1453],[17,27695,27697,27717],{"className":27696},[83,84],[17,27698,27700,27714],{"className":27699},[88],[17,27701,27703],{"className":27702,"style":3253},[92],[17,27704,27705,27708],{"style":27600},[17,27706],{"className":27707,"style":1470},[100],[17,27709,27711],{"className":27710},[1474,1475,1476,1477],[17,27712,27566],{"className":27713},[79,230,1477],[17,27715,136],{"className":27716},[135],[17,27718,27720],{"className":27719},[88],[17,27721,27723],{"className":27722,"style":1490},[92],[17,27724],{},[13,27726,27727],{},"边只从前一层指向后一层。",[13,27729,27730],{},"这种图常用来表示多阶段决策问题。",[506,27732],{},[513,27734,27736],{"id":27735},"_2-最优路径","2. 最优路径",[13,27738,27739,27740,720],{},"从初始顶点到终止顶点的路径中，权值总和最小的路径叫",[645,27741,27742],{},"最优路径",[13,27744,27745],{},"求法通常是动态规划思想：",[1700,27747,27748],{},[13,27749,27750],{},"从后往前，逐层计算每个顶点到终点的最优值。",[506,27752],{},[513,27754,27756],{"id":27755},"_3-核心思想","3. 核心思想",[13,27758,27759,27760,27788,27789,4874],{},"如果从 ",[17,27761,27763,27776],{"className":27762},[24],[17,27764,27766],{"className":27765},[28],[30,27767,27768],{"xmlns":32},[35,27769,27770,27774],{},[38,27771,27772],{},[187,27773,793],{},[59,27775,793],{"encoding":61},[17,27777,27779],{"className":27778,"ariaHidden":53},[66],[17,27780,27782,27785],{"className":27781},[70],[17,27783],{"className":27784,"style":769},[74],[17,27786,793],{"className":27787,"style":818},[79,230]," 出发，可以走到若干后继顶点 ",[17,27790,27792,27830],{"className":27791},[24],[17,27793,27795],{"className":27794},[28],[30,27796,27797],{"xmlns":32},[35,27798,27799,27827],{},[38,27800,27801,27807,27809,27815,27817,27819,27821],{},[1385,27802,27803,27805],{},[187,27804,788],{},[1390,27806,1392],{},[191,27808,202],{"separator":53},[1385,27810,27811,27813],{},[187,27812,788],{},[1390,27814,1401],{},[191,27816,202],{"separator":53},[191,27818,9374],{},[191,27820,202],{"separator":53},[1385,27822,27823,27825],{},[187,27824,788],{},[187,27826,4699],{},[59,27828,27829],{"encoding":61},"u_1,u_2,\\dots,u_k",[17,27831,27833],{"className":27832,"ariaHidden":53},[66],[17,27834,27836,27839,27879,27882,27885,27925,27928,27931,27934,27937,27940,27943],{"className":27835},[70],[17,27837],{"className":27838,"style":406},[74],[17,27840,27842,27845],{"className":27841},[79],[17,27843,788],{"className":27844},[79,230],[17,27846,27848],{"className":27847},[1453],[17,27849,27851,27871],{"className":27850},[83,84],[17,27852,27854,27868],{"className":27853},[88],[17,27855,27857],{"className":27856,"style":1463},[92],[17,27858,27859,27862],{"style":2106},[17,27860],{"className":27861,"style":1470},[100],[17,27863,27865],{"className":27864},[1474,1475,1476,1477],[17,27866,1392],{"className":27867},[79,1477],[17,27869,136],{"className":27870},[135],[17,27872,27874],{"className":27873},[88],[17,27875,27877],{"className":27876,"style":1490},[92],[17,27878],{},[17,27880,202],{"className":27881},[261],[17,27883],{"className":27884,"style":265},[234],[17,27886,27888,27891],{"className":27887},[79],[17,27889,788],{"className":27890},[79,230],[17,27892,27894],{"className":27893},[1453],[17,27895,27897,27917],{"className":27896},[83,84],[17,27898,27900,27914],{"className":27899},[88],[17,27901,27903],{"className":27902,"style":1463},[92],[17,27904,27905,27908],{"style":2106},[17,27906],{"className":27907,"style":1470},[100],[17,27909,27911],{"className":27910},[1474,1475,1476,1477],[17,27912,1401],{"className":27913},[79,1477],[17,27915,136],{"className":27916},[135],[17,27918,27920],{"className":27919},[88],[17,27921,27923],{"className":27922,"style":1490},[92],[17,27924],{},[17,27926,202],{"className":27927},[261],[17,27929],{"className":27930,"style":265},[234],[17,27932,9374],{"className":27933},[9183],[17,27935],{"className":27936,"style":265},[234],[17,27938,202],{"className":27939},[261],[17,27941],{"className":27942,"style":265},[234],[17,27944,27946,27949],{"className":27945},[79],[17,27947,788],{"className":27948},[79,230],[17,27950,27952],{"className":27951},[1453],[17,27953,27955,27975],{"className":27954},[83,84],[17,27956,27958,27972],{"className":27957},[88],[17,27959,27961],{"className":27960,"style":9205},[92],[17,27962,27963,27966],{"style":2106},[17,27964],{"className":27965,"style":1470},[100],[17,27967,27969],{"className":27968},[1474,1475,1476,1477],[17,27970,4699],{"className":27971,"style":4715},[79,230,1477],[17,27973,136],{"className":27974},[135],[17,27976,27978],{"className":27977},[88],[17,27979,27981],{"className":27980,"style":1490},[92],[17,27982],{},[17,27984,27986],{"className":27985},[20],[17,27987,27989,28053],{"className":27988},[24],[17,27990,27992],{"className":27991},[28],[30,27993,27994],{"xmlns":32,"display":33},[35,27995,27996,28050],{},[38,27997,27998,28000,28002,28004,28006,28008,28018],{},[187,27999,14748],{},[191,28001,841],{"stretchy":48},[187,28003,793],{},[191,28005,850],{"stretchy":48},[191,28007,193],{},[4901,28009,28010,28016],{},[38,28011,28012,28014],{},[187,28013,26549],{},[191,28015,26552],{},[187,28017,11429],{},[38,28019,28020,28022,28024,28026,28028,28034,28036,28038,28040,28042,28048],{},[187,28021,22906],{},[191,28023,841],{"stretchy":48},[187,28025,793],{},[191,28027,202],{"separator":53},[1385,28029,28030,28032],{},[187,28031,788],{},[187,28033,11429],{},[191,28035,850],{"stretchy":48},[191,28037,4149],{},[187,28039,14748],{},[191,28041,841],{"stretchy":48},[1385,28043,28044,28046],{},[187,28045,788],{},[187,28047,11429],{},[191,28049,850],{"stretchy":48},[59,28051,28052],{"encoding":61},"F(v)=\\min_i{W(v,u_i)+F(u_i)}",[17,28054,28056,28083],{"className":28055,"ariaHidden":53},[66],[17,28057,28059,28062,28065,28068,28071,28074,28077,28080],{"className":28058},[70],[17,28060],{"className":28061,"style":249},[74],[17,28063,14748],{"className":28064,"style":14790},[79,230],[17,28066,841],{"className":28067},[253],[17,28069,793],{"className":28070,"style":818},[79,230],[17,28072,850],{"className":28073},[282],[17,28075],{"className":28076,"style":235},[234],[17,28078,193],{"className":28079},[239],[17,28081],{"className":28082,"style":235},[234],[17,28084,28086,28090,28137,28140],{"className":28085},[70],[17,28087],{"className":28088,"style":28089},[74],"height:1.4777em;vertical-align:-0.7277em;",[17,28091,28093],{"className":28092},[4973,4974],[17,28094,28096,28128],{"className":28095},[83,84],[17,28097,28099,28125],{"className":28098},[88],[17,28100,28103,28115],{"className":28101,"style":28102},[92],"height:0.6679em;",[17,28104,28106,28109],{"style":28105},"top:-2.3723em;margin-left:0em;",[17,28107],{"className":28108,"style":3390},[100],[17,28110,28112],{"className":28111},[1474,1475,1476,1477],[17,28113,11429],{"className":28114},[79,230,1477],[17,28116,28117,28120],{"style":7829},[17,28118],{"className":28119,"style":3390},[100],[17,28121,28122],{},[17,28123,26549],{"className":28124},[4973],[17,28126,136],{"className":28127},[135],[17,28129,28131],{"className":28130},[88],[17,28132,28135],{"className":28133,"style":28134},[92],"height:0.7277em;",[17,28136],{},[17,28138],{"className":28139,"style":265},[234],[17,28141,28143,28146,28149,28152,28155,28158,28198,28201,28204,28207,28210,28213,28216,28256],{"className":28142},[79],[17,28144,22906],{"className":28145,"style":14790},[79,230],[17,28147,841],{"className":28148},[253],[17,28150,793],{"className":28151,"style":818},[79,230],[17,28153,202],{"className":28154},[261],[17,28156],{"className":28157,"style":265},[234],[17,28159,28161,28164],{"className":28160},[79],[17,28162,788],{"className":28163},[79,230],[17,28165,28167],{"className":28166},[1453],[17,28168,28170,28190],{"className":28169},[83,84],[17,28171,28173,28187],{"className":28172},[88],[17,28174,28176],{"className":28175,"style":11470},[92],[17,28177,28178,28181],{"style":2106},[17,28179],{"className":28180,"style":1470},[100],[17,28182,28184],{"className":28183},[1474,1475,1476,1477],[17,28185,11429],{"className":28186},[79,230,1477],[17,28188,136],{"className":28189},[135],[17,28191,28193],{"className":28192},[88],[17,28194,28196],{"className":28195,"style":1490},[92],[17,28197],{},[17,28199,850],{"className":28200},[282],[17,28202],{"className":28203,"style":257},[234],[17,28205,4149],{"className":28206},[997],[17,28208],{"className":28209,"style":257},[234],[17,28211,14748],{"className":28212,"style":14790},[79,230],[17,28214,841],{"className":28215},[253],[17,28217,28219,28222],{"className":28218},[79],[17,28220,788],{"className":28221},[79,230],[17,28223,28225],{"className":28224},[1453],[17,28226,28228,28248],{"className":28227},[83,84],[17,28229,28231,28245],{"className":28230},[88],[17,28232,28234],{"className":28233,"style":11470},[92],[17,28235,28236,28239],{"style":2106},[17,28237],{"className":28238,"style":1470},[100],[17,28240,28242],{"className":28241},[1474,1475,1476,1477],[17,28243,11429],{"className":28244},[79,230,1477],[17,28246,136],{"className":28247},[135],[17,28249,28251],{"className":28250},[88],[17,28252,28254],{"className":28253,"style":1490},[92],[17,28255],{},[17,28257,850],{"className":28258},[282],[13,28260,5086],{},[1700,28262,28263],{},[13,28264,28265],{},"从当前点出发的最优值 = 走一条边的代价 + 后面最优值 的最小值。",[506,28267],{},[10,28269,28271],{"id":28270},"六pert-图与关键路径","六、PERT 图与关键路径",[13,28273,28274],{},"PERT 图用于工程项目管理。",[513,28276,28278],{"id":28277},"_1-pert-图的特点","1. PERT 图的特点",[13,28280,28281],{},"PERT 图是一种有向无环图。",[150,28283,28284,28287,28290,28293,28296],{},[153,28285,28286],{},"顶点表示事件；",[153,28288,28289],{},"边表示任务；",[153,28291,28292],{},"边权表示完成任务所需时间；",[153,28294,28295],{},"有一个源点；",[153,28297,28298],{},"有一个汇点。",[506,28300],{},[513,28302,28304],{"id":28303},"_2-最早完成时间","2. 最早完成时间",[13,28306,28307,28308,28377],{},"顶点 ",[17,28309,28311,28328],{"className":28310},[24],[17,28312,28314],{"className":28313},[28],[30,28315,28316],{"xmlns":32},[35,28317,28318,28326],{},[38,28319,28320],{},[1385,28321,28322,28324],{},[187,28323,793],{},[187,28325,11429],{},[59,28327,12005],{"encoding":61},[17,28329,28331],{"className":28330,"ariaHidden":53},[66],[17,28332,28334,28337],{"className":28333},[70],[17,28335],{"className":28336,"style":2085},[74],[17,28338,28340,28343],{"className":28339},[79],[17,28341,793],{"className":28342,"style":818},[79,230],[17,28344,28346],{"className":28345},[1453],[17,28347,28349,28369],{"className":28348},[83,84],[17,28350,28352,28366],{"className":28351},[88],[17,28353,28355],{"className":28354,"style":11470},[92],[17,28356,28357,28360],{"style":1466},[17,28358],{"className":28359,"style":1470},[100],[17,28361,28363],{"className":28362},[1474,1475,1476,1477],[17,28364,11429],{"className":28365},[79,230,1477],[17,28367,136],{"className":28368},[135],[17,28370,28372],{"className":28371},[88],[17,28373,28375],{"className":28374,"style":1490},[92],[17,28376],{}," 的最早完成时间记作：",[17,28379,28381],{"className":28380},[20],[17,28382,28384,28410],{"className":28383},[24],[17,28385,28387],{"className":28386},[28],[30,28388,28389],{"xmlns":32,"display":33},[35,28390,28391,28407],{},[38,28392,28393,28395,28397,28399,28405],{},[187,28394,17926],{},[187,28396,205],{},[191,28398,841],{"stretchy":48},[1385,28400,28401,28403],{},[187,28402,793],{},[187,28404,11429],{},[191,28406,850],{"stretchy":48},[59,28408,28409],{"encoding":61},"TE(v_i)",[17,28411,28413],{"className":28412,"ariaHidden":53},[66],[17,28414,28416,28419,28422,28425,28428,28468],{"className":28415},[70],[17,28417],{"className":28418,"style":249},[74],[17,28420,17926],{"className":28421,"style":14790},[79,230],[17,28423,205],{"className":28424,"style":269},[79,230],[17,28426,841],{"className":28427},[253],[17,28429,28431,28434],{"className":28430},[79],[17,28432,793],{"className":28433,"style":818},[79,230],[17,28435,28437],{"className":28436},[1453],[17,28438,28440,28460],{"className":28439},[83,84],[17,28441,28443,28457],{"className":28442},[88],[17,28444,28446],{"className":28445,"style":11470},[92],[17,28447,28448,28451],{"style":1466},[17,28449],{"className":28450,"style":1470},[100],[17,28452,28454],{"className":28453},[1474,1475,1476,1477],[17,28455,11429],{"className":28456},[79,230,1477],[17,28458,136],{"className":28459},[135],[17,28461,28463],{"className":28462},[88],[17,28464,28466],{"className":28465,"style":1490},[92],[17,28467],{},[17,28469,850],{"className":28470},[282],[13,28472,28473,28474,28543],{},"表示在不违反先后顺序的情况下，事件 ",[17,28475,28477,28494],{"className":28476},[24],[17,28478,28480],{"className":28479},[28],[30,28481,28482],{"xmlns":32},[35,28483,28484,28492],{},[38,28485,28486],{},[1385,28487,28488,28490],{},[187,28489,793],{},[187,28491,11429],{},[59,28493,12005],{"encoding":61},[17,28495,28497],{"className":28496,"ariaHidden":53},[66],[17,28498,28500,28503],{"className":28499},[70],[17,28501],{"className":28502,"style":2085},[74],[17,28504,28506,28509],{"className":28505},[79],[17,28507,793],{"className":28508,"style":818},[79,230],[17,28510,28512],{"className":28511},[1453],[17,28513,28515,28535],{"className":28514},[83,84],[17,28516,28518,28532],{"className":28517},[88],[17,28519,28521],{"className":28520,"style":11470},[92],[17,28522,28523,28526],{"style":1466},[17,28524],{"className":28525,"style":1470},[100],[17,28527,28529],{"className":28528},[1474,1475,1476,1477],[17,28530,11429],{"className":28531},[79,230,1477],[17,28533,136],{"className":28534},[135],[17,28536,28538],{"className":28537},[88],[17,28539,28541],{"className":28540,"style":1490},[92],[17,28542],{}," 最早什么时候能发生。",[13,28545,28546],{},"通常：",[17,28548,28550],{"className":28549},[20],[17,28551,28553,28583],{"className":28552},[24],[17,28554,28556],{"className":28555},[28],[30,28557,28558],{"xmlns":32,"display":33},[35,28559,28560,28580],{},[38,28561,28562,28564,28566,28568,28574,28576,28578],{},[187,28563,17926],{},[187,28565,205],{},[191,28567,841],{"stretchy":48},[1385,28569,28570,28572],{},[187,28571,793],{},[1390,28573,1392],{},[191,28575,850],{"stretchy":48},[191,28577,193],{},[1390,28579,47],{},[59,28581,28582],{"encoding":61},"TE(v_1)=0",[17,28584,28586,28653],{"className":28585,"ariaHidden":53},[66],[17,28587,28589,28592,28595,28598,28601,28641,28644,28647,28650],{"className":28588},[70],[17,28590],{"className":28591,"style":249},[74],[17,28593,17926],{"className":28594,"style":14790},[79,230],[17,28596,205],{"className":28597,"style":269},[79,230],[17,28599,841],{"className":28600},[253],[17,28602,28604,28607],{"className":28603},[79],[17,28605,793],{"className":28606,"style":818},[79,230],[17,28608,28610],{"className":28609},[1453],[17,28611,28613,28633],{"className":28612},[83,84],[17,28614,28616,28630],{"className":28615},[88],[17,28617,28619],{"className":28618,"style":1463},[92],[17,28620,28621,28624],{"style":1466},[17,28622],{"className":28623,"style":1470},[100],[17,28625,28627],{"className":28626},[1474,1475,1476,1477],[17,28628,1392],{"className":28629},[79,1477],[17,28631,136],{"className":28632},[135],[17,28634,28636],{"className":28635},[88],[17,28637,28639],{"className":28638,"style":1490},[92],[17,28640],{},[17,28642,850],{"className":28643},[282],[17,28645],{"className":28646,"style":235},[234],[17,28648,193],{"className":28649},[239],[17,28651],{"className":28652,"style":235},[234],[17,28654,28656,28659],{"className":28655},[70],[17,28657],{"className":28658,"style":5244},[74],[17,28660,47],{"className":28661},[79],[13,28663,28664],{},"对其他点：",[17,28666,28668],{"className":28667},[20],[17,28669,28671,28742],{"className":28670},[24],[17,28672,28674],{"className":28673},[28],[30,28675,28676],{"xmlns":32,"display":33},[35,28677,28678,28739],{},[38,28679,28680,28682,28684,28686,28692,28694,28696,28699,28701],{},[187,28681,17926],{},[187,28683,205],{},[191,28685,841],{"stretchy":48},[1385,28687,28688,28690],{},[187,28689,793],{},[187,28691,11429],{},[191,28693,850],{"stretchy":48},[191,28695,193],{},[187,28697,28698],{},"max",[191,28700,26552],{},[38,28702,28703,28705,28707,28709,28715,28717,28719,28721,28723,28729,28731,28737],{},[187,28704,17926],{},[187,28706,205],{},[191,28708,841],{"stretchy":48},[1385,28710,28711,28713],{},[187,28712,793],{},[187,28714,11438],{},[191,28716,850],{"stretchy":48},[191,28718,4149],{},[187,28720,22906],{},[191,28722,841],{"stretchy":48},[1385,28724,28725,28727],{},[187,28726,793],{},[187,28728,11438],{},[191,28730,202],{"separator":53},[1385,28732,28733,28735],{},[187,28734,793],{},[187,28736,11429],{},[191,28738,850],{"stretchy":48},[59,28740,28741],{"encoding":61},"TE(v_i)=\\max{TE(v_j)+W(v_j,v_i)}",[17,28743,28745,28812],{"className":28744,"ariaHidden":53},[66],[17,28746,28748,28751,28754,28757,28760,28800,28803,28806,28809],{"className":28747},[70],[17,28749],{"className":28750,"style":249},[74],[17,28752,17926],{"className":28753,"style":14790},[79,230],[17,28755,205],{"className":28756,"style":269},[