[{"data":1,"prerenderedAt":32987},["ShallowReactive",2],{"note:cs\u002Falgo\u002Fpastpapers\u002F2024-2025-se2":3,"site-search-catalogue":32986},{"id":4,"title":5,"body":6,"description":7751,"extension":32980,"meta":32981,"navigation":29831,"path":32982,"seo":32983,"stem":32984,"__hash__":32985},"notes\u002Fsource\u002Fcs\u002Falgo\u002Fpastpapers\u002F2024-2025-se2.md","2024-2025 第二学期 算法设计与分析",{"type":7,"value":8,"toc":32920},"minimark",[9,13,16,21,26,30,33,40,62,67,92,94,98,101,104,108,157,161,258,260,264,267,270,274,307,311,367,369,373,376,379,384,398,402,416,418,422,425,438,441,446,479,481,484,1322,1325,1330,2433,2435,2438,3003,3006,3011,4729,4731,4734,5152,5155,5159,5584,5586,5590,5689,5692,5696,5914,5916,5920,6193,6196,6200,6439,6441,6445,6457,6460,6464,6474,6476,6480,6491,6494,6498,6535,6537,6541,7049,7052,7056,7365,7367,7371,7383,7386,7390,7417,7419,7423,7426,7429,7432,7444,7461,7463,7466,7469,7472,7477,7680,7682,7685,7745,7833,7836,7864,8109,8111,8114,8444,8447,8602,9339,9341,9344,10456,10459,10473,10812,10814,10818,10821,10824,10897,10967,10970,10975,11198,11203,12749,12751,12754,14471,14544,14547,14961,15033,24400,24464,24658,24693,25930,25932,25935,26114,26122,26125,26130,26243,27662,29769,29771,29775,29778,29781,29789,29792,29797,29871,29876,30244,30246,30249,30426,30612,30615,30618,30623,32650,32655,32916],[10,11,5],"h1",{"id":12},"_2024-2025-第二学期-算法设计与分析",[14,15],"hr",{},[17,18,20],"h2",{"id":19},"一简答题每题5分共20分","一、简答题（每题5分，共20分）",[22,23,25],"h3",{"id":24},"_1-题目内容","1. 题目内容",[27,28,29],"p",{},"简述分治法进行算法设计的三个基本步骤。",[22,31,32],{"id":32},"答案与深度解析",[27,34,35,39],{},[36,37,38],"strong",{},"答案：","\n分治法（Divide and Conquer）的三个基本步骤为：",[41,42,43,50,56],"ol",{},[44,45,46,49],"li",{},[36,47,48],{},"分解（Divide）："," 将原问题分解为若干个规模较小、相互独立且与原问题形式相同的子问题。",[44,51,52,55],{},[36,53,54],{},"解决（Conquer）："," 若子问题规模较小且容易被解决，则直接求解；否则，递归地解决各个子问题。",[44,57,58,61],{},[36,59,60],{},"合并（Combine）："," 将各个子问题的解合并为原问题的解。",[27,63,64],{},[36,65,66],{},"深度解析：",[68,69,70,76,86],"ul",{},[44,71,72,75],{},[36,73,74],{},"核心驱动力："," 面对庞大复杂的问题，计算机处理起来会非常耗时。分治法的底层逻辑是“降维打击”，通过不断缩小问题的规模，直到问题简单到可以直接得出答案（即递归的基线条件）。",[44,77,78,81,82,85],{},[36,79,80],{},"关键点与风险："," 分治法成功的前提是“子问题必须相互独立”。如果子问题之间有重叠（即存在公共子子问题），分治法会进行大量重复计算，此时算法效率极低，应转而考虑",[36,83,84],{},"动态规划","。",[44,87,88,91],{},[36,89,90],{},"应用实例："," 归并排序、快速排序、二分查找都严格遵循了这三个步骤。",[14,93],{},[22,95,97],{"id":96},"_2-题目内容","2. 题目内容",[27,99,100],{},"简述回溯法与分支限界法的异同。",[22,102,32],{"id":103},"答案与深度解析-1",[27,105,106],{},[36,107,38],{},[68,109,110,116],{},[44,111,112,115],{},[36,113,114],{},"相同点："," 两者都是在问题的状态空间树（解空间）上进行搜索的算法；都需要通过设计限界函数（剪枝函数）来避免无效搜索，提高算法效率。",[44,117,118,121],{},[36,119,120],{},"不同点：",[41,122,123,140],{},[44,124,125,128,129,132,133,85],{},[36,126,127],{},"搜索方式不同："," 回溯法采用",[36,130,131],{},"深度优先搜索（DFS）","；分支限界法采用",[36,134,135,136,139],{},"广度优先搜索（BFS）",[36,137,138],{},"或","最小耗费优先（优先队列）搜索",[44,141,142,145,146,138,149,152,153,156],{},[36,143,144],{},"求解目标不同："," 回溯法的目标通常是找出满足约束条件的",[36,147,148],{},"所有解",[36,150,151],{},"任一解","；分支限界法的目标则是找出满足约束条件的一个解，或者是某种意义下的",[36,154,155],{},"最优解","（如最大值或最小值）。",[27,158,159],{},[36,160,66],{},[68,162,163,181],{},[44,164,165,168,169,172,173],{},[36,166,167],{},"形象化理解："," * ",[36,170,171],{},"回溯法","就像是在走迷宫，你顺着一条路一直走到黑（深度优先），遇到死胡同就退回上一个岔路口（回溯），尝试另一条路，直到把所有角落都走遍。\n",[68,174,175],{},[44,176,177,180],{},[36,178,179],{},"分支限界法","像是在雷达扫描，你站在起点，先把周围第一圈的岔路口都看一遍（广度优先），然后评估哪条路看起来最有可能通向宝藏（通过代价函数评估），接着优先去展开那条最有希望的路。",[44,182,183,186,187,257],{},[36,184,185],{},"空间复杂度差异："," 回溯法只需要保存当前从根节点到当前节点的路径，空间复杂度通常为 ",[188,189,192,226],"span",{"className":190},[191],"katex",[188,193,196],{"className":194},[195],"katex-mathml",[197,198,200],"math",{"xmlns":199},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[201,202,203,221],"semantics",{},[204,205,206,210,215,218],"mrow",{},[207,208,209],"mi",{},"O",[211,212,214],"mo",{"stretchy":213},"false","(",[207,216,217],{},"n",[211,219,220],{"stretchy":213},")",[222,223,225],"annotation",{"encoding":224},"application\u002Fx-tex","O(n)",[188,227,231],{"className":228,"ariaHidden":230},[229],"katex-html","true",[188,232,235,240,246,250,253],{"className":233},[234],"base",[188,236],{"className":237,"style":239},[238],"strut","height:1em;vertical-align:-0.25em;",[188,241,209],{"className":242,"style":245},[243,244],"mord","mathnormal","margin-right:0.0278em;",[188,247,214],{"className":248},[249],"mopen",[188,251,217],{"className":252},[243,244],[188,254,220],{"className":255},[256],"mclose","；而分支限界法需要维护一个活结点表（队列），在最坏情况下空间复杂度可能达到指数级。",[14,259],{},[22,261,263],{"id":262},"_3-题目内容","3. 题目内容",[27,265,266],{},"简述拉斯维加斯算法与蒙特卡洛算法的异同。",[22,268,32],{"id":269},"答案与深度解析-2",[27,271,272],{},[36,273,38],{},[68,275,276,281],{},[44,277,278,280],{},[36,279,114],{}," 两者都属于随机化算法，都在算法执行过程中引入了随机数来辅助决策，以期望获得更好的平均性能或绕过最坏情况。",[44,282,283,285],{},[36,284,120],{},[68,286,287,297],{},[44,288,289,292,293,296],{},[36,290,291],{},"拉斯维加斯算法（Las Vegas）："," 只要算法返回了结果，这个结果就",[36,294,295],{},"一定正确","。但它的执行时间是不确定的，有时可能找不到解并宣告失败。",[44,298,299,302,303,306],{},[36,300,301],{},"蒙特卡洛算法（Monte Carlo）："," 算法的执行时间是确定且通常较快的，它一定会给出一个答案，但这个答案",[36,304,305],{},"不一定正确","，获得正确解的概率存在一个界限。",[27,308,309],{},[36,310,66],{},[68,312,313,357],{},[44,314,315,318,319],{},[36,316,317],{},"如何记忆："," * 去“拉斯维加斯”赌场，要么赢钱（拿到绝对正确的解），要么输光离场（找不到解），但赌场绝对不会给你假钞（结果绝对正确）。\n",[68,320,321],{},[44,322,323,324,356],{},"“蒙特卡洛”常用于估算（例如用随机投点法估算圆周率 ",[188,325,327,342],{"className":326},[191],[188,328,330],{"className":329},[195],[197,331,332],{"xmlns":199},[201,333,334,339],{},[204,335,336],{},[207,337,338],{},"π",[222,340,341],{"encoding":224},"\\pi",[188,343,345],{"className":344,"ariaHidden":230},[229],[188,346,348,352],{"className":347},[234],[188,349],{"className":350,"style":351},[238],"height:0.4306em;",[188,353,338],{"className":354,"style":355},[243,244],"margin-right:0.0359em;","），投的点越多，估算越准确，但它始终是一个近似值（有概率犯错）。",[44,358,359,362,363,366],{},[36,360,361],{},"性能提升策略："," 蒙特卡洛算法可以通过",[36,364,365],{},"反复多次执行","来无限逼近 100% 的正确率；而拉斯维加斯算法如果失败，只能重新运行，期望下一次运气好能找到解。",[14,368],{},[22,370,372],{"id":371},"_4-题目内容","4. 题目内容",[27,374,375],{},"简述分支限界法中活结点表的组织方式。",[22,377,32],{"id":378},"答案与深度解析-3",[27,380,381,383],{},[36,382,38],{},"\n分支限界法中，活结点表（用于存放已经被生成但尚未展开的节点）主要有两种组织方式：",[41,385,386,392],{},[44,387,388,391],{},[36,389,390],{},"队列式（FIFO）分支限界法："," 将活结点表组织成一个先进先出的队列。按照节点生成的顺序依次扩展。",[44,393,394,397],{},[36,395,396],{},"优先队列式分支限界法："," 将活结点表组织成一个优先队列（通常用堆来实现）。每个节点都有一个由代价函数计算出的优先级（如成本或价值），算法每次总是从活结点表中选取优先级最高（或代价最小）的节点作为下一个扩展的节点。",[27,399,400],{},[36,401,66],{},[68,403,404,410],{},[44,405,406,409],{},[36,407,408],{},"底层数据结构："," 队列式对应简单的数组队列或链式队列；优先队列式对应数据结构中的“大顶堆”或“小顶堆”。",[44,411,412,415],{},[36,413,414],{},"策略选择："," 在实际解决工程优化问题（如单源最短路径、旅行商问题）时，优先队列式分支限界法应用更广，因为它能更快地引导搜索过程逼近最优解，从而引发更多的“剪枝”，大幅缩减搜索空间。",[14,417],{},[17,419,421],{"id":420},"二选择题每题1分共10分","二、选择题（每题1分，共10分）",[22,423,25],{"id":424},"_1-题目内容-1",[27,426,427,428,431,432,434,435,437],{},"在算法设计中，要求算法对于错误的输入也有相应的处理即要求设计的算法具有（ ）。\nA. 确定性",[429,430],"br",{},"\nB. 健壮性",[429,433],{},"\nC. 可行性",[429,436],{},"\nD. 正确性",[22,439,32],{"id":440},"答案与深度解析-4",[27,442,443],{},[36,444,445],{},"答案：B",[68,447,448],{},[44,449,450,453],{},[36,451,452],{},"分析：",[68,454,455,461,467,473],{},[44,456,457,460],{},[36,458,459],{},"确定性："," 算法的每一步都必须有明确的定义，无二义性。",[44,462,463,466],{},[36,464,465],{},"健壮性（Robustness）："," 也称鲁棒性，指当输入数据非法或出现异常情况时，算法能够适当地做出反应或进行处理，而不会产生莫名其妙的输出或直接崩溃。这正是题干描述的内容。",[44,468,469,472],{},[36,470,471],{},"可行性："," 算法中的操作必须足够基本，能够在有限次内完成。",[44,474,475,478],{},[36,476,477],{},"正确性："," 算法对合法的输入能产生满足要求的正确输出。",[14,480],{},[22,482,97],{"id":483},"_2-题目内容-1",[27,485,486,487,629,630,704,706,707,824,825,900,902,903,629,1033,1132,1134,1135,824,1248],{},"下述表达不正确的选项是（ ）。\nA. ",[188,488,490,526],{"className":489},[191],[188,491,493],{"className":492},[195],[197,494,495],{"xmlns":199},[201,496,497,523],{},[204,498,499,508,512,514,517],{},[500,501,502,504],"msup",{},[207,503,217],{},[505,506,507],"mn",{},"2",[207,509,511],{"mathvariant":510},"normal","\u002F",[505,513,507],{},[211,515,516],{},"+",[500,518,519,521],{},[505,520,507],{},[207,522,217],{},[222,524,525],{"encoding":224},"n^2 \u002F 2 + 2^n",[188,527,529,593],{"className":528,"ariaHidden":230},[229],[188,530,532,536,577,581,586,590],{"className":531},[234],[188,533],{"className":534,"style":535},[238],"height:1.0641em;vertical-align:-0.25em;",[188,537,539,542],{"className":538},[243],[188,540,217],{"className":541},[243,244],[188,543,546],{"className":544},[545],"msupsub",[188,547,550],{"className":548},[549],"vlist-t",[188,551,554],{"className":552},[553],"vlist-r",[188,555,559],{"className":556,"style":558},[557],"vlist","height:0.8141em;",[188,560,562,567],{"style":561},"top:-3.063em;margin-right:0.05em;",[188,563],{"className":564,"style":566},[565],"pstrut","height:2.7em;",[188,568,574],{"className":569},[570,571,572,573],"sizing","reset-size6","size3","mtight",[188,575,507],{"className":576},[243,573],[188,578,580],{"className":579},[243],"\u002F2",[188,582],{"className":583,"style":585},[584],"mspace","margin-right:0.2222em;",[188,587,516],{"className":588},[589],"mbin",[188,591],{"className":592,"style":585},[584],[188,594,596,600],{"className":595},[234],[188,597],{"className":598,"style":599},[238],"height:0.6644em;",[188,601,603,606],{"className":602},[243],[188,604,507],{"className":605},[243],[188,607,609],{"className":608},[545],[188,610,612],{"className":611},[549],[188,613,615],{"className":614},[553],[188,616,618],{"className":617,"style":599},[557],[188,619,620,623],{"style":561},[188,621],{"className":622,"style":566},[565],[188,624,626],{"className":625},[570,571,572,573],[188,627,217],{"className":628},[243,244,573]," 上界函数是 ",[188,631,633,657],{"className":632},[191],[188,634,636],{"className":635},[195],[197,637,638],{"xmlns":199},[201,639,640,654],{},[204,641,642,644,646,652],{},[207,643,209],{},[211,645,214],{"stretchy":213},[500,647,648,650],{},[505,649,507],{},[207,651,217],{},[211,653,220],{"stretchy":213},[222,655,656],{"encoding":224},"O(2^n)",[188,658,660],{"className":659,"ariaHidden":230},[229],[188,661,663,666,669,672,701],{"className":662},[234],[188,664],{"className":665,"style":239},[238],[188,667,209],{"className":668,"style":245},[243,244],[188,670,214],{"className":671},[249],[188,673,675,678],{"className":674},[243],[188,676,507],{"className":677},[243],[188,679,681],{"className":680},[545],[188,682,684],{"className":683},[549],[188,685,687],{"className":686},[553],[188,688,690],{"className":689,"style":599},[557],[188,691,692,695],{"style":561},[188,693],{"className":694,"style":566},[565],[188,696,698],{"className":697},[570,571,572,573],[188,699,217],{"className":700},[243,244,573],[188,702,220],{"className":703},[256],[429,705],{},"\nB. ",[188,708,710,739],{"className":709},[191],[188,711,713],{"className":712},[195],[197,714,715],{"xmlns":199},[201,716,717,737],{},[204,718,719,725,727,729,731],{},[500,720,721,723],{},[207,722,217],{},[505,724,507],{},[207,726,511],{"mathvariant":510},[505,728,507],{},[211,730,516],{},[500,732,733,735],{},[505,734,507],{},[207,736,217],{},[222,738,525],{"encoding":224},[188,740,742,789],{"className":741,"ariaHidden":230},[229],[188,743,745,748,777,780,783,786],{"className":744},[234],[188,746],{"className":747,"style":535},[238],[188,749,751,754],{"className":750},[243],[188,752,217],{"className":753},[243,244],[188,755,757],{"className":756},[545],[188,758,760],{"className":759},[549],[188,761,763],{"className":762},[553],[188,764,766],{"className":765,"style":558},[557],[188,767,768,771],{"style":561},[188,769],{"className":770,"style":566},[565],[188,772,774],{"className":773},[570,571,572,573],[188,775,507],{"className":776},[243,573],[188,778,580],{"className":779},[243],[188,781],{"className":782,"style":585},[584],[188,784,516],{"className":785},[589],[188,787],{"className":788,"style":585},[584],[188,790,792,795],{"className":791},[234],[188,793],{"className":794,"style":599},[238],[188,796,798,801],{"className":797},[243],[188,799,507],{"className":800},[243],[188,802,804],{"className":803},[545],[188,805,807],{"className":806},[549],[188,808,810],{"className":809},[553],[188,811,813],{"className":812,"style":599},[557],[188,814,815,818],{"style":561},[188,816],{"className":817,"style":566},[565],[188,819,821],{"className":820},[570,571,572,573],[188,822,217],{"className":823},[243,244,573]," 的下界函数是 ",[188,826,828,853],{"className":827},[191],[188,829,831],{"className":830},[195],[197,832,833],{"xmlns":199},[201,834,835,850],{},[204,836,837,840,842,848],{},[207,838,839],{"mathvariant":510},"Ω",[211,841,214],{"stretchy":213},[500,843,844,846],{},[505,845,507],{},[207,847,217],{},[211,849,220],{"stretchy":213},[222,851,852],{"encoding":224},"\\Omega(2^n)",[188,854,856],{"className":855,"ariaHidden":230},[229],[188,857,859,862,865,868,897],{"className":858},[234],[188,860],{"className":861,"style":239},[238],[188,863,839],{"className":864},[243],[188,866,214],{"className":867},[249],[188,869,871,874],{"className":870},[243],[188,872,507],{"className":873},[243],[188,875,877],{"className":876},[545],[188,878,880],{"className":879},[549],[188,881,883],{"className":882},[553],[188,884,886],{"className":885,"style":599},[557],[188,887,888,891],{"style":561},[188,889],{"className":890,"style":566},[565],[188,892,894],{"className":893},[570,571,572,573],[188,895,217],{"className":896},[243,244,573],[188,898,220],{"className":899},[256],[429,901],{},"\nC. ",[188,904,906,938],{"className":905},[191],[188,907,909],{"className":908},[195],[197,910,911],{"xmlns":199},[201,912,913,935],{},[204,914,915,928],{},[916,917,918,926],"msub",{},[204,919,920,923],{},[207,921,922],{},"log",[211,924,925],{},"⁡",[505,927,507],{},[500,929,930,932],{},[207,931,217],{},[505,933,934],{},"3",[222,936,937],{"encoding":224},"\\log_2 n^3",[188,939,941],{"className":940,"ariaHidden":230},[229],[188,942,944,948,1000,1004],{"className":943},[234],[188,945],{"className":946,"style":947},[238],"height:1.0582em;vertical-align:-0.2441em;",[188,949,952,960],{"className":950},[951],"mop",[188,953,955,956],{"className":954},[951],"lo",[188,957,959],{"style":958},"margin-right:0.0139em;","g",[188,961,963],{"className":962},[545],[188,964,967,991],{"className":965},[549,966],"vlist-t2",[188,968,970,986],{"className":969},[553],[188,971,974],{"className":972,"style":973},[557],"height:0.207em;",[188,975,977,980],{"style":976},"top:-2.4559em;margin-right:0.05em;",[188,978],{"className":979,"style":566},[565],[188,981,983],{"className":982},[570,571,572,573],[188,984,507],{"className":985},[243,573],[188,987,990],{"className":988},[989],"vlist-s","​",[188,992,994],{"className":993},[553],[188,995,998],{"className":996,"style":997},[557],"height:0.2441em;",[188,999],{},[188,1001],{"className":1002,"style":1003},[584],"margin-right:0.1667em;",[188,1005,1007,1010],{"className":1006},[243],[188,1008,217],{"className":1009},[243,244],[188,1011,1013],{"className":1012},[545],[188,1014,1016],{"className":1015},[549],[188,1017,1019],{"className":1018},[553],[188,1020,1022],{"className":1021,"style":558},[557],[188,1023,1024,1027],{"style":561},[188,1025],{"className":1026,"style":566},[565],[188,1028,1030],{"className":1029},[570,571,572,573],[188,1031,934],{"className":1032},[243,573],[188,1034,1036,1066],{"className":1035},[191],[188,1037,1039],{"className":1038},[195],[197,1040,1041],{"xmlns":199},[201,1042,1043,1063],{},[204,1044,1045,1047,1049,1059,1061],{},[207,1046,209],{},[211,1048,214],{"stretchy":213},[916,1050,1051,1057],{},[204,1052,1053,1055],{},[207,1054,922],{},[211,1056,925],{},[505,1058,507],{},[207,1060,217],{},[211,1062,220],{"stretchy":213},[222,1064,1065],{"encoding":224},"O(\\log_2 n)",[188,1067,1069],{"className":1068,"ariaHidden":230},[229],[188,1070,1072,1075,1078,1081,1123,1126,1129],{"className":1071},[234],[188,1073],{"className":1074,"style":239},[238],[188,1076,209],{"className":1077,"style":245},[243,244],[188,1079,214],{"className":1080},[249],[188,1082,1084,1089],{"className":1083},[951],[188,1085,955,1087],{"className":1086},[951],[188,1088,959],{"style":958},[188,1090,1092],{"className":1091},[545],[188,1093,1095,1115],{"className":1094},[549,966],[188,1096,1098,1112],{"className":1097},[553],[188,1099,1101],{"className":1100,"style":973},[557],[188,1102,1103,1106],{"style":976},[188,1104],{"className":1105,"style":566},[565],[188,1107,1109],{"className":1108},[570,571,572,573],[188,1110,507],{"className":1111},[243,573],[188,1113,990],{"className":1114},[989],[188,1116,1118],{"className":1117},[553],[188,1119,1121],{"className":1120,"style":997},[557],[188,1122],{},[188,1124],{"className":1125,"style":1003},[584],[188,1127,217],{"className":1128},[243,244],[188,1130,220],{"className":1131},[256],[429,1133],{},"\nD. ",[188,1136,1138,1165],{"className":1137},[191],[188,1139,1141],{"className":1140},[195],[197,1142,1143],{"xmlns":199},[201,1144,1145,1163],{},[204,1146,1147,1157],{},[916,1148,1149,1155],{},[204,1150,1151,1153],{},[207,1152,922],{},[211,1154,925],{},[505,1156,507],{},[500,1158,1159,1161],{},[207,1160,217],{},[505,1162,934],{},[222,1164,937],{"encoding":224},[188,1166,1168],{"className":1167,"ariaHidden":230},[229],[188,1169,1171,1174,1216,1219],{"className":1170},[234],[188,1172],{"className":1173,"style":947},[238],[188,1175,1177,1182],{"className":1176},[951],[188,1178,955,1180],{"className":1179},[951],[188,1181,959],{"style":958},[188,1183,1185],{"className":1184},[545],[188,1186,1188,1208],{"className":1187},[549,966],[188,1189,1191,1205],{"className":1190},[553],[188,1192,1194],{"className":1193,"style":973},[557],[188,1195,1196,1199],{"style":976},[188,1197],{"className":1198,"style":566},[565],[188,1200,1202],{"className":1201},[570,571,572,573],[188,1203,507],{"className":1204},[243,573],[188,1206,990],{"className":1207},[989],[188,1209,1211],{"className":1210},[553],[188,1212,1214],{"className":1213,"style":997},[557],[188,1215],{},[188,1217],{"className":1218,"style":1003},[584],[188,1220,1222,1225],{"className":1221},[243],[188,1223,217],{"className":1224},[243,244],[188,1226,1228],{"className":1227},[545],[188,1229,1231],{"className":1230},[549],[188,1232,1234],{"className":1233},[553],[188,1235,1237],{"className":1236,"style":558},[557],[188,1238,1239,1242],{"style":561},[188,1240],{"className":1241,"style":566},[565],[188,1243,1245],{"className":1244},[570,571,572,573],[188,1246,934],{"className":1247},[243,573],[188,1249,1251,1275],{"className":1250},[191],[188,1252,1254],{"className":1253},[195],[197,1255,1256],{"xmlns":199},[201,1257,1258,1272],{},[204,1259,1260,1262,1264,1270],{},[207,1261,839],{"mathvariant":510},[211,1263,214],{"stretchy":213},[500,1265,1266,1268],{},[207,1267,217],{},[505,1269,934],{},[211,1271,220],{"stretchy":213},[222,1273,1274],{"encoding":224},"\\Omega(n^3)",[188,1276,1278],{"className":1277,"ariaHidden":230},[229],[188,1279,1281,1284,1287,1290,1319],{"className":1280},[234],[188,1282],{"className":1283,"style":535},[238],[188,1285,839],{"className":1286},[243],[188,1288,214],{"className":1289},[249],[188,1291,1293,1296],{"className":1292},[243],[188,1294,217],{"className":1295},[243,244],[188,1297,1299],{"className":1298},[545],[188,1300,1302],{"className":1301},[549],[188,1303,1305],{"className":1304},[553],[188,1306,1308],{"className":1307,"style":558},[557],[188,1309,1310,1313],{"style":561},[188,1311],{"className":1312,"style":566},[565],[188,1314,1316],{"className":1315},[570,571,572,573],[188,1317,934],{"className":1318},[243,573],[188,1320,220],{"className":1321},[256],[22,1323,32],{"id":1324},"答案与深度解析-5",[27,1326,1327],{},[36,1328,1329],{},"答案：D",[68,1331,1332],{},[44,1333,1334,1336,1337,1365,1366],{},[36,1335,452],{}," 复杂度分析关注的是当问题规模 ",[188,1338,1340,1353],{"className":1339},[191],[188,1341,1343],{"className":1342},[195],[197,1344,1345],{"xmlns":199},[201,1346,1347,1351],{},[204,1348,1349],{},[207,1350,217],{},[222,1352,217],{"encoding":224},[188,1354,1356],{"className":1355,"ariaHidden":230},[229],[188,1357,1359,1362],{"className":1358},[234],[188,1360],{"className":1361,"style":351},[238],[188,1363,217],{"className":1364},[243,244]," 趋于无穷大时，函数的增长量级。我们在多项式相加时，只保留最高阶项。\n",[68,1367,1368,1787,2296],{},[44,1369,1370,1371,1488,1489,1548,1549,1608,1609,1667,1668,1697,1698,1727,1728,1786],{},"对于 ",[188,1372,1374,1403],{"className":1373},[191],[188,1375,1377],{"className":1376},[195],[197,1378,1379],{"xmlns":199},[201,1380,1381,1401],{},[204,1382,1383,1389,1391,1393,1395],{},[500,1384,1385,1387],{},[207,1386,217],{},[505,1388,507],{},[207,1390,511],{"mathvariant":510},[505,1392,507],{},[211,1394,516],{},[500,1396,1397,1399],{},[505,1398,507],{},[207,1400,217],{},[222,1402,525],{"encoding":224},[188,1404,1406,1453],{"className":1405,"ariaHidden":230},[229],[188,1407,1409,1412,1441,1444,1447,1450],{"className":1408},[234],[188,1410],{"className":1411,"style":535},[238],[188,1413,1415,1418],{"className":1414},[243],[188,1416,217],{"className":1417},[243,244],[188,1419,1421],{"className":1420},[545],[188,1422,1424],{"className":1423},[549],[188,1425,1427],{"className":1426},[553],[188,1428,1430],{"className":1429,"style":558},[557],[188,1431,1432,1435],{"style":561},[188,1433],{"className":1434,"style":566},[565],[188,1436,1438],{"className":1437},[570,571,572,573],[188,1439,507],{"className":1440},[243,573],[188,1442,580],{"className":1443},[243],[188,1445],{"className":1446,"style":585},[584],[188,1448,516],{"className":1449},[589],[188,1451],{"className":1452,"style":585},[584],[188,1454,1456,1459],{"className":1455},[234],[188,1457],{"className":1458,"style":599},[238],[188,1460,1462,1465],{"className":1461},[243],[188,1463,507],{"className":1464},[243],[188,1466,1468],{"className":1467},[545],[188,1469,1471],{"className":1470},[549],[188,1472,1474],{"className":1473},[553],[188,1475,1477],{"className":1476,"style":599},[557],[188,1478,1479,1482],{"style":561},[188,1480],{"className":1481,"style":566},[565],[188,1483,1485],{"className":1484},[570,571,572,573],[188,1486,217],{"className":1487},[243,244,573],"，指数级 ",[188,1490,1492,1510],{"className":1491},[191],[188,1493,1495],{"className":1494},[195],[197,1496,1497],{"xmlns":199},[201,1498,1499,1507],{},[204,1500,1501],{},[500,1502,1503,1505],{},[505,1504,507],{},[207,1506,217],{},[222,1508,1509],{"encoding":224},"2^n",[188,1511,1513],{"className":1512,"ariaHidden":230},[229],[188,1514,1516,1519],{"className":1515},[234],[188,1517],{"className":1518,"style":599},[238],[188,1520,1522,1525],{"className":1521},[243],[188,1523,507],{"className":1524},[243],[188,1526,1528],{"className":1527},[545],[188,1529,1531],{"className":1530},[549],[188,1532,1534],{"className":1533},[553],[188,1535,1537],{"className":1536,"style":599},[557],[188,1538,1539,1542],{"style":561},[188,1540],{"className":1541,"style":566},[565],[188,1543,1545],{"className":1544},[570,571,572,573],[188,1546,217],{"className":1547},[243,244,573]," 的增长速度远远快于多项式 ",[188,1550,1552,1570],{"className":1551},[191],[188,1553,1555],{"className":1554},[195],[197,1556,1557],{"xmlns":199},[201,1558,1559,1567],{},[204,1560,1561],{},[500,1562,1563,1565],{},[207,1564,217],{},[505,1566,507],{},[222,1568,1569],{"encoding":224},"n^2",[188,1571,1573],{"className":1572,"ariaHidden":230},[229],[188,1574,1576,1579],{"className":1575},[234],[188,1577],{"className":1578,"style":558},[238],[188,1580,1582,1585],{"className":1581},[243],[188,1583,217],{"className":1584},[243,244],[188,1586,1588],{"className":1587},[545],[188,1589,1591],{"className":1590},[549],[188,1592,1594],{"className":1593},[553],[188,1595,1597],{"className":1596,"style":558},[557],[188,1598,1599,1602],{"style":561},[188,1600],{"className":1601,"style":566},[565],[188,1603,1605],{"className":1604},[570,571,572,573],[188,1606,507],{"className":1607},[243,573],"。