79,230],[17,28758,841],{"className":28759},[253],[17,28761,28763,28766],{"className":28762},[79],[17,28764,793],{"className":28765,"style":818},[79,230],[17,28767,28769],{"className":28768},[1453],[17,28770,28772,28792],{"className":28771},[83,84],[17,28773,28775,28789],{"className":28774},[88],[17,28776,28778],{"className":28777,"style":11470},[92],[17,28779,28780,28783],{"style":1466},[17,28781],{"className":28782,"style":1470},[100],[17,28784,28786],{"className":28785},[1474,1475,1476,1477],[17,28787,11429],{"className":28788},[79,230,1477],[17,28790,136],{"className":28791},[135],[17,28793,28795],{"className":28794},[88],[17,28796,28798],{"className":28797,"style":1490},[92],[17,28799],{},[17,28801,850],{"className":28802},[282],[17,28804],{"className":28805,"style":235},[234],[17,28807,193],{"className":28808},[239],[17,28810],{"className":28811,"style":235},[234],[17,28813,28815,28818,28821,28824],{"className":28814},[70],[17,28816],{"className":28817,"style":11589},[74],[17,28819,28698],{"className":28820},[4973],[17,28822],{"className":28823,"style":265},[234],[17,28825,28827,28830,28833,28836,28876,28879,28882,28885,28888,28891,28894,28934,28937,28940,28980],{"className":28826},[79],[17,28828,17926],{"className":28829,"style":14790},[79,230],[17,28831,205],{"className":28832,"style":269},[79,230],[17,28834,841],{"className":28835},[253],[17,28837,28839,28842],{"className":28838},[79],[17,28840,793],{"className":28841,"style":818},[79,230],[17,28843,28845],{"className":28844},[1453],[17,28846,28848,28868],{"className":28847},[83,84],[17,28849,28851,28865],{"className":28850},[88],[17,28852,28854],{"className":28853,"style":11470},[92],[17,28855,28856,28859],{"style":1466},[17,28857],{"className":28858,"style":1470},[100],[17,28860,28862],{"className":28861},[1474,1475,1476,1477],[17,28863,11438],{"className":28864,"style":11528},[79,230,1477],[17,28866,136],{"className":28867},[135],[17,28869,28871],{"className":28870},[88],[17,28872,28874],{"className":28873,"style":11538},[92],[17,28875],{},[17,28877,850],{"className":28878},[282],[17,28880],{"className":28881,"style":257},[234],[17,28883,4149],{"className":28884},[997],[17,28886],{"className":28887,"style":257},[234],[17,28889,22906],{"className":28890,"style":14790},[79,230],[17,28892,841],{"className":28893},[253],[17,28895,28897,28900],{"className":28896},[79],[17,28898,793],{"className":28899,"style":818},[79,230],[17,28901,28903],{"className":28902},[1453],[17,28904,28906,28926],{"className":28905},[83,84],[17,28907,28909,28923],{"className":28908},[88],[17,28910,28912],{"className":28911,"style":11470},[92],[17,28913,28914,28917],{"style":1466},[17,28915],{"className":28916,"style":1470},[100],[17,28918,28920],{"className":28919},[1474,1475,1476,1477],[17,28921,11438],{"className":28922,"style":11528},[79,230,1477],[17,28924,136],{"className":28925},[135],[17,28927,28929],{"className":28928},[88],[17,28930,28932],{"className":28931,"style":11538},[92],[17,28933],{},[17,28935,202],{"className":28936},[261],[17,28938],{"className":28939,"style":265},[234],[17,28941,28943,28946],{"className":28942},[79],[17,28944,793],{"className":28945,"style":818},[79,230],[17,28947,28949],{"className":28948},[1453],[17,28950,28952,28972],{"className":28951},[83,84],[17,28953,28955,28969],{"className":28954},[88],[17,28956,28958],{"className":28957,"style":11470},[92],[17,28959,28960,28963],{"style":1466},[17,28961],{"className":28962,"style":1470},[100],[17,28964,28966],{"className":28965},[1474,1475,1476,1477],[17,28967,11429],{"className":28968},[79,230,1477],[17,28970,136],{"className":28971},[135],[17,28973,28975],{"className":28974},[88],[17,28976,28978],{"className":28977,"style":1490},[92],[17,28979],{},[17,28981,850],{"className":28982},[282],[13,28984,28985,28986,5835,29055,29124],{},"其中 ",[17,28987,28989,29006],{"className":28988},[24],[17,28990,28992],{"className":28991},[28],[30,28993,28994],{"xmlns":32},[35,28995,28996,29004],{},[38,28997,28998],{},[1385,28999,29000,29002],{},[187,29001,793],{},[187,29003,11438],{},[59,29005,11934],{"encoding":61},[17,29007,29009],{"className":29008,"ariaHidden":53},[66],[17,29010,29012,29015],{"className":29011},[70],[17,29013],{"className":29014,"style":11451},[74],[17,29016,29018,29021],{"className":29017},[79],[17,29019,793],{"className":29020,"style":818},[79,230],[17,29022,29024],{"className":29023},[1453],[17,29025,29027,29047],{"className":29026},[83,84],[17,29028,29030,29044],{"className":29029},[88],[17,29031,29033],{"className":29032,"style":11470},[92],[17,29034,29035,29038],{"style":1466},[17,29036],{"className":29037,"style":1470},[100],[17,29039,29041],{"className":29040},[1474,1475,1476,1477],[17,29042,11438],{"className":29043,"style":11528},[79,230,1477],[17,29045,136],{"className":29046},[135],[17,29048,29050],{"className":29049},[88],[17,29051,29053],{"className":29052,"style":11538},[92],[17,29054],{},[17,29056,29058,29075],{"className":29057},[24],[17,29059,29061],{"className":29060},[28],[30,29062,29063],{"xmlns":32},[35,29064,29065,29073],{},[38,29066,29067],{},[1385,29068,29069,29071],{},[187,29070,793],{},[187,29072,11429],{},[59,29074,12005],{"encoding":61},[17,29076,29078],{"className":29077,"ariaHidden":53},[66],[17,29079,29081,29084],{"className":29080},[70],[17,29082],{"className":29083,"style":2085},[74],[17,29085,29087,29090],{"className":29086},[79],[17,29088,793],{"className":29089,"style":818},[79,230],[17,29091,29093],{"className":29092},[1453],[17,29094,29096,29116],{"className":29095},[83,84],[17,29097,29099,29113],{"className":29098},[88],[17,29100,29102],{"className":29101,"style":11470},[92],[17,29103,29104,29107],{"style":1466},[17,29105],{"className":29106,"style":1470},[100],[17,29108,29110],{"className":29109},[1474,1475,1476,1477],[17,29111,11429],{"className":29112},[79,230,1477],[17,29114,136],{"className":29115},[135],[17,29117,29119],{"className":29118},[88],[17,29120,29122],{"className":29121,"style":1490},[92],[17,29123],{}," 的前驱顶点。",[506,29126],{},[513,29128,29130],{"id":29129},"_3-最迟完成时间","3. 最迟完成时间",[13,29132,28307,29133,29202],{},[17,29134,29136,29153],{"className":29135},[24],[17,29137,29139],{"className":29138},[28],[30,29140,29141],{"xmlns":32},[35,29142,29143,29151],{},[38,29144,29145],{},[1385,29146,29147,29149],{},[187,29148,793],{},[187,29150,11429],{},[59,29152,12005],{"encoding":61},[17,29154,29156],{"className":29155,"ariaHidden":53},[66],[17,29157,29159,29162],{"className":29158},[70],[17,29160],{"className":29161,"style":2085},[74],[17,29163,29165,29168],{"className":29164},[79],[17,29166,793],{"className":29167,"style":818},[79,230],[17,29169,29171],{"className":29170},[1453],[17,29172,29174,29194],{"className":29173},[83,84],[17,29175,29177,29191],{"className":29176},[88],[17,29178,29180],{"className":29179,"style":11470},[92],[17,29181,29182,29185],{"style":1466},[17,29183],{"className":29184,"style":1470},[100],[17,29186,29188],{"className":29187},[1474,1475,1476,1477],[17,29189,11429],{"className":29190},[79,230,1477],[17,29192,136],{"className":29193},[135],[17,29195,29197],{"className":29196},[88],[17,29198,29200],{"className":29199,"style":1490},[92],[17,29201],{}," 的最迟完成时间记作：",[17,29204,29206],{"className":29205},[20],[17,29207,29209,29236],{"className":29208},[24],[17,29210,29212],{"className":29211},[28],[30,29213,29214],{"xmlns":32,"display":33},[35,29215,29216,29233],{},[38,29217,29218,29220,29223,29225,29231],{},[187,29219,17926],{},[187,29221,29222],{},"L",[191,29224,841],{"stretchy":48},[1385,29226,29227,29229],{},[187,29228,793],{},[187,29230,11429],{},[191,29232,850],{"stretchy":48},[59,29234,29235],{"encoding":61},"TL(v_i)",[17,29237,29239],{"className":29238,"ariaHidden":53},[66],[17,29240,29242,29245,29248,29251,29254,29294],{"className":29241},[70],[17,29243],{"className":29244,"style":249},[74],[17,29246,17926],{"className":29247,"style":14790},[79,230],[17,29249,29222],{"className":29250},[79,230],[17,29252,841],{"className":29253},[253],[17,29255,29257,29260],{"className":29256},[79],[17,29258,793],{"className":29259,"style":818},[79,230],[17,29261,29263],{"className":29262},[1453],[17,29264,29266,29286],{"className":29265},[83,84],[17,29267,29269,29283],{"className":29268},[88],[17,29270,29272],{"className":29271,"style":11470},[92],[17,29273,29274,29277],{"style":1466},[17,29275],{"className":29276,"style":1470},[100],[17,29278,29280],{"className":29279},[1474,1475,1476,1477],[17,29281,11429],{"className":29282},[79,230,1477],[17,29284,136],{"className":29285},[135],[17,29287,29289],{"className":29288},[88],[17,29290,29292],{"className":29291,"style":1490},[92],[17,29293],{},[17,29295,850],{"className":29296},[282],[13,29298,29299,29300,29369],{},"表示在不延误总工期的情况下，事件 ",[17,29301,29303,29320],{"className":29302},[24],[17,29304,29306],{"className":29305},[28],[30,29307,29308],{"xmlns":32},[35,29309,29310,29318],{},[38,29311,29312],{},[1385,29313,29314,29316],{},[187,29315,793],{},[187,29317,11429],{},[59,29319,12005],{"encoding":61},[17,29321,29323],{"className":29322,"ariaHidden":53},[66],[17,29324,29326,29329],{"className":29325},[70],[17,29327],{"className":29328,"style":2085},[74],[17,29330,29332,29335],{"className":29331},[79],[17,29333,793],{"className":29334,"style":818},[79,230],[17,29336,29338],{"className":29337},[1453],[17,29339,29341,29361],{"className":29340},[83,84],[17,29342,29344,29358],{"className":29343},[88],[17,29345,29347],{"className":29346,"style":11470},[92],[17,29348,29349,29352],{"style":1466},[17,29350],{"className":29351,"style":1470},[100],[17,29353,29355],{"className":29354},[1474,1475,1476,1477],[17,29356,11429],{"className":29357},[79,230,1477],[17,29359,136],{"className":29360},[135],[17,29362,29364],{"className":29363},[88],[17,29365,29367],{"className":29366,"style":1490},[92],[17,29368],{}," 最晚什么时候必须发生。",[13,29371,29372],{},"终点：",[17,29374,29376],{"className":29375},[20],[17,29377,29379,29421],{"className":29378},[24],[17,29380,29382],{"className":29381},[28],[30,29383,29384],{"xmlns":32,"display":33},[35,29385,29386,29418],{},[38,29387,29388,29390,29392,29394,29400,29402,29404,29406,29408,29410,29416],{},[187,29389,17926],{},[187,29391,29222],{},[191,29393,841],{"stretchy":48},[1385,29395,29396,29398],{},[187,29397,793],{},[187,29399,3183],{},[191,29401,850],{"stretchy":48},[191,29403,193],{},[187,29405,17926],{},[187,29407,205],{},[191,29409,841],{"stretchy":48},[1385,29411,29412,29414],{},[187,29413,793],{},[187,29415,3183],{},[191,29417,850],{"stretchy":48},[59,29419,29420],{"encoding":61},"TL(v_n)=TE(v_n)",[17,29422,29424,29491],{"className":29423,"ariaHidden":53},[66],[17,29425,29427,29430,29433,29436,29439,29479,29482,29485,29488],{"className":29426},[70],[17,29428],{"className":29429,"style":249},[74],[17,29431,17926],{"className":29432,"style":14790},[79,230],[17,29434,29222],{"className":29435},[79,230],[17,29437,841],{"className":29438},[253],[17,29440,29442,29445],{"className":29441},[79],[17,29443,793],{"className":29444,"style":818},[79,230],[17,29446,29448],{"className":29447},[1453],[17,29449,29451,29471],{"className":29450},[83,84],[17,29452,29454,29468],{"className":29453},[88],[17,29455,29457],{"className":29456,"style":3253},[92],[17,29458,29459,29462],{"style":1466},[17,29460],{"className":29461,"style":1470},[100],[17,29463,29465],{"className":29464},[1474,1475,1476,1477],[17,29466,3183],{"className":29467},[79,230,1477],[17,29469,136],{"className":29470},[135],[17,29472,29474],{"className":29473},[88],[17,29475,29477],{"className":29476,"style":1490},[92],[17,29478],{},[17,29480,850],{"className":29481},[282],[17,29483],{"className":29484,"style":235},[234],[17,29486,193],{"className":29487},[239],[17,29489],{"className":29490,"style":235},[234],[17,29492,29494,29497,29500,29503,29506,29546],{"className":29493},[70],[17,29495],{"className":29496,"style":249},[74],[17,29498,17926],{"className":29499,"style":14790},[79,230],[17,29501,205],{"className":29502,"style":269},[79,230],[17,29504,841],{"className":29505},[253],[17,29507,29509,29512],{"className":29508},[79],[17,29510,793],{"className":29511,"style":818},[79,230],[17,29513,29515],{"className":29514},[1453],[17,29516,29518,29538],{"className":29517},[83,84],[17,29519,29521,29535],{"className":29520},[88],[17,29522,29524],{"className":29523,"style":3253},[92],[17,29525,29526,29529],{"style":1466},[17,29527],{"className":29528,"style":1470},[100],[17,29530,29532],{"className":29531},[1474,1475,1476,1477],[17,29533,3183],{"className":29534},[79,230,1477],[17,29536,136],{"className":29537},[135],[17,29539,29541],{"className":29540},[88],[17,29542,29544],{"className":29543,"style":1490},[92],[17,29545],{},[17,29547,850],{"className":29548},[282],[13,29550,28664],{},[17,29552,29554],{"className":29553},[20],[17,29555,29557,29627],{"className":29556},[24],[17,29558,29560],{"className":29559},[28],[30,29561,29562],{"xmlns":32,"display":33},[35,29563,29564,29624],{},[38,29565,29566,29568,29570,29572,29578,29580,29582,29584,29586],{},[187,29567,17926],{},[187,29569,29222],{},[191,29571,841],{"stretchy":48},[1385,29573,29574,29576],{},[187,29575,793],{},[187,29577,11429],{},[191,29579,850],{"stretchy":48},[191,29581,193],{},[187,29583,26549],{},[191,29585,26552],{},[38,29587,29588,29590,29592,29594,29600,29602,29604,29606,29608,29614,29616,29622],{},[187,29589,17926],{},[187,29591,29222],{},[191,29593,841],{"stretchy":48},[1385,29595,29596,29598],{},[187,29597,793],{},[187,29599,11438],{},[191,29601,850],{"stretchy":48},[191,29603,972],{},[187,29605,22906],{},[191,29607,841],{"stretchy":48},[1385,29609,29610,29612],{},[187,29611,793],{},[187,29613,11429],{},[191,29615,202],{"separator":53},[1385,29617,29618,29620],{},[187,29619,793],{},[187,29621,11438],{},[191,29623,850],{"stretchy":48},[59,29625,29626],{"encoding":61},"TL(v_i)=\\min{TL(v_j)-W(v_i,v_j)}",[17,29628,29630,29697],{"className":29629,"ariaHidden":53},[66],[17,29631,29633,29636,29639,29642,29645,29685,29688,29691,29694],{"className":29632},[70],[17,29634],{"className":29635,"style":249},[74],[17,29637,17926],{"className":29638,"style":14790},[79,230],[17,29640,29222],{"className":29641},[79,230],[17,29643,841],{"className":29644},[253],[17,29646,29648,29651],{"className":29647},[79],[17,29649,793],{"className":29650,"style":818},[79,230],[17,29652,29654],{"className":29653},[1453],[17,29655,29657,29677],{"className":29656},[83,84],[17,29658,29660,29674],{"className":29659},[88],[17,29661,29663],{"className":29662,"style":11470},[92],[17,29664,29665,29668],{"style":1466},[17,29666],{"className":29667,"style":1470},[100],[17,29669,29671],{"className":29670},[1474,1475,1476,1477],[17,29672,11429],{"className":29673},[79,230,1477],[17,29675,136],{"className":29676},[135],[17,29678,29680],{"className":29679},[88],[17,29681,29683],{"className":29682,"style":1490},[92],[17,29684],{},[17,29686,850],{"className":29687},[282],[17,29689],{"className":29690,"style":235},[234],[17,29692,193],{"className":29693},[239],[17,29695],{"className":29696,"style":235},[234],[17,29698,29700,29703,29706,29709],{"className":29699},[70],[17,29701],{"className":29702,"style":11589},[74],[17,29704,26549],{"className":29705},[4973],[17,29707],{"className":29708,"style":265},[234],[17,29710,29712,29715,29718,29721,29761,29764,29767,29770,29773,29776,29779,29819,29822,29825,29865],{"className":29711},[79],[17,29713,17926],{"className":29714,"style":14790},[79,230],[17,29716,29222],{"className":29717},[79,230],[17,29719,841],{"className":29720},[253],[17,29722,29724,29727],{"className":29723},[79],[17,29725,793],{"className":29726,"style":818},[79,230],[17,29728,29730],{"className":29729},[1453],[17,29731,29733,29753],{"className":29732},[83,84],[17,29734,29736,29750],{"className":29735},[88],[17,29737,29739],{"className":29738,"style":11470},[92],[17,29740,29741,29744],{"style":1466},[17,29742],{"className":29743,"style":1470},[100],[17,29745,29747],{"className":29746},[1474,1475,1476,1477],[17,29748,11438],{"className":29749,"style":11528},[79,230,1477],[17,29751,136],{"className":29752},[135],[17,29754,29756],{"className":29755},[88],[17,29757,29759],{"className":29758,"style":11538},[92],[17,29760],{},[17,29762,850],{"className":29763},[282],[17,29765],{"className":29766,"style":257},[234],[17,29768,972],{"className":29769},[997],[17,29771],{"className":29772,"style":257},[234],[17,29774,22906],{"className":29775,"style":14790},[79,230],[17,29777,841],{"className":29778},[253],[17,29780,29782,29785],{"className":29781},[79],[17,29783,793],{"className":29784,"style":818},[79,230],[17,29786,29788],{"className":29787},[1453],[17,29789,29791,29811],{"className":29790},[83,84],[17,29792,29794,29808