因此最高阶项是 ",[188,1610,1612,1629],{"className":1611},[191],[188,1613,1615],{"className":1614},[195],[197,1616,1617],{"xmlns":199},[201,1618,1619,1627],{},[204,1620,1621],{},[500,1622,1623,1625],{},[505,1624,507],{},[207,1626,217],{},[222,1628,1509],{"encoding":224},[188,1630,1632],{"className":1631,"ariaHidden":230},[229],[188,1633,1635,1638],{"className":1634},[234],[188,1636],{"className":1637,"style":599},[238],[188,1639,1641,1644],{"className":1640},[243],[188,1642,507],{"className":1643},[243],[188,1645,1647],{"className":1646},[545],[188,1648,1650],{"className":1649},[549],[188,1651,1653],{"className":1652},[553],[188,1654,1656],{"className":1655,"style":599},[557],[188,1657,1658,1661],{"style":561},[188,1659],{"className":1660,"style":566},[565],[188,1662,1664],{"className":1663},[570,571,572,573],[188,1665,217],{"className":1666},[243,244,573],"。它的上界 ",[188,1669,1671,1684],{"className":1670},[191],[188,1672,1674],{"className":1673},[195],[197,1675,1676],{"xmlns":199},[201,1677,1678,1682],{},[204,1679,1680],{},[207,1681,209],{},[222,1683,209],{"encoding":224},[188,1685,1687],{"className":1686,"ariaHidden":230},[229],[188,1688,1690,1694],{"className":1689},[234],[188,1691],{"className":1692,"style":1693},[238],"height:0.6833em;",[188,1695,209],{"className":1696,"style":245},[243,244]," 和下界 ",[188,1699,1701,1715],{"className":1700},[191],[188,1702,1704],{"className":1703},[195],[197,1705,1706],{"xmlns":199},[201,1707,1708,1712],{},[204,1709,1710],{},[207,1711,839],{"mathvariant":510},[222,1713,1714],{"encoding":224},"\\Omega",[188,1716,1718],{"className":1717,"ariaHidden":230},[229],[188,1719,1721,1724],{"className":1720},[234],[188,1722],{"className":1723,"style":1693},[238],[188,1725,839],{"className":1726},[243]," 都可以是 ",[188,1729,1731,1748],{"className":1730},[191],[188,1732,1734],{"className":1733},[195],[197,1735,1736],{"xmlns":199},[201,1737,1738,1746],{},[204,1739,1740],{},[500,1741,1742,1744],{},[505,1743,507],{},[207,1745,217],{},[222,1747,1509],{"encoding":224},[188,1749,1751],{"className":1750,"ariaHidden":230},[229],[188,1752,1754,1757],{"className":1753},[234],[188,1755],{"className":1756,"style":599},[238],[188,1758,1760,1763],{"className":1759},[243],[188,1761,507],{"className":1762},[243],[188,1764,1766],{"className":1765},[545],[188,1767,1769],{"className":1768},[549],[188,1770,1772],{"className":1771},[553],[188,1773,1775],{"className":1774,"style":599},[557],[188,1776,1777,1780],{"style":561},[188,1778],{"className":1779,"style":566},[565],[188,1781,1783],{"className":1782},[570,571,572,573],[188,1784,217],{"className":1785},[243,244,573],"。A和B表述正确。",[44,1788,1370,1789,1902,1903,1996,1997,2097,2098,2196,2197,85],{},[188,1790,1792,1819],{"className":1791},[191],[188,1793,1795],{"className":1794},[195],[197,1796,1797],{"xmlns":199},[201,1798,1799,1817],{},[204,1800,1801,1811],{},[916,1802,1803,1809],{},[204,1804,1805,1807],{},[207,1806,922],{},[211,1808,925],{},[505,1810,507],{},[500,1812,1813,1815],{},[207,1814,217],{},[505,1816,934],{},[222,1818,937],{"encoding":224},[188,1820,1822],{"className":1821,"ariaHidden":230},[229],[188,1823,1825,1828,1870,1873],{"className":1824},[234],[188,1826],{"className":1827,"style":947},[238],[188,1829,1831,1836],{"className":1830},[951],[188,1832,955,1834],{"className":1833},[951],[188,1835,959],{"style":958},[188,1837,1839],{"className":1838},[545],[188,1840,1842,1862],{"className":1841},[549,966],[188,1843,1845,1859],{"className":1844},[553],[188,1846,1848],{"className":1847,"style":973},[557],[188,1849,1850,1853],{"style":976},[188,1851],{"className":1852,"style":566},[565],[188,1854,1856],{"className":1855},[570,571,572,573],[188,1857,507],{"className":1858},[243,573],[188,1860,990],{"className":1861},[989],[188,1863,1865],{"className":1864},[553],[188,1866,1868],{"className":1867,"style":997},[557],[188,1869],{},[188,1871],{"className":1872,"style":1003},[584],[188,1874,1876,1879],{"className":1875},[243],[188,1877,217],{"className":1878},[243,244],[188,1880,1882],{"className":1881},[545],[188,1883,1885],{"className":1884},[549],[188,1886,1888],{"className":1887},[553],[188,1889,1891],{"className":1890,"style":558},[557],[188,1892,1893,1896],{"style":561},[188,1894],{"className":1895,"style":566},[565],[188,1897,1899],{"className":1898},[570,571,572,573],[188,1900,934],{"className":1901},[243,573],"，根据对数运算法则，它等于 ",[188,1904,1906,1932],{"className":1905},[191],[188,1907,1909],{"className":1908},[195],[197,1910,1911],{"xmlns":199},[201,1912,1913,1929],{},[204,1914,1915,1917,1927],{},[505,1916,934],{},[916,1918,1919,1925],{},[204,1920,1921,1923],{},[207,1922,922],{},[211,1924,925],{},[505,1926,507],{},[207,1928,217],{},[222,1930,1931],{"encoding":224},"3 \\log_2 n",[188,1933,1935],{"className":1934,"ariaHidden":230},[229],[188,1936,1938,1942,1945,1948,1990,1993],{"className":1937},[234],[188,1939],{"className":1940,"style":1941},[238],"height:0.9386em;vertical-align:-0.2441em;",[188,1943,934],{"className":1944},[243],[188,1946],{"className":1947,"style":1003},[584],[188,1949,1951,1956],{"className":1950},[951],[188,1952,955,1954],{"className":1953},[951],[188,1955,959],{"style":958},[188,1957,1959],{"className":1958},[545],[188,1960,1962,1982],{"className":1961},[549,966],[188,1963,1965,1979],{"className":1964},[553],[188,1966,1968],{"className":1967,"style":973},[557],[188,1969,1970,1973],{"style":976},[188,1971],{"className":1972,"style":566},[565],[188,1974,1976],{"className":1975},[570,571,572,573],[188,1977,507],{"className":1978},[243,573],[188,1980,990],{"className":1981},[989],[188,1983,1985],{"className":1984},[553],[188,1986,1988],{"className":1987,"style":997},[557],[188,1989],{},[188,1991],{"className":1992,"style":1003},[584],[188,1994,217],{"className":1995},[243,244],"。常数系数 3 在量级分析中被忽略，因此它的确切量级是 ",[188,1998,2000,2031],{"className":1999},[191],[188,2001,2003],{"className":2002},[195],[197,2004,2005],{"xmlns":199},[201,2006,2007,2028],{},[204,2008,2009,2012,2014,2024,2026],{},[207,2010,2011],{"mathvariant":510},"Θ",[211,2013,214],{"stretchy":213},[916,2015,2016,2022],{},[204,2017,2018,2020],{},[207,2019,922],{},[211,2021,925],{},[505,2023,507],{},[207,2025,217],{},[211,2027,220],{"stretchy":213},[222,2029,2030],{"encoding":224},"\\Theta(\\log_2 n)",[188,2032,2034],{"className":2033,"ariaHidden":230},[229],[188,2035,2037,2040,2043,2046,2088,2091,2094],{"className":2036},[234],[188,2038],{"className":2039,"style":239},[238],[188,2041,2011],{"className":2042},[243],[188,2044,214],{"className":2045},[249],[188,2047,2049,2054],{"className":2048},[951],[188,2050,955,2052],{"className":2051},[951],[188,2053,959],{"style":958},[188,2055,2057],{"className":2056},[545],[188,2058,2060,2080],{"className":2059},[549,966],[188,2061,2063,2077],{"className":2062},[553],[188,2064,2066],{"className":2065,"style":973},[557],[188,2067,2068,2071],{"style":976},[188,2069],{"className":2070,"style":566},[565],[188,2072,2074],{"className":2073},[570,571,572,573],[188,2075,507],{"className":2076},[243,573],[188,2078,990],{"className":2079},[989],[188,2081,2083],{"className":2082},[553],[188,2084,2086],{"className":2085,"style":997},[557],[188,2087],{},[188,2089],{"className":2090,"style":1003},[584],[188,2092,217],{"className":2093},[243,244],[188,2095,220],{"className":2096},[256],"。这意味着它的上界是 ",[188,2099,2101,2130],{"className":2100},[191],[188,2102,2104],{"className":2103},[195],[197,2105,2106],{"xmlns":199},[201,2107,2108,2128],{},[204,2109,2110,2112,2114,2124,2126],{},[207,2111,209],{},[211,2113,214],{"stretchy":213},[916,2115,2116,2122],{},[204,2117,2118,2120],{},[207,2119,922],{},[211,2121,925],{},[505,2123,507],{},[207,2125,217],{},[211,2127,220],{"stretchy":213},[222,2129,1065],{"encoding":224},[188,2131,2133],{"className":2132,"ariaHidden":230},[229],[188,2134,2136,2139,2142,2145,2187,2190,2193],{"className":2135},[234],[188,2137],{"className":2138,"style":239},[238],[188,2140,209],{"className":2141,"style":245},[243,244],[188,2143,214],{"className":2144},[249],[188,2146,2148,2153],{"className":2147},[951],[188,2149,955,2151],{"className":2150},[951],[188,2152,959],{"style":958},[188,2154,2156],{"className":2155},[545],[188,2157,2159,2179],{"className":2158},[549,966],[188,2160,2162,2176],{"className":2161},[553],[188,2163,2165],{"className":2164,"style":973},[557],[188,2166,2167,2170],{"style":976},[188,2168],{"className":2169,"style":566},[565],[188,2171,2173],{"className":2172},[570,571,572,573],[188,2174,507],{"className":2175},[243,573],[188,2177,990],{"className":2178},[989],[188,2180,2182],{"className":2181},[553],[188,2183,2185],{"className":2184,"style":997},[557],[188,2186],{},[188,2188],{"className":2189,"style":1003},[584],[188,2191,217],{"className":2192},[243,244],[188,2194,220],{"className":2195},[256],"，下界是 ",[188,2198,2200,2230],{"className":2199},[191],[188,2201,2203],{"className":2202},[195],[197,2204,2205],{"xmlns":199},[201,2206,2207,2227],{},[204,2208,2209,2211,2213,2223,2225],{},[207,2210,839],{"mathvariant":510},[211,2212,214],{"stretchy":213},[916,2214,2215,2221],{},[204,2216,2217,2219],{},[207,2218,922],{},[211,2220,925],{},[505,2222,507],{},[207,2224,217],{},[211,2226,220],{"stretchy":213},[222,2228,2229],{"encoding":224},"\\Omega(\\log_2 n)",[188,2231,2233],{"className":2232,"ariaHidden":230},[229],[188,2234,2236,2239,2242,2245,2287,2290,2293],{"className":2235},[234],[188,2237],{"className":2238,"style":239},[238],[188,2240,839],{"className":2241},[243],[188,2243,214],{"className":2244},[249],[188,2246,2248,2253],{"className":2247},[951],[188,2249,955,2251],{"className":2250},[951],[188,2252,959],{"style":958},[188,2254,2256],{"className":2255},[545],[188,2257,2259,2279],{"className":2258},[549,966],[188,2260,2262,2276],{"className":2261},[553],[188,2263,2265],{"className":2264,"style":973},[557],[188,2266,2267,2270],{"style":976},[188,2268],{"className":2269,"style":566},[565],[188,2271,2273],{"className":2272},[570,571,572,573],[188,2274,507],{"className":2275},[243,573],[188,2277,990],{"className":2278},[989],[188,2280,2282],{"className":2281},[553],[188,2283,2285],{"className":2284,"style":997},[557],[188,2286],{},[188,2288],{"className":2289,"style":1003},[584],[188,2291,217],{"className":2292},[243,244],[188,2294,220],{"className":2295},[256],[44,2297,2298,2299,2372,2373,2432],{},"选项 D 说下界是 ",[188,2300,2302,2325],{"className":2301},[191],[188,2303,2305],{"className":2304},[195],[197,2306,2307],{"xmlns":199},[201,2308,2309,2323],{},[204,2310,2311,2313,2315,2321],{},[207,2312,839],{"mathvariant":510},[211,2314,214],{"stretchy":213},[500,2316,2317,2319],{},[207,2318,217],{},[505,2320,934],{},[211,2322,220],{"stretchy":213},[222,2324,1274],{"encoding":224},[188,2326,2328],{"className":2327,"ariaHidden":230},[229],[188,2329,2331,2334,2337,2340,2369],{"className":2330},[234],[188,2332],{"className":2333,"style":535},[238],[188,2335,839],{"className":2336},[243],[188,2338,214],{"className":2339},[249],[188,2341,2343,2346],{"className":2342},[243],[188,2344,217],{"className":2345},[243,244],[188,2347,2349],{"className":2348},[545],[188,2350,2352],{"className":2351},[549],[188,2353,2355],{"className":2354},[553],[188,2356,2358],{"className":2357,"style":558},[557],[188,2359,2360,2363],{"style":561},[188,2361],{"className":2362,"style":566},[565],[188,2364,2366],{"className":2365},[570,571,572,573],[188,2367,934],{"className":2368},[243,573],[188,2370,220],{"className":2371},[256],"，即认为该函数的增长速度大于等于 ",[188,2374,2376,2394],{"className":2375},[191],[188,2377,2379],{"className":2378},[195],[197,2380,2381],{"xmlns":199},[201,2382,2383,2391],{},[204,2384,2385],{},[500,2386,2387,2389],{},[207,2388,217],{},[505,2390,934],{},[222,2392,2393],{"encoding":224},"n^3",[188,2395,2397],{"className":2396,"ariaHidden":230},[229],[188,2398,2400,2403],{"className":2399},[234],[188,2401],{"className":2402,"style":558},[238],[188,2404,2406,2409],{"className":2405},[243],[188,2407,217],{"className":2408},[243,244],[188,2410,2412],{"className":2411},[545],[188,2413,2415],{"className":2414},[549],[188,2416,2418],{"className":2417},[553],[188,2419,2421],{"className":2420,"style":558},[557],[188,2422,2423,2426],{"style":561},[188,2424],{"className":2425,"style":566},[565],[188,2427,2429],{"className":2428},[570,571,572,573],[188,2430,934],{"className":2431},[243,573],"，这是极其荒谬的，对数函数的增长极其缓慢，远小于多项式函数。因此 D 错误。",[14,2434],{},[22,2436,263],{"id":2437},"_3-题目内容-1",[27,2439,2440,2441,2656,2657,2700,706,2702,2776,902,2778,2915,1134,2917],{},"某递归算法的时间复杂度公式为：",[188,2442,2444,2503],{"className":2443},[191],[188,2445,2447],{"className":2446},[195],[197,2448,2449],{"xmlns":199},[201,2450,2451,2500],{},[204,2452,2453,2456,2458,2460,2462,2465,2468,2470,2472,2474,2476,2478,2480,2482,2488,2498],{},[207,2454,2455],{},"T",[211,2457,214],{"stretchy":213},[207,2459,217],{},[211,2461,220],{"stretchy":213},[211,2463,2464],{},"=",[505,2466,2467],{},"8",[207,2469,2455],{},[211,2471,214],{"stretchy":213},[207,2473,217],{},[207,2475,511],{"mathvariant":510},[505,2477,934],{},[211,2479,220],{"stretchy":213},[211,2481,516],{},[500,2483,2484,2486],{},[207,2485,217],{},[505,2487,507],{},[916,2489,2490,2496],{},[204,2491,2492,2494],{},[207,2493,922],{},[211,2495,925],{},[505,2497,507],{},[207,2499,217],{},[222,2501,2502],{"encoding":224},"T(n)=8T(n\u002F3)+n^2\\log_2 n",[188,2504,2506,2536,2570],{"className":2505,"ariaHidden":230},[229],[188,2507,2509,2512,2516,2519,2522,2525,2529,2533],{"className":2508},[234],[188,2510],{"className":2511,"style":239},[238],[188,2513,2455],{"className":2514,"style":2515},[243,244],"margin-right:0.1389em;",[188,2517,214],{"className":2518},[249],[188,2520,217],{"className":2521},[243,244],[188,2523,220],{"className":2524},[256],[188,2526],{"className":2527,"style":2528},[584],"margin-right:0.2778em;",[188,2530,2464],{"className":2531},[2532],"mrel",[188,2534],{"className":2535,"style":2528},[584],[188,2537,2539,2542,2545,2548,2551,2554,2558,2561,2564,2567],{"className":2538},[234],[188,2540],{"className":2541,"style":239},[238],[188,2543,2467],{"className":2544},[243],[188,2546,2455],{"className":2547,"style":2515},[243,244],[188,2549,214],{"className":2550},[249],[188,2552,217],{"className":2553},[243,244],[188,2555,2557],{"className":2556},[243],"\u002F3",[188,2559,220],{"className":2560},[256],[188,2562],{"className":2563,"style":585},[584],[188,2565,516],{"className":2566},[589],[188,2568],{"className":2569,"style":585},[584],[188,2571,2573,2576,2605,2608,2650,2653],{"className":2572},[234],[188,2574],{"className":2575,"style":947},[238],[188,2577,2579,2582],{"className":2578},[243],[188,2580,217],{"className":2581},[243,244],[188,2583,2585],{"className":2584},[545],[188,2586,2588],{"className":2587},[549],[188,2589,2591],{"className":2590},[553],[188,2592,2594],{"className":2593,"style":558},[557],[188,2595,2596,2599],{"style":561},[188,2597],{"className":2598,"style":566},[565],[188,2600,2602],{"className":2601},[570,571,572,573],[188,2603,507],{"className":2604},[243,573],[188,2606],{"className":2607,"style":1003},[584],[188,2609,2611,2616],{"className":2610},[951],[188,2612,955,2614],{"className":2613},[951],[188,2615,959],{"style":958},[188,2617,2619],{"className":2618},[545],[188,2620,2622,2642],{"className":2621},[549,966],[188,2623,2625,2639],{"className":2624},[553],[188,2626,2628],{"className":2627,"style":973},[557],[188,2629,2630,2633],{"style":976},[188,2631],{"className":2632,"style":566},[565],[188,2634,2636],{"className":2635},[570,571,572,573],[188,2637,507],{"className":2638},[243,573],[188,2640,990],{"className":2641},[989],[188,2643,2645],{"className":2644},[553],[188,2646,2648],{"className":2647,"style":997},[557],[188,2649],{},[188,2651],{"className":2652,"style":1003},[584],[188,2654,217],{"className":2655},[243,244],"，则该算法的时间复杂度为（ ）。\nA. ",[188,2658,2660,2679],{"className":2659},[191],[188,2661,2663],{"className":2662},[195],[197,2664,2665],{"xmlns":199},[201,2666,2667,2677],{},[204,2668,2669,2671,2673,2675],{},[207,2670,209],{},[211,2672,214],{"stretchy":213},[207,2674,217],{},[211,2676,220],{"stretchy":213},[222,2678,225],{"encoding":224},[188,2680,2682],{"className":2681,"ariaHidden":230},[229],[188,2683,2685,2688,2691,2694,2697],{"className":2684},[234],[188,2686],{"className":2687,"style":239},[238],[188,2689,209],{"className":2690,"style":245},[243,244],[188,2692,214],{"className":2693},[249],[188,2695,217],{"className":2696},[243,244],[188,2698,220],{"className":2699},[256],[429,2701],{},[188,2703,2705,2729],{"className":2704},[191],[188,2706,2708],{"className":2707},[195],[197,2709,2710],{"xmlns":199},[201,2711,2712,2726],{},[204,2713,2714,2716,2718,2724],{},[207,2715,209],{},[211,2717,214],{"stretchy":213},[500,2719,2720,2722],{},[207,2721,217],{},[505,2723,507],{},[211,2725,220],{"stretchy":213},[222,2727,2728],{"encoding":224},"O(n^2)",[188,2730,2732],{"className":2731,"ariaHidden":230},[229],[188,2733,2735,2738,2741,2744,2773],{"className":2734},[234],[188,2736],{"className":2737,"style":535},[238],[188,2739,209],{"className":2740,"style":245},[243,244],[188,2742,214],{"className":2743},[249],[188,2745,2747,2750],{"className":2746},[243],[188,2748,217],{"className":2749},[243,244],[188,2751,2753],{"className":2752},[545],[188,2754,2756],{"className":2755},[549],[188,2757,2759],{"className":2758},[553],[188,2760,2762],{"className":2761,"style":558},[557],[188,2763,2764,2767],{"style":561},[188,2765],{"className":2766,"style":566},[565],[188,2768,2770],{"className":2769},[570,571,572,573],[188,2771,507],{"className":2772},[243,573],[188,2774,220],{"className":2775},[256],[429,2777],{},[188,2779,2781,2817],{"className":2780},[191],[188,2782,2784],{"className":2783},[195],[197,2785,2786],{"xmlns":199},[201,2787,2788,2814],{},[204,2789,2790,2792,2794,2800,2810,2812],{},[207,2791,209],{},[211,2793,214],{"stretchy":213},[500,2795,2796,2798],{},[207,2797,217],{},[505,2799,507],{},[916,2801,2802,2808],{},[204,2803,2804,2806],{},[207,2805,922],{},[211,2807,925],{},[505,2809,507],{},[207,2811,217],{},[211,2813,220],{"stretchy":213},[222,2815,2816],{"encoding":224},"O(n^2 \\log_2 n)",[188,2818,2820],{"className":2819,"ariaHidden":230},[229],[188,2821,2823,2826,2829,2832,2861,2864,2906,2909,2912],{"className":2822},[234],[188,2824],{"className":2825,"style":535},[238],[188,2827,209],{"className":2828,"style":245},[243,244],[188,2830,214],{"className":2831},[249],[188,2833,2835,2838],{"className":2834},[243],[188,2836,217],{"className":2837},[243,244],[188,2839,2841],{"className":2840},[545],[188,2842,2844],{"className":2843},[549],[188,2845,2847],{"className":2846},[553],[188,2848,2850],{"className":2849,"style":558},[557],[188,2851,2852,2855],{"style":561},[188,2853],{"className":2854,"style":566},[565],[188,2856,2858],{"className":2857},[570,571,572,573],[188,2859,507],{"className":2860},[243,573],[188,2862],{"className":2863,"style":1003},[584],[188,2865,2867,2872],{"className":2866},[951],[188,2868,955,2870],{"className":2869},[951],[188,2871,959],{"style":958},[188,2873,2875],{"className":2874},[545],[188,2876,2878,2898],{"className":2877},[549,966],[188,2879,2881,2895],{"className":2880},[553],[188,2882,2884],{"className":2883,"style":973},[557],[188,2885,2886,2889],{"style":976},[188,2887],{"className":2888,"style":566},[565],[188,2890,2892],{"className":2891},[570,571,572,573],[188,2893,507],{"className":2894},[243,573],[188,2896,990],{"className":2897},[989],[188,2899,2901],{"className":2900},[553],[188,2902,2904],{"className":2903,"style":997},[557],[188,2905],{},[188,2907],{"className":2908,"style":1003},[584],[188,2910,217],{"className":2911},[243,244],[188,2913,220],{"className":2914},[256],[429,2916],{},[188,2918,2920,2950],{"className":2919},[191],[188,2921,2923],{"className":2922},[195],[197,2924,2925],{"xmlns":199},[201,2926,2927,2947],{},[204,2928,2929,2931,2933,2945],{},[207,2930,209],{},[211,2932,214],{"stretchy":213},[500,2934,2935,2937],{},[207,2936,217],{},[204,2938,2939,2941,2943],{},[505,2940,2467],{},[207,2942,511],{"mathvariant":510},[505,2944,934],{},[211,2946,220],{"stretchy":213},[222,2948,2949],{"encoding":224},"O(n^{8\u002F3})",[188,2951,2953],{"className":2952,"ariaHidden":230},[229],[188,2954,2956,2960,2963,2966,3000],{"className":2955},[234],[188,2957],{"className":2958,"style":2959},[238],"height:1.138em;vertical-align:-0.25em;",[188,2961,209],{"className":2962,"style":245},[243,244],[188,2964,214],{"className":2965},[249],[188,2967,2969,2972],{"className":2968},[243],[188,2970,217],{"className":2971},[243,244],[188,2973,2975],{"className":2974},[545],[188,2976,2978],{"className":2977},[549],[188,2979,2981],{"className":2980},[553],[188,2982,2985],{"className":2983,"style":2984},[557],"height:0.888em;",[188,2986,2987,2990],{"style":561},[188,2988],{"className":2989,"style":566},[565],[188,2991,2993],{"className":2992},[570,571,572,573],[188,2994,2996],{"className":2995},[243,573],[188,2997,2999],{"className":2998},[243,573],"8\u002F3",[188,3001,220],{"className":3002},[256],[22,3004,32],{"id":3005},"答案与深度解析-6",[27,3007,3008],{},[36,3009,3010],{},"答案：C",[68,3012,3013],{},[44,3014,3015,3017,3018,3021,3022,3159,3160],{},[36,3016,452],{}," 此题考察求解递归式的终极武器——",[36,3019,3020],{},"主定理（Master Theorem）","。\n主定理用于求解形式为 ",[188,3023,3025,3074],{"className":3024},[191],[188,3026,3028],{"className":3027},[195],[197,3029,3030],{"xmlns":199},[201,3031,3032,3071],{},[204,3033,3034,3036,3038,3040,3042,3044,3047,3049,3051,3053,3055,3058,3060,3062,3065,3067,3069],{},[207,3035,2455],{},[211,3037,214],{"stretchy":213},[207,3039,217],{},[211,3041,220],{"stretchy":213},[211,3043,2464],{},[207,3045,3046],{},"a",[207,3048,2455],{},[211,3050,214],{"stretchy":213},[207,3052,217],{},[207,3054,511],{"mathvariant":510},[207,3056,3057],{},"b",[211,3059,220],{"stretchy":213},[211,3061,516],{},[207,3063,3064],{},"f",[211,3066,214],{"stretchy":213},[207,3068,217],{},[211,3070,220],{"stretchy":213},[222,3072,3073],{"encoding":224},"T(n) = aT(n\u002Fb) + f(n)",[188,3075,3077,3104,3140],{"className":3076,"ariaHidden":230},[229],[188,3078,3080,3083,3086,3089,3092,3095,3098,3101],{"className":3079},[234],[188,3081],{"className":3082,"style":239},[238],[188,3084,2455],{"className":3085,"style":2515},[243,244],[188,3087,214],{"className":3088},[249],[188,3090,217],{"className":3091},[243,244],[188,3093,220],{"className":3094},[256],[188,3096],{"className":3097,"style":2528},[584],[188,3099,2464],{"className":3100},[2532],[188,3102],{"className":3103,"style":2528},[584],[188,3105,3107,3110,3113,3116,3119,3122,3125,3128,3131,3134,3137],{"className":3106},[234],[188,3108],{"className":3109,"style":239},[238],[188,3111,3046],{"className":3112},[243,244],[188,3114,2455],{"className":3115,"style":2515},[243,244],[188,3117,214],{"className":3118},[249],[188,3120,217],{"className":3121},[243,244],[188,3123,511],{"className":3124},[243],[188,3126,3057],{"className":3127},[243,244],[188,3129,220],{"className":3130},[256],[188,3132],{"className":3133,"style":585},[584],[188,3135,516],{"className":3136},[589],[188,3138],{"className":3139,"style":585},[584],[188,3141,3143,3146,3150,3153,3156],{"className":3142},[234],[188,3144],{"className":3145,"style":239},[238],[188,3147,3064],{"className":3148,"style":3149},[243,244],"margin-right:0.1076em;",[188,3151,214],{"className":3152},[249],[188,3154,217],{"className":3155},[243,244],[188,3157,220],{"className":3158},[256]," 的递归方程。