],{"className":29793},[88],[17,29795,29797],{"className":29796,"style":11470},[92],[17,29798,29799,29802],{"style":1466},[17,29800],{"className":29801,"style":1470},[100],[17,29803,29805],{"className":29804},[1474,1475,1476,1477],[17,29806,11429],{"className":29807},[79,230,1477],[17,29809,136],{"className":29810},[135],[17,29812,29814],{"className":29813},[88],[17,29815,29817],{"className":29816,"style":1490},[92],[17,29818],{},[17,29820,202],{"className":29821},[261],[17,29823],{"className":29824,"style":265},[234],[17,29826,29828,29831],{"className":29827},[79],[17,29829,793],{"className":29830,"style":818},[79,230],[17,29832,29834],{"className":29833},[1453],[17,29835,29837,29857],{"className":29836},[83,84],[17,29838,29840,29854],{"className":29839},[88],[17,29841,29843],{"className":29842,"style":11470},[92],[17,29844,29845,29848],{"style":1466},[17,29846],{"className":29847,"style":1470},[100],[17,29849,29851],{"className":29850},[1474,1475,1476,1477],[17,29852,11438],{"className":29853,"style":11528},[79,230,1477],[17,29855,136],{"className":29856},[135],[17,29858,29860],{"className":29859},[88],[17,29861,29863],{"className":29862,"style":11538},[92],[17,29864],{},[17,29866,850],{"className":29867},[282],[13,29869,28985,29870,5835,29939,30008],{},[17,29871,29873,29890],{"className":29872},[24],[17,29874,29876],{"className":29875},[28],[30,29877,29878],{"xmlns":32},[35,29879,29880,29888],{},[38,29881,29882],{},[1385,29883,29884,29886],{},[187,29885,793],{},[187,29887,11438],{},[59,29889,11934],{"encoding":61},[17,29891,29893],{"className":29892,"ariaHidden":53},[66],[17,29894,29896,29899],{"className":29895},[70],[17,29897],{"className":29898,"style":11451},[74],[17,29900,29902,29905],{"className":29901},[79],[17,29903,793],{"className":29904,"style":818},[79,230],[17,29906,29908],{"className":29907},[1453],[17,29909,29911,29931],{"className":29910},[83,84],[17,29912,29914,29928],{"className":29913},[88],[17,29915,29917],{"className":29916,"style":11470},[92],[17,29918,29919,29922],{"style":1466},[17,29920],{"className":29921,"style":1470},[100],[17,29923,29925],{"className":29924},[1474,1475,1476,1477],[17,29926,11438],{"className":29927,"style":11528},[79,230,1477],[17,29929,136],{"className":29930},[135],[17,29932,29934],{"className":29933},[88],[17,29935,29937],{"className":29936,"style":11538},[92],[17,29938],{},[17,29940,29942,29959],{"className":29941},[24],[17,29943,29945],{"className":29944},[28],[30,29946,29947],{"xmlns":32},[35,29948,29949,29957],{},[38,29950,29951],{},[1385,29952,29953,29955],{},[187,29954,793],{},[187,29956,11429],{},[59,29958,12005],{"encoding":61},[17,29960,29962],{"className":29961,"ariaHidden":53},[66],[17,29963,29965,29968],{"className":29964},[70],[17,29966],{"className":29967,"style":2085},[74],[17,29969,29971,29974],{"className":29970},[79],[17,29972,793],{"className":29973,"style":818},[79,230],[17,29975,29977],{"className":29976},[1453],[17,29978,29980,30000],{"className":29979},[83,84],[17,29981,29983,29997],{"className":29982},[88],[17,29984,29986],{"className":29985,"style":11470},[92],[17,29987,29988,29991],{"style":1466},[17,29989],{"className":29990,"style":1470},[100],[17,29992,29994],{"className":29993},[1474,1475,1476,1477],[17,29995,11429],{"className":29996},[79,230,1477],[17,29998,136],{"className":29999},[135],[17,30001,30003],{"className":30002},[88],[17,30004,30006],{"className":30005,"style":1490},[92],[17,30007],{}," 的后继顶点。",[506,30010],{},[513,30012,30014],{"id":30013},"_4-关键路径","4. 关键路径",[13,30016,30017],{},"如果某条路径上的顶点都满足：",[17,30019,30021],{"className":30020},[20],[17,30022,30024,30058],{"className":30023},[24],[17,30025,30027],{"className":30026},[28],[30,30028,30029],{"xmlns":32,"display":33},[35,30030,30031,30055],{},[38,30032,30033,30035,30037,30039,30041,30043,30045,30047,30049,30051,30053],{},[187,30034,17926],{},[187,30036,205],{},[191,30038,841],{"stretchy":48},[187,30040,793],{},[191,30042,850],{"stretchy":48},[191,30044,193],{},[187,30046,17926],{},[187,30048,29222],{},[191,30050,841],{"stretchy":48},[187,30052,793],{},[191,30054,850],{"stretchy":48},[59,30056,30057],{"encoding":61},"TE(v)=TL(v)",[17,30059,30061,30091],{"className":30060,"ariaHidden":53},[66],[17,30062,30064,30067,30070,30073,30076,30079,30082,30085,30088],{"className":30063},[70],[17,30065],{"className":30066,"style":249},[74],[17,30068,17926],{"className":30069,"style":14790},[79,230],[17,30071,205],{"className":30072,"style":269},[79,230],[17,30074,841],{"className":30075},[253],[17,30077,793],{"className":30078,"style":818},[79,230],[17,30080,850],{"className":30081},[282],[17,30083],{"className":30084,"style":235},[234],[17,30086,193],{"className":30087},[239],[17,30089],{"className":30090,"style":235},[234],[17,30092,30094,30097,30100,30103,30106,30109],{"className":30093},[70],[17,30095],{"className":30096,"style":249},[74],[17,30098,17926],{"className":30099,"style":14790},[79,230],[17,30101,29222],{"className":30102},[79,230],[17,30104,841],{"className":30105},[253],[17,30107,793],{"className":30108,"style":818},[79,230],[17,30110,850],{"className":30111},[282],[13,30113,30114,30115,720],{},"则这条路径可能是",[645,30116,30117],{},"关键路径",[13,30119,30120],{},"关键路径的长度就是整个工程的最短完成时间。",[506,30122],{},[513,30124,30126],{"id":30125},"_5-关键路径的意义","5. 关键路径的意义",[13,30128,30129],{},"关键路径上的任务不能延误。",[13,30131,30132],{},"只要关键路径上任一任务延误，整个项目就会延误。",[13,30134,30135],{},"非关键路径上的任务通常有一定机动时间。",[506,30137],{},[10,30139,30140],{"id":30140},"第十二章核心公式总结",[287,30142,30143,30153],{},[290,30144,30145],{},[293,30146,30147,30150],{},[296,30148,30149],{},"知识点",[296,30151,30152],{},"公式 \u002F 结论",[303,30154,30155,30292,30365,30512,30520,30577,30612,30858,31102,31257,31502,31950],{},[293,30156,30157,30160],{},[308,30158,30159],{},"无向完全图边数",[308,30161,30162],{},[17,30163,30165,30195],{"className":30164},[24],[17,30166,30168],{"className":30167},[28],[30,30169,30170],{"xmlns":32},[35,30171,30172,30192],{},[38,30173,30174],{},[3304,30175,30176,30190],{},[38,30177,30178,30180,30182,30184,30186,30188],{},[187,30179,3183],{},[191,30181,841],{"stretchy":48},[187,30183,3183],{},[191,30185,972],{},[1390,30187,1392],{},[191,30189,850],{"stretchy":48},[1390,30191,1401],{},[59,30193,30194],{"encoding":61},"\\frac{n(n-1)}{2}",[17,30196,30198],{"className":30197,"ariaHidden":53},[66],[17,30199,30201,30205],{"className":30200},[70],[17,30202],{"className":30203,"style":30204},[74],"height:1.355em;vertical-align:-0.345em;",[17,30206,30208,30211,30289],{"className":30207},[79],[17,30209],{"className":30210},[253,3370],[17,30212,30214],{"className":30213},[3304],[17,30215,30217,30280],{"className":30216},[83,84],[17,30218,30220,30277],{"className":30219},[88],[17,30221,30224,30239,30247],{"className":30222,"style":30223},[92],"height:1.01em;",[17,30225,30227,30230],{"style":30226},"top:-2.655em;",[17,30228],{"className":30229,"style":3390},[100],[17,30231,30233],{"className":30232},[1474,1475,1476,1477],[17,30234,30236],{"className":30235},[79,1477],[17,30237,1401],{"className":30238},[79,1477],[17,30240,30241,30244],{"style":3399},[17,30242],{"className":30243,"style":3390},[100],[17,30245],{"className":30246,"style":3407},[3406],[17,30248,30250,30253],{"style":30249},"top:-3.485em;",[17,30251],{"className":30252,"style":3390},[100],[17,30254,30256],{"className":30255},[1474,1475,1476,1477],[17,30257,30259,30262,30265,30268,30271,30274],{"className":30258},[79,1477],[17,30260,3183],{"className":30261},[79,230,1477],[17,30263,841],{"className":30264},[253,1477],[17,30266,3183],{"className":30267},[79,230,1477],[17,30269,972],{"className":30270},[997,1477],[17,30272,1392],{"className":30273},[79,1477],[17,30275,850],{"className":30276},[282,1477],[17,30278,136],{"className":30279},[135],[17,30281,30283],{"className":30282},[88],[17,30284,30287],{"className":30285,"style":30286},[92],"height:0.345em;",[17,30288],{},[17,30290],{"className":30291},[282,3370],[293,30293,30294,30297],{},[308,30295,30296],{},"有向完全图边数",[308,30298,30299],{},[17,30300,30302,30326],{"className":30301},[24],[17,30303,30305],{"className":30304},[28],[30,30306,30307],{"xmlns":32},[35,30308,30309,30323],{},[38,30310,30311,30313,30315,30317,30319,30321],{},[187,30312,3183],{},[191,30314,841],{"stretchy":48},[187,30316,3183],{},[191,30318,972],{},[1390,30320,1392],{},[191,30322,850],{"stretchy":48},[59,30324,30325],{"encoding":61},"n(n-1)",[17,30327,30329,30353],{"className":30328,"ariaHidden":53},[66],[17,30330,30332,30335,30338,30341,30344,30347,30350],{"className":30331},[70],[17,30333],{"className":30334,"style":249},[74],[17,30336,3183],{"className":30337},[79,230],[17,30339,841],{"className":30340},[253],[17,30342,3183],{"className":30343},[79,230],[17,30345],{"className":30346,"style":257},[234],[17,30348,972],{"className":30349},[997],[17,30351],{"className":30352,"style":257},[234],[17,30354,30356,30359,30362],{"className":30355},[70],[17,30357],{"className":30358,"style":249},[74],[17,30360,1392],{"className":30361},[79],[17,30363,850],{"className":30364},[282],[293,30366,30367,30370],{},[308,30368,30369],{},"握手定理",[308,30371,30372],{},[17,30373,30375,30412],{"className":30374},[24],[17,30376,30378],{"className":30377},[28],[30,30379,30380],{"xmlns":32},[35,30381,30382,30410],{},[38,30383,30384,30396,30398,30400,30402,30404,30406,30408],{},[1385,30385,30386,30388],{},[191,30387,4905],{},[38,30389,30390,30392,30394],{},[187,30391,793],{},[191,30393,1891],{},[187,30395,199],{},[187,30397,3912],{},[191,30399,841],{"stretchy":48},[187,30401,793],{},[191,30403,850],{"stretchy":48},[191,30405,193],{},[1390,30407,1401],{},[187,30409,4859],{},[59,30411,5150],{"encoding":61},[17,30413,30415,30500],{"className":30414,"ariaHidden":53},[66],[17,30416,30418,30422,30476,30479,30482,30485,30488,30491,30494,30497],{"className":30417},[70],[17,30419],{"className":30420,"style":30421},[74],"height:1.0771em;vertical-align:-0.3271em;",[17,30423,30425,30430],{"className":30424},[4973],[17,30426,4905],{"className":30427,"style":30429},[4973,5018,30428],"small-op","position:relative;top:0em;",[17,30431,30433],{"className":30432},[1453],[17,30434,30436,30467],{"className":30435},[83,84],[17,30437,30439,30464],{"className":30438},[88],[17,30440,30443],{"className":30441,"style":30442},[92],"height:0.1786em;",[17,30444,30446,30449],{"style":30445},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[17,30447],{"className":30448,"style":1470},[100],[17,30450,30452],{"className":30451},[1474,1475,1476,1477],[17,30453,30455,30458,30461],{"className":30454},[79,1477],[17,30456,793],{"className":30457,"style":818},[79,230,1477],[17,30459,1891],{"className":30460},[239,1477],[17,30462,199],{"className":30463,"style":257},[79,230,1477],[17,30465,136],{"className":30466},[135],[17,30468,30470],{"className":30469},[88],[17,30471,30474],{"className":30472,"style":30473},[92],"height:0.3271em;",[17,30475],{},[17,30477],{"className":30478,"style":265},[234],[17,30480,3912],{"className":30481},[79,230],[17,30483,841],{"className":30484},[253],[17,30486,793],{"className":30487,"style":818},[79,230],[17,30489,850],{"className":30490},[282],[17,30492],{"className":30493,"style":235},[234],[17,30495,193],{"className":30496},[239],[17,30498],{"className":30499,"style":235},[234],[17,30501,30503,30506,30509],{"className":30502},[70],[17,30504],{"className":30505,"style":5244},[74],[17,30507,1401],{"className":30508},[79],[17,30510,4859],{"className":30511},[79,230],[293,30513,30514,30517],{},[308,30515,30516],{},"奇顶点个数",[308,30518,30519],{},"一定是偶数",[293,30521,30522,30525],{},[308,30523,30524],{},"基本路径最大长度",[308,30526,30527],{},[17,30528,30530,30547],{"className":30529},[24],[17,30531,30533],{"className":30532},[28],[30,30534,30535],{"xmlns":32},[35,30536,30537,30545],{},[38,30538,30539,30541,30543],{},[187,30540,3183],{},[191,30542,972],{},[1390,30544,1392],{},[59,30546,10849],{"encoding":61},[17,30548,30550,30568],{"className":30549,"ariaHidden":53},[66],[17,30551,30553,30556,30559,30562,30565],{"className":30552},[70],[17,30554],{"className":30555,"style":987},[74],[17,30557,3183],{"className":30558},[79,230],[17,30560],{"className":30561,"style":257},[234],[17,30563,972],{"className":30564},[997],[17,30566],{"className":30567,"style":257},[234],[17,30569,30571,30574],{"className":30570},[70],[17,30572],{"className":30573,"style":5244},[74],[17,30575,1392],{"className":30576},[79],[293,30578,30579,30582],{},[308,30580,30581],{},"基本循环最大长度",[308,30583,30584],{},[17,30585,30587,30600],{"className":30586},[24],[17,30588,30590],{"className":30589},[28],[30,30591,30592],{"xmlns":32},[35,30593,30594,30598],{},[38,30595,30596],{},[187,30597,3183],{},[59,30599,3183],{"encoding":61},[17,30601,30603],{"className":30602,"ariaHidden":53},[66],[17,30604,30606,30609],{"className":30605},[70],[17,30607],{"className":30608,"style":769},[74],[17,30610,3183],{"className":30611},[79,230],[293,30613,30614,30617],{},[308,30615,30616],{},"有向图出度",[308,30618,30619],{},[17,30620,30622,30668],{"className":30621},[24],[17,30623,30625],{"className":30624},[28],[30,30626,30627],{"xmlns":32},[35,30628,30629,30665],{},[38,30630,30631,30637,30639,30645,30647,30649,30655],{},[4143,30632,30633,30635],{},[187,30634,3912],{},[191,30636,4149],{},[191,30638,841],{"stretchy":48},[1385,30640,30641,30643],{},[187,30642,793],{},[187,30644,11429],{},[191,30646,850],{"stretchy":48},[191,30648,193],{},[1385,30650,30651,30653],{},[191,30652,4905],{},[187,30654,11438],{},[1385,30656,30657,30659],{},[187,30658,17049],{},[38,30660,30661,30663],{},[187,30662,11429],{},[187,30664,11438],{},[59,30666,30667],{"encoding":61},"d^+(v_i)=\\sum_j a_{ij}",[17,30669,30671,30763],{"className":30670,"ariaHidden":53},[66],[17,30672,30674,30678,30708,30711,30751,30754,30757,30760],{"className":30673},[70],[17,30675],{"className":30676,"style":30677},[74],"height:1.0213em;vertical-align:-0.25em;",[17,30679,30681,30684],{"className":30680},[79],[17,30682,3912],{"className":30683},[79,230],[17,30685,30687],{"className":30686},[1453],[17,30688,30690],{"className":30689},[83],[17,30691,30693],{"className":30692},[88],[17,30694,30697],{"className":30695,"style":30696},[92],"height:0.7713em;",[17,30698,30699,30702],{"style":5822},[17,30700],{"className":30701,"style":1470},[100],[17,30703,30705],{"className":30704},[1474,1475,1476,1477],[17,30706,4149],{"className":30707},[997,1477],[17,30709,841],{"className":30710},[253],[17,30712,30714,30717],{"className":30713},[79],[17,30715,793],{"className":30716,"style":818},[79,230],[17,30718,30720],{"className":30719},[1453],[17,30721,30723,30743],{"className":30722},[83,84],[17,30724,30726,30740],{"className":30725},[88],[17,30727,30729],{"className":30728,"style":11470},[92],[17,30730,30731,30734],{"style":1466},[17,30732],{"className":30733,"style":1470},[100],[17,30735,30737],{"className":30736},[1474,1475,1476,1477],[17,30738,11429],{"className":30739},[79,230,1477],[17,30741,136],{"className":30742},[135],[17,30744,30746],{"className":30745},[88],[17,30747,30749],{"className":30748,"style":1490},[92],[17,30750],{},[17,30752,850],{"className":30753},[282],[17,30755],{"className":30756,"style":235},[234],[17,30758,193],{"className":30759},[239],[17,30761],{"className":30762,"style":235},[234],[17,30764,30766,30770,30812,30815],{"className":30765},[70],[17,30767],{"className":30768,"style":30769},[74],"height:1.1858em;vertical-align:-0.4358em;",[17,30771,30773,30776],{"className":30772},[4973],[17,30774,4905],{"className":30775,"style":30429},[4973,5018,30428],[17,30777,30779],{"className":30778},[1453],[17,30780,30782,30803],{"className":30781},[83,84],[17,30783,30785,30800],{"className":30784},[88],[17,30786,30789],{"className":30787,"style":30788},[92],"height:0.162em;",[17,30790,30791,30794],{"style":30445},[17,30792],{"className":30793,"style":1470},[100],[17,30795,30797],{"className":30796},[1474,1475,1476,1477],[17,30798,11438],{"className":30799,"style":11528},[79,230,1477],[17,30801,136],{"className":30802},[135],[17,30804,30806],{"className":30805},[88],[17,30807,30810],{"className":30808,"style":30809},[92],"height:0.4358em;",[17,30811],{},[17,30813],{"className":30814,"style":265},[234],[17,30816,30818,30821],{"className":30817},[79],[17,30819,17049],{"className":30820},[79,230],[17,30822,30824],{"className":30823},[1453],[17,30825,30827,30850],{"className":30826},[83,84],[17,30828,30830,30847],{"className":30829},[88],[17,30831,30833],{"className":30832,"style":11470},[92],[17,30834,30835,30838],{"style":2106},[17,30836],{"className":30837,"style":1470},[100],[17,30839,30841],{"className":30840},[1474,1475,1476,1477],[17,30842,30844],{"className":30843},[79,1477],[17,30845,14842],{"className":30846,"style":11528},[79,230,1477],[17,30848,136],{"className":30849},[135],[17,30851,30853],{"className":30852},[88],[17,30854,30856],{"className":30855,"style":11538},[92],[17,30857],{},[293,30859,30860,30863],{},[308,30861,30862],{},"有向图入度",[308,30864,30865],{},[17,30866,30868,30914],{"className":30867},[24],[17,30869,30871],{"className":30870},[28],[30,30872,30873],{"xmlns":32},[35,30874,30875,30911],{},[38,30876,30877,30883,30885,30891,30893,30895,30901],{},[4143,30878,30879,30881],{},[187,30880,3912],{},[191,30882,972],{},[191,30884,841],{"stretchy":48},[1385,30886,30887,30889],{},[187,30888,793],{},[187,30890,11429],{},[191,30892,850],{"stretchy":48},[191,30894,193],{},[1385,30896,30897,30899],{},[191,30898,4905],{},[187,30900,11438],{},[1385,30902,30903,30905],{},[187,30904,17049],{},[38,30906,30907,30909],{},[187,30908,11438],{},[187,30910,11429],{},[59,30912,30913],{"encoding":61},"d^-(v_i)=\\sum_j a_{ji}",[17,30915,30917,31007],{"className":30916,"ariaHidden":53},[66],[17,30918,30920,30923,30952,30955,30995,30998,31001,31004],{"className":30919},[70],[17,30921],{"className":30922,"style":30677},[74],[17,30924,30926,30929],{"className":30925},[79],[17,30927,3912],{"className":30928},[79,230],[17,30930,30932],{"className":30931},[1453],[17,30933,30935],{"className":30934},[83],[17,30936,30938],{"className":30937},[88],[17,30939,30941],{"className":30940,"style":30696},[92],[17,30942,30943,30946],{"style":5822},[17,30944],{"className":30945,"style":1470},[100],[17,30947,30949],{"className":30948},[1474,1475,1476,1477],[17,30950,972],{"className":30951},[997,1477],[17,30953,841],{"className":30954},[253],[17,30956,30958,30961],{"className":30957},[79],[17,30959,793],{"className":30960,"style":818},[79,230],[17,30962,30964],{"className":30963},[1453],[17,30965,30967,30987],{"className":30966},[83,84],[17,30968,30970,30984],{"className":30969},[88],[17,30971,30973],{"className":30972,"style":11470},[92],[17,30974,30975,30978],{"style":1466},[17,30976],{"className":30977,"style":1470},[100],[17,30979,30981],{"className":30980},[1474,1475,1476,1477],[17,30982,11429],{"className":30983},[79,230,1477],[17,30985,136],{"className":30986},[135],[17,30988,30990],{"className":30989},[88],[17,30991,30993],{"className":30992,"style":1490},[92],[17,30994],{},[17,30996,850],{"className":30997},[282],[17,30999],{"className":31000,"style":235},[234],[17,31002,193],{"className":31003},[239],[17,31005],{"className":31006,"style":235},[234],[17,31008,31010,31013,31053,31056],{"className":31009},[70],[17,31011],{"className":31012,"style":30769},[74],[17,31014,31016,31019],{"className":31015},[4973],[17,31017,4905],{"className":31018,"style":30429},[4973,5018,30428],[17,31020,31022],{"className":31021},[1453],[17,31023,31025,31045],{"className":31024},[83,84],[17,31026,31028,31042],{"className":31027},[88],[17,31029,31031],{"className":31030,"style":30788},[92],[17,31032,31033,31036],{"style":30445},[17,31034],{"className":31035,"style":1470},[100],[17,31037,31039],{"className":31038},[1474,1475,1476,1477],[17,31040,11438],{"className":31041,"style":11528},[79,230,1477],[17,31043,136],{"className":31044},[135],[17,31046,31048],{"className":31047},[88],[17,31049,31051],{"className":31050,"style":30809},[92],[17,31052],{},[17,31054],{"className":31055,"style":265},[234],[17,31057,31059,31062],{"className":31058},[79],[17,31060,17049],{"className":31061},[79,230],[17,31063,31065],{"className":31064},[1453],[17,31066,31068,31094],{"className":31067},[83,84],[17,31069,31071,31091],{"className":31070},[88],[17,31072,31074],{"className":31073,"style":11470},[92],[17,31075,31076,31079],{"style":2106},[17,31077],{"className":31078,"style":1470},[100],[17,31080,31082],{"className":31081},[1474,1475,1476,1477],[17,31083,31085,31088],{"className":31084},[79,1477],[17,31086,11438],{"className":31087,"style":11528},[79,230,1477],[17,31089,11429],{"className":31090},[79,230,1477],[17,31092,136],{"className":31093},[135],[17,31095,31097],{"className":31096},[88],[17,31098,31100],{"className":31099,"style":11538},[92],[17,31101],{},[293,31103,31104,31107],{},[308,31105,31106],{},"邻接矩阵幂",[308,31108,31109,31227,31228,31256],{},[17,31110,31112,31142],{"className":31111},[24],[17,31113,31115],{"className":31114},[28],[30,31116,31117],{"xmlns":32},[35,31118,31119,31139],{},[38,31120,31121,31123,31129],{},[191,31122,841],{"stretchy":48},[4143,31124,31125,31127],{},[187,31126,17040],{},[187,31128,4859],{},[1385,31130,31131,31133],{},[191,31132,850],{"stretchy":48},[38,31134,31135,31137],{},[187,31136,11429],{},[187,31138,11438],{},[59,31140,31141],{"encoding":61},"(A^m)_{ij}",[17,31143,31145],{"className":31144,"ariaHidden":53},[66],[17,31146,31148,31151,31154,31184],{"className":31147},[70],[17,31149],{"className":31150,"style":11589},[74],[17,31152,841],{"className":31153},[253],[17,31155,31157,31160],{"className":31156},[79],[17,31158,17040],{"className":31159},[79,230],[17,31161,31163],{"className":31162},[1453],[17,31164,31166],{"className":31165},[83],[17,31167,31169],{"className":31168},[88],[17,31170,31173],{"className":31171,"style":31172},[92],"height:0.6644em;",[17,31174,31175,31178],{"style":5822},[17,31176],{"className":31177,"style":1470},[100],[17,31179,31181],{"className":31180},[1474,1475,1476,1477],[17,31182,4859],{"className":31183},[79,230,1477],[17,31185,31187,31190],{"className":31186},[282],[17,31188,850],{"className":31189},[282],[17,31191,31193],{"className":31192},[1453],[17,31194,31196,31219],{"className":31195},[83,84],[17,31197,31199,31216],{"className":31198},[88],[17,31200,31202],{"className":31201,"style":11470},[92],[17,31203,31204,31207],{"style":2106},[17,31205],{"className":31206,"style":1470},[100],[17,31208,31210],{"className":31209},[1474,1475,1476,1477],[17,31211,31213],{"className":31212},[79,1477],[17,31214,14842],{"className":31215,"style":11528},[79,230,1477],[17,31217,136],{"className":31218},[135],[17,31220,31222],{"className":31221},[88],[17,31223,31225],{"className":31224,"style":11538},[92],[17,31226],{}," 表示长度为 ",[17,31229,31231,31244],{"className":31230},[24],[17,31232,31234],{"className":31233},[28],[30,31235,31236],{"xmlns":32},[35,31237,31238,31242],{},[38,31239,31240],{},[187,31241,4859],{},[59,31243,4859],{"encoding":61},[17,31245,31247],{"className":31246,"ariaHidden":53},[66],[17,31248,31250,31253],{"className":31249},[70],[17,31251],{"className":31252,"style":769},[74],[17,31254,4859],{"className":31255},[79,230]," 的路径条数",[293,31258,31259,31262],{},[308,31260,31261],{},"可达矩阵",[308,31263,31264],{},[17,31265,31267,31324],{"className":31266},[24],[17,31268,31270],{"className":31269},[28],[30,31271,31272],{"xmlns":32},[35,31273,31274,31322],{},[38,31275,31276,31278,31280,31282,31284,31286,31288,31300,31302,31304,31306],{},[187,31277,19908],{},[191,31279,193],{},[187,31281,21012],{},[191,31283,21015],{},[187,31285,17040],{},[191,31287,21015],{},[4143,31289,31290,31292],{},[187,31291,17040],{},[38,31293,31294,31296,31298],{},[191,31295,841],{"stretchy":48},[1390,31297,1401],{},[191,31299,850],{"stretchy":48},[191,31301,21015],{},[191,31303,8934],{},[191,31305,21015],{},[4143,31307,31308,31310],{},[187,31309,17040],{},[38,31311,31312,31314,31316,31318,31320],{},[191,31313,841],{"stretchy":48},[187,31315,3183],{},[191,31317,972],{},[1390,31319,1392],{},[191,31321,850],{"stretchy":48},[59,31323,21056],{"encoding":61},[17,31325,31327,31345,31363,31381,31434,31452],{"className":31326,"ariaHidden":53},[66],[17,31328,31330,31333,31336,31339,31342],{"className":31329},[70],[17,31331],{"className":31332,"style":226},[74],[17,31334,19908],{"className":31335,"style":14790},[79,230],[17,31337],{"className":31338,"style":235},[234],[17,31340,193],{"className":31341},[239],[17,31343],{"className":31344,"style":235},[234],[17,31346,31348,31351,31354,31357,31360],{"className":31347},[70],[17,31349],{"className":31350,"style":226},[74],[17,31352,21012],{"className":31353,"style":21087},[79,230],[17,31355],{"className":31356,"style":257},[234],[17,31358,21015],{"className":31359},[997],[17,31361],{"className":31362,"style":257},[234],[17,31364,31366,31369,31372,31375,31378],{"className":31365},[70],[17,31367],{"className":31368,"style":226},[74],[17,31370,17040],{"className":31371},[79,230],[17,31373],{"className":31374,"style":257},[234],[17,31376,21015],{"className":31377},[997],[17,31379],{"className":31380,"style":257},[234],[17,31382,31384,31387,31425,31428,31431],{"className":31383},[70],[17,31385],{"className":31386,"style":21311},[74],[17,31388,31390,31393],{"className":31389},[79],[17,31391,17040],{"className":31392},[79,230],[17,31394,31396],{"className":31395},[1453],[17,31397,31399],{"className":31398},[83],[17,31400,31402],{"className":31401},[88],[17,31403,31405],{"className":31404,"style":21311},[92],[17,31406,31407,31410],{"style":5822},[17,31408],{"className":31409,"style":1470},[100],[17,31411,31413],{"className":31412},[1474,1475,1476,1477],[17,31414,31416,31419,31422],{"className":31415},[79,1477],[17,31417,841],{"className":31418},[253,1477],[17,31420,1401],{"className":31421},[79,1477],[17,31423,850],{"className":31424},[282,1477],[17,31426],{"className":31427,"style":257},[234],[17,31429,21015],{"className":31430},[997],[17,31432],{"className":31433,"style":257},[234],[17,31435,31437,31440,31443,31446,31449],{"className":31436},[70],[17,31438],{"className":31439,"style":21175},[74],[17,31441,8934],{"className":31442},[9183],[17,31444],{"className":31445,"style":257},[234],[17,31447,21015],{"className":31448},[997],[17,31450],{"className":31451,"style":257},[234],[17,31453,31455,31458],{"className":31454},[70],[17,31456],{"className":31457,"style":21311},[74],[17,31459,31461,31464],{"className":31460},[79],[17,31462,17040],{"className":31463},[79,230],[17,31465,31467],{"className":31466},[1453],[17,31468,31470],{"className":31469},[83],[17,31471,31473],{"className":31472},[88],[17,31474,31476],{"className":31475,"style":21311},[92],[17,31477,31478,31481],{"style":5822},[17,31479],{"className":31480,"style":1470},[100],[17,31482,31484],{"className":31483},[1474,1475,1476,1477],[17,31485,31487,31490,31493,31496,31499],{"className":31486},[79,1477],[17,31488,841],{"className":31489},[253,1477],[17,31491,3183],{"className":31492},[79,230,1477],[17,31494,972],{"className":31495},[997,1477],[17,31497,1392],{"className":31498},[79,1477],[17,31500,850],{"className":31501},[282,1477],[293,31503,31504,31507],{},[308,31505,31506],{},"Floyd 更新",[308,31508,31509],{},[17,31510,31512,31622],{"className":31511},[24],[17,31513,31515],{"className":31514},[28],[30,31516,31517],{"xmlns":32},[35,31518,31519,31619],{},[38,31520,31521,31539,31541,31543,31545,31547,31569,31571,31593,31595,31617],{},[3526,31522,31523,31525,31531],{},[187,31524,3912],{},[38,31526,31527,31529],{},[187,31528,11429],{},[187,31530,11438],{},[38,31532,31533,31535,31537],{},[191,31534,841],{"stretchy":48},[187,31536,4699],{},[191,31538,850],{"stretchy":48},[191,31540,193],{},[187,31542,26549],{},[191,31544,26552],{},[191,31546,841],{"stretchy":48},[3526,31548,31549,31551,31557],{},[187,31550,3912],{},[38,31552,31553,31555],{},[187,31554,11429],{},[187,31556,11438],{},[38,31558,31559,31561,31563,31565,31567],{},[191,31560,841],{"stretchy":48},[187,31562,4699],{},[191,31564,972],{},[1390,31566,1392],{},[191,31568,850],{"stretchy":48},[191,31570,202],{"separator":53},[3526,31572,31573,31575,31581],{},[187,31574,3912],{},[38,31576,31577,31579],{},[187,31578,11429],{},[187,31580,4699],{},[38,31582,31583,31585,31587,31589,31591],{},[191,31584,841],{"stretchy":48},[187,31586,4699],{},[191,31588,972],{},[1390,31590,1392],{},[191,31592,850],{"stretchy":48},[191,31594,4149],{},[3526,31596,31597,31599,31605],{},[187,31598,3912],{},[38,31600,31601,31603],{},[187,31602,4699],{},[187,31604,11438],{},[38,31606,31607,31609,31611,31613,31615],{},[191,31608,841],{"stretchy":48},[187,31610,4699],{},[191,31612,972],{},[1390,31614,1392],{},[191,31616,850],{"stretchy":48},[191,31618,850],{"stretchy":48},[59,31620,31621],{"encoding":61},"d_{ij}^{(k)}=\\min(d_{ij}^{(k-1)},d_{ik}^{(k-1)}+d_{kj}^{(k-1)})",[17,31623,31625,31703,31868],{"className":31624,"ariaHidden":53},[66],[17,31626,31628,31631,31694,31697,31700],{"className":31627},[70],[17,31629],{"className":31630,"style":25851},[74],[17,31632,31634,31637],{"className":31633},[79],[17,31635,3912],{"className":31636},[79,230],[17,31638,31640],{"className":31639},[1453],[17,31641,31643,31686],{"className":31642},[83,84],[17,31644,31646,31683],{"className":31645},[88],[17,31647,31649,31663],{"className":31648,"style":25873},[92],[17,31650,31651,31654],{"style":25876},[17,31652],{"className":31653,"style":1470},[100],[17,31655,31657],{"className":31656},[1474,1475,1476,1477],[17,31658,31660],{"className":31659},[79,1477],[17,31661,14842],{"className":31662,"style":11528},[79,230,1477],[17,31664,31665,31668],{"style":25891},[17,31666],{"className":31667,"style":1470},[100],[17,31669,31671],{"className":31670},[1474,1475,1476,1477],[17,31672,31674,31677,31680],{"className":31673},[79,1477],[17,31675,841],{"className":31676},[253,1477],[17,31678,4699],{"className":31679,"style":4715},[79,230,1477],[17,31681,850],{"className":31682},[282,1477],[17,31684,136],{"className":31685},[135],[17,31687,31689],{"className":31688},[88],[17,31690,31692],{"className":31691,"style":25919},[92],[17,31693],{},[17,31695],{"className":31696,"style":235},[234],[17,31698,193],{"className":31699},[239],[17,31701],{"className":31702,"style":235},[234],[17,31704,31706,31709,31712,31715,31784,31787,31790,31859,31862,31865],{"className":31705},[70],[17,31707],{"className":31708,"style":25851},[74],[17,31710,26549],{"className":31711},[4973],[17,31713,841],{"className":31714},[253],[17,31716,31718,31721],{"className":31717},[79],[17,31719,3912],{"className":31720},[79,230],[17,31722,31724],{"className":31723},[1453],[17,31725,31727,31776],{"className":31726},[83,84],[17,31728,31730,31773],{"className":31729},[88],[17,31731,31733,31747],{"className":31732,"style":25873},[92],[17,31734,31735,31738],{"style":25876},[17,31736],{"className":31737,"style":1470},[100],[17,31739,31741],{"className":31740},[1474,1475,1476,1477],[17,31742,31744],{"className":31743},[79,1477],[17,31745,14842],{"className":31746,"style":11528},[79,230,1477],[17,31748,31749,31752],{"style":25891},[17,31750],{"className":31751,"style":1470},[100],[17,31753,31755],{"className":31754},[1474,1475,1476,1477],[17,31756,31758,31761,31764,31767,31770],{"className":31757},[79,1477],[17,31759,841],{"className":31760},[253,1477],[17,31762,4699],{"className":31763,"style":4715},[79,230,1477],[17,31765,972],{"className":31766},[997,1477],[17,31768,1392],{"className":31769},[79,1477],[17,31771,850],{"className":31772},[282,1477],[17,31774,136],{"className":31775},[135],[17,31777,31779],{"className":31778},[88],[17,31780,31782],{"className":31781,"style":25919},[92],[17,31783],{},[17,31785,202],{"className":31786},[261],[17,31788],{"className":31789,"style":265},[234],[17,31791,31793,31796],{"className":31792},[79],[17,31794,3912],{"className":31795},[79,230],[17,31797,31799],{"className":31798},[1453],[17,31800,31802,31851],{"className":31801},[83,84],[17,31803,31805,31848],{"className":31804},[88],[17,31806,31808,31822],{"className":31807,"style":25873},[92],[17,31809,31810,31813],{"style":26858},[17,31811],{"className":31812,"style":1470},[100],[17,31814,31816],{"className":31815},[1474,1475,1476,1477],[17,31817,31819],{"className":31818},[79,1477],[17,31820,26871],{"className":31821,"style":4715},[79,230,1477],[17,31823,31824,31827],{"style":25891},[17,31825],{"className":31826,"style":1470},[100],[17,31828,31830],{"className":31829},[1474,1475,1476,1477],[17,31831,31833,31836,31839,31842,31845],{"className":31832},[79,1477],[17,31834,841],{"className":31835},[253,1477],[17,31837,4699],{"className":31838,"style":4715},[79,230,1477],[17,31840,972],{"className":31841},[997,1477],[17,31843,1392],{"className":31844},[79,1477],[17,31846,850],{"className":31847},[282,1477],[17,31849,136],{"className":31850},[135],[17,31852,31854],{"className":31853},[88],[17,31855,31857],{"className":31856,"style":26907},[92],[17,31858],{},[17,31860],{"className":31861,"style":257},[234],[17,31863,4149],{"className":31864},[997],[17,31866],{"className":31867,"style":257},[234],[17,31869,31871,31875,31947],{"className":31870},[70],[17,31872],{"className":31873,"style":31874},[74],"height:1.4822em;vertical-align:-0.4374em;",[17,31876,31878,31881],{"className":31877},[79],[17,31879,3912],{"className":31880},[79,230],[17,31882,31884],{"className":31883},[1453],[17,31885,31887,31939],{"className":31886},[83,84],[17,31888,31890,31936],{"className":31889},[88],[17,31891,31893,31910],{"className":31892,"style":25873},[92],[17,31894,31895,31898],{"style":26858},[17,31896],{"className":31897,"style":1470},[100],[17,31899,31901],{"className":31900},[1474,1475,1476,1477],[17,31902,31904,31907],{"className":31903},[79,1477],[17,31905,4699],{"className":31906,"style":4715},[79,230,1477],[17,31908,11438],{"className":31909,"style":11528},[79,230,1477],[17,31911,31912,31915],{"style":25891},[17,31913],{"className":31914,"style":1470},[100],[17,31916,31918],{"className":31917},[1474,1475,1476,1477],[17,31919,31921,31924,31927,31930,31933],{"className":31920},[79,1477],[17,31922,841],{"className":31923},[253,1477],[17,31925,4699],{"className":31926,"style":4715},[79,230,1477],[17,31928,972],{"className":31929},[997,1477],[17,31931,1392],{"className":31932},[79,1477],[17,31934,850],{"className":31935},[282,1477],[17,31937,136],{"className":31938},[135],[17,31940,31942],{"className":31941},[88],[17,31943,31945],{"className":31944,"style":26989},[92],[17,31946],{},[17,31948,850],{"className":31949},[282],[293,31951,31952,31955],{},[308,31953,31954],{},"路径权长",[308,31956,31957],{},[17,31958,31960,31996],{"className":31959},[24],[17,31961,31963],{"className":31962},[28],[30,31964,31965],{"xmlns":32},[35,31966,31967,31993],{},[38,31968,31969,31971,31973,31975,31977,31979,31981,31983,31985,31991],{},[187,31970,23189],{},[191,31972,841],{"stretchy":48},[187,31974,8899],{},[191,31976,850],{"stretchy":48},[191,31978,193],{},[191,31980,4905],{},[187,31982,22906],{},[191,31984,841],{"stretchy":48},[1385,31986,31987,31989],{},[187,31988,757],{},[187,31990,11429],{},[191,31992,850],{"stretchy":48},[59,31994,31995],{"encoding":61},"l(\\mu)=\\sum