\n",[41,3161,3162,3431,3954,4451,4502],{},[44,3163,3164,3165,3217,3218,3270,3271,3430],{},"提取参数：题干中 ",[188,3166,3168,3186],{"className":3167},[191],[188,3169,3171],{"className":3170},[195],[197,3172,3173],{"xmlns":199},[201,3174,3175,3183],{},[204,3176,3177,3179,3181],{},[207,3178,3046],{},[211,3180,2464],{},[505,3182,2467],{},[222,3184,3185],{"encoding":224},"a = 8",[188,3187,3189,3207],{"className":3188,"ariaHidden":230},[229],[188,3190,3192,3195,3198,3201,3204],{"className":3191},[234],[188,3193],{"className":3194,"style":351},[238],[188,3196,3046],{"className":3197},[243,244],[188,3199],{"className":3200,"style":2528},[584],[188,3202,2464],{"className":3203},[2532],[188,3205],{"className":3206,"style":2528},[584],[188,3208,3210,3214],{"className":3209},[234],[188,3211],{"className":3212,"style":3213},[238],"height:0.6444em;",[188,3215,2467],{"className":3216},[243],"（子问题个数），",[188,3219,3221,3239],{"className":3220},[191],[188,3222,3224],{"className":3223},[195],[197,3225,3226],{"xmlns":199},[201,3227,3228,3236],{},[204,3229,3230,3232,3234],{},[207,3231,3057],{},[211,3233,2464],{},[505,3235,934],{},[222,3237,3238],{"encoding":224},"b = 3",[188,3240,3242,3261],{"className":3241,"ariaHidden":230},[229],[188,3243,3245,3249,3252,3255,3258],{"className":3244},[234],[188,3246],{"className":3247,"style":3248},[238],"height:0.6944em;",[188,3250,3057],{"className":3251},[243,244],[188,3253],{"className":3254,"style":2528},[584],[188,3256,2464],{"className":3257},[2532],[188,3259],{"className":3260,"style":2528},[584],[188,3262,3264,3267],{"className":3263},[234],[188,3265],{"className":3266,"style":3213},[238],[188,3268,934],{"className":3269},[243],"（问题规模缩小的比例），",[188,3272,3274,3314],{"className":3273},[191],[188,3275,3277],{"className":3276},[195],[197,3278,3279],{"xmlns":199},[201,3280,3281,3311],{},[204,3282,3283,3285,3287,3289,3291,3293,3299,3309],{},[207,3284,3064],{},[211,3286,214],{"stretchy":213},[207,3288,217],{},[211,3290,220],{"stretchy":213},[211,3292,2464],{},[500,3294,3295,3297],{},[207,3296,217],{},[505,3298,507],{},[916,3300,3301,3307],{},[204,3302,3303,3305],{},[207,3304,922],{},[211,3306,925],{},[505,3308,507],{},[207,3310,217],{},[222,3312,3313],{"encoding":224},"f(n) = n^2 \\log_2 n",[188,3315,3317,3344],{"className":3316,"ariaHidden":230},[229],[188,3318,3320,3323,3326,3329,3332,3335,3338,3341],{"className":3319},[234],[188,3321],{"className":3322,"style":239},[238],[188,3324,3064],{"className":3325,"style":3149},[243,244],[188,3327,214],{"className":3328},[249],[188,3330,217],{"className":3331},[243,244],[188,3333,220],{"className":3334},[256],[188,3336],{"className":3337,"style":2528},[584],[188,3339,2464],{"className":3340},[2532],[188,3342],{"className":3343,"style":2528},[584],[188,3345,3347,3350,3379,3382,3424,3427],{"className":3346},[234],[188,3348],{"className":3349,"style":947},[238],[188,3351,3353,3356],{"className":3352},[243],[188,3354,217],{"className":3355},[243,244],[188,3357,3359],{"className":3358},[545],[188,3360,3362],{"className":3361},[549],[188,3363,3365],{"className":3364},[553],[188,3366,3368],{"className":3367,"style":558},[557],[188,3369,3370,3373],{"style":561},[188,3371],{"className":3372,"style":566},[565],[188,3374,3376],{"className":3375},[570,571,572,573],[188,3377,507],{"className":3378},[243,573],[188,3380],{"className":3381,"style":1003},[584],[188,3383,3385,3390],{"className":3384},[951],[188,3386,955,3388],{"className":3387},[951],[188,3389,959],{"style":958},[188,3391,3393],{"className":3392},[545],[188,3394,3396,3416],{"className":3395},[549,966],[188,3397,3399,3413],{"className":3398},[553],[188,3400,3402],{"className":3401,"style":973},[557],[188,3403,3404,3407],{"style":976},[188,3405],{"className":3406,"style":566},[565],[188,3408,3410],{"className":3409},[570,571,572,573],[188,3411,507],{"className":3412},[243,573],[188,3414,990],{"className":3415},[989],[188,3417,3419],{"className":3418},[553],[188,3420,3422],{"className":3421,"style":997},[557],[188,3423],{},[188,3425],{"className":3426,"style":1003},[584],[188,3428,217],{"className":3429},[243,244],"（分解和合并的代价）。",[44,3432,3433,3434,3570,3571,3698,3699,3805,3806,3890,3891,85],{},"计算参照项：计算 ",[188,3435,3437,3467],{"className":3436},[191],[188,3438,3440],{"className":3439},[195],[197,3441,3442],{"xmlns":199},[201,3443,3444,3464],{},[204,3445,3446],{},[500,3447,3448,3450],{},[207,3449,217],{},[204,3451,3452,3462],{},[916,3453,3454,3460],{},[204,3455,3456,3458],{},[207,3457,922],{},[211,3459,925],{},[207,3461,3057],{},[207,3463,3046],{},[222,3465,3466],{"encoding":224},"n^{\\log_b a}",[188,3468,3470],{"className":3469,"ariaHidden":230},[229],[188,3471,3473,3477],{"className":3472},[234],[188,3474],{"className":3475,"style":3476},[238],"height:0.8491em;",[188,3478,3480,3483],{"className":3479},[243],[188,3481,217],{"className":3482},[243,244],[188,3484,3486],{"className":3485},[545],[188,3487,3489],{"className":3488},[549],[188,3490,3492],{"className":3491},[553],[188,3493,3495],{"className":3494,"style":3476},[557],[188,3496,3497,3500],{"style":561},[188,3498],{"className":3499,"style":566},[565],[188,3501,3503],{"className":3502},[570,571,572,573],[188,3504,3506,3563,3567],{"className":3505},[243,573],[188,3507,3509,3523],{"className":3508},[951,573],[188,3510,3512,3516,3520],{"className":3511},[951,573],[188,3513,3515],{"className":3514},[573],"l",[188,3517,3519],{"className":3518},[573],"o",[188,3521,959],{"className":3522,"style":958},[573],[188,3524,3526],{"className":3525},[545],[188,3527,3529,3554],{"className":3528},[549,966],[188,3530,3532,3551],{"className":3531},[553],[188,3533,3536],{"className":3534,"style":3535},[557],"height:0.2302em;",[188,3537,3539,3543],{"style":3538},"top:-2.2341em;margin-right:0.0714em;",[188,3540],{"className":3541,"style":3542},[565],"height:2.5em;",[188,3544,3548],{"className":3545},[570,3546,3547,573],"reset-size3","size1",[188,3549,3057],{"className":3550},[243,244,573],[188,3552,990],{"className":3553},[989],[188,3555,3557],{"className":3556},[553],[188,3558,3561],{"className":3559,"style":3560},[557],"height:0.2659em;",[188,3562],{},[188,3564],{"className":3565,"style":3566},[584,573],"margin-right:0.1952em;",[188,3568,3046],{"className":3569},[243,244,573],"，即 ",[188,3572,3574,3604],{"className":3573},[191],[188,3575,3577],{"className":3576},[195],[197,3578,3579],{"xmlns":199},[201,3580,3581,3601],{},[204,3582,3583],{},[500,3584,3585,3587],{},[207,3586,217],{},[204,3588,3589,3599],{},[916,3590,3591,3597],{},[204,3592,3593,3595],{},[207,3594,922],{},[211,3596,925],{},[505,3598,934],{},[505,3600,2467],{},[222,3602,3603],{"encoding":224},"n^{\\log_3 8}",[188,3605,3607],{"className":3606,"ariaHidden":230},[229],[188,3608,3610,3613],{"className":3609},[234],[188,3611],{"className":3612,"style":3476},[238],[188,3614,3616,3619],{"className":3615},[243],[188,3617,217],{"className":3618},[243,244],[188,3620,3622],{"className":3621},[545],[188,3623,3625],{"className":3624},[549],[188,3626,3628],{"className":3627},[553],[188,3629,3631],{"className":3630,"style":3476},[557],[188,3632,3633,3636],{"style":561},[188,3634],{"className":3635,"style":566},[565],[188,3637,3639],{"className":3638},[570,571,572,573],[188,3640,3642,3692,3695],{"className":3641},[243,573],[188,3643,3645,3657],{"className":3644},[951,573],[188,3646,3648,3651,3654],{"className":3647},[951,573],[188,3649,3515],{"className":3650},[573],[188,3652,3519],{"className":3653},[573],[188,3655,959],{"className":3656,"style":958},[573],[188,3658,3660],{"className":3659},[545],[188,3661,3663,3684],{"className":3662},[549,966],[188,3664,3666,3681],{"className":3665},[553],[188,3667,3670],{"className":3668,"style":3669},[557],"height:0.1944em;",[188,3671,3672,3675],{"style":3538},[188,3673],{"className":3674,"style":3542},[565],[188,3676,3678],{"className":3677},[570,3546,3547,573],[188,3679,934],{"className":3680},[243,573],[188,3682,990],{"className":3683},[989],[188,3685,3687],{"className":3686},[553],[188,3688,3690],{"className":3689,"style":3560},[557],[188,3691],{},[188,3693],{"className":3694,"style":3566},[584,573],[188,3696,2467],{"className":3697},[243,573],"。因为 ",[188,3700,3702,3730],{"className":3701},[191],[188,3703,3705],{"className":3704},[195],[197,3706,3707],{"xmlns":199},[201,3708,3709,3727],{},[204,3710,3711,3717,3719,3722,3725],{},[500,3712,3713,3715],{},[505,3714,934],{},[505,3716,507],{},[211,3718,2464],{},[505,3720,3721],{},"9",[211,3723,3724],{},">",[505,3726,2467],{},[222,3728,3729],{"encoding":224},"3^2 = 9 > 8",[188,3731,3733,3777,3796],{"className":3732,"ariaHidden":230},[229],[188,3734,3736,3739,3768,3771,3774],{"className":3735},[234],[188,3737],{"className":3738,"style":558},[238],[188,3740,3742,3745],{"className":3741},[243],[188,3743,934],{"className":3744},[243],[188,3746,3748],{"className":3747},[545],[188,3749,3751],{"className":3750},[549],[188,3752,3754],{"className":3753},[553],[188,3755,3757],{"className":3756,"style":558},[557],[188,3758,3759,3762],{"style":561},[188,3760],{"className":3761,"style":566},[565],[188,3763,3765],{"className":3764},[570,571,572,573],[188,3766,507],{"className":3767},[243,573],[188,3769],{"className":3770,"style":2528},[584],[188,3772,2464],{"className":3773},[2532],[188,3775],{"className":3776,"style":2528},[584],[188,3778,3780,3784,3787,3790,3793],{"className":3779},[234],[188,3781],{"className":3782,"style":3783},[238],"height:0.6835em;vertical-align:-0.0391em;",[188,3785,3721],{"className":3786},[243],[188,3788],{"className":3789,"style":2528},[584],[188,3791,3724],{"className":3792},[2532],[188,3794],{"className":3795,"style":2528},[584],[188,3797,3799,3802],{"className":3798},[234],[188,3800],{"className":3801,"style":3213},[238],[188,3803,2467],{"className":3804},[243],"，所以 ",[188,3807,3809,3833],{"className":3808},[191],[188,3810,3812],{"className":3811},[195],[197,3813,3814],{"xmlns":199},[201,3815,3816,3830],{},[204,3817,3818,3828],{},[916,3819,3820,3826],{},[204,3821,3822,3824],{},[207,3823,922],{},[211,3825,925],{},[505,3827,934],{},[505,3829,2467],{},[222,3831,3832],{"encoding":224},"\\log_3 8",[188,3834,3836],{"className":3835,"ariaHidden":230},[229],[188,3837,3839,3842,3884,3887],{"className":3838},[234],[188,3840],{"className":3841,"style":1941},[238],[188,3843,3845,3850],{"className":3844},[951],[188,3846,955,3848],{"className":3847},[951],[188,3849,959],{"style":958},[188,3851,3853],{"className":3852},[545],[188,3854,3856,3876],{"className":3855},[549,966],[188,3857,3859,3873],{"className":3858},[553],[188,3860,3862],{"className":3861,"style":973},[557],[188,3863,3864,3867],{"style":976},[188,3865],{"className":3866,"style":566},[565],[188,3868,3870],{"className":3869},[570,571,572,573],[188,3871,934],{"className":3872},[243,573],[188,3874,990],{"className":3875},[989],[188,3877,3879],{"className":3878},[553],[188,3880,3882],{"className":3881,"style":997},[557],[188,3883],{},[188,3885],{"className":3886,"style":1003},[584],[188,3888,2467],{"className":3889},[243]," 的值略小于 2（约为 1.89）。即参照项约为 ",[188,3892,3894,3913],{"className":3893},[191],[188,3895,3897],{"className":3896},[195],[197,3898,3899],{"xmlns":199},[201,3900,3901,3910],{},[204,3902,3903],{},[500,3904,3905,3907],{},[207,3906,217],{},[505,3908,3909],{},"1.89",[222,3911,3912],{"encoding":224},"n^{1.89}",[188,3914,3916],{"className":3915,"ariaHidden":230},[229],[188,3917,3919,3922],{"className":3918},[234],[188,3920],{"className":3921,"style":558},[238],[188,3923,3925,3928],{"className":3924},[243],[188,3926,217],{"className":3927},[243,244],[188,3929,3931],{"className":3930},[545],[188,3932,3934],{"className":3933},[549],[188,3935,3937],{"className":3936},[553],[188,3938,3940],{"className":3939,"style":558},[557],[188,3941,3942,3945],{"style":561},[188,3943],{"className":3944,"style":566},[565],[188,3946,3948],{"className":3947},[570,571,572,573],[188,3949,3951],{"className":3950},[243,573],[188,3952,3909],{"className":3953},[243,573],[44,3955,3956,3957,4001,4002,4160,4161,4222,4223,4281,4282,4325,4326,85],{},"比较 ",[188,3958,3960,3980],{"className":3959},[191],[188,3961,3963],{"className":3962},[195],[197,3964,3965],{"xmlns":199},[201,3966,3967,3977],{},[204,3968,3969,3971,3973,3975],{},[207,3970,3064],{},[211,3972,214],{"stretchy":213},[207,3974,217],{},[211,3976,220],{"stretchy":213},[222,3978,3979],{"encoding":224},"f(n)",[188,3981,3983],{"className":3982,"ariaHidden":230},[229],[188,3984,3986,3989,3992,3995,3998],{"className":3985},[234],[188,3987],{"className":3988,"style":239},[238],[188,3990,3064],{"className":3991,"style":3149},[243,244],[188,3993,214],{"className":3994},[249],[188,3996,217],{"className":3997},[243,244],[188,3999,220],{"className":4000},[256]," 与参照项：我们将 ",[188,4003,4005,4044],{"className":4004},[191],[188,4006,4008],{"className":4007},[195],[197,4009,4010],{"xmlns":199},[201,4011,4012,4042],{},[204,4013,4014,4016,4018,4020,4022,4024,4030,4040],{},[207,4015,3064],{},[211,4017,214],{"stretchy":213},[207,4019,217],{},[211,4021,220],{"stretchy":213},[211,4023,2464],{},[500,4025,4026,4028],{},[207,4027,217],{},[505,4029,507],{},[916,4031,4032,4038],{},[204,4033,4034,4036],{},[207,4035,922],{},[211,4037,925],{},[505,4039,507],{},[207,4041,217],{},[222,4043,3313],{"encoding":224},[188,4045,4047,4074],{"className":4046,"ariaHidden":230},[229],[188,4048,4050,4053,4056,4059,4062,4065,4068,4071],{"className":4049},[234],[188,4051],{"className":4052,"style":239},[238],[188,4054,3064],{"className":4055,"style":3149},[243,244],[188,4057,214],{"className":4058},[249],[188,4060,217],{"className":4061},[243,244],[188,4063,220],{"className":4064},[256],[188,4066],{"className":4067,"style":2528},[584],[188,4069,2464],{"className":4070},[2532],[188,4072],{"className":4073,"style":2528},[584],[188,4075,4077,4080,4109,4112,4154,4157],{"className":4076},[234],[188,4078],{"className":4079,"style":947},[238],[188,4081,4083,4086],{"className":4082},[243],[188,4084,217],{"className":4085},[243,244],[188,4087,4089],{"className":4088},[545],[188,4090,4092],{"className":4091},[549],[188,4093,4095],{"className":4094},[553],[188,4096,4098],{"className":4097,"style":558},[557],[188,4099,4100,4103],{"style":561},[188,4101],{"className":4102,"style":566},[565],[188,4104,4106],{"className":4105},[570,571,572,573],[188,4107,507],{"className":4108},[243,573],[188,4110],{"className":4111,"style":1003},[584],[188,4113,4115,4120],{"className":4114},[951],[188,4116,955,4118],{"className":4117},[951],[188,4119,959],{"style":958},[188,4121,4123],{"className":4122},[545],[188,4124,4126,4146],{"className":4125},[549,966],[188,4127,4129,4143],{"className":4128},[553],[188,4130,4132],{"className":4131,"style":973},[557],[188,4133,4134,4137],{"style":976},[188,4135],{"className":4136,"style":566},[565],[188,4138,4140],{"className":4139},[570,571,572,573],[188,4141,507],{"className":4142},[243,573],[188,4144,990],{"className":4145},[989],[188,4147,4149],{"className":4148},[553],[188,4150,4152],{"className":4151,"style":997},[557],[188,4153],{},[188,4155],{"className":4156,"style":1003},[584],[188,4158,217],{"className":4159},[243,244]," 与 ",[188,4162,4164,4181],{"className":4163},[191],[188,4165,4167],{"className":4166},[195],[197,4168,4169],{"xmlns":199},[201,4170,4171,4179],{},[204,4172,4173],{},[500,4174,4175,4177],{},[207,4176,217],{},[505,4178,3909],{},[222,4180,3912],{"encoding":224},[188,4182,4184],{"className":4183,"ariaHidden":230},[229],[188,4185,4187,4190],{"className":4186},[234],[188,4188],{"className":4189,"style":558},[238],[188,4191,4193,4196],{"className":4192},[243],[188,4194,217],{"className":4195},[243,244],[188,4197,4199],{"className":4198},[545],[188,4200,4202],{"className":4201},[549],[188,4203,4205],{"className":4204},[553],[188,4206,4208],{"className":4207,"style":558},[557],[188,4209,4210,4213],{"style":561},[188,4211],{"className":4212,"style":566},[565],[188,4214,4216],{"className":4215},[570,571,572,573],[188,4217,4219],{"className":4218},[243,573],[188,4220,3909],{"className":4221},[243,573]," 比较。显然 ",[188,4224,4226,4243],{"className":4225},[191],[188,4227,4229],{"className":4228},[195],[197,4230,4231],{"xmlns":199},[201,4232,4233,4241],{},[204,4234,4235],{},[500,4236,4237,4239],{},[207,4238,217],{},[505,4240,507],{},[222,4242,1569],{"encoding":224},[188,4244,4246],{"className":4245,"ariaHidden":230},[229],[188,4247,4249,4252],{"className":4248},[234],[188,4250],{"className":4251,"style":558},[238],[188,4253,4255,4258],{"className":4254},[243],[188,4256,217],{"className":4257},[243,244],[188,4259,4261],{"className":4260},[545],[188,4262,4264],{"className":4263},[549],[188,4265,4267],{"className":4266},[553],[188,4268,4270],{"className":4269,"style":558},[557],[188,4271,4272,4275],{"style":561},[188,4273],{"className":4274,"style":566},[565],[188,4276,4278],{"className":4277},[570,571,572,573],[188,4279,507],{"className":4280},[243,573]," 的多项式阶数 2 大于 1.89。所以 ",[188,4283,4285,4304],{"className":4284},[191],[188,4286,4288],{"className":4287},[195],[197,4289,4290],{"xmlns":199},[201,4291,4292,4302],{},[204,4293,4294,4296,4298,4300],{},[207,4295,3064],{},[211,4297,214],{"stretchy":213},[207,4299,217],{},[211,4301,220],{"stretchy":213},[222,4303,3979],{"encoding":224},[188,4305,4307],{"className":4306,"ariaHidden":230},[229],[188,4308,4310,4313,4316,4319,4322],{"className":4309},[234],[188,4311],{"className":4312,"style":239},[238],[188,4314,3064],{"className":4315,"style":3149},[243,244],[188,4317,214],{"className":4318},[249],[188,4320,217],{"className":4321},[243,244],[188,4323,220],{"className":4324},[256]," 在多项式意义上大于 ",[188,4327,4329,4358],{"className":4328},[191],[188,4330,4332],{"className":4331},[195],[197,4333,4334],{"xmlns":199},[201,4335,4336,4356],{},[204,4337,4338],{},[500,4339,4340,4342],{},[207,4341,217],{},[204,4343,4344,4354],{},[916,4345,4346,4352],{},[204,4347,4348,4350],{},[207,4349,922],{},[211,4351,925],{},[207,4353,3057],{},[207,4355,3046],{},[222,4357,3466],{"encoding":224},[188,4359,4361],{"className":4360,"ariaHidden":230},[229],[188,4362,4364,4367],{"className":4363},[234],[188,4365],{"className":4366,"style":3476},[238],[188,4368,4370,4373],{"className":4369},[243],[188,4371,217],{"className":4372},[243,244],[188,4374,4376],{"className":4375},[545],[188,4377,4379],{"className":4378},[549],[188,4380,4382],{"className":4381},[553],[188,4383,4385],{"className":4384,"style":3476},[557],[188,4386,4387,4390],{"style":561},[188,4388],{"className":4389,"style":566},[565],[188,4391,4393],{"className":4392},[570,571,572,573],[188,4394,4396,4445,4448],{"className":4395},[243,573],[188,4397,4399,4411],{"className":4398},[951,573],[188,4400,4402,4405,4408],{"className":4401},[951,573],[188,4403,3515],{"className":4404},[573],[188,4406,3519],{"className":4407},[573],[188,4409,959],{"className":4410,"style":958},[573],[188,4412,4414],{"className":4413},[545],[188,4415,4417,4437],{"className":4416},[549,966],[188,4418,4420,4434],{"className":4419},[553],[188,4421,4423],{"className":4422,"style":3535},[557],[188,4424,4425,4428],{"style":3538},[188,4426],{"className":4427,"style":3542},[565],[188,4429,4431],{"className":4430},[570,3546,3547,573],[188,4432,3057],{"className":4433},[243,244,573],[188,4435,990],{"className":4436},[989],[188,4438,4440],{"className":4439},[553],[188,4441,4443],{"className":4442,"style":3560},[557],[188,4444],{},[188,4446],{"className":4447,"style":3566},[584,573],[188,4449,3046],{"className":4450},[243,244,573],[44,4452,4453,4454,4457,4458,4501],{},"匹配主定理情况：这属于主定理的",[36,4455,4456],{},"第三种情况","（根节点的计算量占主导地位）。算法的时间复杂度由 ",[188,4459,4461,4480],{"className":4460},[191],[188,4462,4464],{"className":4463},[195],[197,4465,4466],{"xmlns":199},[201,4467,4468,4478],{},[204,4469,4470,4472,4474,4476],{},[207,4471,3064],{},[211,4473,214],{"stretchy":213},[207,4475,217],{},[211,4477,220],{"stretchy":213},[222,4479,3979],{"encoding":224},[188,4481,4483],{"className":4482,"ariaHidden":230},[229],[188,4484,4486,4489,4492,4495,4498],{"className":4485},[234],[188,4487],{"className":4488,"style":239},[238],[188,4490,3064],{"className":4491,"style":3149},[243,244],[188,4493,214],{"className":4494},[249],[188,4496,217],{"className":4497},[243,244],[188,4499,220],{"className":4500},[256]," 决定。",[44,4503,4504,4505,85],{},"结论：",[188,4506,4508,4570],{"className":4507},[191],[188,4509,4511],{"className":4510},[195],[197,4512,4513],{"xmlns":199},[201,4514,4515,4567],{},[204,4516,4517,4519,4521,4523,4525,4527,4529,4531,4533,4535,4537,4539,4541,4543,4545,4547,4553,4563,4565],{},[207,4518,2455],{},[211,4520,214],{"stretchy":213},[207,4522,217],{},[211,4524,220],{"stretchy":213},[211,4526,2464],{},[207,4528,2011],{"mathvariant":510},[211,4530,214],{"stretchy":213},[207,4532,3064],{},[211,4534,214],{"stretchy":213},[207,4536,217],{},[211,4538,220],{"stretchy":213},[211,4540,220],{"stretchy":213},[211,4542,2464],{},[207,4544,209],{},[211,4546,214],{"stretchy":213},[500,4548,4549,4551],{},[207,4550,217],{},[505,4552,507],{},[916,4554,4555,4561],{},[204,4556,4557,4559],{},[207,4558,922],{},[211,4560,925],{},[505,4562,507],{},[207,4564,217],{},[211,4566,220],{"stretchy":213},[222,4568,4569],{"encoding":224},"T(n) = \\Theta(f(n)) = O(n^2 \\log_2 n)",[188,4571,4573,4600,4634],{"className":4572,"ariaHidden":230},[229],[188,4574,4576,4579,4582,4585,4588,4591,4594,4597],{"className":4575},[234],[188,4577],{"className":4578,"style":239},[238],[188,4580,2455],{"className":4581,"style":2515},[243,244],[188,4583,214],{"className":4584},[249],[188,4586,217],{"className":4587},[243,244],[188,4589,220],{"className":4590},[256],[188,4592],{"className":4593,"style":2528},[584],[188,4595,2464],{"className":4596},[2532],[188,4598],{"className":4599,"style":2528},[584],[188,4601,4603,4606,4609,4612,4615,4618,4621,4625,4628,4631],{"className":4602},[234],[188,4604],{"className":4605,"style":239},[238],[188,4607,2011],{"className":4608},[243],[188,4610,214],{"className":4611},[249],[188,4613,3064],{"className":4614,"style":3149},[243,244],[188,4616,214],{"className":4617},[249],[188,4619,217],{"className":4620},[243,244],[188,4622,4624],{"className":4623},[256],"))",[188,4626],{"className":4627,"style":2528},[584],[188,4629,2464],{"className":4630},[2532],[188,4632],{"className":4633,"style":2528},[584],[188,4635,4637,4640,4643,4646,4675,4678,4720,4723,4726],{"className":4636},[234],[188,4638],{"className":4639,"style":535},[238],[188,4641,209],{"className":4642,"style":245},[243,244],[188,4644,214],{"className":4645},[249],[188,4647,4649,4652],{"className":4648},[243],[188,4650,217],{"className":4651},[243,244],[188,4653,4655],{"className":4654},[545],[188,4656,4658],{"className":4657},[549],[188,4659,4661],{"className":4660},[553],[188,4662,4664],{"className":4663,"style":558},[557],[188,4665,4666,4669],{"style":561},[188,4667],{"className":4668,"style":566},[565],[188,4670,4672],{"className":4671},[570,571,572,573],[188,4673,507],{"className":4674},[243,573],[188,4676],{"className":4677,"style":1003},[584],[188,4679,4681,4686],{"className":4680},[951],[188,4682,955,4684],{"className":4683},[951],[188,4685,959],{"style":958},[188,4687,4689],{"className":4688},[545],[188,4690,4692,4712],{"className":4691},[549,966],[188,4693,4695,4709],{"className":4694},[553],[188,4696,4698],{"className":4697,"style":973},[557],[188,4699,4700,4703],{"style":976},[188,4701],{"className":4702,"style":566},[565],[188,4704,4706],{"className":4705},[570,571,572,573],[188,4707,507],{"className":4708},[243,573],[188,4710,990],{"className":4711},[989],[188,4713,4715],{"className":4714},[553],[188,4716,4718],{"className":4717,"style":997},[557],[188,4719],{},[188,4721],{"className":4722,"style":1003},[584],[188,4724,217],{"className":4725},[243,244],[188,4727,220],{"className":4728},[256],[14,4730],{},[22,4732,372],{"id":4733},"_4-题目内容-1",[27,4735,4736,4737,4852,4853,4921,706,4923,5023,902,5025,5084,1134,5086],{},"在棋盘覆盖问题中，关于 ",[188,4738,4740,4768],{"className":4739},[191],[188,4741,4743],{"className":4742},[195],[197,4744,4745],{"xmlns":199},[201,4746,4747,4765],{},[204,4748,4749,4756,4759],{},[500,4750,4751,4753],{},[505,4752,507],{},[207,4754,4755],{},"k",[211,4757,4758],{},"×",[500,4760,4761,4763],{},[505,4762,507],{},[207,4764,4755],{},[222,4766,4767],{"encoding":224},"2^k \\times 2^k",[188,4769,4771,4817],{"className":4770,"ariaHidden":230},[229],[188,4772,4774,4778,4808,4811,4814],{"className":4773},[234],[188,4775],{"className":4776,"style":4777},[238],"height:0.9324em;vertical-align:-0.0833em;",[188,4779,4781,4784],{"className":4780},[243],[188,4782,507],{"className":4783},[243],[188,4785,4787],{"className":4786},[545],[188,4788,4790],{"className":4789},[549],[188,4791,4793],{"className":4792},[553],[188,4794,4796],{"className":4795,"style":3476},[557],[188,4797,4798,4801],{"style":561},[188,4799],{"className":4800,"style":566},[565],[188,4802,4804],{"className":4803},[570,571,572,573],[188,4805,4755],{"className":4806,"style":4807},[243,244,573],"margin-right:0.0315em;",[188,4809],{"className":4810,"style":585},[584],[188,4812,4758],{"className":4813},[589],[188,4815],{"className":4816,"style":585},[584],[188,4818,4820,4823],{"className":4819},[234],[188,4821],{"className":4822,"style":3476},[238],[188,4824,4826,4829],{"className":4825},[243],[188,4827,507],{"className":4828},[243],[188,4830,4832],{"className":4831},[545],[188,4833,4835],{"className":4834},[549],[188,4836,4838],{"className":4837},[553],[188,4839,4841],{"className":4840,"style":3476},[557],[188,4842,4843,4846],{"style":561},[188,4844],{"className":4845,"style":566},[565],[188,4847,4849],{"className":4848},[570,571,572,573],[188,4850,4755],{"className":4851,"style":4807},[243,244,573]," 的特殊棋盘（有一个特殊方块），所需的L型牌（可以覆盖3个方格）的个数是（ ）。