W(e_i)",[17,31997,31999,32026],{"className":31998,"ariaHidden":53},[66],[17,32000,32002,32005,32008,32011,32014,32017,32020,32023],{"className":32001},[70],[17,32003],{"className":32004,"style":249},[74],[17,32006,23189],{"className":32007,"style":23257},[79,230],[17,32009,841],{"className":32010},[253],[17,32012,8899],{"className":32013},[79,230],[17,32015,850],{"className":32016},[282],[17,32018],{"className":32019,"style":235},[234],[17,32021,193],{"className":32022},[239],[17,32024],{"className":32025,"style":235},[234],[17,32027,32029,32032,32035,32038,32041,32044,32084],{"className":32028},[70],[17,32030],{"className":32031,"style":249},[74],[17,32033,4905],{"className":32034,"style":30429},[4973,5018,30428],[17,32036],{"className":32037,"style":265},[234],[17,32039,22906],{"className":32040,"style":14790},[79,230],[17,32042,841],{"className":32043},[253],[17,32045,32047,32050],{"className":32046},[79],[17,32048,757],{"className":32049},[79,230],[17,32051,32053],{"className":32052},[1453],[17,32054,32056,32076],{"className":32055},[83,84],[17,32057,32059,32073],{"className":32058},[88],[17,32060,32062],{"className":32061,"style":11470},[92],[17,32063,32064,32067],{"style":2106},[17,32065],{"className":32066,"style":1470},[100],[17,32068,32070],{"className":32069},[1474,1475,1476,1477],[17,32071,11429],{"className":32072},[79,230,1477],[17,32074,136],{"className":32075},[135],[17,32077,32079],{"className":32078},[88],[17,32080,32082],{"className":32081,"style":1490},[92],[17,32083],{},[17,32085,850],{"className":32086},[282],[506,32088],{},[10,32090,32091],{"id":32091},"第十二章常考题型",[513,32093,32095],{"id":32094},"题型一判断图的类型","题型一：判断图的类型",[13,32097,32098],{},"常问：",[150,32100,32101,32104,32107,32110,32113,32116],{},[153,32102,32103],{},"是无向图还是有向图？",[153,32105,32106],{},"是简单图还是多重图？",[153,32108,32109],{},"有没有自环？",[153,32111,32112],{},"有没有重边？",[153,32114,32115],{},"是不是完全图？",[153,32117,32118],{},"是不是正则图？",[13,32120,32121],{},"口诀：",[17,32123,32125],{"className":32124},[20],[17,32126,32128,32151],{"className":32127},[24],[17,32129,32131],{"className":32130},[28],[30,32132,32133],{"xmlns":32,"display":33},[35,32134,32135,32148],{},[38,32136,32137],{},[41,32138,32139],{"notation":43},[45,32140,32141],{"scriptlevel":47,"displaystyle":48},[45,32142,32143],{"scriptlevel":47,"displaystyle":48},[45,32144,32145],{"scriptlevel":47,"displaystyle":53},[55,32146,32147],{},"简单图：无自环、无重边",[59,32149,32150],{"encoding":61},"\\boxed{\\text{简单图：无自环、无重边}}",[17,32152,32154],{"className":32153,"ariaHidden":53},[66],[17,32155,32157,32160],{"className":32156},[70],[17,32158],{"className":32159,"style":75},[74],[17,32161,32163],{"className":32162},[79],[17,32164,32166,32203],{"className":32165},[83,84],[17,32167,32169,32200],{"className":32168},[88],[17,32170,32172,32192],{"className":32171,"style":93},[92],[17,32173,32174,32177],{"style":96},[17,32175],{"className":32176,"style":101},[100],[17,32178,32180],{"className":32179},[105],[17,32181,32183],{"className":32182},[79],[17,32184,32186],{"className":32185},[79],[17,32187,32189],{"className":32188},[79,115],[17,32190,32147],{"className":32191},[79,119],[17,32193,32194,32197],{"style":122},[17,32195],{"className":32196,"style":101},[100],[17,32198],{"className":32199,"style":131},[129,130],[17,32201,136],{"className":32202},[135],[17,32204,32206],{"className":32205},[88],[17,32207,32209],{"className":32208,"style":143},[92],[17,32210],{},[17,32212,32214],{"className":32213},[20],[17,32215,32217,32240],{"className":32216},[24],[17,32218,32220],{"className":32219},[28],[30,32221,32222],{"xmlns":32,"display":33},[35,32223,32224,32237],{},[38,32225,32226],{},[41,32227,32228],{"notation":43},[45,32229,32230],{"scriptlevel":47,"displaystyle":48},[45,32231,32232],{"scriptlevel":47,"displaystyle":48},[45,32233,32234],{"scriptlevel":47,"displaystyle":53},[55,32235,32236],{},"完全图：任意两点都有边",[59,32238,32239],{"encoding":61},"\\boxed{\\text{完全图：任意两点都有边}}",[17,32241,32243],{"className":32242,"ariaHidden":53},[66],[17,32244,32246,32249],{"className":32245},[70],[17,32247],{"className":32248,"style":75},[74],[17,32250,32252],{"className":32251},[79],[17,32253,32255,32292],{"className":32254},[83,84],[17,32256,32258,32289],{"className":32257},[88],[17,32259,32261,32281],{"className":32260,"style":93},[92],[17,32262,32263,32266],{"style":96},[17,32264],{"className":32265,"style":101},[100],[17,32267,32269],{"className":32268},[105],[17,32270,32272],{"className":32271},[79],[17,32273,32275],{"className":32274},[79],[17,32276,32278],{"className":32277},[79,115],[17,32279,32236],{"className":32280},[79,119],[17,32282,32283,32286],{"style":122},[17,32284],{"className":32285,"style":101},[100],[17,32287],{"className":32288,"style":131},[129,130],[17,32290,136],{"className":32291},[135],[17,32293,32295],{"className":32294},[88],[17,32296,32298],{"className":32297,"style":143},[92],[17,32299],{},[506,32301],{},[513,32303,32305],{"id":32304},"题型二求顶点的度","题型二：求顶点的度",[13,32307,14730],{},[150,32309,32310,32313],{},[153,32311,32312],{},"普通边贡献 1；",[153,32314,32315],{},"自环贡献 2。",[13,32317,17022],{},[150,32319,32320,32323,32326],{},[153,32321,32322],{},"出边算出度；",[153,32324,32325],{},"入边算入度；",[153,32327,32328],{},"总度 = 出度 + 入度。",[506,32330],{},[513,32332,32334],{"id":32333},"题型三用握手定理判断图是否存在","题型三：用握手定理判断图是否存在",[13,32336,32337],{},"给出度数序列，问是否可能构成无向图。",[13,32339,32340],{},"先看：",[17,32342,32344],{"className":32343},[20],[17,32345,32347,32369],{"className":32346},[24],[17,32348,32350],{"className":32349},[28],[30,32351,32352],{"xmlns":32,"display":33},[35,32353,32354,32366],{},[38,32355,32356,32358,32360,32362,32364],{},[191,32357,4905],{},[187,32359,3912],{},[191,32361,841],{"stretchy":48},[187,32363,793],{},[191,32365,850],{"stretchy":48},[59,32367,32368],{"encoding":61},"\\sum d(v)",[17,32370,32372],{"className":32371,"ariaHidden":53},[66],[17,32373,32375,32379,32382,32385,32388,32391,32394],{"className":32374},[70],[17,32376],{"className":32377,"style":32378},[74],"height:1.6em;vertical-align:-0.55em;",[17,32380,4905],{"className":32381,"style":30429},[4973,5018,5019],[17,32383],{"className":32384,"style":265},[234],[17,32386,3912],{"className":32387},[79,230],[17,32389,841],{"className":32390},[253],[17,32392,793],{"className":32393,"style":818},[79,230],[17,32395,850],{"className":32396},[282],[13,32398,32399],{},"是否为偶数。",[13,32401,32402],{},"如果是奇数，必不可能。",[13,32404,32405],{},"还要看是否违反简单图条件，比如某个顶点度数超过：",[17,32407,32409],{"className":32408},[20],[17,32410,32412,32429],{"className":32411},[24],[17,32413,32415],{"className":32414},[28],[30,32416,32417],{"xmlns":32,"display":33},[35,32418,32419,32427],{},[38,32420,32421,32423,32425],{},[187,32422,3183],{},[191,32424,972],{},[1390,32426,1392],{},[59,32428,10849],{"encoding":61},[17,32430,32432,32450],{"className":32431,"ariaHidden":53},[66],[17,32433,32435,32438,32441,32444,32447],{"className":32434},[70],[17,32436],{"className":32437,"style":987},[74],[17,32439,3183],{"className":32440},[79,230],[17,32442],{"className":32443,"style":257},[234],[17,32445,972],{"className":32446},[997],[17,32448],{"className":32449,"style":257},[234],[17,32451,32453,32456],{"className":32452},[70],[17,32454],{"className":32455,"style":5244},[74],[17,32457,1392],{"className":32458},[79],[506,32460],{},[513,32462,32464],{"id":32463},"题型四判断子图","题型四：判断子图",[13,32466,32467],{},"要看：",[17,32469,32471],{"className":32470},[20],[17,32472,32474,32509],{"className":32473},[24],[17,32475,32477],{"className":32476},[28],[30,32478,32479],{"xmlns":32,"display":33},[35,32480,32481,32507],{},[38,32482,32483,32489,32491,32493,32495,32497,32503,32505],{},[4143,32484,32485,32487],{},[187,32486,199],{},[191,32488,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,32490,5629],{},[187,32492,199],{},[191,32494,202],{"separator":53},[234,32496],{"width":2053},[4143,32498,32499,32501],{},[187,32500,205],{},[191,32502,5401],{"mathvariant":2754,"lspace":5400,"rspace":5400},[191,32504,5629],{},[187,32506,205],{},[59,32508,5648],{"encoding":61},[17,32510,32512,32559,32618],{"className":32511,"ariaHidden":53},[66],[17,32513,32515,32518,32550,32553,32556],{"className":32514},[70],[17,32516],{"className":32517,"style":5658},[74],[17,32519,32521,32524],{"className":32520},[79],[17,32522,199],{"className":32523,"style":257},[79,230],[17,32525,32527],{"className":32526},[1453],[17,32528,32530],{"className":32529},[83],[17,32531,32533],{"className":32532},[88],[17,32534,32536],{"className":32535,"style":5498},[92],[17,32537,32538,32541],{"style":3601},[17,32539],{"className":32540,"style":1470},[100],[17,32542,32544],{"className":32543},[1474,1475,1476,1477],[17,32545,32547],{"className":32546},[79,1477],[17,32548,5401],{"className":32549},[79,1477],[17,32551],{"className":32552,"style":235},[234],[17,32554,5629],{"className":32555},[239],[17,32557],{"className":32558,"style":235},[234],[17,32560,32562,32565,32568,32571,32574,32577,32609,32612,32615],{"className":32561},[70],[17,32563],{"className":32564,"style":5706},[74],[17,32566,199],{"className":32567,"style":257},[79,230],[17,32569,202],{"className":32570},[261],[17,32572],{"className":32573,"style":2166},[234],[17,32575],{"className":32576,"style":265},[234],[17,32578,32580,32583],{"className":32579},[79],[17,32581,205],{"className":32582,"style":269},[79,230],[17,32584,32586],{"className":32585},[1453],[17,32587,32589],{"className":32588},[83],[17,32590,32592],{"className":32591},[88],[17,32593,32595],{"className":32594,"style":5498},[92],[17,32596,32597,32600],{"style":3601},[17,32598],{"className":32599,"style":1470},[100],[17,32601,32603],{"className":32602},[1474,1475,1476,1477],[17,32604,32606],{"className":32605},[79,1477],[17,32607,5401],{"className":32608},[79,1477],[17,32610],{"className":32611,"style":235},[234],[17,32613,5629],{"className":32614},[239],[17,32616],{"className":32617,"style":235},[234],[17,32619,32621,32624],{"className":32620},[70],[17,32622],{"className":32623,"style":226},[74],[17,32625,205],{"className":32626,"style":269},[79,230],[13,32628,32629],{},"生成子图看顶点是否全部保留。",[13,32631,32632],{},"导出子图看是否保留了对应的所有边。",[506,32634],{},[513,32636,32638],{"id":32637},"题型五判断图同构","题型五：判断图同构",[13,32640,32641],{},"先查：",[8696,32643,32644,32647,32650,32653,32656,32659],{},[153,32645,32646],{},"顶点数；",[153,32648,32649],{},"边数；",[153,32651,32652],{},"度数序列；",[153,32654,32655],{},"是否连通；",[153,32657,32658],{},"是否有自环、重边；",[153,32660,32661],{},"是否有三角形、孤立点、割点等结构。",[13,32663,32664],{},"如果这些不同，肯定不同构。",[13,32666,32667],{},"如果都相同，还要进一步找顶点对应关系。",[506,32669],{},[513,32671,32673],{"id":32672},"题型六判断连通性","题型六：判断连通性",[13,32675,32676],{},"无向图：",[17,32678,32680],{"className":32679},[20],[17,32681,32683,32713],{"className":32682},[24],[17,32684,32686],{"className":32685},[28],[30,32687,32688],{"xmlns":32,"display":33},[35,32689,32690,32710],{},[38,32691,32692],{},[41,32693,32694],{"notation":43},[45,32695,32696],{"scriptlevel":47,"displaystyle":48},[45,32697,32698],{"scriptlevel":47,"displaystyle":48},[45,32699,32700],{"scriptlevel":47,"displaystyle":53},[38,32701,32702,32705,32707],{},[55,32703,32704],{},"任意两点有路径",[191,32706,13906],{},[55,32708,32709],{},"连通",[59,32711,32712],{"encoding":61},"\\boxed{\\text{任意两点有路径} \\Rightarrow \\text{连通}}",[17,32714,32716],{"className":32715,"ariaHidden":53},[66],[17,32717,32719,32722],{"className":32718},[70],[17,32720],{"className":32721,"style":75},[74],[17,32723,32725],{"className":32724},[79],[17,32726,32728,32780],{"className":32727},[83,84],[17,32729,32731,32777],{"className":32730},[88],[17,32732,32734,32769],{"className":32733,"style":93},[92],[17,32735,32736,32739],{"style":96},[17,32737],{"className":32738,"style":101},[100],[17,32740,32742],{"className":32741},[105],[17,32743,32745],{"className":32744},[79],[17,32746,32748,32754,32757,32760,32763],{"className":32747},[79],[17,32749,32751],{"className":32750},[79,115],[17,32752,32704],{"className":32753},[79,119],[17,32755],{"className":32756,"style":235},[234],[17,32758,13906],{"className":32759},[239],[17,32761],{"className":32762,"style":235},[234],[17,32764,32766],{"className":32765},[79,115],[17,32767,32709],{"className":32768},[79,119],[17,32770,32771,32774],{"style":122},[17,32772],{"className":32773,"style":101},[100],[17,32775],{"className":32776,"style":131},[129,130],[17,32778,136],{"className":32779},[135],[17,32781,32783],{"className":32782},[88],[17,32784,32786],{"className":32785,"style":143},[92],[17,32787],{},[13,32789,32790],{},"有向图：",[17,32792,32794],{"className":32793},[20],[17,32795,32797,32828],{"className":32796},[24],[17,32798,32800],{"className":32799},[28],[30,32801,32802],{"xmlns":32,"display":33},[35,32803,32804,32826],{},[38,32805,32806],{},[41,32807,32808],{"notation":43},[45,32809,32810],{"scriptlevel":47,"displaystyle":48},[45,32811,32812],{"scriptlevel":47,"displaystyle":48},[45,32813,32814],{"scriptlevel":47,"displaystyle":53},[38,32815,32816,32818,32820,32822,32824],{},[55,32817,13903],{},[191,32819,13906],{},[55,32821,13909],{},[191,32823,13906],{},[55,32825,13914],{},[59,32827,13917],{"encoding":61},[17,32829,32831],{"className":32830,"ariaHidden":53},[66],[17,32832,32834,32837],{"className":32833},[70],[17,32835],{"className":32836,"style":75},[74],[17,32838,32840],{"className":32839},[79],[17,32841,32843,32910],{"className":32842},[83,84],[17,32844,32846,32907],{"className":32845},[88],[17,32847,32849,32899],{"className":32848,"style":93},[92],[17,32850,32851,32854],{"style":96},[17,32852],{"className":32853,"style":101},[100],[17,32855,32857],{"className":32856},[105],[17,32858,32860],{"className":32859},[79],[17,32861,32863,32869,32872,32875,32878,32884,32887,32890,32893],{"className":32862},[79],[17,32864,32866],{"className":32865},[79,115],[17,32867,13903],{"className":32868},[79,119],[17,32870],{"className":32871,"style":235},[234],[17,32873,13906],{"className":32874},[239],[17,32876],{"className":32877,"style":235},[234],[17,32879,32881],{"className":32880},[79,115],[17,32882,13909],{"className":32883},[79,119],[17,32885],{"className":32886,"style":235},[234],[17,32888,13906],{"className":32889},[239],[17,32891],{"className":32892,"style":235},[234],[17,32894,32896],{"className":32895},[79,115],[17,32897,13914],{"className":32898},[79,119],[17,32900,32901,32904],{"style":122},[17,32902],{"className":32903,"style":101},[100],[17,32905],{"className":32906,"style":131},[129,130],[17,32908,136],{"className":32909},[135],[17,32911,32913],{"className":32912},[88],[17,32914,32916],{"className":32915,"style":143},[92],[17,32917],{},[506,32919],{},[513,32921,32923],{"id":32922},"题型七求邻接矩阵关联矩阵","题型七：求邻接矩阵、关联矩阵",[13,32925,32926],{},"邻接矩阵：",[17,32928,32930],{"className":32929},[20],[17,32931,32933,32950],{"className":32932},[24],[17,32934,32936],{"className":32935},[28],[30,32937,32938],{"xmlns":32,"display":33},[35,32939,32940,32948],{},[38,32941,32942,32944,32946],{},[187,32943,3183],{},[191,32945,14680],{},[187,32947,3183],{},[59,32949,16981],{"encoding":61},[17,32951,32953,32971],{"className":32952,"ariaHidden":53},[66],[17,32954,32956,32959,32962,32965,32968],{"className":32955},[70],[17,32957],{"className":32958,"style":987},[74],[17,32960,3183],{"className":32961},[79,230],[17,32963],{"className":32964,"style":257},[234],[17,32966,14680],{"className":32967},[997],[17,32969],{"className":32970,"style":257},[234],[17,32972,32974,32977],{"className":32973},[70],[17,32975],{"className":32976,"style":769},[74],[17,32978,3183],{"className":32979},[79,230],[13,32981,32982],{},"表示顶点和顶点关系。",[13,32984,32985],{},"关联矩阵：",[17,32987,32989],{"className":32988},[20],[17,32990,32992,33009],{"className":32991},[24],[17,32993,32995],{"className":32994},[28],[30,32996,32997],{"xmlns":32,"display":33},[35,32998,32999,33007],{},[38,33000,33001,33003,33005],{},[187,33002,3183],{},[191,33004,14680],{},[187,33006,4859],{},[59,33008,14685],{"encoding":61},[17,33010,33012,33030],{"className":33011,"ariaHidden":53},[66],[17,33013,33015,33018,33021,33024,33027],{"className":33014},[70],[17,33016],{"className":33017,"style":987},[74],[17,33019,3183],{"className":33020},[79,230],[17,33022],{"className":33023,"style":257},[234],[17,33025,14680],{"className":33026},[997],[17,33028],{"className":33029,"style":257},[234],[17,33031,33033,33036],{"className":33032},[70],[17,33034],{"className":33035,"style":769},[74],[17,33037,4859],{"className":33038},[79,230],[13,33040,33041],{},"表示顶点和边关系。",[506,33043],{},[513,33045,33047],{"id":33046},"题型八用矩阵求路径条数","题型八：用矩阵求路径条数",[13,33049,33050],{},"如果题目问：",[13,33052,33053,33054,12578,33123,33192,33193,33221],{},"“从 ",[17,33055,33057,33074],{"className":33056},[24],[17,33058,33060],{"className":33059},[28],[30,33061,33062],{"xmlns":32},[35,33063,33064,33072],{},[38,33065,33066],{},[1385,33067,33068,33070],{},[187,33069,793],{},[187,33071,11429],{},[59,33073,12005],{"encoding":61},[17,33075,33077],{"className":33076,"ariaHidden":53},[66],[17,33078,33080,33083],{"className":33079},[70],[17,33081],{"className":33082,"style":2085},[74],[17,33084,33086,33089],{"className":33085},[79],[17,33087,793],{"className":33088,"style":818},[79,230],[17,33090,33092],{"className":33091},[1453],[17,33093,33095,33115],{"className":33094},[83,84],[17,33096,33098,33112],{"className":33097},[88],[17,33099,33101],{"className":33100,"style":11470},[92],[17,33102,33103,33106],{"style":1466},[17,33104],{"className":33105,"style":1470},[100],[17,33107,33109],{"className":33108},[1474,1475,1476,1477],[17,33110,11429],{"className":33111},[79,230,1477],[17,33113,136],{"className":33114},[135],[17,33116,33118],{"className":33117},[88],[17,33119,33121],{"className":33120,"style":1490},[92],[17,33122],{},[17,33124,33126,33143],{"className":33125},[24],[17,33127,33129],{"className":33128},[28],[30,33130,33131],{"xmlns":32},[35,33132,33133,33141],{},[38,33134,33135],{},[1385,33136,33137,33139],{},[187,33138,793],{},[187,33140,11438],{},[59,33142,11934],{"encoding":61},[17,33144,33146],{"className":33145,"ariaHidden":53},[66],[17,33147,33149,33152],{"className":33148},[70],[17,33150],{"className":33151,"style":11451},[74],[17,33153,33155,33158],{"className":33154},[79],[17,33156,793],{"className":33157,"style":818},[79,230],[17,33159,33161],{"className":33160},[1453],[17,33162,33164,33184],{"className":33163},[83,84],[17,33165,33167,33181],{"className":33166},[88],[17,33168,33170],{"className":33169,"style":11470},[92],[17,33171,33172,33175],{"style":1466},[17,33173],{"className":33174,"style":1470},[100],[17,33176,33178],{"className":33177},[1474,1475,1476,1477],[17,33179,11438],{"className":33180,"style":11528},[79,230,1477],[17,33182,136],{"className":33183},[135],[17,33185,33187],{"className":33186},[88],[17,33188,33190],{"className":33189,"style":11538},[92],[17,33191],{}," 长度为 ",[17,33194,33196,33209],{"className":33195},[24],[17,33197,33199],{"className":33198},[28],[30,33200,33201],{"xmlns":32},[35,33202,33203,33207],{},[38,33204,33205],{},[187,33206,4859],{},[59,33208,4859],{"encoding":61},[17,33210,33212],{"className":33211,"ariaHidden":53},[66],[17,33213,33215,33218],{"className":33214},[70],[17,33216],{"className":33217,"style":769},[74],[17,33219,4859],{"className":33220},[79,230]," 的路径有几条？”",[13,33223,33224],{},"就看：",[17,33226,33228],{"className":33227},[20],[17,33229,33231,33260],{"className":33230},[24],[17,33232,33234],{"className":33233},[28],[30,33235,33236],{"xmlns":32,"display":33},[35,33237,33238,33258],{},[38,33239,33240,33242,33248],{},[191,33241,841],{"stretchy":48},[4143,33243,33244,33246],{},[187,33245,17040],{},[187,33247,4859],{},[1385,33249,33250,33252],{},[191,33251,850],{"stretchy":48},[38,33253,33254,33256],{},[187,33255,11429],{},[187,33257,11438],{},[59,33259,31141],{"encoding":61},[17,33261,33263],{"className":33262,"ariaHidden":53},[66],[17,33264,33266,33269,33272,33301],{"className":33265},[70],[17,33267],{"className":33268,"style":11589},[74],[17,33270,841],{"className":33271},[253],[17,33273,33275,33278],{"className":33274},[79],[17,33276,17040],{"className":33277},[79,230],[17,33279,33281],{"className":33280},[1453],[17,33282,33284],{"className":33283},[83],[17,33285,33287],{"className":33286},[88],[17,33288,33290],{"className":33289,"style":19000},[92],[17,33291,33292,33295],{"style":3601},[17,33293],{"className":33294,"style":1470},[100],[17,33296,33298],{"className":33297},[1474,1475,1476,1477],[17,33299,4859],{"className":33300},[79,230,1477],[17,33302,33304,33307],{"className":33303},[282],[17,33305,850],{"className":33306},[282],[17,33308,33310],{"className":33309},[1453],[17,33311,33313,33336],{"className":33312},[83,84],[17,33314,33316,33333],{"className":33315},[88],[17,33317,33319],{"className":33318,"style":11470},[92],[17,33320,33321,33324],{"style":2106},[17,33322],{"className":33323,"style":1470},[100],[17,33325,33327],{"className":33326},[1474,1475,1476,1477],[17,33328,33330],{"className":33329},[79,1477],[17,33331,14842],{"className":33332,"style":11528},[79,230,1477],[17,33334,136],{"className":33335},[135],[17,33337,33339],{"className":33338},[88],[17,33340,33342],{"className":33341,"style":11538},[92],[17,33343],{},[506,33345],{},[513,33347,33349],{"id":33348},"题型九求可达矩阵","题型九：求可达矩阵",[13,33351,33352],{},"用：",[17,33354,33356],{"className":33355},[20],[17,33357,33359,33416],{"className":33358},[24],[17,33360,33362],{"className":33361},[28],[30,33363,33364],{"xmlns":32,"display":33},[35,33365,33366,33414],{},[38,33367,33368,33370,33372,33374,33376,33378,33380,33392,33394,33396,33398],{},[187,33369,19908],{},[191,33371,193],{},[187,33373,21012],{},[191,33375,21015],{},[187,33377,17040],{},[191,33379,21015],{},[4143,33381,33382,33384],{},[187,33383,17040],{},[38,33385,33386,33388,33390],{},[191,33387,841],{"stretchy":48},[1390,33389,1401],{},[191,33391,850],{"stretchy":48},[191,33393,21015],{},[191,33395,8934],{},[191,33397,21015],{},[4143,33399,33400,33402],{},[187,33401,17040],{},[38,33403,33404,33406,33408,33410,33412],{},[191,33405,841],{"stretchy":48},[187,33407,3183],{},[191,33409,972],{},[1390,33411,1392],{},[191,33413,850],{"stretchy":48},[59,33415,21056],{"encoding":61},[17,33417,33419,33437,33455,33473,33526,33544],{"className":33418,"ariaHidden":53},[66],[17,33420,33422,33425,33428,33431,33434],{"className":33421},[70],[17,33423],{"className":33424,"style":226},[74],[17,33426,19908],{"className":33427,"style":14790},[79,230],[17,33429],{"className":33430,"style":235},[234],[17,33432,193],{"className":33433},[239],[17,33435],{"className":33436,"style":235},[234],[17,33438,33440,33443,33446,33449,33452],{"className":33439},[70],[17,33441],{"className":33442,"style":226},[74],[17,33444,21012],{"className":33445,"style":21087},[79,230],[17,33447],{"className":33448,"style":257},[234],[17,33450,21015],{"className":33451},[997],[17,33453],{"className":33454,"style":257},[234],[17,33456,33458,33461,33464,33467,33470],{"className":33457},[70],[17,33459],{"className":33460,"style":226},[74],[17,33462,17040],{"className":33463},[79,230],[17,33465],{"className":33466,"style":257},[234],[17,33468,21015],{"className":33469},[997],[17,33471],{"className":33472,"style":257},[234],[17,33474,33476,33479,33517,33520,33523],{"className":33475},[70],[17,33477],{"className":33478,"style":21121},[74],[17,33480,33482,33485],{"className":33481},[79],[17,33483,17040],{"className":33484},[79,230],[17,33486,33488],{"className":33487},[1453],[17,33489,33491],{"className":33490},[83],[17,33492,33494],{"className":33493},[88],[17,33495,33497],{"className":33496,"style":21121},[92],[17,33498,33499,33502],{"style":3601},[17,33500],{"className":33501,"style":1470},[100],[17,33503,33505],{"className":33504},[1474,1475,1476,1477],[17,33506,33508,33511,33514],{"className":33507},[79,1477],[17,33509,841],{"className":33510},[253,1477],[17,33512,1401],{"className":33513},[79,1477],[17,33515,850],{"className":33516},[282,1477],[17,33518],{"className":33519,"style":257},[234],[17,33521,21015],{"className":33522},[997],[17,33524],{"className":33525,"style":257},[234],[17,33527,33529,33532,33535,33538,33541],{"className":33528},[70],[17,33530],{"className":33531,"style":21175},[74],[17,33533,8934],{"className":33534},[9183],[17,33536],{"className":33537,"style":257},[234],[17,33539,21015],{"className":33540},[997],[17,33542],{"className":33543,"style":257},[234],[17,33545,33547,33550],{"className":33546},[70],[17,33548],{"className":33549,"style":21121},[74],[17,33551,33553,33556],{"className":33552},[79],[17,33554,17040],{"className":33555},[79,230],[17,33557,33559],{"className":33558},[1453],[17,33560,33562],{"className":33561},[83],[17,33563,33565],{"className":33564},[88],[17,33566,33568],{"className":33567,"style":21121},[92],[17,33569,33570,33573],{"style":3601},[17,33571],{"className":33572,"style":1470},[100],[17,33574,33576],{"className":33575},[1474,1475,1476,1477],[17,33577,33579,33582,33585,33588,33591],{"className":33578},[79,1477],[17,33580,841],{"className":33581},[253,1477],[17,33583,3183],{"className":33584},[79,230,1477],[17,33586,972],{"className":33587},[997,1477],[17,33589,1392],{"className":33590},[79,1477],[17,33592,850],{"className":33593},[282,1477],[13,33595,33596],{},"或用 Warshall 类方法。",[506,33598],{},[513,33600,33602],{"id":33601},"题型十最短路径","题型十：最短路径",[13,33604,33605],{},"单源最短路径：",[17,33607,33609],{"className":33608},[20],[17,33610,33612,33634],{"className":33611},[24],[17,33613,33615],{"className":33614},[28],[30,33616,33617],{"xmlns":32,"display":33},[35,33618,33619,33631],{},[38,33620,33621],{},[41,33622,33623],{"notation":43},[45,33624,33625],{"scriptlevel":47,"displaystyle":48},[45,33626,33627],{"scriptlevel":47,"displaystyle":48},[45,33628,33629],{"scriptlevel":47,"displaystyle":53},[55,33630,27388],{},[59,33632,33633],{"encoding":61},"\\boxed{\\text{Dijkstra}}",[17,33635,33637],{"className":33636,"ariaHidden":53},[66],[17,33638,33640,33643],{"className":33639},[70],[17,33641],{"className":33642,"style":27441},[74],[17,33644,33646],{"className":33645},[79],[17,33647,33649,33686],{"className":33648},[83,84],[17,33650,33652,33683],{"className":33651},[88],[17,33653,33655,33675],{"className":33654,"style":9663},[92],[17,33656,33657,33660],{"style":27456},[17,33658],{"className":33659,"style":27460},[100],[17,33661,33663],{"className":33662},[105],[17,33664,33666],{"className":33665},[79],[17,33667,33669],{"className":33668},[79],[17,33670,33672],{"className":33671},[79,115],[17,33673,27388],{"className":33674},[79],[17,33676,33677,33680],{"style":9685},[17,33678],{"className":33679,"style":27460},[100],[17,33681],{"className":33682,"style":27497},[129,130],[17,33684,136],{"className":33685},[135],[17,33687,33689],{"className":33688},[88],[17,33690,33692],{"className":33691,"style":16629},[92],[17,33693],{},[13,33695,33696],{},"任意两点最短路径：",[17,33698,33700],{"className":33699},[20],[17,33701,33703,33725],{"className":33702},[24],[17,33704,33706],{"className":33705},[28],[30,33707,33708],{"xmlns":32,"display":33},[35,33709,33710,33722],{},[38,33711,33712],{},[41,33713,33714],{"notation":43},[45,33715,33716],{"scriptlevel":47,"displaystyle":48},[45,33717,33718],{"scriptlevel":47,"displaystyle":48},[45,33719,33720],{"scriptlevel":47,"displaystyle":53},[55,33721,27396],{},[59,33723,33724],{"encoding":61},"\\boxed{\\text{Floyd}}",[17,33726,33728],{"className":33727,"ariaHidden":53},[66],[17,33729,33731,33734],{"className":33730},[70],[17,33732],{"className":33733,"style":27441},[74],[17,33735,33737],{"className":33736},[79],[17,33738,33740,33777],{"className":33739},[83,84],[17,33741,33743,33774],{"className":33742},[88],[17,33744,33746,33766],{"className":33745,"style":9663},[92],[17,33747,33748,33751],{"style":27456},[17,33749],{"className":33750,"style":27460},[100],[17,33752,33754],{"className":33753},[105],[17,33755,33757],{"className":33756},[79],[17,33758,33760],{"className":33759},[79],[17,33761,33763],{"className":33762},[79,115],[17,33764,27396],{"className":33765},[79],[17,33767,33768,33771],{"style":9685},[17,33769],{"className":33770,"style":27460},[100],[17,33772],{"className":33773,"style":27497},[129,130],[17,33775,136],{"className":33776},[135],[17,33778,33780],{"className":33779},[88],[17,33781,33783],{"className":33782,"style":16629},[92],[17,33784],{},[506,33786],{},[10,33788,33789],{"id":33789},"最容易混的点",[513,33791,33793],{"id":33792},"_1-路径简单路径基本路径","1. 路径、简单路径、基本路径",[287,33795,33796,33806],{},[290,33797,33798],{},[293,33799,33800,33803],{},[296,33801,33802],{},"名称",[296,33804,33805],{},"要求",[303,33807,33808,33816,33823],{},[293,33809,33810,33813],{},[308,33811,33812],{},"路径",[308,33814,33815],{},"可以重复边、重复点",[293,33817,33818,33820],{},[308,33819,10193],{},[308,33821,33822],{},"边不重复",[293,33824,33825,33827],{},[308,33826,10208],{},[308,33828,33829],{},"顶点不重复",[13,33831,33832],{},"所以：",[17,33834,33836],{"className":33835},[20],[17,33837,33839,33862],{"className":33838},[24],[17,33840,33842],{"className":33841},[28],[30,33843,33844],{"xmlns":32,"display":33},[35,33845,33846,33859],{},[38,33847,33848],{},[41,33849,33850],{"notation":43},[45,33851,33852],{"scriptlevel":47,"displaystyle":48},[45,33853,33854],{"scriptlevel":47,"displaystyle":48},[45,33855,33856],{"scriptlevel":47,"displaystyle":53},[55,33857,33858],{},"基本路径一定是简单路径，反之不一定",[59,33860,33861],{"encoding":61},"\\boxed{\\text{基本路径一定是简单路径，反之不一定}}",[17,33863,33865],{"className":33864,"ariaHidden":53},[66],[17,33866,33868,33871],{"className":33867},[70],[17,33869],{"className":33870,"style":75},[74],[17,33872,33874],{"className":33873},[79],[17,33875,33877,33914],{"className":33876},[83,84],[17,33878,33880,33911],{"className":33879},[88],[17,33881,33883,33903],{"className":33882,"style":93},[92],[17,33884,33885,33888],{"style":96},[17,33886],{"className":33887,"style":101},[100],[17,33889,33891],{"className":33890},[105],[17,33892,33894],{"className":33893},[79],[17,33895,33897],{"className":33896},[79],[17,33898,33900],{"className":33899},[79,115],[17,33901,33858],{"className":33902},[79,119],[17,33904,33905,33908],{"style":122},[17,33906],{"className":33907,"style":101},[100],[17,33909],{"className":33910,"style":131},[129,130],[17,33912,136],{"className":33913},[135],[17,33915,33917],{"className":33916},[88],[17,33918,33920],{"className":33919,"style":143},[92],[17,33921],{},[506,33923],{},[513,33925,33927],{"id":33926},"_2-循环简单循环基本循环","2. 循环、简单循环、基本循环",[287,33929,33930,33938],{},[290,33931,33932],{},[293,33933,33934,33936],{},[296,33935,33802],{},[296,33937,33805],{},[303,33939,33940,33947,33953],{},[293,33941,33942,33944],{},[308,33943,10458],{},[308,33945,33946],{},"起点终点相同",[293,33948,33949,33951],{},[308,33950,10473],{},[308,33952,33822],{},[293,33954,33955,33957],{},[308,33956,10485],{},[308,33958,33959],{},"除起点终点外，顶点不重复",[506,33961],{},[513,33963,33965],{"id":33964},"_3-强连通单向连通弱连通","3. 