\nA. ",[188,4854,4856,4879],{"className":4855},[191],[188,4857,4859],{"className":4858},[195],[197,4860,4861],{"xmlns":199},[201,4862,4863,4876],{},[204,4864,4865,4872,4874],{},[500,4866,4867,4870],{},[505,4868,4869],{},"4",[207,4871,4755],{},[207,4873,511],{"mathvariant":510},[505,4875,934],{},[222,4877,4878],{"encoding":224},"4^k \u002F 3",[188,4880,4882],{"className":4881,"ariaHidden":230},[229],[188,4883,4885,4889,4918],{"className":4884},[234],[188,4886],{"className":4887,"style":4888},[238],"height:1.0991em;vertical-align:-0.25em;",[188,4890,4892,4895],{"className":4891},[243],[188,4893,4869],{"className":4894},[243],[188,4896,4898],{"className":4897},[545],[188,4899,4901],{"className":4900},[549],[188,4902,4904],{"className":4903},[553],[188,4905,4907],{"className":4906,"style":3476},[557],[188,4908,4909,4912],{"style":561},[188,4910],{"className":4911,"style":566},[565],[188,4913,4915],{"className":4914},[570,571,572,573],[188,4916,4755],{"className":4917,"style":4807},[243,244,573],[188,4919,2557],{"className":4920},[243],[429,4922],{},[188,4924,4926,4958],{"className":4925},[191],[188,4927,4929],{"className":4928},[195],[197,4930,4931],{"xmlns":199},[201,4932,4933,4955],{},[204,4934,4935,4937,4943,4946,4949,4951,4953],{},[211,4936,214],{"stretchy":213},[500,4938,4939,4941],{},[505,4940,4869],{},[207,4942,4755],{},[211,4944,4945],{},"−",[505,4947,4948],{},"1",[211,4950,220],{"stretchy":213},[207,4952,511],{"mathvariant":510},[505,4954,934],{},[222,4956,4957],{"encoding":224},"(4^k - 1) \u002F 3",[188,4959,4961,5008],{"className":4960,"ariaHidden":230},[229],[188,4962,4964,4967,4970,4999,5002,5005],{"className":4963},[234],[188,4965],{"className":4966,"style":4888},[238],[188,4968,214],{"className":4969},[249],[188,4971,4973,4976],{"className":4972},[243],[188,4974,4869],{"className":4975},[243],[188,4977,4979],{"className":4978},[545],[188,4980,4982],{"className":4981},[549],[188,4983,4985],{"className":4984},[553],[188,4986,4988],{"className":4987,"style":3476},[557],[188,4989,4990,4993],{"style":561},[188,4991],{"className":4992,"style":566},[565],[188,4994,4996],{"className":4995},[570,571,572,573],[188,4997,4755],{"className":4998,"style":4807},[243,244,573],[188,5000],{"className":5001,"style":585},[584],[188,5003,4945],{"className":5004},[589],[188,5006],{"className":5007,"style":585},[584],[188,5009,5011,5014,5017,5020],{"className":5010},[234],[188,5012],{"className":5013,"style":239},[238],[188,5015,4948],{"className":5016},[243],[188,5018,220],{"className":5019},[256],[188,5021,2557],{"className":5022},[243],[429,5024],{},[188,5026,5028,5046],{"className":5027},[191],[188,5029,5031],{"className":5030},[195],[197,5032,5033],{"xmlns":199},[201,5034,5035,5043],{},[204,5036,5037],{},[500,5038,5039,5041],{},[505,5040,4869],{},[207,5042,4755],{},[222,5044,5045],{"encoding":224},"4^k",[188,5047,5049],{"className":5048,"ariaHidden":230},[229],[188,5050,5052,5055],{"className":5051},[234],[188,5053],{"className":5054,"style":3476},[238],[188,5056,5058,5061],{"className":5057},[243],[188,5059,4869],{"className":5060},[243],[188,5062,5064],{"className":5063},[545],[188,5065,5067],{"className":5066},[549],[188,5068,5070],{"className":5069},[553],[188,5071,5073],{"className":5072,"style":3476},[557],[188,5074,5075,5078],{"style":561},[188,5076],{"className":5077,"style":566},[565],[188,5079,5081],{"className":5080},[570,571,572,573],[188,5082,4755],{"className":5083,"style":4807},[243,244,573],[429,5085],{},[188,5087,5089,5111],{"className":5088},[191],[188,5090,5092],{"className":5091},[195],[197,5093,5094],{"xmlns":199},[201,5095,5096,5108],{},[204,5097,5098,5104,5106],{},[500,5099,5100,5102],{},[505,5101,507],{},[207,5103,4755],{},[207,5105,511],{"mathvariant":510},[505,5107,934],{},[222,5109,5110],{"encoding":224},"2^k \u002F 3",[188,5112,5114],{"className":5113,"ariaHidden":230},[229],[188,5115,5117,5120,5149],{"className":5116},[234],[188,5118],{"className":5119,"style":4888},[238],[188,5121,5123,5126],{"className":5122},[243],[188,5124,507],{"className":5125},[243],[188,5127,5129],{"className":5128},[545],[188,5130,5132],{"className":5131},[549],[188,5133,5135],{"className":5134},[553],[188,5136,5138],{"className":5137,"style":3476},[557],[188,5139,5140,5143],{"style":561},[188,5141],{"className":5142,"style":566},[565],[188,5144,5146],{"className":5145},[570,571,572,573],[188,5147,4755],{"className":5148,"style":4807},[243,244,573],[188,5150,2557],{"className":5151},[243],[22,5153,32],{"id":5154},"答案与深度解析-7",[27,5156,5157],{},[36,5158,445],{},[68,5160,5161],{},[44,5162,5163,5165,5166],{},[36,5164,452],{}," 这是一个纯粹的数学逻辑题，不需要死记硬背算法。\n",[41,5167,5168,5394,5397,5481,5484],{},[44,5169,5170,5171,5230,5231,85],{},"棋盘的边长是 ",[188,5172,5174,5192],{"className":5173},[191],[188,5175,5177],{"className":5176},[195],[197,5178,5179],{"xmlns":199},[201,5180,5181,5189],{},[204,5182,5183],{},[500,5184,5185,5187],{},[505,5186,507],{},[207,5188,4755],{},[222,5190,5191],{"encoding":224},"2^k",[188,5193,5195],{"className":5194,"ariaHidden":230},[229],[188,5196,5198,5201],{"className":5197},[234],[188,5199],{"className":5200,"style":3476},[238],[188,5202,5204,5207],{"className":5203},[243],[188,5205,507],{"className":5206},[243],[188,5208,5210],{"className":5209},[545],[188,5211,5213],{"className":5212},[549],[188,5214,5216],{"className":5215},[553],[188,5217,5219],{"className":5218,"style":3476},[557],[188,5220,5221,5224],{"style":561},[188,5222],{"className":5223,"style":566},[565],[188,5225,5227],{"className":5226},[570,571,572,573],[188,5228,4755],{"className":5229,"style":4807},[243,244,573],"，因此总方格数是边长乘边长：",[188,5232,5234,5268],{"className":5233},[191],[188,5235,5237],{"className":5236},[195],[197,5238,5239],{"xmlns":199},[201,5240,5241,5265],{},[204,5242,5243,5249,5251,5257,5259],{},[500,5244,5245,5247],{},[505,5246,507],{},[207,5248,4755],{},[211,5250,4758],{},[500,5252,5253,5255],{},[505,5254,507],{},[207,5256,4755],{},[211,5258,2464],{},[500,5260,5261,5263],{},[505,5262,4869],{},[207,5264,4755],{},[222,5266,5267],{"encoding":224},"2^k \\times 2^k = 4^k",[188,5269,5271,5315,5359],{"className":5270,"ariaHidden":230},[229],[188,5272,5274,5277,5306,5309,5312],{"className":5273},[234],[188,5275],{"className":5276,"style":4777},[238],[188,5278,5280,5283],{"className":5279},[243],[188,5281,507],{"className":5282},[243],[188,5284,5286],{"className":5285},[545],[188,5287,5289],{"className":5288},[549],[188,5290,5292],{"className":5291},[553],[188,5293,5295],{"className":5294,"style":3476},[557],[188,5296,5297,5300],{"style":561},[188,5298],{"className":5299,"style":566},[565],[188,5301,5303],{"className":5302},[570,571,572,573],[188,5304,4755],{"className":5305,"style":4807},[243,244,573],[188,5307],{"className":5308,"style":585},[584],[188,5310,4758],{"className":5311},[589],[188,5313],{"className":5314,"style":585},[584],[188,5316,5318,5321,5350,5353,5356],{"className":5317},[234],[188,5319],{"className":5320,"style":3476},[238],[188,5322,5324,5327],{"className":5323},[243],[188,5325,507],{"className":5326},[243],[188,5328,5330],{"className":5329},[545],[188,5331,5333],{"className":5332},[549],[188,5334,5336],{"className":5335},[553],[188,5337,5339],{"className":5338,"style":3476},[557],[188,5340,5341,5344],{"style":561},[188,5342],{"className":5343,"style":566},[565],[188,5345,5347],{"className":5346},[570,571,572,573],[188,5348,4755],{"className":5349,"style":4807},[243,244,573],[188,5351],{"className":5352,"style":2528},[584],[188,5354,2464],{"className":5355},[2532],[188,5357],{"className":5358,"style":2528},[584],[188,5360,5362,5365],{"className":5361},[234],[188,5363],{"className":5364,"style":3476},[238],[188,5366,5368,5371],{"className":5367},[243],[188,5369,4869],{"className":5370},[243],[188,5372,5374],{"className":5373},[545],[188,5375,5377],{"className":5376},[549],[188,5378,5380],{"className":5379},[553],[188,5381,5383],{"className":5382,"style":3476},[557],[188,5384,5385,5388],{"style":561},[188,5386],{"className":5387,"style":566},[565],[188,5389,5391],{"className":5390},[570,571,572,573],[188,5392,4755],{"className":5393,"style":4807},[243,244,573],[44,5395,5396],{},"题目说棋盘是“特殊棋盘”，意味着其中有 1 个方格是特殊方格（不需要被覆盖）。",[44,5398,5399,5400,85],{},"需要被L型牌覆盖的剩余方格总数为：",[188,5401,5403,5425],{"className":5402},[191],[188,5404,5406],{"className":5405},[195],[197,5407,5408],{"xmlns":199},[201,5409,5410,5422],{},[204,5411,5412,5418,5420],{},[500,5413,5414,5416],{},[505,5415,4869],{},[207,5417,4755],{},[211,5419,4945],{},[505,5421,4948],{},[222,5423,5424],{"encoding":224},"4^k - 1",[188,5426,5428,5472],{"className":5427,"ariaHidden":230},[229],[188,5429,5431,5434,5463,5466,5469],{"className":5430},[234],[188,5432],{"className":5433,"style":4777},[238],[188,5435,5437,5440],{"className":5436},[243],[188,5438,4869],{"className":5439},[243],[188,5441,5443],{"className":5442},[545],[188,5444,5446],{"className":5445},[549],[188,5447,5449],{"className":5448},[553],[188,5450,5452],{"className":5451,"style":3476},[557],[188,5453,5454,5457],{"style":561},[188,5455],{"className":5456,"style":566},[565],[188,5458,5460],{"className":5459},[570,571,572,573],[188,5461,4755],{"className":5462,"style":4807},[243,244,573],[188,5464],{"className":5465,"style":585},[584],[188,5467,4945],{"className":5468},[589],[188,5470],{"className":5471,"style":585},[584],[188,5473,5475,5478],{"className":5474},[234],[188,5476],{"className":5477,"style":3213},[238],[188,5479,4948],{"className":5480},[243],[44,5482,5483],{},"每一块L型骨牌刚好覆盖 3 个方格。",[44,5485,5486,5487,85],{},"因此所需骨牌数量为：",[188,5488,5490,5519],{"className":5489},[191],[188,5491,5493],{"className":5492},[195],[197,5494,5495],{"xmlns":199},[201,5496,5497,5517],{},[204,5498,5499,5501,5507,5509,5511,5513,5515],{},[211,5500,214],{"stretchy":213},[500,5502,5503,5505],{},[505,5504,4869],{},[207,5506,4755],{},[211,5508,4945],{},[505,5510,4948],{},[211,5512,220],{"stretchy":213},[207,5514,511],{"mathvariant":510},[505,5516,934],{},[222,5518,4957],{"encoding":224},[188,5520,5522,5569],{"className":5521,"ariaHidden":230},[229],[188,5523,5525,5528,5531,5560,5563,5566],{"className":5524},[234],[188,5526],{"className":5527,"style":4888},[238],[188,5529,214],{"className":5530},[249],[188,5532,5534,5537],{"className":5533},[243],[188,5535,4869],{"className":5536},[243],[188,5538,5540],{"className":5539},[545],[188,5541,5543],{"className":5542},[549],[188,5544,5546],{"className":5545},[553],[188,5547,5549],{"className":5548,"style":3476},[557],[188,5550,5551,5554],{"style":561},[188,5552],{"className":5553,"style":566},[565],[188,5555,5557],{"className":5556},[570,571,572,573],[188,5558,4755],{"className":5559,"style":4807},[243,244,573],[188,5561],{"className":5562,"style":585},[584],[188,5564,4945],{"className":5565},[589],[188,5567],{"className":5568,"style":585},[584],[188,5570,5572,5575,5578,5581],{"className":5571},[234],[188,5573],{"className":5574,"style":239},[238],[188,5576,4948],{"className":5577},[243],[188,5579,220],{"className":5580},[256],[188,5582,2557],{"className":5583},[243],[14,5585],{},[22,5587,5589],{"id":5588},"_5-题目内容","5. 题目内容",[27,5591,5592,5593,5621,5622,5650,5651,5679,5680,5682,5683,5685,5686,5688],{},"在求解 ",[188,5594,5596,5609],{"className":5595},[191],[188,5597,5599],{"className":5598},[195],[197,5600,5601],{"xmlns":199},[201,5602,5603,5607],{},[204,5604,5605],{},[207,5606,217],{},[222,5608,217],{"encoding":224},[188,5610,5612],{"className":5611,"ariaHidden":230},[229],[188,5613,5615,5618],{"className":5614},[234],[188,5616],{"className":5617,"style":351},[238],[188,5619,217],{"className":5620},[243,244]," 个元素中第 ",[188,5623,5625,5638],{"className":5624},[191],[188,5626,5628],{"className":5627},[195],[197,5629,5630],{"xmlns":199},[201,5631,5632,5636],{},[204,5633,5634],{},[207,5635,4755],{},[222,5637,4755],{"encoding":224},[188,5639,5641],{"className":5640,"ariaHidden":230},[229],[188,5642,5644,5647],{"className":5643},[234],[188,5645],{"className":5646,"style":3248},[238],[188,5648,4755],{"className":5649,"style":4807},[243,244]," 小元素问题中，假设利用快速排序算法思想对 ",[188,5652,5654,5667],{"className":5653},[191],[188,5655,5657],{"className":5656},[195],[197,5658,5659],{"xmlns":199},[201,5660,5661,5665],{},[204,5662,5663],{},[207,5664,217],{},[222,5666,217],{"encoding":224},[188,5668,5670],{"className":5669,"ariaHidden":230},[229],[188,5671,5673,5676],{"className":5672},[234],[188,5674],{"className":5675,"style":351},[238],[188,5677,217],{"className":5678},[243,244]," 个元素进行划分，应如何选择划分基准（ ）。\nA. 随机选择一个元素作为划分基准",[429,5681],{},"\nB. 取子序列的第一个元素作为划分基准",[429,5684],{},"\nC. 用中位数的中位数方式寻觅划分基准",[429,5687],{},"\nD. 以上皆可行，但不同方式，算法复杂度上界可能不同",[22,5690,32],{"id":5691},"答案与深度解析-8",[27,5693,5694],{},[36,5695,1329],{},[68,5697,5698],{},[44,5699,5700,5702,5703,5731,5732],{},[36,5701,452],{}," 求解第 ",[188,5704,5706,5719],{"className":5705},[191],[188,5707,5709],{"className":5708},[195],[197,5710,5711],{"xmlns":199},[201,5712,5713,5717],{},[204,5714,5715],{},[207,5716,4755],{},[222,5718,4755],{"encoding":224},[188,5720,5722],{"className":5721,"ariaHidden":230},[229],[188,5723,5725,5728],{"className":5724},[234],[188,5726],{"className":5727,"style":3248},[238],[188,5729,4755],{"className":5730,"style":4807},[243,244]," 小元素的经典算法是“快速选择算法”（Quickselect），它的核心也是划分（Partition）。\n",[68,5733,5734,5857,5911],{},[44,5735,5736,5739,5740,5783,5784,85],{},[36,5737,5738],{},"取第一个元素（B）或随机取元素（A）："," 很容易实现，平均时间复杂度很好，是 ",[188,5741,5743,5762],{"className":5742},[191],[188,5744,5746],{"className":5745},[195],[197,5747,5748],{"xmlns":199},[201,5749,5750,5760],{},[204,5751,5752,5754,5756,5758],{},[207,5753,209],{},[211,5755,214],{"stretchy":213},[207,5757,217],{},[211,5759,220],{"stretchy":213},[222,5761,225],{"encoding":224},[188,5763,5765],{"className":5764,"ariaHidden":230},[229],[188,5766,5768,5771,5774,5777,5780],{"className":5767},[234],[188,5769],{"className":5770,"style":239},[238],[188,5772,209],{"className":5773,"style":245},[243,244],[188,5775,214],{"className":5776},[249],[188,5778,217],{"className":5779},[243,244],[188,5781,220],{"className":5782},[256],"。但如果是极端恶劣的数据（例如已经排好序的数组，且每次取第一个），最坏情况下的时间复杂度会退化到 ",[188,5785,5787,5810],{"className":5786},[191],[188,5788,5790],{"className":5789},[195],[197,5791,5792],{"xmlns":199},[201,5793,5794,5808],{},[204,5795,5796,5798,5800,5806],{},[207,5797,209],{},[211,5799,214],{"stretchy":213},[500,5801,5802,5804],{},[207,5803,217],{},[505,5805,507],{},[211,5807,220],{"stretchy":213},[222,5809,2728],{"encoding":224},[188,5811,5813],{"className":5812,"ariaHidden":230},[229],[188,5814,5816,5819,5822,5825,5854],{"className":5815},[234],[188,5817],{"className":5818,"style":535},[238],[188,5820,209],{"className":5821,"style":245},[243,244],[188,5823,214],{"className":5824},[249],[188,5826,5828,5831],{"className":5827},[243],[188,5829,217],{"className":5830},[243,244],[188,5832,5834],{"className":5833},[545],[188,5835,5837],{"className":5836},[549],[188,5838,5840],{"className":5839},[553],[188,5841,5843],{"className":5842,"style":558},[557],[188,5844,5845,5848],{"style":561},[188,5846],{"className":5847,"style":566},[565],[188,5849,5851],{"className":5850},[570,571,572,573],[188,5852,507],{"className":5853},[243,573],[188,5855,220],{"className":5856},[256],[44,5858,5859,5862,5863,5866,5867,5910],{},[36,5860,5861],{},"中位数的中位数（C）："," 这是著名的 BFPRT 算法（线性时间选择算法）。它通过复杂的逻辑强制找到一个相对居中的元素作为基准。虽然常数项较大，但它能保证在",[36,5864,5865],{},"最坏情况","下依然具有 ",[188,5868,5870,5889],{"className":5869},[191],[188,5871,5873],{"className":5872},[195],[197,5874,5875],{"xmlns":199},[201,5876,5877,5887],{},[204,5878,5879,5881,5883,5885],{},[207,5880,209],{},[211,5882,214],{"stretchy":213},[207,5884,217],{},[211,5886,220],{"stretchy":213},[222,5888,225],{"encoding":224},[188,5890,5892],{"className":5891,"ariaHidden":230},[229],[188,5893,5895,5898,5901,5904,5907],{"className":5894},[234],[188,5896],{"className":5897,"style":239},[238],[188,5899,209],{"className":5900,"style":245},[243,244],[188,5902,214],{"className":5903},[249],[188,5905,217],{"className":5906},[243,244],[188,5908,220],{"className":5909},[256]," 的时间复杂度上界。",[44,5912,5913],{},"因此，这三种方法在工程上和理论上都是可行的，只是它们的最坏时间复杂度上界存在差异。选项 D 描述最为客观全面。",[14,5915],{},[22,5917,5919],{"id":5918},"_6-题目内容","6. 题目内容",[27,5921,5922,5923,5997,706,5999,6057,902,6059,6094,1134,6096],{},"用回溯法求解子集树问题，最坏情形下其解空间的叶结点数量为（ ）。\nA. ",[188,5924,5926,5950],{"className":5925},[191],[188,5927,5929],{"className":5928},[195],[197,5930,5931],{"xmlns":199},[201,5932,5933,5947],{},[204,5934,5935],{},[500,5936,5937,5939],{},[505,5938,507],{},[204,5940,5941,5943,5945],{},[207,5942,217],{},[211,5944,4945],{},[505,5946,4948],{},[222,5948,5949],{"encoding":224},"2^{n-1}",[188,5951,5953],{"className":5952,"ariaHidden":230},[229],[188,5954,5956,5959],{"className":5955},[234],[188,5957],{"className":5958,"style":558},[238],[188,5960,5962,5965],{"className":5961},[243],[188,5963,507],{"className":5964},[243],[188,5966,5968],{"className":5967},[545],[188,5969,5971],{"className":5970},[549],[188,5972,5974],{"className":5973},[553],[188,5975,5977],{"className":5976,"style":558},[557],[188,5978,5979,5982],{"style":561},[188,5980],{"className":5981,"style":566},[565],[188,5983,5985],{"className":5984},[570,571,572,573],[188,5986,5988,5991,5994],{"className":5987},[243,573],[188,5989,217],{"className":5990},[243,244,573],[188,5992,4945],{"className":5993},[589,573],[188,5995,4948],{"className":5996},[243,573],[429,5998],{},[188,6000,6002,6019],{"className":6001},[191],[188,6003,6005],{"className":6004},[195],[197,6006,6007],{"xmlns":199},[201,6008,6009,6017],{},[204,6010,6011],{},[500,6012,6013,6015],{},[505,6014,507],{},[207,6016,217],{},[222,6018,1509],{"encoding":224},[188,6020,6022],{"className":6021,"ariaHidden":230},[229],[188,6023,6025,6028],{"className":6024},[234],[188,6026],{"className":6027,"style":599},[238],[188,6029,6031,6034],{"className":6030},[243],[188,6032,507],{"className":6033},[243],[188,6035,6037],{"className":6036},[545],[188,6038,6040],{"className":6039},[549],[188,6041,6043],{"className":6042},[553],[188,6044,6046],{"className":6045,"style":599},[557],[188,6047,6048,6051],{"style":561},[188,6049],{"className":6050,"style":566},[565],[188,6052,6054],{"className":6053},[570,571,572,573],[188,6055,217],{"className":6056},[243,244,573],[429,6058],{},[188,6060,6062,6079],{"className":6061},[191],[188,6063,6065],{"className":6064},[195],[197,6066,6067],{"xmlns":199},[201,6068,6069,6076],{},[204,6070,6071,6073],{},[207,6072,217],{},[211,6074,6075],{"stretchy":213},"!",[222,6077,6078],{"encoding":224},"n!",[188,6080,6082],{"className":6081,"ariaHidden":230},[229],[188,6083,6085,6088,6091],{"className":6084},[234],[188,6086],{"className":6087,"style":3248},[238],[188,6089,217],{"className":6090},[243,244],[188,6092,6075],{"className":6093},[256],[429,6095],{},[188,6097,6099,6127],{"className":6098},[191],[188,6100,6102],{"className":6101},[195],[197,6103,6104],{"xmlns":199},[201,6105,6106,6124],{},[204,6107,6108,6120,6122],{},[500,6109,6110,6112],{},[505,6111,507],{},[204,6113,6114,6116,6118],{},[207,6115,217],{},[211,6117,516],{},[505,6119,4948],{},[211,6121,4945],{},[505,6123,4948],{},[222,6125,6126],{"encoding":224},"2^{n+1}-1",[188,6128,6130,6184],{"className":6129,"ariaHidden":230},[229],[188,6131,6133,6137,6175,6178,6181],{"className":6132},[234],[188,6134],{"className":6135,"style":6136},[238],"height:0.8974em;vertical-align:-0.0833em;",[188,6138,6140,6143],{"className":6139},[243],[188,6141,507],{"className":6142},[243],[188,6144,6146],{"className":6145},[545],[188,6147,6149],{"className":6148},[549],[188,6150,6152],{"className":6151},[553],[188,6153,6155],{"className":6154,"style":558},[557],[188,6156,6157,6160],{"style":561},[188,6158],{"className":6159,"style":566},[565],[188,6161,6163],{"className":6162},[570,571,572,573],[188,6164,6166,6169,6172],{"className":6165},[243,573],[188,6167,217],{"className":6168},[243,244,573],[188,6170,516],{"className":6171},[589,573],[188,6173,4948],{"className":6174},[243,573],[188,6176],{"className":6177,"style":585},[584],[188,6179,4945],{"className":6180},[589],[188,6182],{"className":6183,"style":585},[584],[188,6185,6187,6190],{"className":6186},[234],[188,6188],{"className":6189,"style":3213},[238],[188,6191,4948],{"className":6192},[243],[22,6194,32],{"id":6195},"答案与深度解析-9",[27,6197,6198],{},[36,6199,445],{},[68,6201,6202],{},[44,6203,6204,6206],{},[36,6205,452],{},[68,6207,6208,6243,6275,6365],{},[44,6209,6210,6213,6214,6242],{},[36,6211,6212],{},"子集树（Subset Tree）："," 当问题是从 ",[188,6215,6217,6230],{"className":6216},[191],[188,6218,6220],{"className":6219},[195],[197,6221,6222],{"xmlns":199},[201,6223,6224,6228],{},[204,6225,6226],{},[207,6227,217],{},[222,6229,217],{"encoding":224},[188,6231,6233],{"className":6232,"ariaHidden":230},[229],[188,6234,6236,6239],{"className":6235},[234],[188,6237],{"className":6238,"style":351},[238],[188,6240,217],{"className":6241},[243,244]," 个元素的集合中找出满足某种性质的子集时（例如 0\u002F1 背包问题、装载问题），每个元素只有两种状态：选（1）或不选（0）。",[44,6244,6245,6246,6274],{},"这相当于做了 ",[188,6247,6249,6262],{"className":6248},[191],[188,6250,6252],{"className":6251},[195],[197,6253,6254],{"xmlns":199},[201,6255,6256,6260],{},[204,6257,6258],{},[207,6259,217],{},[222,6261,217],{"encoding":224},[188,6263,6265],{"className":6264,"ariaHidden":230},[229],[188,6266,6268,6271],{"className":6267},[234],[188,6269],{"className":6270,"style":351},[238],[188,6272,217],{"className":6273},[243,244]," 次决策，每次决策有 2 个分支。",[44,6276,6277,6278,6306,6307,85],{},"画出一棵完整的状态树，第 1 层有 2 个节点，第 2 层有 4 个……到了第 ",[188,6279,6281,6294],{"className":6280},[191],[188,6282,6284],{"className":6283},[195],[197,6285,6286],{"xmlns":199},[201,6287,6288,6292],{},[204,6289,6290],{},[207,6291,217],{},[222,6293,217],{"encoding":224},[188,6295,6297],{"className":6296,"ariaHidden":230},[229],[188,6298,6300,6303],{"className":6299},[234],[188,6301],{"className":6302,"style":351},[238],[188,6304,217],{"className":6305},[243,244]," 层结束时，底部的叶子节点数量正好是所有可能的子集数量，即 ",[188,6308,6310,6327],{"className":6309},[191],[188,6311,6313],{"className":6312},[195],[197,6314,6315],{"xmlns":199},[201,6316,6317,6325],{},[204,6318,6319],{},[500,6320,6321,6323],{},[505,6322,507],{},[207,6324,217],{},[222,6326,1509],{"encoding":224},[188,6328,6330],{"className":6329,"ariaHidden":230},[229],[188,6331,6333,6336],{"className":6332},[234],[188,6334],{"className":6335,"style":599},[238],[188,6337,6339,6342],{"className":6338},[243],[188,6340,507],{"className":6341},[243],[188,6343,6345],{"className":6344},[545],[188,6346,6348],{"className":6347},[549],[188,6349,6351],{"className":6350},[553],[188,6352,6354],{"className":6353,"style":599},[557],[188,6355,6356,6359],{"style":561},[188,6357],{"className":6358,"style":566},[565],[188,6360,6362],{"className":6361},[570,571,572,573],[188,6363,217],{"className":6364},[243,244,573],[44,6366,6367,6368,6371,6372,6405,6406,85],{},"补充知识：如果题目问的是",[36,6369,6370],{},"排列树","（例如旅行商问题、N皇后问题），所有可能的排列方式有 ",[188,6373,6375,6390],{"className":6374},[191],[188,6376,6378],{"className":6377},[195],[197,6379,6380],{"xmlns":199},[201,6381,6382,6388],{},[204,6383,6384,6386],{},[207,6385,217],{},[211,6387,6075],{"stretchy":213},[222,6389,6078],{"encoding":224},[188,6391,6393],{"className":6392,"ariaHidden":230},[229],[188,6394,6396,6399,6402],{"className":6395},[234],[188,6397],{"className":6398,"style":3248},[238],[188,6400,217],{"className":6401},[243,244],[188,6403,6075],{"className":6404},[256]," 种，此时叶节点数量为 ",[188,6407,6409,6424],{"className":6408},[191],[188,6410,6412],{"className":6411},[195],[197,6413,6414],{"xmlns":199},[201,6415,6416,6422],{},[204,6417,6418,6420],{},[207,6419,217],{},[211,6421,6075],{"stretchy":213},[222,6423,6078],{"encoding":224},[188,6425,6427],{"className":6426,"ariaHidden":230},[229],[188,6428,6430,6433,6436],{"className":6429},[234],[188,6431],{"className":6432,"style":3248},[238],[188,6434,217],{"className":6435},[243,244],[188,6437,6075],{"className":6438},[256],[14,6440],{},[22,6442,6444],{"id":6443},"_7-题目内容","7. 题目内容",[27,6446,6447,6448,6450,6451,6453,6454,6456],{},"以深度优先方式对解空间进行搜索的算法是（ ）。\nA. 分支限界",[429,6449],{},"\nB. 贪心算法",[429,6452],{},"\nC. 动态规划",[429,6455],{},"\nD. 回溯法",[22,6458,32],{"id":6459},"答案与深度解析-10",[27,6461,6462],{},[36,6463,1329],{},[68,6465,6466],{},[44,6467,6468,6470,6471,6473],{},[36,6469,452],{}," 这是一道概念识记题。正如简答题第 2 题所分析的：回溯法的核心引擎就是",[36,6472,131],{},"，再辅以剪枝函数。分支限界法是广度优先或优先队列。贪心和动态规划通常不直接描述为对树结构的穷举搜索。",[14,6475],{},[22,6477,6479],{"id":6478},"_8-题目内容","8. 题目内容",[27,6481,6482,6483,6450,6485,6487,6488,6490],{},"备忘录算法是（ ）的变形。\nA. 分治法",[429,6484],{},[429,6486],{},"\nC. 动态规划法",[429,6489],{},"\nD. 分支限界法",[22,6492,32],{"id":6493},"答案与深度解析-11",[27,6495,6496],{},[36,6497,3010],{},[68,6499,6500],{},[44,6501,6502,6504],{},[36,6503,452],{},[68,6505,6506,6509,6532],{},[44,6507,6508],{},"动态规划的核心痛点是“重叠子问题”，如果用普通递归，会引发指数级的重复计算。",[44,6510,6511,6512],{},"解决重复计算有两种路线：\n",[41,6513,6514,6523],{},[44,6515,6516,6519,6520,6522],{},[36,6517,6518],{},"自底向上："," 也就是狭义上的",[36,6521,84],{},"。先从最小的子问题开始算，用表格存起来，慢慢推导到大问题。",[44,6524,6525,6528,6529,85],{},[36,6526,6527],{},"自顶向下："," 依然保持自然的递归写法，但是准备一个“备忘录”（通常是一个数组或哈希表）。每次递归计算出一个子问题的答案时，把它记在备忘录里；下次再遇到完全相同的子问题，直接查备忘录拿答案，不用再算一遍。这就是",[36,6530,6531],{},"备忘录算法（Memoization）",[44,6533,6534],{},"因此，备忘录算法本质上是动态规划思想的“自顶向下”实现方式。",[14,6536],{},[22,6538,6540],{"id":6539},"_9-题目内容","9. 题目内容",[27,6542,6543,6544,6572,6573,6602,6603,6631,6632,6709,6710,6753,706,6755,6828,902,6830,6937,1134,6939],{},"利用贪心算法求解 ",[188,6545,6547,6560],{"className":6546},[191],[188,6548,6550],{"className":6549},[195],[197,6551,6552],{"xmlns":199},[201,6553,6554,6558],{},[204,6555,6556],{},[207,6557,217],{},[222,6559,217],{"encoding":224},[188,6561,6563],{"className":6562,"ariaHidden":230},[229],[188,6564,6566,6569],{"className":6565},[234],[188,6567],{"className":6568,"style":351},[238],[188,6570,217],{"className":6571},[243,244]," 个集装箱最优装载问题（已知轮船载重量为 ",[188,6574,6576,6590],{"className":6575},[191],[188,6577,6579],{"className":6578},[195],[197,6580,6581],{"xmlns":199},[201,6582,6583,6588],{},[204,6584,6585],{},[207,6586,6587],{},"W",[222,6589,6587],{"encoding":224},[188,6591,6593],{"className":6592,"ariaHidden":230},[229],[188,6594,6596,6599],{"className":6595},[234],[188,6597],{"className":6598,"style":1693},[238],[188,6600,6587],{"className":6601,"style":2515},[243,244],"，有 ",[188,6604,6606,6619],{"className":6605},[191],[188,6607,6609],{"className":6608},[195],[197,6610,6611],{"xmlns":199},[201,6612,6613,6617],{},[204,6614,6615],{},[207,6616,217],{},[222,6618,217],{"encoding":224},[188,6620,6622],{"className":6621,"ariaHidden":230},[229],[188,6623,6625,6628],{"className":6624},[234],[188,6626],{"className":6627,"style":351},[238],[188,6629,217],{"className":6630},[243,244]," 个集装箱重量分别为 ",[188,6633,6635,6655],{"className":6634},[191],[188,6636,6638],{"className":6637},[195],[197,6639,6640],{"xmlns":199},[201,6641,6642,6652],{},[204,6643,6644],{},[916,6645,6646,6649],{},[207,6647,6648],{},"w",[207,6650,6651],{},"i",[222,6653,6654],{"encoding":224},"w_i",[188,6656,6658],{"className":6657,"ariaHidden":230},[229],[188,6659,6661,6665],{"className":6660},[234],[188,6662],{"className":6663,"style":6664},[238],"height:0.5806em;vertical-align:-0.15em;",[188,6666,6668,6672],{"className":6667},[243],[188,6669,6648],{"className":6670,"style":6671},[243,244],"margin-right:0.0269em;",[188,6673,6675],{"className":6674},[545],[188,6676,6678,6700],{"className":6677},[549,966],[188,6679,6681,6697],{"className":6680},[553],[188,6682,6685],{"className":6683,"style":6684},[557],"height:0.3117em;",[188,6686,6688,6691],{"style":6687},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[188,6689],{"className":6690,"style":566},[565],[188,6692,6694],{"className":6693},[570,571,572,573],[188,6695,6651],{"className":6696},[243,244,573],[188,6698,990],{"className":6699},[989],[188,6701,6703],{"className":6702},[553],[188,6704,6707],{"className":6705,"style":6706},[557],"height:0.15em;",[188,6708],{},"，设计使得轮船上能装载更多的集装箱）时间复杂度的是（ ）。\nA. ",[188,6711,6713,6732],{"className":6712},[191],[188,6714,6716],{"className":6715},[195],[197,6717,6718],{"xmlns":199},[201,6719,6720,6730],{},[204,6721,6722,6724,6726,6728],{},[207,6723,209],{},[211,6725,214],{"stretchy":213},[207,6727,217],{},[211,6729,220],{"stretchy":213},[222,6731,225],{"encoding":224},[188,6733,6735],{"className":6734,"ariaHidden":230},[229],[188,6736,6738,6741,6744,6747,6750],{"className":6737},[234],[188,6739],{"className":6740,"style":239},[238],[188,6742,209],{"className":6743,"style":245},[243,244],[188,6745,214],{"className":6746},[249],[188,6748,217],{"className":6749},[243,244],[188,6751,220],{"className":6752},[256],[429,6754],{},[188,6756,6758,6781],{"className":6757},[191],[188,6759,6761],{"className":6760},[195],[197,6762,6763],{"xmlns":199},[201,6764,6765,6779],{},[204,6766,6767,6769,6771,6777],{},[207,6768,209],{},[211,6770,214],{"stretchy":213},[500,6772,6773,6775],{},[207,6774,217],{},[505,6776,507],{},[211,6778,220],{"stretchy":213},[222,6780,2728],{"encoding":224},[188,6782,6784],{"className":6783,"ariaHidden":230},[229],[188,6785,6787,6790,6793,6796,6825],{"className":6786},[234],[188,6788],{"className":6789,"style":535},[238],[188,6791,209],{"className":6792,"style":245},[243,244],[188,6794,214],{"className":6795},[249],[188,6797,6799,6802],{"className":6798},[243],[188,6800,217],{"className":6801},[243,244],[188,6803,6805],{"className":6804},[545],[188,6806,6808],{"className":6807},[549],[188,6809,6811],{"className":6810},[553],[188,6812,6814],{"className":6813,"style":558},[557],[188,6815,6816,6819],{"style":561},[188,6817],{"className":6818,"style":566},[565],[188,6820,6822],{"className":6821},[570,571,572,573],[188,6823,507],{"className":6824},[243,573],[188,6826,220],{"className":6827},[256],[429,6829],{},[188,6831,6833,6865],{"className":6832},[191],[188,6834,6836],{"className":6835},[195],[197,6837,6838],{"xmlns":199},[201,6839,6840,6862],{},[204,6841,6842,6844,6846,6848,6858,6860],{},[207,6843,209],{},[211,6845,214],{"stretchy":213},[207,6847,217],{},[916,6849,6850,6856],{},[204,6851,6852,6854],{},[207,6853,922],{},[211,6855,925],{},[505,6857,507],{},[207,6859,217],{},[211,6861,220],{"stretchy":213},[222,6863,6864],{"encoding":224},"O(n\\log_2 n)",[188,6866,6868],{"className":6867,"ariaHidden":230},[229],[188,6869,6871,6874,6877,6880,6883,6886,6928,6931,6934],{"className":6870},[234],[188,6872],{"className":6873,"style":239},[238],[188,6875,209],{"className":6876,"style":245},[243,244],[188,6878,214],{"className":6879},[249],[188,6881,217],{"className":6882},[243,244],[188,6884],{"className":6885,"style":1003},[584],[188,6887,6889,6894],{"className":6888},[951],[188,6890,955,6892],{"className":6891},[951],[188,6893,959],{"style":958},[188,6895,6897],{"className":6896},[545],[188,6898,6900,6920],{"className":6899},[549,966],[188,6901,6903,6917],{"className":6902},[553],[188,6904,6906],{"className":6905,"style":973},[557],[188,6907,6908,6911],{"style":976},[188,6909],{"className":6910,"style":566},[565],[188,6912,6914],{"className":6913},[570,571,572,573],[188,6915,507],{"className":6916},[243,573],[188,6918,990],{"className":6919},[989],[188,6921,6923],{"className":6922},[553],[188,6924,6926],{"className":6925,"style":997},[557],[188,6927],{},[188,6929],{"className":6930,"style":1003},[584],[188,6932,217],{"className":6933},[243,244],[188,6935,220],{"className":6936},[256],[429,6938],{},[188,6940,6942,6965],{"className":6941},[191],[188,6943,6945],{"className":6944},[195],[197,6946,6947],{"xmlns":199},[201,6948,6949,6962],{},[204,6950,6951,6953,6955,6960],{},[207,6952,209],{},[211,6954,214],{"stretchy":213},[6956,6957,6958],"msqrt",{},[207,6959,217],{},[211,6961,220],{"stretchy":213},[222,6963,6964],{"encoding":224},"O(\\sqrt{n})",[188,6966,6968],{"className":6967,"ariaHidden":230},[229],[188,6969,6971,6975,6978,6981,7046],{"className":6970},[234],[188,6972],{"className":6973,"style":6974},[238],"height:1.0503em;vertical-align:-0.25em;",[188,6976,209],{"className":6977,"style":245},[243,244],[188,6979,214],{"className":6980},[249],[188,6982,6985],{"className":6983},[243,6984],"sqrt",[188,6986,6988,7037],{"className":6987},[549,966],[188,6989,6991,7034],{"className":6990},[553],[188,6992,6995,7011],{"className":6993,"style":6994},[557],"height:0.8003em;",[188,6996,7000,7004],{"className":6997,"style":6999},[6998],"svg-align","top:-3em;",[188,7001],{"className":7002,"style":7003},[565],"height:3em;",[188,7005,7008],{"className":7006,"style":7007},[243],"padding-left:0.833em;",[188,7009,217],{"className":7010},[243,244],[188,7012,7014,7017],{"style":7013},"top:-2.7603em;",[188,7015],{"className":7016,"style":7003},[565],[188,7018,7022],{"className":7019,"style":7021},[7020],"hide-tail","min-width:0.853em;height:1.08em;",[7023,7024,7030],"svg",{"xmlns":7025,"width":7026,"height":7027,"viewBox":7028,"preserveAspectRatio":7029},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[7031,7032],"path",{"d":7033},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[188,7035,990],{"className":7036},[989],[188,7038,7040],{"className":7039},[553],[188,7041,7044],{"className":7042,"style":7043},[557],"height:0.2397em;",[188,7045],{},[188,7047,220],{"className":7048},[256],[22,7050,32],{"id":7051},"答案与深度解析-12",[27,7053,7054],{},[36,7055,3010],{},[68,7057,7058],{},[44,7059,7060,7062,7063,7066,7067,7070,7071,7099,7100,7103,7104,7107,7108,7214,7215,7258,7259,85],{},[36,7061,452],{}," 1.  ",[36,7064,7065],{},"贪心策略："," 要想装载“最多”数量的集装箱，最直观且正确的策略就是：优先挑最轻的装。轻的占用的载重量少，留给后面集装箱的额度就多。\n2.  ",[36,7068,7069],{},"算法执行步骤："," 第一步，必须对 ",[188,7072,7074,7087],{"className":7073},[191],[188,7075,7077],{"className":7076},[195],[197,7078,7079],{"xmlns":199},[201,7080,7081,7085],{},[204,7082,7083],{},[207,7084,217],{},[222,7086,217],{"encoding":224},[188,7088,7090],{"className":7089,"ariaHidden":230},[229],[188,7091,7093,7096],{"className":7092},[234],[188,7094],{"className":7095,"style":351},[238],[188,7097,217],{"className":7098},[243,244]," 个集装箱的重量进行",[36,7101,7102],{},"从小到大排序","。第二步，从轻到重依次遍历，只要没超重就装进去。\n3.  ",[36,7105,7106],{},"时间复杂度分析："," 最优的比较排序算法（如快速排序、归并排序）的时间复杂度为 ",[188,7109,7111,7142],{"className":7110},[191],[188,7112,7114],{"className":7113},[195],[197,7115,7116],{"xmlns":199},[201,7117,7118,7140],{},[204,7119,7120,7122,7124,7126,7136,7138],{},[207,7121,209],{},[211,7123,214],{"stretchy":213},[207,7125,217],{},[916,7127,7128,7134],{},[204,7129,7130,7132],{},[207,7131,922],{},[211,7133,925],{},[505,7135,507],{},[207,7137,217],{},[211,7139,220],{"stretchy":213},[222,7141,6864],{"encoding":224},[188,7143,7145],{"className":7144,"ariaHidden":230},[229],[188,7146,7148,7151,7154,7157,7160,7163,7205,7208,7211],{"className":7147},[234],[188,7149],{"className":7150,"style":239},[238],[188,7152,209],{"className":7153,"style":245},[243,244],[188,7155,214],{"className":7156},[249],[188,7158,217],{"className":7159},[243,244],[188,7161],{"className":7162,"style":1003},[584],[188,7164,7166,7171],{"className":7165},[951],[188,7167,955,7169],{"className":7168},[951],[188,7170,959],{"style":958},[188,7172,7174],{"className":7173},[545],[188,7175,7177,7197],{"className":7176},[549,966],[188,7178,7180,7194],{"className":7179},[553],[188,7181,7183],{"className":7182,"style":973},[557],[188,7184,7185,7188],{"style":976},[188,7186],{"className":7187,"style":566},[565],[188,7189,7191],{"className":7190},[570,571,572,573],[188,7192,507],{"className":7193},[243,573],[188,7195,990],{"className":7196},[989],[188,7198,7200],{"className":7199},[553],[188,7201,7203],{"className":7202,"style":997},[557],[188,7204],{},[188,7206],{"className":7207,"style":1003},[584],[188,7209,217],{"className":7210},[243,244],[188,7212,220],{"className":7213},[256],"。第二步的遍历只需扫描一次，复杂度为 ",[188,7216,7218,7237],{"className":7217},[191],[188,7219,7221],{"className":7220},[195],[197,7222,7223],{"xmlns":199},[201,7224,7225,7235],{},[204,7226,7227,7229,7231,7233],{},[207,7228,209],{},[211,7230,214],{"stretchy":213},[207,7232,217],{},[211,7234,220],{"stretchy":213},[222,7236,225],{"encoding":224},[188,7238,7240],{"className":7239,"ariaHidden":230},[229],[188,7241,7243,7246,7249,7252,7255],{"className":7242},[234],[188,7244],{"className":7245,"style":239},[238],[188,7247,209],{"className":7248,"style":245},[243,244],[188,7250,214],{"className":7251},[249],[188,7253,217],{"className":7254},[243,244],[188,7256,220],{"className":7257},[256],"。两者相加，排序步骤主导了整体时间耗费，因此总时间复杂度为 ",[188,7260,7262,7293],{"className":7261},[191],[188,7263,7265],{"className":7264},[195],[197,7266,7267],{"xmlns":199},[201,7268,7269,7291],{},[204,7270,7271,7273,7275,7277,7287,7289],{},[207,7272,209],{},[211,7274,214],{"stretchy":213},[207,7276,217],{},[916,7278,7279,7285],{},[204,7280,7281,7283],{},[207,7282,922],{},[211,7284,925],{},[505,7286,507],{},[207,7288,217],{},[211,7290,220],{"stretchy":213},[222,7292,6864],{"encoding":224},[188,7294,7296],{"className":7295,"ariaHidden":230},[229],[188,7297,7299,7302,7305,7308,7311,7314,7356,7359,7362],{"className":7298},[234],[188,7300],{"className":7301,"style":239},[238],[188,7303,209],{"className":7304,"style":245},[243,244],[188,7306,214],{"className":7307},[249],[188,7309,217],{"className":7310},[243,244],[188,7312],{"className":7313,"style":1003},[584],[188,7315,7317,7322],{"className":7316},[951],[188,7318,955,7320],{"className":7319},[951],[188,7321,959],{"style":958},[188,7323,7325],{"className":7324},[545],[188,7326,7328,7348],{"className":7327},[549,966],[188,7329,7331,7345],{"className":7330},[553],[188,7332,7334],{"className":7333,"style":973},[557],[188,7335,7336,7339],{"style":976},[188,7337],{"className":7338,"style":566},[565],[188,7340,7342],{"className":7341},[570,571,572,573],[188,7343,507],{"className":7344},[243,573],[188,7346,990],{"className":7347},[989],[188,7349,7351],{"className":7350},[553],[188,7352,7354],{"className":7353,"style":997},[557],[188,7355],{},[188,7357],{"className":7358,"style":1003},[584],[188,7360,217],{"className":7361},[243,244],[188,7363,220],{"className":7364},[256],[14,7366],{},[22,7368,7370],{"id":7369},"_10-题目内容","10. 题目内容",[27,7372,7373,7374,7376,7377,7379,7380,7382],{},"调用一次下列随机算法进行问题求解时，可能成功也可能失败的是（ ）。\nA. 蒙特卡洛算法",[429,7375],{},"\nB. 拉斯维加斯算法",[429,7378],{},"\nC. 舍伍德算法",[429,7381],{},"\nD. 数值概率算法",[22,7384,32],{"id":7385},"答案与深度解析-13",[27,7387,7388],{},[36,7389,445],{},[68,7391,7392],{},[44,7393,7394,7396,7397],{},[36,7395,452],{}," 结合简答题第 3 题的知识：\n",[68,7398,7399,7405,7411],{},[44,7400,7401,7404],{},[36,7402,7403],{},"拉斯维加斯算法","最大的特征就是：一旦它输出结果，结果绝对正确（100%）。但它不能保证在限定时间内一定能找到解，如果运气不好走入死胡同，它会返回“失败”（无解）。这完全契合题目描述的“可能成功也可能失败”。",[44,7406,7407,7410],{},[36,7408,7409],{},"蒙特卡洛算法","必定会返回一个答案（一定成功运行），只是答案可能是错的。",[44,7412,7413,7416],{},[36,7414,7415],{},"舍伍德算法","是为了消除最坏情况而引入随机性（例如随机选择快速排序的基准元素），它总能求得正确解，且必定成功。",[14,7418],{},[17,7420,7422],{"id":7421},"三填空题每空2分共20分","三、填空题（每空2分，共20分）",[22,7424,25],{"id":7425},"_1-题目内容-2",[27,7427,7428],{},"求解 0\u002F1 背包问题可采用动态规划法、回溯法和分支限界法，其中需要按照单位重量价值比进行排序以提高算法效率的是 _____，不需要进行排序的是 _____ 。",[22,7430,32],{"id":7431},"答案与深度解析-14",[27,7433,7434,7436,7437,7440,7441],{},[36,7435,38],{},"\n第一空：",[36,7438,7439],{},"回溯法和分支限界法","\n第二空：",[36,7442,7443],{},"动态规划法",[68,7445,7446],{},[44,7447,7448,7450,7451],{},[36,7449,66],{}," * 为什么回溯和分支限界需要排序？因为这两种方法本质是在枚举所有组合。为了能尽早剪去不可能产生最优解的枝丫，我们需要一个强有力的“上界函数”。将物品按性价比（价值\u002F重量）降序排列，可以让我们用贪心思想迅速估算出一个“理想状态下的最大可能收益”，如果这个理想收益都比不过当前已经找到的解，直接砍掉这个搜索分支，大幅提升效率。\n",[68,7452,7453],{},[44,7454,7455,7456,7460],{},"为什么动态规划不需要？动态规划是基于状态转移方程 ",[7457,7458,7459],"code",{},"dp[i][j] = max(dp[i-1][j], dp[i-1][j-w[i]] + v[i])","，它通过穷尽表格所有容量状态来获得绝对最优解，物品出现的先后顺序不影响最终表格右下角的答案，因此排序纯属多此一举。",[14,7462],{},[22,7464,97],{"id":7465},"_2-题目内容-2",[27,7467,7468],{},"标识主元素的蒙特卡洛算法，获得正确解的概率为 0.5，则调用该算法 3 次可以将获得正确解的概率提高到 _____ 。",[22,7470,32],{"id":7471},"答案与深度解析-15",[27,7473,7474],{},[36,7475,7476],{},"答案：0.875 （或 87.5%、7\u002F8）",[68,7478,7479],{},[44,7480,7481,7483,7484],{},[36,7482,66],{}," 这是一个基础概率论计算题，需要逆向思维。\n",[68,7485,7486,7492,7502,7603],{},[44,7487,7488,7489,85],{},"算法运行 1 次，正确的概率是 0.5，",[36,7490,7491],{},"错误的概率是 1 - 0.5 = 0.5",[44,7493,7494,7495,7498,7499,85],{},"“调用 3 次且最终拿到正确解”的含义是：只要这 3 次中",[36,7496,7497],{},"有任意一次","是正确的，我们就成功了。它的反面是：",[36,7500,7501],{},"3 次全部都算错了",[44,7503,7504,7505,85],{},"3 次全部算错的概率是：",[188,7506,7508,7536],{"className":7507},[191],[188,7509,7511],{"className":7510},[195],[197,7512,7513],{"xmlns":199},[201,7514,7515,7533],{},[204,7516,7517,7520,7522,7524,7526,7528,7530],{},[505,7518,7519],{},"0.5",[211,7521,4758],{},[505,7523,7519],{},[211,7525,4758],{},[505,7527,7519],{},[211,7529,2464],{},[505,7531,7532],{},"0.125",[222,7534,7535],{"encoding":224},"0.5 \\times 0.5 \\times 0.5 = 0.125",[188,7537,7539,7558,7576,7594],{"className":7538,"ariaHidden":230},[229],[188,7540,7542,7546,7549,7552,7555],{"className":7541},[234],[188,7543],{"className":7544,"style":7545},[238],"height:0.7278em;vertical-align:-0.0833em;",[188,7547,7519],{"className":7548},[243],[188,7550],{"className":7551,"style":585},[584],[188,7553,4758],{"className":7554},[589],[188,7556],{"className":7557,"style":585},[584],[188,7559,7561,7564,7567,7570,7573],{"className":7560},[234],[188,7562],{"className":7563,"style":7545},[238],[188,7565,7519],{"className":7566},[243],[188,7568],{"className":7569,"style":585},[584],[188,7571,4758],{"className":7572},[589],[188,7574],{"className":7575,"style":585},[584],[188,7577,7579,7582,7585,7588,7591],{"className":7578},[234],[188,7580],{"className":7581,"style":3213},[238],[188,7583,7519],{"className":7584},[243],[188,7586],{"className":7587,"style":2528},[584],[188,7589,2464],{"className":7590},[2532],[188,7592],{"className":7593,"style":2528},[584],[188,7595,7597,7600],{"className":7596},[234],[188,7598],{"className":7599,"style":3213},[238],[188,7601,7532],{"className":7602},[243],[44,7604,7605,7606,85],{},"那么至少有一次算对（即最终获得正确解）的概率就是：",[188,7607,7609,7632],{"className":7608},[191],[188,7610,7612],{"className":7611},[195],[197,7613,7614],{"xmlns":199},[201,7615,7616,7629],{},[204,7617,7618,7620,7622,7624,7626],{},[505,7619,4948],{},[211,7621,4945],{},[505,7623,7532],{},[211,7625,2464],{},[505,7627,7628],{},"0.875",[222,7630,7631],{"encoding":224},"1 - 0.125 = 0.875",[188,7633,7635,7653,7671],{"className":7634,"ariaHidden":230},[229],[188,7636,7638,7641,7644,7647,7650],{"className":7637},[234],[188,7639],{"className":7640,"style":7545},[238],[188,7642,4948],{"className":7643},[243],[188,7645],{"className":7646,"style":585},[584],[188,7648,4945],{"className":7649},[589],[188,7651],{"className":7652,"style":585},[584],[188,7654,7656,7659,7662,7665,7668],{"className":7655},[234],[188,7657],{"className":7658,"style":3213},[238],[188,7660,7532],{"className":7661},[243],[188,7663],{"className":7664,"style":2528},[584],[188,7666,2464],{"className":7667},[2532],[188,7669],{"className":7670,"style":2528},[584],[188,7672,7674,7677],{"className":7673},[234],[188,7675],{"className":7676,"style":3213},[238],[188,7678,7628],{"className":7679},[243],[14,7681],{},[22,7683,263],{"id":7684},"_3-题目内容-2",[27,7686,7687,7715,7716,7744],{},[188,7688,7690,7703],{"className":7689},[191],[188,7691,7693],{"className":7692},[195],[197,7694,7695],{"xmlns":199},[201,7696,7697,7701],{},[204,7698,7699],{},[207,7700,217],{},[222,7702,217],{"encoding":224},[188,7704,7706],{"className":7705,"ariaHidden":230},[229],[188,7707,7709,7712],{"className":7708},[234],[188,7710],{"className":7711,"style":351},[238],[188,7713,217],{"className":7714},[243,244]," 皇后问题的满 ",[188,7717,7719,7732],{"className":7718},[191],[188,7720,7722],{"className":7721},[195],[197,7723,7724],{"xmlns":199},[201,7725,7726,7730],{},[204,7727,7728],{},[207,7729,217],{},[222,7731,217],{"encoding":224},[188,7733,7735],{"className":7734,"ariaHidden":230},[229],[188,7736,7738,7741],{"className":7737},[234],[188,7739],{"className":7740,"style":351},[238],[188,7742,217],{"className":7743},[243,244]," 叉树的求解算法的框架如下，补充完整该算法：",[7746,7747,7752],"pre",{"className":7748,"code":7749,"language":7750,"meta":7751,"style":7751},"language-c shiki shiki-themes github-light github-dark","int sum = 0; \u002F\u002F sum 用于记录可行解个数\nvoid queen(int t) \u002F\u002F 放第 t 个皇后\n{\n    if (t > n)\n        _____(1)_____;\n    else\n        for (int j = 1; ____(2)____; j++)\n        {\n            ____(3)_____; \n            if (place(t))\n                ____(4)_____; \n        }\n}\n","c","",[7457,7753,7754,7761,7767,7773,7779,7785,7791,7797,7803,7809,7815,7821,7827],{"__ignoreMap":7751},[188,7755,7758],{"class":7756,"line":7757},"line",1,[188,7759,7760],{},"int sum = 0; \u002F\u002F sum 用于记录可行解个数\n",[188,7762,7764],{"class":7756,"line":7763},2,[188,7765,7766],{},"void queen(int t) \u002F\u002F 放第 t 个皇后\n",[188,7768,7770],{"class":7756,"line":7769},3,[188,7771,7772],{},"{\n",[188,7774,7776],{"class":7756,"line":7775},4,[188,7777,7778],{},"    if (t > n)\n",[188,7780,7782],{"class":7756,"line":7781},5,[188,7783,7784],{},"        _____(1)_____;\n",[188,7786,7788],{"class":7756,"line":7787},6,[188,7789,7790],{},"    else\n",[188,7792,7794],{"class":7756,"line":7793},7,[188,7795,7796],{},"        for (int j = 1; ____(2)____; j++)\n",[188,7798,7800],{"class":7756,"line":7799},8,[188,7801,7802],{},"        {\n",[188,7804,7806],{"class":7756,"line":7805},9,[188,7807,7808],{},"            ____(3)_____; \n",[188,7810,7812],{"class":7756,"line":7811},10,[188,7813,7814],{},"            if (place(t))\n",[188,7816,7818],{"class":7756,"line":7817},11,[188,7819,7820],{},"                ____(4)_____; \n",[188,7822,7824],{"class":7756,"line":7823},12,[188,7825,7826],{},"        }\n",[188,7828,7830],{"class":7756,"line":7829},13,[188,7831,7832],{},"}\n",[22,7834,32],{"id":7835},"答案与深度解析-16",[27,7837,7838,7840,7841,7844,7845,7848,7849,7852,7853,7856,7857,7860,7861],{},[36,7839,38],{},"\n(1) ",[7457,7842,7843],{},"sum++","\n(2) ",[7457,7846,7847],{},"j \u003C= n","\n(3) ",[7457,7850,7851],{},"x[t] = j"," （这里假设用于记录第 ",[7457,7854,7855],{},"t"," 个皇后所在的列号的全局数组名为 ",[7457,7858,7859],{},"x","，这是极其通用的约定写法）\n(4) ",[7457,7862,7863],{},"queen(t + 1)",[68,7865,7866],{},[44,7867,7868,7870,7871],{},[36,7869,66],{}," 这是经典的回溯法框架。我们一行一行从零梳理逻辑：\n",[68,7872,7873,7883,8002,8076,8099],{},[44,7874,7875,7876,7879,7880,7882],{},"函数 ",[7457,7877,7878],{},"queen(t)"," 的意义是：去决定第 ",[7457,7881,7855],{}," 行的皇后应该放在哪一列。",[44,7884,7885,7888,7889,7917,7918,7970,7971,7999,8000,85],{},[36,7886,7887],{},"第(1)空："," 递归的终止条件。