强连通、单向连通、弱连通",[17,33967,33969],{"className":33968},[20],[17,33970,33972,33995],{"className":33971},[24],[17,33973,33975],{"className":33974},[28],[30,33976,33977],{"xmlns":32,"display":33},[35,33978,33979,33992],{},[38,33980,33981],{},[41,33982,33983],{"notation":43},[45,33984,33985],{"scriptlevel":47,"displaystyle":48},[45,33986,33987],{"scriptlevel":47,"displaystyle":48},[45,33988,33989],{"scriptlevel":47,"displaystyle":53},[55,33990,33991],{},"强：双向可达",[59,33993,33994],{"encoding":61},"\\boxed{\\text{强：双向可达}}",[17,33996,33998],{"className":33997,"ariaHidden":53},[66],[17,33999,34001,34004],{"className":34000},[70],[17,34002],{"className":34003,"style":75},[74],[17,34005,34007],{"className":34006},[79],[17,34008,34010,34047],{"className":34009},[83,84],[17,34011,34013,34044],{"className":34012},[88],[17,34014,34016,34036],{"className":34015,"style":93},[92],[17,34017,34018,34021],{"style":96},[17,34019],{"className":34020,"style":101},[100],[17,34022,34024],{"className":34023},[105],[17,34025,34027],{"className":34026},[79],[17,34028,34030],{"className":34029},[79],[17,34031,34033],{"className":34032},[79,115],[17,34034,33991],{"className":34035},[79,119],[17,34037,34038,34041],{"style":122},[17,34039],{"className":34040,"style":101},[100],[17,34042],{"className":34043,"style":131},[129,130],[17,34045,136],{"className":34046},[135],[17,34048,34050],{"className":34049},[88],[17,34051,34053],{"className":34052,"style":143},[92],[17,34054],{},[17,34056,34058],{"className":34057},[20],[17,34059,34061,34084],{"className":34060},[24],[17,34062,34064],{"className":34063},[28],[30,34065,34066],{"xmlns":32,"display":33},[35,34067,34068,34081],{},[38,34069,34070],{},[41,34071,34072],{"notation":43},[45,34073,34074],{"scriptlevel":47,"displaystyle":48},[45,34075,34076],{"scriptlevel":47,"displaystyle":48},[45,34077,34078],{"scriptlevel":47,"displaystyle":53},[55,34079,34080],{},"单向：至少一个方向可达",[59,34082,34083],{"encoding":61},"\\boxed{\\text{单向：至少一个方向可达}}",[17,34085,34087],{"className":34086,"ariaHidden":53},[66],[17,34088,34090,34093],{"className":34089},[70],[17,34091],{"className":34092,"style":75},[74],[17,34094,34096],{"className":34095},[79],[17,34097,34099,34136],{"className":34098},[83,84],[17,34100,34102,34133],{"className":34101},[88],[17,34103,34105,34125],{"className":34104,"style":93},[92],[17,34106,34107,34110],{"style":96},[17,34108],{"className":34109,"style":101},[100],[17,34111,34113],{"className":34112},[105],[17,34114,34116],{"className":34115},[79],[17,34117,34119],{"className":34118},[79],[17,34120,34122],{"className":34121},[79,115],[17,34123,34080],{"className":34124},[79,119],[17,34126,34127,34130],{"style":122},[17,34128],{"className":34129,"style":101},[100],[17,34131],{"className":34132,"style":131},[129,130],[17,34134,136],{"className":34135},[135],[17,34137,34139],{"className":34138},[88],[17,34140,34142],{"className":34141,"style":143},[92],[17,34143],{},[17,34145,34147],{"className":34146},[20],[17,34148,34150,34173],{"className":34149},[24],[17,34151,34153],{"className":34152},[28],[30,34154,34155],{"xmlns":32,"display":33},[35,34156,34157,34170],{},[38,34158,34159],{},[41,34160,34161],{"notation":43},[45,34162,34163],{"scriptlevel":47,"displaystyle":48},[45,34164,34165],{"scriptlevel":47,"displaystyle":48},[45,34166,34167],{"scriptlevel":47,"displaystyle":53},[55,34168,34169],{},"弱：去掉方向后连通",[59,34171,34172],{"encoding":61},"\\boxed{\\text{弱：去掉方向后连通}}",[17,34174,34176],{"className":34175,"ariaHidden":53},[66],[17,34177,34179,34182],{"className":34178},[70],[17,34180],{"className":34181,"style":75},[74],[17,34183,34185],{"className":34184},[79],[17,34186,34188,34225],{"className":34187},[83,84],[17,34189,34191,34222],{"className":34190},[88],[17,34192,34194,34214],{"className":34193,"style":93},[92],[17,34195,34196,34199],{"style":96},[17,34197],{"className":34198,"style":101},[100],[17,34200,34202],{"className":34201},[105],[17,34203,34205],{"className":34204},[79],[17,34206,34208],{"className":34207},[79],[17,34209,34211],{"className":34210},[79,115],[17,34212,34169],{"className":34213},[79,119],[17,34215,34216,34219],{"style":122},[17,34217],{"className":34218,"style":101},[100],[17,34220],{"className":34221,"style":131},[129,130],[17,34223,136],{"className":34224},[135],[17,34226,34228],{"className":34227},[88],[17,34229,34231],{"className":34230,"style":143},[92],[17,34232],{},[506,34234],{},[513,34236,34238],{"id":34237},"_4-关联矩阵和邻接矩阵","4. 关联矩阵和邻接矩阵",[287,34240,34241,34257],{},[290,34242,34243],{},[293,34244,34245,34248,34251,34254],{},[296,34246,34247],{},"矩阵",[296,34249,34250],{},"行",[296,34252,34253],{},"列",[296,34255,34256],{},"表示",[303,34258,34259,34271],{},[293,34260,34261,34264,34266,34268],{},[308,34262,34263],{},"关联矩阵",[308,34265,647],{},[308,34267,682],{},[308,34269,34270],{},"顶点与边是否关联",[293,34272,34273,34276,34278,34280],{},[308,34274,34275],{},"邻接矩阵",[308,34277,647],{},[308,34279,647],{},[308,34281,34282],{},"顶点之间是否有边",[506,34284],{},[513,34286,34288],{"id":34287},"_5-dijkstra-和-floyd","5. Dijkstra 和 Floyd",[287,34290,34291,34300],{},[290,34292,34293],{},[293,34294,34295,34297],{},[296,34296,27378],{},[296,34298,34299],{},"用途",[303,34301,34302,34309],{},[293,34303,34304,34306],{},[308,34305,27388],{},[308,34307,34308],{},"一个点到其他点",[293,34310,34311,34313],{},[308,34312,27396],{},[308,34314,34315],{},"所有点到所有点",[506,34317],{},[10,34319,34320],{"id":34320},"第十二章一句话总结",[13,34322,34323],{},"第十二章就是图论入门，核心主线是：",[17,34325,34327],{"className":34326},[20],[17,34328,34330,34353],{"className":34329},[24],[17,34331,34333],{"className":34332},[28],[30,34334,34335],{"xmlns":32,"display":33},[35,34336,34337,34350],{},[38,34338,34339],{},[41,34340,34341],{"notation":43},[45,34342,34343],{"scriptlevel":47,"displaystyle":48},[45,34344,34345],{"scriptlevel":47,"displaystyle":48},[45,34346,34347],{"scriptlevel":47,"displaystyle":53},[55,34348,34349],{},"图是什么",[59,34351,34352],{"encoding":61},"\\boxed{\\text{图是什么}}",[17,34354,34356],{"className":34355,"ariaHidden":53},[66],[17,34357,34359,34362],{"className":34358},[70],[17,34360],{"className":34361,"style":75},[74],[17,34363,34365],{"className":34364},[79],[17,34366,34368,34405],{"className":34367},[83,84],[17,34369,34371,34402],{"className":34370},[88],[17,34372,34374,34394],{"className":34373,"style":93},[92],[17,34375,34376,34379],{"style":96},[17,34377],{"className":34378,"style":101},[100],[17,34380,34382],{"className":34381},[105],[17,34383,34385],{"className":34384},[79],[17,34386,34388],{"className":34387},[79],[17,34389,34391],{"className":34390},[79,115],[17,34392,34349],{"className":34393},[79,119],[17,34395,34396,34399],{"style":122},[17,34397],{"className":34398,"style":101},[100],[17,34400],{"className":34401,"style":131},[129,130],[17,34403,136],{"className":34404},[135],[17,34406,34408],{"className":34407},[88],[17,34409,34411],{"className":34410,"style":143},[92],[17,34412],{},[17,34414,34416],{"className":34415},[20],[17,34417,34419,34442],{"className":34418},[24],[17,34420,34422],{"className":34421},[28],[30,34423,34424],{"xmlns":32,"display":33},[35,34425,34426,34439],{},[38,34427,34428],{},[41,34429,34430],{"notation":43},[45,34431,34432],{"scriptlevel":47,"displaystyle":48},[45,34433,34434],{"scriptlevel":47,"displaystyle":48},[45,34435,34436],{"scriptlevel":47,"displaystyle":53},[55,34437,34438],{},"图有哪些基本结构",[59,34440,34441],{"encoding":61},"\\boxed{\\text{图有哪些基本结构}}",[17,34443,34445],{"className":34444,"ariaHidden":53},[66],[17,34446,34448,34451],{"className":34447},[70],[17,34449],{"className":34450,"style":75},[74],[17,34452,34454],{"className":34453},[79],[17,34455,34457,34494],{"className":34456},[83,84],[17,34458,34460,34491],{"className":34459},[88],[17,34461,34463,34483],{"className":34462,"style":93},[92],[17,34464,34465,34468],{"style":96},[17,34466],{"className":34467,"style":101},[100],[17,34469,34471],{"className":34470},[105],[17,34472,34474],{"className":34473},[79],[17,34475,34477],{"className":34476},[79],[17,34478,34480],{"className":34479},[79,115],[17,34481,34438],{"className":34482},[79,119],[17,34484,34485,34488],{"style":122},[17,34486],{"className":34487,"style":101},[100],[17,34489],{"className":34490,"style":131},[129,130],[17,34492,136],{"className":34493},[135],[17,34495,34497],{"className":34496},[88],[17,34498,34500],{"className":34499,"style":143},[92],[17,34501],{},[17,34503,34505],{"className":34504},[20],[17,34506,34508,34531],{"className":34507},[24],[17,34509,34511],{"className":34510},[28],[30,34512,34513],{"xmlns":32,"display":33},[35,34514,34515,34528],{},[38,34516,34517],{},[41,34518,34519],{"notation":43},[45,34520,34521],{"scriptlevel":47,"displaystyle":48},[45,34522,34523],{"scriptlevel":47,"displaystyle":48},[45,34524,34525],{"scriptlevel":47,"displaystyle":53},[55,34526,34527],{},"图中能不能走通",[59,34529,34530],{"encoding":61},"\\boxed{\\text{图中能不能走通}}",[17,34532,34534],{"className":34533,"ariaHidden":53},[66],[17,34535,34537,34540],{"className":34536},[70],[17,34538],{"className":34539,"style":75},[74],[17,34541,34543],{"className":34542},[79],[17,34544,34546,34583],{"className":34545},[83,84],[17,34547,34549,34580],{"className":34548},[88],[17,34550,34552,34572],{"className":34551,"style":93},[92],[17,34553,34554,34557],{"style":96},[17,34555],{"className":34556,"style":101},[100],[17,34558,34560],{"className":34559},[105],[17,34561,34563],{"className":34562},[79],[17,34564,34566],{"className":34565},[79],[17,34567,34569],{"className":34568},[79,115],[17,34570,34527],{"className":34571},[79,119],[17,34573,34574,34577],{"style":122},[17,34575],{"className":34576,"style":101},[100],[17,34578],{"className":34579,"style":131},[129,130],[17,34581,136],{"className":34582},[135],[17,34584,34586],{"className":34585},[88],[17,34587,34589],{"className":34588,"style":143},[92],[17,34590],{},[17,34592,34594],{"className":34593},[20],[17,34595,34597,34620],{"className":34596},[24],[17,34598,34600],{"className":34599},[28],[30,34601,34602],{"xmlns":32,"display":33},[35,34603,34604,34617],{},[38,34605,34606],{},[41,34607,34608],{"notation":43},[45,34609,34610],{"scriptlevel":47,"displaystyle":48},[45,34611,34612],{"scriptlevel":47,"displaystyle":48},[45,34613,34614],{"scriptlevel":47,"displaystyle":53},[55,34615,34616],{},"如何用矩阵表示图",[59,34618,34619],{"encoding":61},"\\boxed{\\text{如何用矩阵表示图}}",[17,34621,34623],{"className":34622,"ariaHidden":53},[66],[17,34624,34626,34629],{"className":34625},[70],[17,34627],{"className":34628,"style":75},[74],[17,34630,34632],{"className":34631},[79],[17,34633,34635,34672],{"className":34634},[83,84],[17,34636,34638,34669],{"className":34637},[88],[17,34639,34641,34661],{"className":34640,"style":93},[92],[17,34642,34643,34646],{"style":96},[17,34644],{"className":34645,"style":101},[100],[17,34647,34649],{"className":34648},[105],[17,34650,34652],{"className":34651},[79],[17,34653,34655],{"className":34654},[79],[17,34656,34658],{"className":34657},[79,115],[17,34659,34616],{"className":34660},[79,119],[17,34662,34663,34666],{"style":122},[17,34664],{"className":34665,"style":101},[100],[17,34667],{"className":34668,"style":131},[129,130],[17,34670,136],{"className":34671},[135],[17,34673,34675],{"className":34674},[88],[17,34676,34678],{"className":34677,"style":143},[92],[17,34679],{},[17,34681,34683],{"className":34682},[20],[17,34684,34686,34709],{"className":34685},[24],[17,34687,34689],{"className":34688},[28],[30,34690,34691],{"xmlns":32,"display":33},[35,34692,34693,34706],{},[38,34694,34695],{},[41,34696,34697],{"notation":43},[45,34698,34699],{"scriptlevel":47,"displaystyle":48},[45,34700,34701],{"scriptlevel":47,"displaystyle":48},[45,34702,34703],{"scriptlevel":47,"displaystyle":53},[55,34704,34705],{},"如何解决最短路径和关键路径问题",[59,34707,34708],{"encoding":61},"\\boxed{\\text{如何解决最短路径和关键路径问题}}",[17,34710,34712],{"className":34711,"ariaHidden":53},[66],[17,34713,34715,34718],{"className":34714},[70],[17,34716],{"className":34717,"style":75},[74],[17,34719,34721],{"className":34720},[79],[17,34722,34724,34761],{"className":34723},[83,84],[17,34725,34727,34758],{"className":34726},[88],[17,34728,34730,34750],{"className":34729,"style":93},[92],[17,34731,34732,34735],{"style":96},[17,34733],{"className":34734,"style":101},[100],[17,34736,34738],{"className":34737},[105],[17,34739,34741],{"className":34740},[79],[17,34742,34744],{"className":34743},[79],[17,34745,34747],{"className":34746},[79,115],[17,34748,34705],{"className":34749},[79,119],[17,34751,34752,34755],{"style":122},[17,34753],{"className":34754,"style":101},[100],[17,34756],{"className":34757,"style":131},[129,130],[17,34759,136],{"className":34760},[135],[17,34762,34764],{"className":34763},[88],[17,34765,34767],{"className":34766,"style":143},[92],[17,34768],{},[13,34770,34771],{},"最该背的是：",[17,34773,34775],{"className":34774},[20],[17,34776,34778,34825],{"className":34777},[24],[17,34779,34781],{"className":34780},[28],[30,34782,34783],{"xmlns":32,"display":33},[35,34784,34785,34823],{},[38,34786,34787],{},[41,34788,34789],{"notation":43},[45,34790,34791],{"scriptlevel":47,"displaystyle":48},[45,34792,34793],{"scriptlevel":47,"displaystyle":48},[45,34794,34795],{"scriptlevel":47,"displaystyle":53},[38,34796,34797,34809,34811,34813,34815,34817,34819,34821],{},[4901,34798,34799,34801],{},[191,34800,4905],{},[38,34802,34803,34805,34807],{},[187,34804,793],{},[191,34806,1891],{},[187,34808,199],{},[187,34810,3912],{},[191,34812,841],{"stretchy":48},[187,34814,793],{},[191,34816,850],{"stretchy":48},[191,34818,193],{},[1390,34820,1401],{},[187,34822,4859],{},[59,34824,4930],{"encoding":61},[17,34826,34828],{"className":34827,"ariaHidden":53},[66],[17,34829,34831,34834],{"className":34830},[70],[17,34832],{"className":34833,"style":4940},[74],[17,34835,34837],{"className":34836},[79],[17,34838,34840,34954],{"className":34839},[83,84],[17,34841,34843,34951],{"className":34842},[88],[17,34844,34846,34943],{"className":34845,"style":4953},[92],[17,34847,34848,34851],{"style":4956},[17,34849],{"className":34850,"style":4960},[100],[17,34852,34854],{"className":34853},[105],[17,34855,34857],{"className":34856},[79],[17,34858,34860,34913,34916,34919,34922,34925,34928,34931,34934,34937,34940],{"className":34859},[79],[17,34861,34863],{"className":34862},[4973,4974],[17,34864,34866,34905],{"className":34865},[83,84],[17,34867,34869,34902],{"className":34868},[88],[17,34870,34872,34892],{"className":34871,"style":4984},[92],[17,34873,34874,34877],{"style":4987},[17,34875],{"className":34876,"style":4991},[100],[17,34878,34880],{"className":34879},[1474,1475,1476,1477],[17,34881,34883,34886,34889],{"className":34882},[79,1477],[17,34884,793],{"className":34885,"style":818},[79,230,1477],[17,34887,1891],{"className":34888},[239,1477],[17,34890,199],{"className":34891,"style":257},[79,230,1477],[17,34893,34894,34897],{"style":5009},[17,34895],{"className":34896,"style":4991},[100],[17,34898,34899],{},[17,34900,4905],{"className":34901},[4973,5018,5019],[17,34903,136],{"className":34904},[135],[17,34906,34908],{"className":34907},[88],[17,34909,34911],{"className":34910,"style":5029},[92],[17,34912],{},[17,34914],{"className":34915,"style":265},[234],[17,34917,3912],{"className":34918},[79,230],[17,34920,841],{"className":34921},[253],[17,34923,793],{"className":34924,"style":818},[79,230],[17,34926,850],{"className":34927},[282],[17,34929],{"className":34930,"style":235},[234],[17,34932,193],{"className":34933},[239],[17,34935],{"className":34936,"style":235},[234],[17,34938,1401],{"className":34939},[79],[17,34941,4859],{"className":34942},[79,230],[17,34944,34945,34948],{"style":5064},[17,34946],{"className":34947,"style":4960},[100],[17,34949],{"className":34950,"style":5071},[129,130],[17,34952,136],{"className":34953},[135],[17,34955,34957],{"className":34956},[88],[17,34958,34960],{"className":34959,"style":5081},[92],[17,34961],{},[17,34963,34965],{"className":34964},[20],[17,34966,34968,34991],{"className":34967},[24],[17,34969,34971],{"className":34970},[28],[30,34972,34973],{"xmlns":32,"display":33},[35,34974,34975,34988],{},[38,34976,34977],{},[41,34978,34979],{"notation":43},[45,34980,34981],{"scriptlevel":47,"displaystyle":48},[45,34982,34983],{"scriptlevel":47,"displaystyle":48},[45,34984,34985],{"scriptlevel":47,"displaystyle":53},[55,34986,34987],{},"奇度顶点个数一定为偶数",[59,34989,34990],{"encoding":61},"\\boxed{\\text{奇度顶点个数一定为偶数}}",[17,34992,34994],{"className":34993,"ariaHidden":53},[66],[17,34995,34997,35000],{"className":34996},[70],[17,34998],{"className":34999,"style":75},[74],[17,35001,35003],{"className":35002},[79],[17,35004,35006,35043],{"className":35005},[83,84],[17,35007,35009,35040],{"className":35008},[88],[17,35010,35012,35032],{"className":35011,"style":93},[92],[17,35013,35014,35017],{"style":96},[17,35015],{"className":35016,"style":101},[100],[17,35018,35020],{"className":35019},[105],[17,35021,35023],{"className":35022},[79],[17,35024,35026],{"className":35025},[79],[17,35027,35029],{"className":35028},[79,115],[17,35030,34987],{"className":35031},[79,119],[17,35033,35034,35037],{"style":122},[17,35035],{"className":35036,"style":101},[100],[17,35038],{"className":35039,"style":131},[129,130],[17,35041,136],{"className":35042},[135],[17,35044,35046],{"className":35045},[88],[17,35047,35049],{"className":35048,"style":143},[92],[17,35050],{},[17,35052,35054],{"className":35053},[20],[17,35055,35057,35091],{"className":35056},[24],[17,35058,35060],{"className":35059},[28],[30,35061,35062],{"xmlns":32,"display":33},[35,35063,35064,35088],{},[38,35065,35066],{},[41,35067,35068],{"notation":43},[45,35069,35070],{"scriptlevel":47,"displaystyle":48},[45,35071,35072],{"scriptlevel":47,"displaystyle":48},[45,35073,35074],{"scriptlevel":47,"displaystyle":53},[38,35075,35076,35079,35082,35084,35086],{},[55,35077,35078],{},"基本路径长度",[191,35080,35081],{},"≤",[187,35083,3183],{},[191,35085,972],{},[1390,35087,1392],{},[59,35089,35090],{"encoding":61},"\\boxed{\\text{基本路径长度}\\leq