题目说一共有 ",[188,7890,7892,7905],{"className":7891},[191],[188,7893,7895],{"className":7894},[195],[197,7896,7897],{"xmlns":199},[201,7898,7899,7903],{},[204,7900,7901],{},[207,7902,217],{},[222,7904,217],{"encoding":224},[188,7906,7908],{"className":7907,"ariaHidden":230},[229],[188,7909,7911,7914],{"className":7910},[234],[188,7912],{"className":7913,"style":351},[238],[188,7915,217],{"className":7916},[243,244]," 个皇后，如果此时传入的 ",[188,7919,7921,7939],{"className":7920},[191],[188,7922,7924],{"className":7923},[195],[197,7925,7926],{"xmlns":199},[201,7927,7928,7936],{},[204,7929,7930,7932,7934],{},[207,7931,7855],{},[211,7933,3724],{},[207,7935,217],{},[222,7937,7938],{"encoding":224},"t > n",[188,7940,7942,7961],{"className":7941,"ariaHidden":230},[229],[188,7943,7945,7949,7952,7955,7958],{"className":7944},[234],[188,7946],{"className":7947,"style":7948},[238],"height:0.6542em;vertical-align:-0.0391em;",[188,7950,7855],{"className":7951},[243,244],[188,7953],{"className":7954,"style":2528},[584],[188,7956,3724],{"className":7957},[2532],[188,7959],{"className":7960,"style":2528},[584],[188,7962,7964,7967],{"className":7963},[234],[188,7965],{"className":7966,"style":351},[238],[188,7968,217],{"className":7969},[243,244],"，说明第 1 到第 ",[188,7972,7974,7987],{"className":7973},[191],[188,7975,7977],{"className":7976},[195],[197,7978,7979],{"xmlns":199},[201,7980,7981,7985],{},[204,7982,7983],{},[207,7984,217],{},[222,7986,217],{"encoding":224},[188,7988,7990],{"className":7989,"ariaHidden":230},[229],[188,7991,7993,7996],{"className":7992},[234],[188,7994],{"className":7995,"style":351},[238],[188,7997,217],{"className":7998},[243,244]," 个皇后都已经成功放置在棋盘上了，这意味着我们找到了一个合法的可行解。此时当然要让解的计数器增加：",[7457,8001,7843],{},[44,8003,8004,8007,8008,8011,8012,8040,8041,8043,8044,8072,8073,85],{},[36,8005,8006],{},"第(2)空："," ",[7457,8009,8010],{},"else"," 块表示还在放置前 ",[188,8013,8015,8028],{"className":8014},[191],[188,8016,8018],{"className":8017},[195],[197,8019,8020],{"xmlns":199},[201,8021,8022,8026],{},[204,8023,8024],{},[207,8025,217],{},[222,8027,217],{"encoding":224},[188,8029,8031],{"className":8030,"ariaHidden":230},[229],[188,8032,8034,8037],{"className":8033},[234],[188,8035],{"className":8036,"style":351},[238],[188,8038,217],{"className":8039},[243,244]," 个皇后。要在第 ",[7457,8042,7855],{}," 行放皇后，她能放在哪里呢？棋盘的列数是从第 1 列到第 ",[188,8045,8047,8060],{"className":8046},[191],[188,8048,8050],{"className":8049},[195],[197,8051,8052],{"xmlns":199},[201,8053,8054,8058],{},[204,8055,8056],{},[207,8057,217],{},[222,8059,217],{"encoding":224},[188,8061,8063],{"className":8062,"ariaHidden":230},[229],[188,8064,8066,8069],{"className":8065},[234],[188,8067],{"className":8068,"style":351},[238],[188,8070,217],{"className":8071},[243,244]," 列。所以我们要遍历所有的列尝试放置：",[7457,8074,8075],{},"for (int j = 1; j \u003C= n; j++)",[44,8077,8078,8081,8082,8084,8085,8088,8089,8092,8093,8096,8097,85],{},[36,8079,8080],{},"第(3)空："," 我们尝试把第 ",[7457,8083,7855],{}," 个皇后放在第 ",[7457,8086,8087],{},"j"," 列。必须有一个数组把这个尝试记录下来，系统后面的 ",[7457,8090,8091],{},"place(t)"," 函数才知道去哪里检查冲突。通常这个数组叫 ",[7457,8094,8095],{},"x[]","。记录动作是 ",[7457,8098,7851],{},[44,8100,8101,8007,8104,8106,8107,85],{},[36,8102,8103],{},"第(4)空：",[7457,8105,8091],{}," 是检查函数，如果刚才放的位置（不和前面几行的皇后同列、同对角线）是安全的（返回 true），那该怎么办？当然是继续去放下一行的皇后了，即递归调用：",[7457,8108,7863],{},[14,8110],{},[22,8112,372],{"id":8113},"_4-题目内容-2",[27,8115,8116,8117,8177,8178,8206,8207,8235,8236,8288,8289,8377,8378,8443],{},"利用分治法求解正整数的划分数问题时，",[188,8118,8120,8146],{"className":8119},[191],[188,8121,8123],{"className":8122},[195],[197,8124,8125],{"xmlns":199},[201,8126,8127,8143],{},[204,8128,8129,8131,8133,8135,8138,8141],{},[207,8130,3064],{},[211,8132,214],{"stretchy":213},[207,8134,217],{},[211,8136,8137],{"separator":230},",",[207,8139,8140],{},"m",[211,8142,220],{"stretchy":213},[222,8144,8145],{"encoding":224},"f(n,m)",[188,8147,8149],{"className":8148,"ariaHidden":230},[229],[188,8150,8152,8155,8158,8161,8164,8168,8171,8174],{"className":8151},[234],[188,8153],{"className":8154,"style":239},[238],[188,8156,3064],{"className":8157,"style":3149},[243,244],[188,8159,214],{"className":8160},[249],[188,8162,217],{"className":8163},[243,244],[188,8165,8137],{"className":8166},[8167],"mpunct",[188,8169],{"className":8170,"style":1003},[584],[188,8172,8140],{"className":8173},[243,244],[188,8175,220],{"className":8176},[256]," 表示将正整数 ",[188,8179,8181,8194],{"className":8180},[191],[188,8182,8184],{"className":8183},[195],[197,8185,8186],{"xmlns":199},[201,8187,8188,8192],{},[204,8189,8190],{},[207,8191,217],{},[222,8193,217],{"encoding":224},[188,8195,8197],{"className":8196,"ariaHidden":230},[229],[188,8198,8200,8203],{"className":8199},[234],[188,8201],{"className":8202,"style":351},[238],[188,8204,217],{"className":8205},[243,244]," 划分成最大正整数不超过 ",[188,8208,8210,8223],{"className":8209},[191],[188,8211,8213],{"className":8212},[195],[197,8214,8215],{"xmlns":199},[201,8216,8217,8221],{},[204,8218,8219],{},[207,8220,8140],{},[222,8222,8140],{"encoding":224},[188,8224,8226],{"className":8225,"ariaHidden":230},[229],[188,8227,8229,8232],{"className":8228},[234],[188,8230],{"className":8231,"style":351},[238],[188,8233,8140],{"className":8234},[243,244]," 的划分数，当 ",[188,8237,8239,8257],{"className":8238},[191],[188,8240,8242],{"className":8241},[195],[197,8243,8244],{"xmlns":199},[201,8245,8246,8254],{},[204,8247,8248,8250,8252],{},[207,8249,217],{},[211,8251,3724],{},[207,8253,8140],{},[222,8255,8256],{"encoding":224},"n>m",[188,8258,8260,8279],{"className":8259,"ariaHidden":230},[229],[188,8261,8263,8267,8270,8273,8276],{"className":8262},[234],[188,8264],{"className":8265,"style":8266},[238],"height:0.5782em;vertical-align:-0.0391em;",[188,8268,217],{"className":8269},[243,244],[188,8271],{"className":8272,"style":2528},[584],[188,8274,3724],{"className":8275},[2532],[188,8277],{"className":8278,"style":2528},[584],[188,8280,8282,8285],{"className":8281},[234],[188,8283],{"className":8284,"style":351},[238],[188,8286,8140],{"className":8287},[243,244]," 时（",[188,8290,8292,8319],{"className":8291},[191],[188,8293,8295],{"className":8294},[195],[197,8296,8297],{"xmlns":199},[201,8298,8299,8316],{},[204,8300,8301,8303,8305,8308,8310,8312,8314],{},[207,8302,217],{},[211,8304,3724],{},[505,8306,8307],{},"0",[211,8309,8137],{"separator":230},[207,8311,8140],{},[211,8313,3724],{},[505,8315,8307],{},[222,8317,8318],{"encoding":224},"n>0, m>0",[188,8320,8322,8340,8368],{"className":8321,"ariaHidden":230},[229],[188,8323,8325,8328,8331,8334,8337],{"className":8324},[234],[188,8326],{"className":8327,"style":8266},[238],[188,8329,217],{"className":8330},[243,244],[188,8332],{"className":8333,"style":2528},[584],[188,8335,3724],{"className":8336},[2532],[188,8338],{"className":8339,"style":2528},[584],[188,8341,8343,8347,8350,8353,8356,8359,8362,8365],{"className":8342},[234],[188,8344],{"className":8345,"style":8346},[238],"height:0.8389em;vertical-align:-0.1944em;",[188,8348,8307],{"className":8349},[243],[188,8351,8137],{"className":8352},[8167],[188,8354],{"className":8355,"style":1003},[584],[188,8357,8140],{"className":8358},[243,244],[188,8360],{"className":8361,"style":2528},[584],[188,8363,3724],{"className":8364},[2532],[188,8366],{"className":8367,"style":2528},[584],[188,8369,8371,8374],{"className":8370},[234],[188,8372],{"className":8373,"style":3213},[238],[188,8375,8307],{"className":8376},[243],"），",[188,8379,8381,8407],{"className":8380},[191],[188,8382,8384],{"className":8383},[195],[197,8385,8386],{"xmlns":199},[201,8387,8388,8404],{},[204,8389,8390,8392,8394,8396,8398,8400,8402],{},[207,8391,3064],{},[211,8393,214],{"stretchy":213},[207,8395,217],{},[211,8397,8137],{"separator":230},[207,8399,8140],{},[211,8401,220],{"stretchy":213},[211,8403,2464],{},[222,8405,8406],{"encoding":224},"f(n, m)=",[188,8408,8410],{"className":8409,"ariaHidden":230},[229],[188,8411,8413,8416,8419,8422,8425,8428,8431,8434,8437,8440],{"className":8412},[234],[188,8414],{"className":8415,"style":239},[238],[188,8417,3064],{"className":8418,"style":3149},[243,244],[188,8420,214],{"className":8421},[249],[188,8423,217],{"className":8424},[243,244],[188,8426,8137],{"className":8427},[8167],[188,8429],{"className":8430,"style":1003},[584],[188,8432,8140],{"className":8433},[243,244],[188,8435,220],{"className":8436},[256],[188,8438],{"className":8439,"style":2528},[584],[188,8441,2464],{"className":8442},[2532]," _____",[22,8445,32],{"id":8446},"答案与深度解析-17",[27,8448,8449],{},[36,8450,38,8451],{},[188,8452,8454,8500],{"className":8453},[191],[188,8455,8457],{"className":8456},[195],[197,8458,8459],{"xmlns":199},[201,8460,8461,8497],{},[204,8462,8463,8465,8467,8469,8471,8473,8475,8477,8479,8481,8483,8485,8487,8489,8491,8493,8495],{},[207,8464,3064],{},[211,8466,214],{"stretchy":213},[207,8468,217],{},[211,8470,8137],{"separator":230},[207,8472,8140],{},[211,8474,4945],{},[505,8476,4948],{},[211,8478,220],{"stretchy":213},[211,8480,516],{},[207,8482,3064],{},[211,8484,214],{"stretchy":213},[207,8486,217],{},[211,8488,4945],{},[207,8490,8140],{},[211,8492,8137],{"separator":230},[207,8494,8140],{},[211,8496,220],{"stretchy":213},[222,8498,8499],{"encoding":224},"f(n, m-1) + f(n-m, m)",[188,8501,8503,8536,8557,8581],{"className":8502,"ariaHidden":230},[229],[188,8504,8506,8509,8512,8515,8518,8521,8524,8527,8530,8533],{"className":8505},[234],[188,8507],{"className":8508,"style":239},[238],[188,8510,3064],{"className":8511,"style":3149},[243,244],[188,8513,214],{"className":8514},[249],[188,8516,217],{"className":8517},[243,244],[188,8519,8137],{"className":8520},[8167],[188,8522],{"className":8523,"style":1003},[584],[188,8525,8140],{"className":8526},[243,244],[188,8528],{"className":8529,"style":585},[584],[188,8531,4945],{"className":8532},[589],[188,8534],{"className":8535,"style":585},[584],[188,8537,8539,8542,8545,8548,8551,8554],{"className":8538},[234],[188,8540],{"className":8541,"style":239},[238],[188,8543,4948],{"className":8544},[243],[188,8546,220],{"className":8547},[256],[188,8549],{"className":8550,"style":585},[584],[188,8552,516],{"className":8553},[589],[188,8555],{"className":8556,"style":585},[584],[188,8558,8560,8563,8566,8569,8572,8575,8578],{"className":8559},[234],[188,8561],{"className":8562,"style":239},[238],[188,8564,3064],{"className":8565,"style":3149},[243,244],[188,8567,214],{"className":8568},[249],[188,8570,217],{"className":8571},[243,244],[188,8573],{"className":8574,"style":585},[584],[188,8576,4945],{"className":8577},[589],[188,8579],{"className":8580,"style":585},[584],[188,8582,8584,8587,8590,8593,8596,8599],{"className":8583},[234],[188,8585],{"className":8586,"style":239},[238],[188,8588,8140],{"className":8589},[243,244],[188,8591,8137],{"className":8592},[8167],[188,8594],{"className":8595,"style":1003},[584],[188,8597,8140],{"className":8598},[243,244],[188,8600,220],{"className":8601},[256],[68,8603,8604],{},[44,8605,8606,8608,8609,8612,8613,8641,8642,8670,8671,8722,8723,8726,8727],{},[36,8607,66],{}," 这是一个非常经典的递归数学模型。所谓划分，比如数字 5 划分且最大数不超过 3，可以是 ",[7457,8610,8611],{},"3+2, 3+1+1, 2+2+1, 2+1+1+1, 1+1+1+1+1","。\n当要划分数字 ",[188,8614,8616,8629],{"className":8615},[191],[188,8617,8619],{"className":8618},[195],[197,8620,8621],{"xmlns":199},[201,8622,8623,8627],{},[204,8624,8625],{},[207,8626,217],{},[222,8628,217],{"encoding":224},[188,8630,8632],{"className":8631,"ariaHidden":230},[229],[188,8633,8635,8638],{"className":8634},[234],[188,8636],{"className":8637,"style":351},[238],[188,8639,217],{"className":8640},[243,244],"，且允许使用的最大数字是 ",[188,8643,8645,8658],{"className":8644},[191],[188,8646,8648],{"className":8647},[195],[197,8649,8650],{"xmlns":199},[201,8651,8652,8656],{},[204,8653,8654],{},[207,8655,8140],{},[222,8657,8140],{"encoding":224},[188,8659,8661],{"className":8660,"ariaHidden":230},[229],[188,8662,8664,8667],{"className":8663},[234],[188,8665],{"className":8666,"style":351},[238],[188,8668,8140],{"className":8669},[243,244]," 时（前提 ",[188,8672,8674,8692],{"className":8673},[191],[188,8675,8677],{"className":8676},[195],[197,8678,8679],{"xmlns":199},[201,8680,8681,8689],{},[204,8682,8683,8685,8687],{},[207,8684,217],{},[211,8686,3724],{},[207,8688,8140],{},[222,8690,8691],{"encoding":224},"n > m",[188,8693,8695,8713],{"className":8694,"ariaHidden":230},[229],[188,8696,8698,8701,8704,8707,8710],{"className":8697},[234],[188,8699],{"className":8700,"style":8266},[238],[188,8702,217],{"className":8703},[243,244],[188,8705],{"className":8706,"style":2528},[584],[188,8708,3724],{"className":8709},[2532],[188,8711],{"className":8712,"style":2528},[584],[188,8714,8716,8719],{"className":8715},[234],[188,8717],{"className":8718,"style":351},[238],[188,8720,8140],{"className":8721},[243,244],"），我们可以把所有可能的情况强制分为",[36,8724,8725],{},"互不重叠的两大类","：\n",[68,8728,8729,8924,9186],{},[44,8730,8731,8762,8763,8791,8792,8844,8845,85],{},[36,8732,8733,8734,85],{},"类别一：我们划分的过程中，打死都不用数字 ",[188,8735,8737,8750],{"className":8736},[191],[188,8738,8740],{"className":8739},[195],[197,8741,8742],{"xmlns":199},[201,8743,8744,8748],{},[204,8745,8746],{},[207,8747,8140],{},[222,8749,8140],{"encoding":224},[188,8751,8753],{"className":8752,"ariaHidden":230},[229],[188,8754,8756,8759],{"className":8755},[234],[188,8757],{"className":8758,"style":351},[238],[188,8760,8140],{"className":8761},[243,244]," 既然不用 ",[188,8764,8766,8779],{"className":8765},[191],[188,8767,8769],{"className":8768},[195],[197,8770,8771],{"xmlns":199},[201,8772,8773,8777],{},[204,8774,8775],{},[207,8776,8140],{},[222,8778,8140],{"encoding":224},[188,8780,8782],{"className":8781,"ariaHidden":230},[229],[188,8783,8785,8788],{"className":8784},[234],[188,8786],{"className":8787,"style":351},[238],[188,8789,8140],{"className":8790},[243,244],"，那我们能用的最大数字就降级成了 ",[188,8793,8795,8813],{"className":8794},[191],[188,8796,8798],{"className":8797},[195],[197,8799,8800],{"xmlns":199},[201,8801,8802,8810],{},[204,8803,8804,8806,8808],{},[207,8805,8140],{},[211,8807,4945],{},[505,8809,4948],{},[222,8811,8812],{"encoding":224},"m-1",[188,8814,8816,8835],{"className":8815,"ariaHidden":230},[229],[188,8817,8819,8823,8826,8829,8832],{"className":8818},[234],[188,8820],{"className":8821,"style":8822},[238],"height:0.6667em;vertical-align:-0.0833em;",[188,8824,8140],{"className":8825},[243,244],[188,8827],{"className":8828,"style":585},[584],[188,8830,4945],{"className":8831},[589],[188,8833],{"className":8834,"style":585},[584],[188,8836,8838,8841],{"className":8837},[234],[188,8839],{"className":8840,"style":3213},[238],[188,8842,4948],{"className":8843},[243],"。这种情况下，划分方式的数目等价于 ",[188,8846,8848,8876],{"className":8847},[191],[188,8849,8851],{"className":8850},[195],[197,8852,8853],{"xmlns":199},[201,8854,8855,8873],{},[204,8856,8857,8859,8861,8863,8865,8867,8869,8871],{},[207,8858,3064],{},[211,8860,214],{"stretchy":213},[207,8862,217],{},[211,8864,8137],{"separator":230},[207,8866,8140],{},[211,8868,4945],{},[505,8870,4948],{},[211,8872,220],{"stretchy":213},[222,8874,8875],{"encoding":224},"f(n, m-1)",[188,8877,8879,8912],{"className":8878,"ariaHidden":230},[229],[188,8880,8882,8885,8888,8891,8894,8897,8900,8903,8906,8909],{"className":8881},[234],[188,8883],{"className":8884,"style":239},[238],[188,8886,3064],{"className":8887,"style":3149},[243,244],[188,8889,214],{"className":8890},[249],[188,8892,217],{"className":8893},[243,244],[188,8895,8137],{"className":8896},[8167],[188,8898],{"className":8899,"style":1003},[584],[188,8901,8140],{"className":8902},[243,244],[188,8904],{"className":8905,"style":585},[584],[188,8907,4945],{"className":8908},[589],[188,8910],{"className":8911,"style":585},[584],[188,8913,8915,8918,8921],{"className":8914},[234],[188,8916],{"className":8917,"style":239},[238],[188,8919,4948],{"className":8920},[243],[188,8922,220],{"className":8923},[256],[44,8925,8926,8957,8958,8986,8987,9015,9016,9077,9078,9106,9107,85],{},[36,8927,8928,8929,85],{},"类别二：我们划分的过程中，至少使用了一个数字 ",[188,8930,8932,8945],{"className":8931},[191],[188,8933,8935],{"className":8934},[195],[197,8936,8937],{"xmlns":199},[201,8938,8939,8943],{},[204,8940,8941],{},[207,8942,8140],{},[222,8944,8140],{"encoding":224},[188,8946,8948],{"className":8947,"ariaHidden":230},[229],[188,8949,8951,8954],{"className":8950},[234],[188,8952],{"className":8953,"style":351},[238],[188,8955,8140],{"className":8956},[243,244]," 既然确定至少包含一个 ",[188,8959,8961,8974],{"className":8960},[191],[188,8962,8964],{"className":8963},[195],[197,8965,8966],{"xmlns":199},[201,8967,8968,8972],{},[204,8969,8970],{},[207,8971,8140],{},[222,8973,8140],{"encoding":224},[188,8975,8977],{"className":8976,"ariaHidden":230},[229],[188,8978,8980,8983],{"className":8979},[234],[188,8981],{"className":8982,"style":351},[238],[188,8984,8140],{"className":8985},[243,244],"，那么把这个 ",[188,8988,8990,9003],{"className":8989},[191],[188,8991,8993],{"className":8992},[195],[197,8994,8995],{"xmlns":199},[201,8996,8997,9001],{},[204,8998,8999],{},[207,9000,8140],{},[222,9002,8140],{"encoding":224},[188,9004,9006],{"className":9005,"ariaHidden":230},[229],[188,9007,9009,9012],{"className":9008},[234],[188,9010],{"className":9011,"style":351},[238],[188,9013,8140],{"className":9014},[243,244]," 先剥离出来，我们要面临的新问题就是如何把剩下的总数 ",[188,9017,9019,9041],{"className":9018},[191],[188,9020,9022],{"className":9021},[195],[197,9023,9024],{"xmlns":199},[201,9025,9026,9038],{},[204,9027,9028,9030,9032,9034,9036],{},[211,9029,214],{"stretchy":213},[207,9031,217],{},[211,9033,4945],{},[207,9035,8140],{},[211,9037,220],{"stretchy":213},[222,9039,9040],{"encoding":224},"(n-m)",[188,9042,9044,9065],{"className":9043,"ariaHidden":230},[229],[188,9045,9047,9050,9053,9056,9059,9062],{"className":9046},[234],[188,9048],{"className":9049,"style":239},[238],[188,9051,214],{"className":9052},[249],[188,9054,217],{"className":9055},[243,244],[188,9057],{"className":9058,"style":585},[584],[188,9060,4945],{"className":9061},[589],[188,9063],{"className":9064,"style":585},[584],[188,9066,9068,9071,9074],{"className":9067},[234],[188,9069],{"className":9070,"style":239},[238],[188,9072,8140],{"className":9073},[243,244],[188,9075,220],{"className":9076},[256]," 继续进行划分。此时允许使用的最大数字依然是 ",[188,9079,9081,9094],{"className":9080},[191],[188,9082,9084],{"className":9083},[195],[197,9085,9086],{"xmlns":199},[201,9087,9088,9092],{},[204,9089,9090],{},[207,9091,8140],{},[222,9093,8140],{"encoding":224},[188,9095,9097],{"className":9096,"ariaHidden":230},[229],[188,9098,9100,9103],{"className":9099},[234],[188,9101],{"className":9102,"style":351},[238],[188,9104,8140],{"className":9105},[243,244],"。这种情况下，划分数目等价于 ",[188,9108,9110,9138],{"className":9109},[191],[188,9111,9113],{"className":9112},[195],[197,9114,9115],{"xmlns":199},[201,9116,9117,9135],{},[204,9118,9119,9121,9123,9125,9127,9129,9131,9133],{},[207,9120,3064],{},[211,9122,214],{"stretchy":213},[207,9124,217],{},[211,9126,4945],{},[207,9128,8140],{},[211,9130,8137],{"separator":230},[207,9132,8140],{},[211,9134,220],{"stretchy":213},[222,9136,9137],{"encoding":224},"f(n-m, m)",[188,9139,9141,9165],{"className":9140,"ariaHidden":230},[229],[188,9142,9144,9147,9150,9153,9156,9159,9162],{"className":9143},[234],[188,9145],{"className":9146,"style":239},[238],[188,9148,3064],{"className":9149,"style":3149},[243,244],[188,9151,214],{"className":9152},[249],[188,9154,217],{"className":9155},[243,244],[188,9157],{"className":9158,"style":585},[584],[188,9160,4945],{"className":9161},[589],[188,9163],{"className":9164,"style":585},[584],[188,9166,9168,9171,9174,9177,9180,9183],{"className":9167},[234],[188,9169],{"className":9170,"style":239},[238],[188,9172,8140],{"className":9173},[243,244],[188,9175,8137],{"className":9176},[8167],[188,9178],{"className":9179,"style":1003},[584],[188,9181,8140],{"className":9182},[243,244],[188,9184,220],{"className":9185},[256],[44,9187,9188,9189,85],{},"由于这两类覆盖了所有情况且互斥，运用加法原理，总数就是 ",[188,9190,9192,9237],{"className":9191},[191],[188,9193,9195],{"className":9194},[195],[197,9196,9197],{"xmlns":199},[201,9198,9199,9235],{},[204,9200,9201,9203,9205,9207,9209,9211,9213,9215,9217,9219,9221,9223,9225,9227,9229,9231,9233],{},[207,9202,3064],{},[211,9204,214],{"stretchy":213},[207,9206,217],{},[211,9208,8137],{"separator":230},[207,9210,8140],{},[211,9212,4945],{},[505,9214,4948],{},[211,9216,220],{"stretchy":213},[211,9218,516],{},[207,9220,3064],{},[211,9222,214],{"stretchy":213},[207,9224,217],{},[211,9226,4945],{},[207,9228,8140],{},[211,9230,8137],{"separator":230},[207,9232,8140],{},[211,9234,220],{"stretchy":213},[222,9236,8499],{"encoding":224},[188,9238,9240,9273,9294,9318],{"className":9239,"ariaHidden":230},[229],[188,9241,9243,9246,9249,9252,9255,9258,9261,9264,9267,9270],{"className":9242},[234],[188,9244],{"className":9245,"style":239},[238],[188,9247,3064],{"className":9248,"style":3149},[243,244],[188,9250,214],{"className":9251},[249],[188,9253,217],{"className":9254},[243,244],[188,9256,8137],{"className":9257},[8167],[188,9259],{"className":9260,"style":1003},[584],[188,9262,8140],{"className":9263},[243,244],[188,9265],{"className":9266,"style":585},[584],[188,9268,4945],{"className":9269},[589],[188,9271],{"className":9272,"style":585},[584],[188,9274,9276,9279,9282,9285,9288,9291],{"className":9275},[234],[188,9277],{"className":9278,"style":239},[238],[188,9280,4948],{"className":9281},[243],[188,9283,220],{"className":9284},[256],[188,9286],{"className":9287,"style":585},[584],[188,9289,516],{"className":9290},[589],[188,9292],{"className":9293,"style":585},[584],[188,9295,9297,9300,9303,9306,9309,9312,9315],{"className":9296},[234],[188,9298],{"className":9299,"style":239},[238],[188,9301,3064],{"className":9302,"style":3149},[243,244],[188,9304,214],{"className":9305},[249],[188,9307,217],{"className":9308},[243,244],[188,9310],{"className":9311,"style":585},[584],[188,9313,4945],{"className":9314},[589],[188,9316],{"className":9317,"style":585},[584],[188,9319,9321,9324,9327,9330,9333,9336],{"className":9320},[234],[188,9322],{"className":9323,"style":239},[238],[188,9325,8140],{"className":9326},[243,244],[188,9328,8137],{"className":9329},[8167],[188,9331],{"className":9332,"style":1003},[584],[188,9334,8140],{"className":9335},[243,244],[188,9337,220],{"className":9338},[256],[14,9340],{},[22,9342,5589],{"id":9343},"_5-题目内容-1",[27,9345,9346,9347,9414,9415,9480,9481,9510,9511,9541,9542,9750,9751,9510,9780,9541,9809,10017,10018,10143,10144,10216,10217,10384,10385,8443],{},"利用动态规划法求解最长公共子序列问题时，设计动态规划数组 ",[188,9348,9350,9381],{"className":9349},[191],[188,9351,9353],{"className":9352},[195],[197,9354,9355],{"xmlns":199},[201,9356,9357,9378],{},[204,9358,9359,9362,9364,9367,9369,9372,9374,9376],{},[207,9360,9361],{},"d",[207,9363,27],{},[211,9365,9366],{"stretchy":213},"[",[207,9368,8140],{},[211,9370,9371],{"stretchy":213},"]",[211,9373,9366],{"stretchy":213},[207,9375,217],{},[211,9377,9371],{"stretchy":213},[222,9379,9380],{"encoding":224},"dp[m][n]",[188,9382,9384],{"className":9383,"ariaHidden":230},[229],[188,9385,9387,9390,9393,9396,9399,9402,9405,9408,9411],{"className":9386},[234],[188,9388],{"className":9389,"style":239},[238],[188,9391,9361],{"className":9392},[243,244],[188,9394,27],{"className":9395},[243,244],[188,9397,9366],{"className":9398},[249],[188,9400,8140],{"className":9401},[243,244],[188,9403,9371],{"className":9404},[256],[188,9406,9366],{"className":9407},[249],[188,9409,217],{"className":9410},[243,244],[188,9412,9371],{"className":9413},[256],"。其中 ",[188,9416,9418,9446],{"className":9417},[191],[188,9419,9421],{"className":9420},[195],[197,9422,9423],{"xmlns":199},[201,9424,9425,9443],{},[204,9426,9427,9429,9431,9433,9435,9437,9439,9441],{},[207,9428,9361],{},[207,9430,27],{},[211,9432,9366],{"stretchy":213},[207,9434,6651],{},[211,9436,9371],{"stretchy":213},[211,9438,9366],{"stretchy":213},[207,9440,8087],{},[211,9442,9371],{"stretchy":213},[222,9444,9445],{"encoding":224},"dp[i][j]",[188,9447,9449],{"className":9448,"ariaHidden":230},[229],[188,9450,9452,9455,9458,9461,9464,9467,9470,9473,9477],{"className":9451},[234],[188,9453],{"className":9454,"style":239},[238],[188,9456,9361],{"className":9457},[243,244],[188,9459,27],{"className":9460},[243,244],[188,9462,9366],{"className":9463},[249],[188,9465,6651],{"className":9466},[243,244],[188,9468,9371],{"className":9469},[256],[188,9471,9366],{"className":9472},[249],[188,9474,8087],{"className":9475,"style":9476},[243,244],"margin-right:0.0572em;",[188,9478,9371],{"className":9479},[256]," 为：长度为 ",[188,9482,9484,9497],{"className":9483},[191],[188,9485,9487],{"className":9486},[195],[197,9488,9489],{"xmlns":199},[201,9490,9491,9495],{},[204,9492,9493],{},[207,9494,6651],{},[222,9496,6651],{"encoding":224},[188,9498,9500],{"className":9499,"ariaHidden":230},[229],[188,9501,9503,9507],{"className":9502},[234],[188,9504],{"className":9505,"style":9506},[238],"height:0.6595em;",[188,9508,6651],{"className":9509},[243,244]," 的 ",[188,9512,9514,9528],{"className":9513},[191],[188,9515,9517],{"className":9516},[195],[197,9518,9519],{"xmlns":199},[201,9520,9521,9526],{},[204,9522,9523],{},[207,9524,9525],{},"X",[222,9527,9525],{"encoding":224},[188,9529,9531],{"className":9530,"ariaHidden":230},[229],[188,9532,9534,9537],{"className":9533},[234],[188,9535],{"className":9536,"style":1693},[238],[188,9538,9525],{"className":9539,"style":9540},[243,244],"margin-right:0.0785em;"," 子序列 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和长度为 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的最长公共子序列的长度。若 ",[188,10019,10021,10059],{"className":10020},[191],[188,10022,10024],{"className":10023},[195],[197,10025,10026],{"xmlns":199},[201,10027,10028,10056],{},[204,10029,10030,10032,10034,10036,10038,10040,10042,10044,10046,10048,10050,10052,10054],{},[207,10031,7859],{},[211,10033,9366],{"stretchy":213},[207,10035,6651],{},[211,10037,4945],{},[505,10039,4948],{},[211,10041,9371],{"stretchy":213},[211,10043,2464],{},[207,10045,9827],{},[211,10047,9366],{"stretchy":213},[207,10049,8087],{},[211,10051,4945],{},[505,10053,4948],{},[211,10055,9371],{"stretchy":213},[222,10057,10058],{"encoding":224},"x[i-1] = y[j-1]",[188,10060,10062,10086,10107,10131],{"className":10061,"ariaHidden":230},[229],[188,10063,10065,10068,10071,10074,10077,10080,10083],{"className":10064},[234],[188,10066],{"className":10067,"style":239},[238],[188,10069,7859],{"className":10070},[243,244],[188,10072,9366],{"className":10073},[249],[188,10075,6651],{"className":10076},[243,244],[188,10078],{"className":10079,"style":585},[584],[188,10081,4945],{"className":10082},[589],[188,10084],{"className":10085,"style":585},[584],[188,10087,10089,10092,10095,10098,10101,10104],{"className":10088},[234],[188,10090],{"className":10091,"style":239},[238],[188,10093,4948],{"className":10094},[243],[188,10096,9371],{"className":10097},[256],[188,10099],{"className":10100,"style":2528},[584],[188,10102,2464],{"className":10103},[2532],[188,10105],{"className":10106,"style":2528},[584],[188,10108,10110,10113,10116,10119,10122,10125,10128],{"className":10109},[234],[188,10111],{"className":10112,"style":239},[238],[188,10114,9827],{"className":10115,"style":355},[243,244],[188,10117,9366],{"className":10118},[249],[188,10120,8087],{"className":10121,"style":9476},[243,244],[188,10123],{"className":10124,"style":585},[584],[188,10126,4945],{"className":10127},[589],[188,10129],{"className":10130,"style":585},[584],[188,10132,10134,10137,10140],{"className":10133},[234],[188,10135],{"className":10136,"style":239},[238],[188,10138,4948],{"className":10139},[243],[188,10141,9371],{"className":10142},[256],"（当前两个字符相同）则 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_____ ；若 ",[188,10218,10220,10259],{"className":10219},[191],[188,10221,10223],{"className":10222},[195],[197,10224,10225],{"xmlns":199},[201,10226,10227,10256],{},[204,10228,10229,10231,10233,10235,10237,10239,10241,10244,10246,10248,10250,10252,10254],{},[207,10230,7859],{},[211,10232,9366],{"stretchy":213},[207,10234,6651],{},[211,10236,4945],{},[505,10238,4948],{},[211,10240,9371],{"stretchy":213},[211,10242,10243],{"mathvariant":510},"≠",[207,10245,9827],{},[211,10247,9366],{"stretchy":213},[207,10249,8087],{},[211,10251,4945],{},[505,10253,4948],{},[211,10255,9371],{"stretchy":213},[222,10257,10258],{"encoding":224},"x[i-1] \\neq 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则 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+ 1",[36,10469,10470],{},[7457,10471,10472],{},"max(dp[i-1][j], dp[i][j-1])",[68,10474,10475],{},[44,10476,10477,10479,10480],{},[36,10478,66],{}," 动态规划的核心在于推导“状态转移方程”。我们用白话进行逻辑推演：\n",[68,10481,10482,10491,10632],{},[44,10483,10484,10486,10487,10490],{},[7457,10485,9445],{}," 就像是两个指针，分别指着字符串 X 的第 i 个字符，和字符串 Y 的第 j 个字符（注意题目给的暗示：C语言数组下标通常从0开始，所以第 i 个字符对应 ",[7457,10488,10489],{},"x[i-1]","）。",[44,10492,10493,10625,10626,10629,10630,85],{},[36,10494,10495,10496,10624],{},"情景一：两边的末尾字符竟然一模一样（",[188,10497,10499,10539],{"className":10498},[191],[188,10500,10502],{"className":10501},[195],[197,10503,10504],{"xmlns":199},[201,10505,10506,10536],{},[204,10507,10508,10510,10512,10514,10516,10518,10520,10522,10524,10526,10528,10530,10532,10534],{},[207,10509,7859],{},[211,10511,9366],{"stretchy":213},[207,10513,6651],{},[211,10515,4945],{},[505,10517,4948],{},[211,10519,9371],{"stretchy":213},[211,10521,2464],{},[211,10523,2464],{},[207,10525,9827],{},[211,10527,9366],{"stretchy":213},[207,10529,8087],{},[211,10531,4945],{},[505,10533,4948],{},[211,10535,9371],{"stretchy":213},[222,10537,10538],{"encoding":224},"x[i-1] == y[j-1]",[188,10540,10542,10566,10588,10612],{"className":10541,"ariaHidden":230},[229],[188,10543,10545,10548,10551,10554,10557,10560,10563],{"className":10544},[234],[188,10546],{"className":10547,"style":239},[238],[188,10549,7859],{"className":10550},[243,244],[188,10552,9366],{"className":10553},[249],[188,10555,6651],{"className":10556},[243,244],[188,10558],{"className":10559,"style":585},[584],[188,10561,4945],{"className":10562},[589],[188,10564],{"className":10565,"style":585},[584],[188,10567,10569,10572,10575,10578,10581,10585],{"className":10568},[234],[188,10570],{"className":10571,"style":239},[238],[188,10573,4948],{"className":10574},[243],[188,10576,9371],{"className":10577},[256],[188,10579],{"className":10580,"style":2528},[584],[188,10582,10584],{"className":10583},[2532],"==",[188,10586],{"className":10587,"style":2528},[584],[188,10589,10591,10594,10597,10600,10603,10606,10609],{"className":10590},[234],[188,10592],{"className":10593,"style":239},[238],[188,10595,9827],{"className":10596,"style":355},[243,244],[188,10598,9366],{"className":10599},[249],[188,10601,8087],{"className":10602,"style":9476},[243,244],[188,10604],{"className":10605,"style":585},[584],[188,10607,4945],{"className":10608},[589],[188,10610],{"className":10611,"style":585},[584],[188,10613,10615,10618,10621],{"className":10614},[234],[188,10616],{"className":10617,"style":239},[238],[188,10619,4948],{"className":10620},[243],[188,10622,9371],{"className":10623},[256],"）！"," 这简直是天上掉馅饼，这两个字符必定能成为公共子序列的最后一个字符。那么现在的长度，等于把这两个字符都扔掉后，前面剩余部分的公共长度再加上这1个字符。前面剩余部分的长度就是 ",[7457,10627,10628],{},"dp[i-1][j-1]","。所以是 ",[7457,10631,10467],{},[44,10633,10634,10794,10795],{},[36,10635,10636,10637,10490],{},"情景二：两边的末尾字符不一样（",[188,10638,10640,10677],{"className":10639},[191],[188,10641,10643],{"className":10642},[195],[197,10644,10645],{"xmlns":199},[201,10646,10647,10675],{},[204,10648,10649,10651,10653,10655,10657,10659,10661,10663,10665,10667,10669,10671,10673],{},[207,10650,7859],{},[211,10652,9366],{"stretchy":213},[207,10654,6651],{},[211,10656,4945],{},[505,10658,4948],{},[211,10660,9371],{"stretchy":213},[211,10662,10243],{"mathvariant":510},[207,10664,9827],{},[211,10666,9366],{"stretchy":213},[207,10668,8087],{},[211,10670,4945],{},[505,10672,4948],{},[211,10674,9371],{"stretchy":213},[222,10676,10258],{"encoding":224},[188,10678,10680,10704,10758,10782],{"className":10679,"ariaHidden":230},[229],[188,10681,10683,10686,10689,10692,10695,10698,10701],{"className":10682},[234],[188,10684],{"className":10685,"style":239},[238],[188,10687,7859],{"className":10688},[243,244],[188,10690,9366],{"className":10691},[249],[188,10693,6651],{"className":10694},[243,244],[188,10696],{"className":10697,"style":585},[584],[188,10699,4945],{"className":10700},[589],[188,10702],{"className":10703,"style":585},[584],[188,10705,10707,10710,10713,10716,10719,10755],{"className":10706},[234],[188,10708],{"className":10709,"style":239},[238],[188,10711,4948],{"className":10712},[243],[188,10714,9371],{"className":10715},[256],[188,10717],{"className":10718,"style":2528},[584],[188,10720,10722,10749,10752],{"className":10721},[2532],[188,10723,10725],{"className":10724},[2532],[188,10726,10728],{"className":10727},[243,10310],[188,10729,10731],{"className":10730},[10314],[188,10732,10734,10737,10746],{"className":10733},[10318],[188,10735],{"className":10736,"style":10322},[238],[188,10738,10740],{"className":10739},[10326],[188,10741,10743],{"className":10742},[243],[188,10744,10333],{"className":10745},[2532],[188,10747],{"className":10748},[10337],[188,10750],{"className":10751},[584,10341],[188,10753,2464],{"className":10754},[2532],[188,10756],{"className":10757,"style":2528},[584],[188,10759,10761,10764,10767,10770,10773,10776,10779],{"className":10760},[234],[188,10762],{"className":10763,"style":239},[238],[188,10765,9827],{"className":10766,"style":355},[243,244],[188,10768,9366],{"className":10769},[249],[188,10771,8087],{"className":10772,"style":9476},[243,244],[188,10774],{"className":10775,"style":585},[584],[188,10777,4945],{"className":10778},[589],[188,10780],{"className":10781,"style":585},[584],[188,10783,10785,10788,10791],{"className":10784},[234],[188,10786],{"className":10787,"style":239},[238],[188,10789,4948],{"className":10790},[243],[188,10792,9371],{"className":10793},[256]," 既然不一样，这两个字符绝对不可能同时出现在最长公共子序列的末尾。我们只能做取舍：\n",[68,10796,10797,10803],{},[44,10798,10799,10800,85],{},"要么抛弃 X 的末尾字符，看 X 的前 i-1 个字符和 Y 的前 j 个字符能凑出多长：",[7457,10801,10802],{},"dp[i-1][j]",[44,10804,10805,10806,10809,10810,85],{},"要么抛弃 Y 的末尾字符，看 X 的前 i 个字符和 Y 的前 j-1 个字符能凑出多长：",[7457,10807,10808],{},"dp[i][j-1]","。\n既然要求“最长”，我们就取这两种取舍方案中的较大值：",[7457,10811,10472],{},[14,10813],{},[17,10815,10817],{"id":10816},"四分析与构造题每题10分共30分","四、分析与构造题（每题10分，共30分）",[22,10819,25],{"id":10820},"_1-题目内容-3",[27,10822,10823],{},"根据如下算法，回答问题。",[7746,10825,10827],{"className":7748,"code":10826,"language":7750,"meta":7751,"style":7751},"void fun(int a[], int i, int n) \u002F\u002F 首次调用时: i为1\n{\n    int j, k;\n    if (i == n) return;\n    else\n    {\n        k = i;\n        for (j = i + 1; j \u003C= n; j++)\n            if (a[j] \u003C a[k]) k = j;\n        if (k != i)\n            swap(a[i], a[k]);\n        fun(a, i + 1, n);\n    }\n}\n",[7457,10828,10829,10834,10838,10843,10848,10852,10857,10862,10867,10872,10877,10882,10887,10892],{"__ignoreMap":7751},[188,10830,10831],{"class":7756,"line":7757},[188,10832,10833],{},"void fun(int a[], int i, int n) \u002F\u002F 首次调用时: i为1\n",[188,10835,10836],{"class":7756,"line":7763},[188,10837,7772],{},[188,10839,10840],{"class":7756,"line":7769},[188,10841,10842],{},"    int j, k;\n",[188,10844,10845],{"class":7756,"line":7775},[188,10846,10847],{},"    if (i == n) return;\n",[188,10849,10850],{"class":7756,"line":7781},[188,10851,7790],{},[188,10853,10854],{"class":7756,"line":7787},[188,10855,10856],{},"    {\n",[188,10858,10859],{"class":7756,"line":7793},[188,10860,10861],{},"        k = i;\n",[188,10863,10864],{"class":7756,"line":7799},[188,10865,10866],{},"        for (j = i + 1; j \u003C= n; j++)\n",[188,10868,10869],{"class":7756,"line":7805},[188,10870,10871],{},"            if (a[j] \u003C a[k]) k = j;\n",[188,10873,10874],{"class":7756,"line":7811},[188,10875,10876],{},"        if (k != i)\n",[188,10878,10879],{"class":7756,"line":7817},[188,10880,10881],{},"            swap(a[i], a[k]);\n",[188,10883,10884],{"class":7756,"line":7823},[188,10885,10886],{},"        fun(a, i + 1, n);\n",[188,10888,10889],{"class":7756,"line":7829},[188,10890,10891],{},"    }\n",[188,10893,10895],{"class":7756,"line":10894},14,[188,10896,7832],{},[41,10898,10899,10964],{},[44,10900,10901,10902,10930,10931,10934,10935,10963],{},"若 ",[188,10903,10905,10918],{"className":10904},[191],[188,10906,10908],{"className":10907},[195],[197,10909,10910],{"xmlns":199},[201,10911,10912,10916],{},[204,10913,10914],{},[207,10915,3046],{},[222,10917,3046],{"encoding":224},[188,10919,10921],{"className":10920,"ariaHidden":230},[229],[188,10922,10924,10927],{"className":10923},[234],[188,10925],{"className":10926,"style":351},[238],[188,10928,3046],{"className":10929},[243,244]," 数组中元素依次为 4, 9, 1, 3, 5, 6，分析并写出调用 ",[7457,10932,10933],{},"fun(a,1,6)"," 后 ",[188,10936,10938,10951],{"className":10937},[191],[188,10939,10941],{"className":10940},[195],[197,10942,10943],{"xmlns":199},[201,10944,10945,10949],{},[204,10946,10947],{},[207,10948,3046],{},[222,10950,3046],{"encoding":224},[188,10952,10954],{"className":10953,"ariaHidden":230},[229],[188,10955,10957,10960],{"className":10956},[234],[188,10958],{"className":10959,"style":351},[238],[188,10961,3046],{"className":10962},[243,244]," 数组中元素值，并回答该算法完成的功能。（5分）",[44,10965,10966],{},"给出该算法时间复杂度递归方程（仅针对元素比较次数分析即可）并分析该算法的最坏时间复杂度。（5分）",[22,10968,32],{"id":10969},"答案与深度解析-19",[27,10971,10972],{},[36,10973,10974],{},"1) 数组变化及功能分析：",[68,10976,10977,11181,11189],{},[44,10978,10979,10982,10983,10985,10986,10988,10989,10991,10992,10995,10996],{},[36,10980,10981],{},"模拟推理（从零推演）：","\n题目明确 ",[7457,10984,3046],{}," 的元素是 4, 9, 1, 3, 5, 6。从代码的界限 ",[7457,10987,6651],{}," 到 ",[7457,10990,217],{},"（从 1 到 6），说明该题目将数组视为从索引 1 开始存数据的（即 ",[7457,10993,10994],{},"a[1]=4, a[2]=9, ... a[6]=6","）。\n",[68,10997,10998,11043,11078,11106,11137,11166],{},[44,10999,11000,8007,11007,11010,11011,11014,11015,11018,11019,11022,11023,11026,11027,11030,11031],{},[36,11001,11002,11003,11006],{},"第一次调用 ",[7457,11004,11005],{},"fun(a, 1, 6)","：",[7457,11008,11009],{},"i=1","。内层循环从 ",[7457,11012,11013],{},"j=2"," 到 6，寻找其中最小的元素。找到了 ",[7457,11016,11017],{},"a[3]=1"," 是最小的，因此记录下标 ",[7457,11020,11021],{},"k=3","。将 ",[7457,11024,11025],{},"a[1]"," 和 ",[7457,11028,11029],{},"a[3]"," 交换。\n",[68,11032,11033],{},[44,11034,11035,11036,11039,11040,85],{},"数组变为：",[36,11037,11038],{},"1, 9, 4, 3, 5, 6","。随后递归调用 ",[7457,11041,11042],{},"fun(a, 2, 6)",[44,11044,11045,8007,11050,11053,11054,11057,11058,11022,11061,11026,11064,11030,11067],{},[36,11046,11047,11048,11006],{},"第二次调用 ",[7457,11049,11042],{},[7457,11051,11052],{},"i=2","。此时数组有效区域是索引 2 到 6。寻找这部分最小元素。发现 ",[7457,11055,11056],{},"a[4]=3"," 最小，记录 ",[7457,11059,11060],{},"k=4",[7457,11062,11063],{},"a[2]",[7457,11065,11066],{},"a[4]",[68,11068,11069],{},[44,11070,11035,11071,11074,11075,85],{},[36,11072,11073],{},"1, 3, 4, 9, 5, 6","。递归调用 ",[7457,11076,11077],{},"fun(a, 3, 6)",[44,11079,11080,8007,11085,11088,11089,11092,11093,11095,11096],{},[36,11081,11082,11083,11006],{},"第三次调用 ",[7457,11084,11077],{},[7457,11086,11087],{},"i=3","。寻找到 3..6 中最小的是 ",[7457,11090,11091],{},"a[3]=4"," 本身，",[7457,11094,11021],{},"，不交换。\n",[68,11097,11098],{},[44,11099,11100,11101,11074,11103,85],{},"数组保持：",[36,11102,11073],{},[7457,11104,11105],{},"fun(a, 4, 6)",[44,11107,11108,8007,11113,11116,11117,11120,11121,11026,11123,11126,11127],{},[36,11109,11110,11111,11006],{},"第四次调用 ",[7457,11112,11105],{},[7457,11114,11115],{},"i=4","。寻找 4..6 中最小元素，发现 ",[7457,11118,11119],{},"a[5]=5"," 最小，交换 ",[7457,11122,11066],{},[7457,11124,11125],{},"a[5]","。\n",[68,11128,11129],{},[44,11130,11035,11131,11074,11134,85],{},[36,11132,11133],{},"1, 3, 4, 5, 9, 6",[7457,11135,11136],{},"fun(a, 5, 6)",[44,11138,11139,8007,11144,11147,11148,11120,11151,11026,11153,11126,11156],{},[36,11140,11141,11142,11006],{},"第五次调用 ",[7457,11143,11136],{},[7457,11145,11146],{},"i=5","。寻找 5..6 最小元素，发现 ",[7457,11149,11150],{},"a[6]=6",[7457,11152,11125],{},[7457,11154,11155],{},"a[6]",[68,11157,11158],{},[44,11159,11035,11160,11074,11163,85],{},[36,11161,11162],{},"1, 3, 4, 5, 6, 9",[7457,11164,11165],{},"fun(a, 6, 6)",[44,11167,11168,8007,11173,11176,11177,11180],{},[36,11169,11170,11171,11006],{},"第六次调用 ",[7457,11172,11165],{},[7457,11174,11175],{},"i=n"," 满足界限条件，直接 ",[7457,11178,11179],{},"return","，递归终止。",[44,11182,11183,11186,11187,85],{},[36,11184,11185],{},"最终结果："," 经过算法处理，数组变为：",[36,11188,11162],{},[44,11190,11191,11194,11195,85],{},[36,11192,11193],{},"算法功能结论："," 这是一个递归实现的",[36,11196,11197],{},"选择排序（从小到大排序）",[27,11199,11200],{},[36,11201,11202],{},"2) 时间复杂度分析：",[68,11204,11205,11793,12668],{},[44,11206,11207,11210,11211,11255,11256,11284,11285,11313,11314],{},[36,11208,11209],{},"建立递归方程："," 设 ",[188,11212,11214,11234],{"className":11213},[191],[188,11215,11217],{"className":11216},[195],[197,11218,11219],{"xmlns":199},[201,11220,11221,11231],{},[204,11222,11223,11225,11227,11229],{},[207,11224,2455],{},[211,11226,214],{"stretchy":213},[207,11228,217],{},[211,11230,220],{"stretchy":213},[222,11232,11233],{"encoding":224},"T(n)",[188,11235,11237],{"className":11236,"ariaHidden":230},[229],[188,11238,11240,11243,11246,11249,11252],{"className":11239},[234],[188,11241],{"className":11242,"style":239},[238],[188,11244,2455],{"className":11245,"style":2515},[243,244],[188,11247,214],{"className":11248},[249],[188,11250,217],{"className":11251},[243,244],[188,11253,220],{"className":11254},[256]," 为处理规模为 ",[188,11257,11259,11272],{"className":11258},[191],[188,11260,11262],{"className":11261},[195],[197,11263,11264],{"xmlns":199},[201,11265,11266,11270],{},[204,11267,11268],{},[207,11269,217],{},[222,11271,217],{"encoding":224},[188,11273,11275],{"className":11274,"ariaHidden":230},[229],[188,11276,11278,11281],{"className":11277},[234],[188,11279],{"className":11280,"style":351},[238],[188,11282,217],{"className":11283},[243,244]," 的数组（这里 ",[188,11286,11288,11301],{"className":11287},[191],[188,11289,11291],{"className":11290},[195],[197,11292,11293],{"xmlns":199},[201,11294,11295,11299],{},[204,11296,11297],{},[207,11298,217],{},[222,11300,217],{"encoding":224},[188,11302,11304],{"className":11303,"ariaHidden":230},[229],[188,11305,11307,11310],{"className":11306},[234],[188,11308],{"className":11309,"style":351},[238],[188,11311,217],{"className":11312},[243,244]," 代表待排序的剩余元素个数）所需要的比较次数。\n",[68,11315,11316,11389,11568],{},[44,11317,11318,11319,11322,11323,85],{},"当剩余 1 个元素时（即 ",[7457,11320,11321],{},"i == n","），比较次数为 0，即 ",[188,11324,11326,11350],{"className":11325},[191],[188,11327,11329],{"className":11328},[195],[197,11330,11331],{"xmlns":199},[201,11332,11333,11347],{},[204,11334,11335,11337,11339,11341,11343,11345],{},[207,11336,2455],{},[211,11338,214],{"stretchy":213},[505,11340,4948],{},[211,11342,220],{"stretchy":213},[211,11344,2464],{},[505,11346,8307],{},[222,11348,11349],{"encoding":224},"T(1) = 0",[188,11351,11353,11380],{"className":11352,"ariaHidden":230},[229],[188,11354,11356,11359,11362,11365,11368,11371,11374,11377],{"className":11355},[234],[188,11357],{"className":11358,"style":239},[238],[188,11360,2455],{"className":11361,"style":2515},[243,244],[188,11363,214],{"className":11364},[249],[188,11366,4948],{"className":11367},[243],[188,11369,220],{"className":11370},[256],[188,11372],{"className":11373,"style":2528},[584],[188,11375,2464],{"className":11376},[2532],[188,11378],{"className":11379,"style":2528},[584],[188,11381,11383,11386],{"className":11382},[234],[188,11384],{"className":11385,"style":3213},[238],[188,11387,8307],{"className":11388},[243],[44,11390,11391,11392,11420,11421,11424,11425,11453,11454,11515,11516,11567],{},"对于规模为 ",[188,11393,11395,11408],{"className":11394},[191],[188,11396,11398],{"className":11397},[195],[197,11399,11400],{"xmlns":199},[201,11401,11402,11406],{},[204,11403,11404],{},[207,11405,217],{},[222,11407,217],{"encoding":224},[188,11409,11411],{"className":11410,"ariaHidden":230},[229],[188,11412,11414,11417],{"className":11413},[234],[188,11415],{"className":11416,"style":351},[238],[188,11418,217],{"className":11419},[243,244]," 的问题，我们要用 ",[7457,11422,11423],{},"for"," 循环寻找当前 ",[188,11426,11428,11441],{"className":11427},[191],[188,11429,11431],{"className":11430},[195],[197,11432,11433],{"xmlns":199},[201,11434,11435,11439],{},[204,11436,11437],{},[207,11438,217],{},[222,11440,217],{"encoding":224},[188,11442,11444],{"className":11443,"ariaHidden":230},[229],[188,11445,11447,11450],{"className":11446},[234],[188,11448],{"className":11449,"style":351},[238],[188,11451,217],{"className":11452},[243,244]," 个元素中的最小值，需要进行 ",[188,11455,11457,11479],{"className":11456},[191],[188,11458,11460],{"className":11459},[195],[197,11461,11462],{"xmlns":199},[201,11463,11464,11476],{},[204,11465,11466,11468,11470,11472,11474],{},[211,11467,214],{"stretchy":213},[207,11469,217],{},[211,11471,4945],{},[505,11473,4948],{},[211,11475,220],{"stretchy":213},[222,11477,11478],{"encoding":224},"(n-1)",[188,11480,11482,11503],{"className":11481,"ariaHidden":230},[229],[188,11483,11485,11488,11491,11494,11497,11500],{"className":11484},[234],[188,11486],{"className":11487,"style":239},[238],[188,11489,214],{"className":11490},[249],[188,11492,217],{"className":11493},[243,244],[188,11495],{"className":11496,"style":585},[584],[188,11498,4945],{"className":11499},[589],[188,11501],{"className":11502,"style":585},[584],[188,11504,11506,11509,11512],{"className":11505},[234],[188,11507],{"className":11508,"style":239},[238],[188,11510,4948],{"className":11511},[243],[188,11513,220],{"className":11514},[256]," 次比较。