n-1}",[17,35092,35094],{"className":35093,"ariaHidden":53},[66],[17,35095,35097,35101],{"className":35096},[70],[17,35098],{"className":35099,"style":35100},[74],"height:1.4993em;vertical-align:-0.476em;",[17,35102,35104],{"className":35103},[79],[17,35105,35107,35171],{"className":35106},[83,84],[17,35108,35110,35168],{"className":35109},[88],[17,35111,35113,35159],{"className":35112,"style":93},[92],[17,35114,35116,35120],{"style":35115},"top:-3.4993em;",[17,35117],{"className":35118,"style":35119},[100],"height:3.4993em;",[17,35121,35123],{"className":35122},[105],[17,35124,35126],{"className":35125},[79],[17,35127,35129,35135,35138,35141,35144,35147,35150,35153,35156],{"className":35128},[79],[17,35130,35132],{"className":35131},[79,115],[17,35133,35078],{"className":35134},[79,119],[17,35136],{"className":35137,"style":235},[234],[17,35139,35081],{"className":35140},[239],[17,35142],{"className":35143,"style":235},[234],[17,35145,3183],{"className":35146},[79,230],[17,35148],{"className":35149,"style":257},[234],[17,35151,972],{"className":35152},[997],[17,35154],{"className":35155,"style":257},[234],[17,35157,1392],{"className":35158},[79],[17,35160,35161,35164],{"style":122},[17,35162],{"className":35163,"style":35119},[100],[17,35165],{"className":35166,"style":35167},[129,130],"height:1.4993em;border-style:solid;border-width:0.04em;",[17,35169,136],{"className":35170},[135],[17,35172,35174],{"className":35173},[88],[17,35175,35178],{"className":35176,"style":35177},[92],"height:0.476em;",[17,35179],{},[17,35181,35183],{"className":35182},[20],[17,35184,35186,35251],{"className":35185},[24],[17,35187,35189],{"className":35188},[28],[30,35190,35191],{"xmlns":32,"display":33},[35,35192,35193,35248],{},[38,35194,35195],{},[41,35196,35197],{"notation":43},[45,35198,35199],{"scriptlevel":47,"displaystyle":48},[45,35200,35201],{"scriptlevel":47,"displaystyle":48},[45,35202,35203],{"scriptlevel":47,"displaystyle":53},[38,35204,35205,35207,35213,35223,35226,35232,35234,35240,35243,35245],{},[191,35206,841],{"stretchy":48},[4143,35208,35209,35211],{},[187,35210,17040],{},[187,35212,4859],{},[1385,35214,35215,35217],{},[191,35216,850],{"stretchy":48},[38,35218,35219,35221],{},[187,35220,11429],{},[187,35222,11438],{},[55,35224,35225],{}," 表示从 ",[1385,35227,35228,35230],{},[187,35229,793],{},[187,35231,11429],{},[55,35233,19112],{},[1385,35235,35236,35238],{},[187,35237,793],{},[187,35239,11438],{},[55,35241,35242],{}," 长度为 ",[187,35244,4859],{},[55,35246,35247],{}," 的路径数",[59,35249,35250],{"encoding":61},"\\boxed{(A^m)_{ij}\\text{ 表示从 }v_i\\text{ 到 }v_j\\text{ 长度为 }m\\text{ 的路径数}}",[17,35252,35254],{"className":35253,"ariaHidden":53},[66],[17,35255,35257,35261],{"className":35256},[70],[17,35258],{"className":35259,"style":35260},[74],"height:1.7161em;vertical-align:-0.6261em;",[17,35262,35264],{"className":35263},[79],[17,35265,35267,35507],{"className":35266},[83,84],[17,35268,35270,35504],{"className":35269},[88],[17,35271,35273,35495],{"className":35272,"style":3787},[92],[17,35274,35276,35280],{"style":35275},"top:-3.7161em;",[17,35277],{"className":35278,"style":35279},[100],"height:3.7161em;",[17,35281,35283],{"className":35282},[105],[17,35284,35286],{"className":35285},[79],[17,35287,35289,35292,35321,35364,35377,35417,35429,35469,35482,35485],{"className":35288},[79],[17,35290,841],{"className":35291},[253],[17,35293,35295,35298],{"className":35294},[79],[17,35296,17040],{"className":35297},[79,230],[17,35299,35301],{"className":35300},[1453],[17,35302,35304],{"className":35303},[83],[17,35305,35307],{"className":35306},[88],[17,35308,35310],{"className":35309,"style":19000},[92],[17,35311,35312,35315],{"style":3601},[17,35313],{"className":35314,"style":1470},[100],[17,35316,35318],{"className":35317},[1474,1475,1476,1477],[17,35319,4859],{"className":35320},[79,230,1477],[17,35322,35324,35327],{"className":35323},[282],[17,35325,850],{"className":35326},[282],[17,35328,35330],{"className":35329},[1453],[17,35331,35333,35356],{"className":35332},[83,84],[17,35334,35336,35353],{"className":35335},[88],[17,35337,35339],{"className":35338,"style":11470},[92],[17,35340,35341,35344],{"style":2106},[17,35342],{"className":35343,"style":1470},[100],[17,35345,35347],{"className":35346},[1474,1475,1476,1477],[17,35348,35350],{"className":35349},[79,1477],[17,35351,14842],{"className":35352,"style":11528},[79,230,1477],[17,35354,136],{"className":35355},[135],[17,35357,35359],{"className":35358},[88],[17,35360,35362],{"className":35361,"style":11538},[92],[17,35363],{},[17,35365,35367,35370,35374],{"className":35366},[79,115],[17,35368,4056],{"className":35369},[79],[17,35371,35373],{"className":35372},[79,119],"表示从",[17,35375,4056],{"className":35376},[79],[17,35378,35380,35383],{"className":35379},[79],[17,35381,793],{"className":35382,"style":818},[79,230],[17,35384,35386],{"className":35385},[1453],[17,35387,35389,35409],{"className":35388},[83,84],[17,35390,35392,35406],{"className":35391},[88],[17,35393,35395],{"className":35394,"style":11470},[92],[17,35396,35397,35400],{"style":1466},[17,35398],{"className":35399,"style":1470},[100],[17,35401,35403],{"className":35402},[1474,1475,1476,1477],[17,35404,11429],{"className":35405},[79,230,1477],[17,35407,136],{"className":35408},[135],[17,35410,35412],{"className":35411},[88],[17,35413,35415],{"className":35414,"style":1490},[92],[17,35416],{},[17,35418,35420,35423,35426],{"className":35419},[79,115],[17,35421,4056],{"className":35422},[79],[17,35424,19227],{"className":35425},[79,119],[17,35427,4056],{"className":35428},[79],[17,35430,35432,35435],{"className":35431},[79],[17,35433,793],{"className":35434,"style":818},[79,230],[17,35436,35438],{"className":35437},[1453],[17,35439,35441,35461],{"className":35440},[83,84],[17,35442,35444,35458],{"className":35443},[88],[17,35445,35447],{"className":35446,"style":11470},[92],[17,35448,35449,35452],{"style":1466},[17,35450],{"className":35451,"style":1470},[100],[17,35453,35455],{"className":35454},[1474,1475,1476,1477],[17,35456,11438],{"className":35457,"style":11528},[79,230,1477],[17,35459,136],{"className":35460},[135],[17,35462,35464],{"className":35463},[88],[17,35465,35467],{"className":35466,"style":11538},[92],[17,35468],{},[17,35470,35472,35475,35479],{"className":35471},[79,115],[17,35473,4056],{"className":35474},[79],[17,35476,35478],{"className":35477},[79,119],"长度为",[17,35480,4056],{"className":35481},[79],[17,35483,4859],{"className":35484},[79,230],[17,35486,35488,35491],{"className":35487},[79,115],[17,35489,4056],{"className":35490},[79],[17,35492,35494],{"className":35493},[79,119],"的路径数",[17,35496,35497,35500],{"style":3830},[17,35498],{"className":35499,"style":35279},[100],[17,35501],{"className":35502,"style":35503},[129,130],"height:1.7161em;border-style:solid;border-width:0.04em;",[17,35505,136],{"className":35506},[135],[17,35508,35510],{"className":35509},[88],[17,35511,35513],{"className":35512,"style":19315},[92],[17,35514],{},[17,35516,35518],{"className":35517},[20],[17,35519,35521,35553],{"className":35520},[24],[17,35522,35524],{"className":35523},[28],[30,35525,35526],{"xmlns":32,"display":33},[35,35527,35528,35550],{},[38,35529,35530],{},[41,35531,35532],{"notation":43},[45,35533,35534],{"scriptlevel":47,"displaystyle":48},[45,35535,35536],{"scriptlevel":47,"displaystyle":48},[45,35537,35538],{"scriptlevel":47,"displaystyle":53},[38,35539,35540,35542,35544,35546,35548],{},[55,35541,13903],{},[191,35543,13906],{},[55,35545,13909],{},[191,35547,13906],{},[55,35549,13914],{},[59,35551,35552],{"encoding":61},"\\boxed{\\text{强连通}\\Rightarrow\\text{单向连通}\\Rightarrow\\text{弱连通}}",[17,35554,35556],{"className":35555,"ariaHidden":53},[66],[17,35557,35559,35562],{"className":35558},[70],[17,35560],{"className":35561,"style":75},[74],[17,35563,35565],{"className":35564},[79],[17,35566,35568,35635],{"className":35567},[83,84],[17,35569,35571,35632],{"className":35570},[88],[17,35572,35574,35624],{"className":35573,"style":93},[92],[17,35575,35576,35579],{"style":96},[17,35577],{"className":35578,"style":101},[100],[17,35580,35582],{"className":35581},[105],[17,35583,35585],{"className":35584},[79],[17,35586,35588,35594,35597,35600,35603,35609,35612,35615,35618],{"className":35587},[79],[17,35589,35591],{"className":35590},[79,115],[17,35592,13903],{"className":35593},[79,119],[17,35595],{"className":35596,"style":235},[234],[17,35598,13906],{"className":35599},[239],[17,35601],{"className":35602,"style":235},[234],[17,35604,35606],{"className":35605},[79,115],[17,35607,13909],{"className":35608},[79,119],[17,35610],{"className":35611,"style":235},[234],[17,35613,13906],{"className":35614},[239],[17,35616],{"className":35617,"style":235},[234],[17,35619,35621],{"className":35620},[79,115],[17,35622,13914],{"className":35623},[79,119],[17,35625,35626,35629],{"style":122},[17,35627],{"className":35628,"style":101},[100],[17,35630],{"className":35631,"style":131},[129,130],[17,35633,136],{"className":35634},[135],[17,35636,35638],{"className":35637},[88],[17,35639,35641],{"className":35640,"style":143},[92],[17,35642],{},[17,35644,35646],{"className":35645},[20],[17,35647,35649,35672],{"className":35648},[24],[17,35650,35652],{"className":35651},[28],[30,35653,35654],{"xmlns":32,"display":33},[35,35655,35656,35669],{},[38,35657,35658],{},[41,35659,35660],{"notation":43},[45,35661,35662],{"scriptlevel":47,"displaystyle":48},[45,35663,35664],{"scriptlevel":47,"displaystyle":48},[45,35665,35666],{"scriptlevel":47,"displaystyle":53},[55,35667,35668],{},"Dijkstra 求单源最短路，Floyd 求任意两点最短路",[59,35670,35671],{"encoding":61},"\\boxed{\\text{Dijkstra 求单源最短路，Floyd 求任意两点最短路}}",[17,35673,35675],{"className":35674,"ariaHidden":53},[66],[17,35676,35678,35681],{"className":35677},[70],[17,35679],{"className":35680,"style":27441},[74],[17,35682,35684],{"className":35683},[79],[17,35685,35687,35735],{"className":35686},[83,84],[17,35688,35690,35732],{"className":35689},[88],[17,35691,35693,35724],{"className":35692,"style":9663},[92],[17,35694,35695,35698],{"style":27456},[17,35696],{"className":35697,"style":27460},[100],[17,35699,35701],{"className":35700},[105],[17,35702,35704],{"className":35703},[79],[17,35705,35707],{"className":35706},[79],[17,35708,35710,35713,35717,35720],{"className":35709},[79,115],[17,35711,27476],{"className":35712},[79],[17,35714,35716],{"className":35715},[79,119],"求单源最短路，",[17,35718,27484],{"className":35719},[79],[17,35721,35723],{"className":35722},[79,119],"求任意两点最短路",[17,35725,35726,35729],{"style":9685},[17,35727],{"className":35728,"style":27460},[100],[17,35730],{"className":35731,"style":27497},[129,130],[17,35733,136],{"className":35734},[135],[17,35736,35738],{"className":35737},[88],[17,35739,35741],{"className":35740,"style":16629},[92],[17,35742],{},[13,35744,35745,35746],{},"这章概念很多，但逻辑很清楚：",[645,35747,35748],{},"先认识图，再研究走法，再用矩阵计算，最后拿去解路径问题。",{"title":35750,"searchDepth":11911,"depth":11911,"links":35751},"",[35752,35753,35754,35755,35756,35757,35758,35759,35760,35761,35762,35763,35764,35765,35766,35767,35768,35769,35770,35775,35776,35777,35778,35779,35780,35781,35782,35783,35784,35785,35786,35787,35788,35789,35790,35791,35792,35793,35794,35795,35796,35797,35798,35799,35800,35801,35802,35803,35804,35805,35806,35807,35808,35809,35810,35811,35812,35813,35814,35815,35816,35817,35818,35819,35820,35825,35826,35827,35828,35829,35830,35831,35832,35838,35839,35840,35841,35842,35843,35844,35845,35846,35847,35848,35849,35850,35851,35852,35853,35854,35855,35856,35857,35858,35859,35860,35861,35862,35863,35864,35865],{"id":515,"depth":11911,"text":516},{"id":731,"depth":11911,"text":732},{"id":735,"depth":11911,"text":736},{"id":1075,"depth":11911,"text":1076},{"id":1350,"depth":11911,"text":1351},{"id":1592,"depth":11911,"text":1593},{"id":1609,"depth":11911,"text":1610},{"id":1854,"depth":11911,"text":1855},{"id":2006,"depth":11911,"text":2007},{"id":2404,"depth":11911,"text":2405},{"id":2499,"depth":11911,"text":2500},{"id":2915,"depth":11911,"text":2916},{"id":2934,"depth":11911,"text":2935},{"id":3006,"depth":11911,"text":3007},{"id":3018,"depth":11911,"text":3019},{"id":3033,"depth":11911,"text":3034},{"id":3158,"depth":11911,"text":3159},{"id":3858,"depth":11911,"text":3859},{"id":4086,"depth":11911,"text":4087,"children":35771},[35772,35773,35774],{"id":4094,"depth":12223,"text":4094},{"id":4210,"depth":12223,"text":4210},{"id":4322,"depth":12223,"text":4322},{"id":4508,"depth":11911,"text":4509},{"id":4680,"depth":11911,"text":4681},{"id":5102,"depth":11911,"text":5103},{"id":5871,"depth":11911,"text":5872},{"id":6308,"depth":11911,"text":6309},{"id":6597,"depth":11911,"text":6598},{"id":6852,"depth":11911,"text":6853},{"id":7032,"depth":11911,"text":7033},{"id":7334,"depth":11911,"text":7335},{"id":7577,"depth":11911,"text":7578},{"id":7672,"depth":11911,"text":7673},{"id":7686,"depth":11911,"text":7687},{"id":8261,"depth":11911,"text":8262},{"id":8690,"depth":11911,"text":8691},{"id":8720,"depth":11911,"text":8721},{"id":9708,"depth":11911,"text":9709},{"id":10186,"depth":11911,"text":10187},{"id":10201,"depth":11911,"text":10202},{"id":10466,"depth":11911,"text":10467},{"id":10478,"depth":11911,"text":10479},{"id":10490,"depth":11911,"text":10491},{"id":10651,"depth":11911,"text":10652},{"id":10885,"depth":11911,"text":10886},{"id":10992,"depth":11911,"text":10993},{"id":11185,"depth":11911,"text":11186},{"id":11197,"depth":11911,"text":11198},{"id":12653,"depth":11911,"text":12654},{"id":12976,"depth":11911,"text":12977},{"id":13047,"depth":11911,"text":13048},{"id":13213,"depth":11911,"text":13214},{"id":13377,"depth":11911,"text":13378},{"id":13535,"depth":11911,"text":13536},{"id":13705,"depth":11911,"text":13706},{"id":13862,"depth":11911,"text":13863},{"id":13874,"depth":11911,"text":13875},{"id":14032,"depth":11911,"text":14033},{"id":14044,"depth":11911,"text":14045},{"id":14056,"depth":11911,"text":14057},{"id":14068,"depth":11911,"text":14069},{"id":14726,"depth":11911,"text":14727},{"id":15590,"depth":11911,"text":15591},{"id":15610,"depth":11911,"text":15611},{"id":17018,"depth":11911,"text":17019},{"id":17577,"depth":11911,"text":17578},{"id":17855,"depth":11911,"text":17856},{"id":17991,"depth":11911,"text":17992,"children":35821},[35822,35823,35824],{"id":17997,"depth":12223,"text":4094},{"id":18310,"depth":12223,"text":4210},{"id":18619,"depth":12223,"text":4322},{"id":19549,"depth":11911,"text":19549},{"id":20547,"depth":11911,"text":20548},{"id":20904,"depth":11911,"text":20905},{"id":21596,"depth":11911,"text":21597},{"id":22847,"depth":11911,"text":8262},{"id":22964,"depth":11911,"text":22965},{"id":23582,"depth":11911,"text":23583},{"id":23836,"depth":11911,"text":23837,"children":35833},[35834,35835,35836,35837],{"id":23912,"depth":12223,"text":23913},{"id":24652,"depth":12223,"text":24653},{"id":24788,"depth":12223,"text":24789},{"id":25537,"depth":12223,"text":25538},{"id":25603,"depth":11911,"text":25604},{"id":25730,"depth":11911,"text":25731},{"id":26497,"depth":11911,"text":26498},{"id":27176,"depth":11911,"text":27177},{"id":27368,"depth":11911,"text":27369},{"id":27517,"depth":11911,"text":27518},{"id":27735,"depth":11911,"text":27736},{"id":27755,"depth":11911,"text":27756},{"id":28277,"depth":11911,"text":28278},{"id":28303,"depth":11911,"text":28304},{"id":29129,"depth":11911,"text":29130},{"id":30013,"depth":11911,"text":30014},{"id":30125,"depth":11911,"text":30126},{"id":32094,"depth":11911,"text":32095},{"id":32304,"depth":11911,"text":32305},{"id":32333,"depth":11911,"text":32334},{"id":32463,"depth":11911,"text":32464},{"id":32637,"depth":11911,"text":32638},{"id":32672,"depth":11911,"text":32673},{"id":32922,"depth":11911,"text":32923},{"id":33046,"depth":11911,"text":33047},{"id":33348,"depth":11911,"text":33349},{"id":33601,"depth":11911,"text":33602},{"id":33792,"depth":11911,"text":33793},{"id":33926,"depth":11911,"text":33927},{"id":33964,"depth":11911,"text":33965},{"id":34237,"depth":11911,"text":34238},{"id":34287,"depth":11911,"text":34288},"md",{},true,"\u002Fsource\u002Fcs\u002Fdm\u002Fnote\u002Fchap12",{"title":5,"description":15},"source\u002Fcs\u002Fdm\u002Fnote\u002Fchap12","aVgceQjeZVBIEoTo23guCsr5_ckxMyhGSdkvSn7XNvs",null,1784032891311]