然后针对剩下的 ",[188,11517,11519,11537],{"className":11518},[191],[188,11520,11522],{"className":11521},[195],[197,11523,11524],{"xmlns":199},[201,11525,11526,11534],{},[204,11527,11528,11530,11532],{},[207,11529,217],{},[211,11531,4945],{},[505,11533,4948],{},[222,11535,11536],{"encoding":224},"n-1",[188,11538,11540,11558],{"className":11539,"ariaHidden":230},[229],[188,11541,11543,11546,11549,11552,11555],{"className":11542},[234],[188,11544],{"className":11545,"style":8822},[238],[188,11547,217],{"className":11548},[243,244],[188,11550],{"className":11551,"style":585},[584],[188,11553,4945],{"className":11554},[589],[188,11556],{"className":11557,"style":585},[584],[188,11559,11561,11564],{"className":11560},[234],[188,11562],{"className":11563,"style":3213},[238],[188,11565,4948],{"className":11566},[243]," 个元素进行递归。",[44,11569,11570,11571,11728],{},"由此得出严谨的递归方程：\n",[188,11572,11574,11620],{"className":11573},[191],[188,11575,11577],{"className":11576},[195],[197,11578,11579],{"xmlns":199},[201,11580,11581,11617],{},[204,11582,11583,11585,11587,11589,11591,11593,11595,11597,11599,11601,11603,11605,11607,11609,11611,11613,11615],{},[207,11584,2455],{},[211,11586,214],{"stretchy":213},[207,11588,217],{},[211,11590,220],{"stretchy":213},[211,11592,2464],{},[207,11594,2455],{},[211,11596,214],{"stretchy":213},[207,11598,217],{},[211,11600,4945],{},[505,11602,4948],{},[211,11604,220],{"stretchy":213},[211,11606,516],{},[211,11608,214],{"stretchy":213},[207,11610,217],{},[211,11612,4945],{},[505,11614,4948],{},[211,11616,220],{"stretchy":213},[222,11618,11619],{"encoding":224},"T(n) = T(n-1) + (n-1)",[188,11621,11623,11650,11674,11695,11716],{"className":11622,"ariaHidden":230},[229],[188,11624,11626,11629,11632,11635,11638,11641,11644,11647],{"className":11625},[234],[188,11627],{"className":11628,"style":239},[238],[188,11630,2455],{"className":11631,"style":2515},[243,244],[188,11633,214],{"className":11634},[249],[188,11636,217],{"className":11637},[243,244],[188,11639,220],{"className":11640},[256],[188,11642],{"className":11643,"style":2528},[584],[188,11645,2464],{"className":11646},[2532],[188,11648],{"className":11649,"style":2528},[584],[188,11651,11653,11656,11659,11662,11665,11668,11671],{"className":11652},[234],[188,11654],{"className":11655,"style":239},[238],[188,11657,2455],{"className":11658,"style":2515},[243,244],[188,11660,214],{"className":11661},[249],[188,11663,217],{"className":11664},[243,244],[188,11666],{"className":11667,"style":585},[584],[188,11669,4945],{"className":11670},[589],[188,11672],{"className":11673,"style":585},[584],[188,11675,11677,11680,11683,11686,11689,11692],{"className":11676},[234],[188,11678],{"className":11679,"style":239},[238],[188,11681,4948],{"className":11682},[243],[188,11684,220],{"className":11685},[256],[188,11687],{"className":11688,"style":585},[584],[188,11690,516],{"className":11691},[589],[188,11693],{"className":11694,"style":585},[584],[188,11696,11698,11701,11704,11707,11710,11713],{"className":11697},[234],[188,11699],{"className":11700,"style":239},[238],[188,11702,214],{"className":11703},[249],[188,11705,217],{"className":11706},[243,244],[188,11708],{"className":11709,"style":585},[584],[188,11711,4945],{"className":11712},[589],[188,11714],{"className":11715,"style":585},[584],[188,11717,11719,11722,11725],{"className":11718},[234],[188,11720],{"className":11721,"style":239},[238],[188,11723,4948],{"className":11724},[243],[188,11726,220],{"className":11727},[256],[188,11729,11731,11754],{"className":11730},[191],[188,11732,11734],{"className":11733},[195],[197,11735,11736],{"xmlns":199},[201,11737,11738,11752],{},[204,11739,11740,11742,11744,11746,11748,11750],{},[207,11741,2455],{},[211,11743,214],{"stretchy":213},[505,11745,4948],{},[211,11747,220],{"stretchy":213},[211,11749,2464],{},[505,11751,8307],{},[222,11753,11349],{"encoding":224},[188,11755,11757,11784],{"className":11756,"ariaHidden":230},[229],[188,11758,11760,11763,11766,11769,11772,11775,11778,11781],{"className":11759},[234],[188,11761],{"className":11762,"style":239},[238],[188,11764,2455],{"className":11765,"style":2515},[243,244],[188,11767,214],{"className":11768},[249],[188,11770,4948],{"className":11771},[243],[188,11773,220],{"className":11774},[256],[188,11776],{"className":11777,"style":2528},[584],[188,11779,2464],{"className":11780},[2532],[188,11782],{"className":11783,"style":2528},[584],[188,11785,11787,11790],{"className":11786},[234],[188,11788],{"className":11789,"style":3213},[238],[188,11791,8307],{"className":11792},[243],[44,11794,11795,11798,11799,12010,12275,12276,12532,12533,85],{},[36,11796,11797],{},"求解与渐进复杂度：","\n不断展开这个方程：\n",[188,11800,11802,11860],{"className":11801},[191],[188,11803,11805],{"className":11804},[195],[197,11806,11807],{"xmlns":199},[201,11808,11809,11857],{},[204,11810,11811,11813,11815,11817,11819,11821,11823,11825,11827,11829,11831,11833,11835,11837,11839,11841,11843,11845,11847,11849,11851,11853,11855],{},[207,11812,2455],{},[211,11814,214],{"stretchy":213},[207,11816,217],{},[211,11818,220],{"stretchy":213},[211,11820,2464],{},[207,11822,2455],{},[211,11824,214],{"stretchy":213},[207,11826,217],{},[211,11828,4945],{},[505,11830,507],{},[211,11832,220],{"stretchy":213},[211,11834,516],{},[211,11836,214],{"stretchy":213},[207,11838,217],{},[211,11840,4945],{},[505,11842,507],{},[211,11844,220],{"stretchy":213},[211,11846,516],{},[211,11848,214],{"stretchy":213},[207,11850,217],{},[211,11852,4945],{},[505,11854,4948],{},[211,11856,220],{"stretchy":213},[222,11858,11859],{"encoding":224},"T(n) = T(n-2) + (n-2) + (n-1)",[188,11861,11863,11890,11914,11935,11956,11977,11998],{"className":11862,"ariaHidden":230},[229],[188,11864,11866,11869,11872,11875,11878,11881,11884,11887],{"className":11865},[234],[188,11867],{"className":11868,"style":239},[238],[188,11870,2455],{"className":11871,"style":2515},[243,244],[188,11873,214],{"className":11874},[249],[188,11876,217],{"className":11877},[243,244],[188,11879,220],{"className":11880},[256],[188,11882],{"className":11883,"style":2528},[584],[188,11885,2464],{"className":11886},[2532],[188,11888],{"className":11889,"style":2528},[584],[188,11891,11893,11896,11899,11902,11905,11908,11911],{"className":11892},[234],[188,11894],{"className":11895,"style":239},[238],[188,11897,2455],{"className":11898,"style":2515},[243,244],[188,11900,214],{"className":11901},[249],[188,11903,217],{"className":11904},[243,244],[188,11906],{"className":11907,"style":585},[584],[188,11909,4945],{"className":11910},[589],[188,11912],{"className":11913,"style":585},[584],[188,11915,11917,11920,11923,11926,11929,11932],{"className":11916},[234],[188,11918],{"className":11919,"style":239},[238],[188,11921,507],{"className":11922},[243],[188,11924,220],{"className":11925},[256],[188,11927],{"className":11928,"style":585},[584],[188,11930,516],{"className":11931},[589],[188,11933],{"className":11934,"style":585},[584],[188,11936,11938,11941,11944,11947,11950,11953],{"className":11937},[234],[188,11939],{"className":11940,"style":239},[238],[188,11942,214],{"className":11943},[249],[188,11945,217],{"className":11946},[243,244],[188,11948],{"className":11949,"style":585},[584],[188,11951,4945],{"className":11952},[589],[188,11954],{"className":11955,"style":585},[584],[188,11957,11959,11962,11965,11968,11971,11974],{"className":11958},[234],[188,11960],{"className":11961,"style":239},[238],[188,11963,507],{"className":11964},[243],[188,11966,220],{"className":11967},[256],[188,11969],{"className":11970,"style":585},[584],[188,11972,516],{"className":11973},[589],[188,11975],{"className":11976,"style":585},[584],[188,11978,11980,11983,11986,11989,11992,11995],{"className":11979},[234],[188,11981],{"className":11982,"style":239},[238],[188,11984,214],{"className":11985},[249],[188,11987,217],{"className":11988},[243,244],[188,11990],{"className":11991,"style":585},[584],[188,11993,4945],{"className":11994},[589],[188,11996],{"className":11997,"style":585},[584],[188,11999,12001,12004,12007],{"className":12000},[234],[188,12002],{"className":12003,"style":239},[238],[188,12005,4948],{"className":12006},[243],[188,12008,220],{"className":12009},[256],[188,12011,12013,12083],{"className":12012},[191],[188,12014,12016],{"className":12015},[195],[197,12017,12018],{"xmlns":199},[201,12019,12020,12080],{},[204,12021,12022,12024,12026,12028,12030,12032,12034,12036,12038,12040,12042,12044,12046,12048,12050,12052,12054,12056,12058,12060,12062,12064,12066,12068,12070,12072,12074,12076,12078],{},[207,12023,2455],{},[211,12025,214],{"stretchy":213},[207,12027,217],{},[211,12029,220],{"stretchy":213},[211,12031,2464],{},[207,12033,2455],{},[211,12035,214],{"stretchy":213},[207,12037,217],{},[211,12039,4945],{},[505,12041,934],{},[211,12043,220],{"stretchy":213},[211,12045,516],{},[211,12047,214],{"stretchy":213},[207,12049,217],{},[211,12051,4945],{},[505,12053,934],{},[211,12055,220],{"stretchy":213},[211,12057,516],{},[211,12059,214],{"stretchy":213},[207,12061,217],{},[211,12063,4945],{},[505,12065,507],{},[211,12067,220],{"stretchy":213},[211,12069,516],{},[211,12071,214],{"stretchy":213},[207,12073,217],{},[211,12075,4945],{},[505,12077,4948],{},[211,12079,220],{"stretchy":213},[222,12081,12082],{"encoding":224},"T(n) = T(n-3) + (n-3) + (n-2) + (n-1)",[188,12084,12086,12113,12137,12158,12179,12200,12221,12242,12263],{"className":12085,"ariaHidden":230},[229],[188,12087,12089,12092,12095,12098,12101,12104,12107,12110],{"className":12088},[234],[188,12090],{"className":12091,"style":239},[238],[188,12093,2455],{"className":12094,"style":2515},[243,244],[188,12096,214],{"className":12097},[249],[188,12099,217],{"className":12100},[243,244],[188,12102,220],{"className":12103},[256],[188,12105],{"className":12106,"style":2528},[584],[188,12108,2464],{"className":12109},[2532],[188,12111],{"className":12112,"style":2528},[584],[188,12114,12116,12119,12122,12125,12128,12131,12134],{"className":12115},[234],[188,12117],{"className":12118,"style":239},[238],[188,12120,2455],{"className":12121,"style":2515},[243,244],[188,12123,214],{"className":12124},[249],[188,12126,217],{"className":12127},[243,244],[188,12129],{"className":12130,"style":585},[584],[188,12132,4945],{"className":12133},[589],[188,12135],{"className":12136,"style":585},[584],[188,12138,12140,12143,12146,12149,12152,12155],{"className":12139},[234],[188,12141],{"className":12142,"style":239},[238],[188,12144,934],{"className":12145},[243],[188,12147,220],{"className":12148},[256],[188,12150],{"className":12151,"style":585},[584],[188,12153,516],{"className":12154},[589],[188,12156],{"className":12157,"style":585},[584],[188,12159,12161,12164,12167,12170,12173,12176],{"className":12160},[234],[188,12162],{"className":12163,"style":239},[238],[188,12165,214],{"className":12166},[249],[188,12168,217],{"className":12169},[243,244],[188,12171],{"className":12172,"style":585},[584],[188,12174,4945],{"className":12175},[589],[188,12177],{"className":12178,"style":585},[584],[188,12180,12182,12185,12188,12191,12194,12197],{"className":12181},[234],[188,12183],{"className":12184,"style":239},[238],[188,12186,934],{"className":12187},[243],[188,12189,220],{"className":12190},[256],[188,12192],{"className":12193,"style":585},[584],[188,12195,516],{"className":12196},[589],[188,12198],{"className":12199,"style":585},[584],[188,12201,12203,12206,12209,12212,12215,12218],{"className":12202},[234],[188,12204],{"className":12205,"style":239},[238],[188,12207,214],{"className":12208},[249],[188,12210,217],{"className":12211},[243,244],[188,12213],{"className":12214,"style":585},[584],[188,12216,4945],{"className":12217},[589],[188,12219],{"className":12220,"style":585},[584],[188,12222,12224,12227,12230,12233,12236,12239],{"className":12223},[234],[188,12225],{"className":12226,"style":239},[238],[188,12228,507],{"className":12229},[243],[188,12231,220],{"className":12232},[256],[188,12234],{"className":12235,"style":585},[584],[188,12237,516],{"className":12238},[589],[188,12240],{"className":12241,"style":585},[584],[188,12243,12245,12248,12251,12254,12257,12260],{"className":12244},[234],[188,12246],{"className":12247,"style":239},[238],[188,12249,214],{"className":12250},[249],[188,12252,217],{"className":12253},[243,244],[188,12255],{"className":12256,"style":585},[584],[188,12258,4945],{"className":12259},[589],[188,12261],{"className":12262,"style":585},[584],[188,12264,12266,12269,12272],{"className":12265},[234],[188,12267],{"className":12268,"style":239},[238],[188,12270,4948],{"className":12271},[243],[188,12273,220],{"className":12274},[256],"\n...\n",[188,12277,12279,12346],{"className":12278},[191],[188,12280,12282],{"className":12281},[195],[197,12283,12284],{"xmlns":199},[201,12285,12286,12343],{},[204,12287,12288,12290,12292,12294,12296,12298,12300,12302,12304,12306,12308,12310,12312,12314,12316,12319,12321,12323,12325,12327,12329,12331,12333,12335,12337,12339,12341],{},[207,12289,2455],{},[211,12291,214],{"stretchy":213},[207,12293,217],{},[211,12295,220],{"stretchy":213},[211,12297,2464],{},[207,12299,2455],{},[211,12301,214],{"stretchy":213},[505,12303,4948],{},[211,12305,220],{"stretchy":213},[211,12307,516],{},[505,12309,4948],{},[211,12311,516],{},[505,12313,507],{},[211,12315,516],{},[211,12317,12318],{},"⋯",[211,12320,516],{},[211,12322,214],{"stretchy":213},[207,12324,217],{},[211,12326,4945],{},[505,12328,507],{},[211,12330,220],{"stretchy":213},[211,12332,516],{},[211,12334,214],{"stretchy":213},[207,12336,217],{},[211,12338,4945],{},[505,12340,4948],{},[211,12342,220],{"stretchy":213},[222,12344,12345],{"encoding":224},"T(n) = T(1) + 1 + 2 + \\dots + (n-2) + (n-1)",[188,12347,12349,12376,12403,12421,12439,12457,12478,12499,12520],{"className":12348,"ariaHidden":230},[229],[188,12350,12352,12355,12358,12361,12364,12367,12370,12373],{"className":12351},[234],[188,12353],{"className":12354,"style":239},[238],[188,12356,2455],{"className":12357,"style":2515},[243,244],[188,12359,214],{"className":12360},[249],[188,12362,217],{"className":12363},[243,244],[188,12365,220],{"className":12366},[256],[188,12368],{"className":12369,"style":2528},[584],[188,12371,2464],{"className":12372},[2532],[188,12374],{"className":12375,"style":2528},[584],[188,12377,12379,12382,12385,12388,12391,12394,12397,12400],{"className":12378},[234],[188,12380],{"className":12381,"style":239},[238],[188,12383,2455],{"className":12384,"style":2515},[243,244],[188,12386,214],{"className":12387},[249],[188,12389,4948],{"className":12390},[243],[188,12392,220],{"className":12393},[256],[188,12395],{"className":12396,"style":585},[584],[188,12398,516],{"className":12399},[589],[188,12401],{"className":12402,"style":585},[584],[188,12404,12406,12409,12412,12415,12418],{"className":12405},[234],[188,12407],{"className":12408,"style":7545},[238],[188,12410,4948],{"className":12411},[243],[188,12413],{"className":12414,"style":585},[584],[188,12416,516],{"className":12417},[589],[188,12419],{"className":12420,"style":585},[584],[188,12422,12424,12427,12430,12433,12436],{"className":12423},[234],[188,12425],{"className":12426,"style":7545},[238],[188,12428,507],{"className":12429},[243],[188,12431],{"className":12432,"style":585},[584],[188,12434,516],{"className":12435},[589],[188,12437],{"className":12438,"style":585},[584],[188,12440,12442,12445,12448,12451,12454],{"className":12441},[234],[188,12443],{"className":12444,"style":8822},[238],[188,12446,12318],{"className":12447},[9697],[188,12449],{"className":12450,"style":585},[584],[188,12452,516],{"className":12453},[589],[188,12455],{"className":12456,"style":585},[584],[188,12458,12460,12463,12466,12469,12472,12475],{"className":12459},[234],[188,12461],{"className":12462,"style":239},[238],[188,12464,214],{"className":12465},[249],[188,12467,217],{"className":12468},[243,244],[188,12470],{"className":12471,"style":585},[584],[188,12473,4945],{"className":12474},[589],[188,12476],{"className":12477,"style":585},[584],[188,12479,12481,12484,12487,12490,12493,12496],{"className":12480},[234],[188,12482],{"className":12483,"style":239},[238],[188,12485,507],{"className":12486},[243],[188,12488,220],{"className":12489},[256],[188,12491],{"className":12492,"style":585},[584],[188,12494,516],{"className":12495},[589],[188,12497],{"className":12498,"style":585},[584],[188,12500,12502,12505,12508,12511,12514,12517],{"className":12501},[234],[188,12503],{"className":12504,"style":239},[238],[188,12506,214],{"className":12507},[249],[188,12509,217],{"className":12510},[243,244],[188,12512],{"className":12513,"style":585},[584],[188,12515,4945],{"className":12516},[589],[188,12518],{"className":12519,"style":585},[584],[188,12521,12523,12526,12529],{"className":12522},[234],[188,12524],{"className":12525,"style":239},[238],[188,12527,4948],{"className":12528},[243],[188,12530,220],{"className":12531},[256],"\n根据等差数列求和公式，总比较次数为 ",[188,12534,12536,12567],{"className":12535},[191],[188,12537,12539],{"className":12538},[195],[197,12540,12541],{"xmlns":199},[201,12542,12543,12564],{},[204,12544,12545],{},[12546,12547,12548,12562],"mfrac",{},[204,12549,12550,12552,12554,12556,12558,12560],{},[207,12551,217],{},[211,12553,214],{"stretchy":213},[207,12555,217],{},[211,12557,4945],{},[505,12559,4948],{},[211,12561,220],{"stretchy":213},[505,12563,507],{},[222,12565,12566],{"encoding":224},"\\frac{n(n-1)}{2}",[188,12568,12570],{"className":12569,"ariaHidden":230},[229],[188,12571,12573,12577],{"className":12572},[234],[188,12574],{"className":12575,"style":12576},[238],"height:1.355em;vertical-align:-0.345em;",[188,12578,12580,12584,12665],{"className":12579},[243],[188,12581],{"className":12582},[249,12583],"nulldelimiter",[188,12585,12587],{"className":12586},[12546],[188,12588,12590,12656],{"className":12589},[549,966],[188,12591,12593,12653],{"className":12592},[553],[188,12594,12597,12612,12623],{"className":12595,"style":12596},[557],"height:1.01em;",[188,12598,12600,12603],{"style":12599},"top:-2.655em;",[188,12601],{"className":12602,"style":7003},[565],[188,12604,12606],{"className":12605},[570,571,572,573],[188,12607,12609],{"className":12608},[243,573],[188,12610,507],{"className":12611},[243,573],[188,12613,12615,12618],{"style":12614},"top:-3.23em;",[188,12616],{"className":12617,"style":7003},[565],[188,12619],{"className":12620,"style":12622},[12621],"frac-line","border-bottom-width:0.04em;",[188,12624,12626,12629],{"style":12625},"top:-3.485em;",[188,12627],{"className":12628,"style":7003},[565],[188,12630,12632],{"className":12631},[570,571,572,573],[188,12633,12635,12638,12641,12644,12647,12650],{"className":12634},[243,573],[188,12636,217],{"className":12637},[243,244,573],[188,12639,214],{"className":12640},[249,573],[188,12642,217],{"className":12643},[243,244,573],[188,12645,4945],{"className":12646},[589,573],[188,12648,4948],{"className":12649},[243,573],[188,12651,220],{"className":12652},[256,573],[188,12654,990],{"className":12655},[989],[188,12657,12659],{"className":12658},[553],[188,12660,12663],{"className":12661,"style":12662},[557],"height:0.345em;",[188,12664],{},[188,12666],{"className":12667},[256,12583],[44,12669,12670,12673,12674,85],{},[36,12671,12672],{},"最坏时间复杂度："," 无论数组原本是否有序，这套寻找最小值的循环必须雷打不动地执行完。因此，最坏时间复杂度（实际上也是最好和平均情况）均为 ",[36,12675,12676],{},[188,12677,12679,12702],{"className":12678},[191],[188,12680,12682],{"className":12681},[195],[197,12683,12684],{"xmlns":199},[201,12685,12686,12700],{},[204,12687,12688,12690,12692,12698],{},[207,12689,209],{},[211,12691,214],{"stretchy":213},[500,12693,12694,12696],{},[207,12695,217],{},[505,12697,507],{},[211,12699,220],{"stretchy":213},[222,12701,2728],{"encoding":224},[188,12703,12705],{"className":12704,"ariaHidden":230},[229],[188,12706,12708,12711,12714,12717,12746],{"className":12707},[234],[188,12709],{"className":12710,"style":535},[238],[188,12712,209],{"className":12713,"style":245},[243,244],[188,12715,214],{"className":12716},[249],[188,12718,12720,12723],{"className":12719},[243],[188,12721,217],{"className":12722},[243,244],[188,12724,12726],{"className":12725},[545],[188,12727,12729],{"className":12728},[549],[188,12730,12732],{"className":12731},[553],[188,12733,12735],{"className":12734,"style":558},[557],[188,12736,12737,12740],{"style":561},[188,12738],{"className":12739,"style":566},[565],[188,12741,12743],{"className":12742},[570,571,572,573],[188,12744,507],{"className":12745},[243,573],[188,12747,220],{"className":12748},[256],[14,12750],{},[22,12752,97],{"id":12753},"_2-题目内容-3",[27,12755,12756,12757,12785,12786,12983,12984,4160,13055,13142,13143,13912,13916,13917,11006],{},"给定 ",[188,12758,12760,12773],{"className":12759},[191],[188,12761,12763],{"className":12762},[195],[197,12764,12765],{"xmlns":199},[201,12766,12767,12771],{},[204,12768,12769],{},[207,12770,217],{},[222,12772,217],{"encoding":224},[188,12774,12776],{"className":12775,"ariaHidden":230},[229],[188,12777,12779,12782],{"className":12778},[234],[188,12780],{"className":12781,"style":351},[238],[188,12783,217],{"className":12784},[243,244]," 个矩阵 ",[188,12787,12789,12828],{"className":12788},[191],[188,12790,12792],{"className":12791},[195],[197,12793,12794],{"xmlns":199},[201,12795,12796,12825],{},[204,12797,12798,12805,12807,12813,12815,12817,12819],{},[916,12799,12800,12803],{},[207,12801,12802],{},"A",[505,12804,4948],{},[211,12806,8137],{"separator":230},[916,12808,12809,12811],{},[207,12810,12802],{},[505,12812,507],{},[211,12814,8137],{"separator":230},[211,12816,9574],{},[211,12818,8137],{"separator":230},[916,12820,12821,12823],{},[207,12822,12802],{},[207,12824,217],{},[222,12826,12827],{"encoding":224},"A_1, A_2, \\dots, A_n",[188,12829,12831],{"className":12830,"ariaHidden":230},[229],[188,12832,12834,12838,12878,12881,12884,12924,12927,12930,12933,12936,12939,12942],{"className":12833},[234],[188,12835],{"className":12836,"style":12837},[238],"height:0.8778em;vertical-align:-0.1944em;",[188,12839,12841,12844],{"className":12840},[243],[188,12842,12802],{"className":12843},[243,244],[188,12845,12847],{"className":12846},[545],[188,12848,12850,12870],{"className":12849},[549,966],[188,12851,12853,12867],{"className":12852},[553],[188,12854,12856],{"className":12855,"style":9618},[557],[188,12857,12858,12861],{"style":9621},[188,12859],{"className":12860,"style":566},[565],[188,12862,12864],{"className":12863},[570,571,572,573],[188,12865,4948],{"className":12866},[243,573],[188,12868,990],{"className":12869},[989],[188,12871,12873],{"className":12872},[553],[188,12874,12876],{"className":12875,"style":6706},[557],[188,12877],{},[188,12879,8137],{"className":12880},[8167],[188,12882],{"className":12883,"style":1003},[584],[188,12885,12887,12890],{"className":12886},[243],[188,12888,12802],{"className":12889},[243,244],[188,12891,12893],{"className":12892},[545],[188,12894,12896,12916],{"className":12895},[549,966],[188,12897,12899,12913],{"className":12898},[553],[188,12900,12902],{"className":12901,"style":9618},[557],[188,12903,12904,12907],{"style":9621},[188,12905],{"className":12906,"style":566},[565],[188,12908,12910],{"className":12909},[570,571,572,573],[188,12911,507],{"className":12912},[243,573],[188,12914,990],{"className":12915},[989],[188,12917,12919],{"className":12918},[553],[188,12920,12922],{"className":12921,"style":6706},[557],[188,12923],{},[188,12925,8137],{"className":12926},[8167],[188,12928],{"className":12929,"style":1003},[584],[188,12931,9574],{"className":12932},[9697],[188,12934],{"className":12935,"style":1003},[584],[188,12937,8137],{"className":12938},[8167],[188,12940],{"className":12941,"style":1003},[584],[188,12943,12945,12948],{"className":12944},[243],[188,12946,12802],{"className":12947},[243,244],[188,12949,12951],{"className":12950},[545],[188,12952,12954,12975],{"className":12953},[549,966],[188,12955,12957,12972],{"className":12956},[553],[188,12958,12961],{"className":12959,"style":12960},[557],"height:0.1514em;",[188,12962,12963,12966],{"style":9621},[188,12964],{"className":12965,"style":566},[565],[188,12967,12969],{"className":12968},[570,571,572,573],[188,12970,217],{"className":12971},[243,244,573],[188,12973,990],{"className":12974},[989],[188,12976,12978],{"className":12977},[553],[188,12979,12981],{"className":12980,"style":6706},[557],[188,12982],{},"，其中 ",[188,12985,12987,13005],{"className":12986},[191],[188,12988,12990],{"className":12989},[195],[197,12991,12992],{"xmlns":199},[201,12993,12994,13002],{},[204,12995,12996],{},[916,12997,12998,13000],{},[207,12999,12802],{},[207,13001,6651],{},[222,13003,13004],{"encoding":224},"A_i",[188,13006,13008],{"className":13007,"ariaHidden":230},[229],[188,13009,13011,13015],{"className":13010},[234],[188,13012],{"className":13013,"style":13014},[238],"height:0.8333em;vertical-align:-0.15em;",[188,13016,13018,13021],{"className":13017},[243],[188,13019,12802],{"className":13020},[243,244],[188,13022,13024],{"className":13023},[545],[188,13025,13027,13047],{"className":13026},[549,966],[188,13028,13030,13044],{"className":13029},[553],[188,13031,13033],{"className":13032,"style":6684},[557],[188,13034,13035,13038],{"style":9621},[188,13036],{"className":13037,"style":566},[565],[188,13039,13041],{"className":13040},[570,571,572,573],[188,13042,6651],{"className":13043},[243,244,573],[188,13045,990],{"className":13046},[989],[188,13048,13050],{"className":13049},[553],[188,13051,13053],{"className":13052,"style":6706},[557],[188,13054],{},[188,13056,13058,13082],{"className":13057},[191],[188,13059,13061],{"className":13060},[195],[197,13062,13063],{"xmlns":199},[201,13064,13065,13079],{},[204,13066,13067],{},[916,13068,13069,13071],{},[207,13070,12802],{},[204,13072,13073,13075,13077],{},[207,13074,6651],{},[211,13076,516],{},[505,13078,4948],{},[222,13080,13081],{"encoding":224},"A_{i+1}",[188,13083,13085],{"className":13084,"ariaHidden":230},[229],[188,13086,13088,13092],{"className":13087},[234],[188,13089],{"className":13090,"style":13091},[238],"height:0.8917em;vertical-align:-0.2083em;",[188,13093,13095,13098],{"className":13094},[243],[188,13096,12802],{"className":13097},[243,244],[188,13099,13101],{"className":13100},[545],[188,13102,13104,13133],{"className":13103},[549,966],[188,13105,13107,13130],{"className":13106},[553],[188,13108,13110],{"className":13109,"style":6684},[557],[188,13111,13112,13115],{"style":9621},[188,13113],{"className":13114,"style":566},[565],[188,13116,13118],{"className":13117},[570,571,572,573],[188,13119,13121,13124,13127],{"className":13120},[243,573],[188,13122,6651],{"className":13123},[243,244,573],[188,13125,516],{"className":13126},[589,573],[188,13128,4948],{"className":13129},[243,573],[188,13131,990],{"className":13132},[989],[188,13134,13136],{"className":13135},[553],[188,13137,13140],{"className":13138,"style":13139},[557],"height:0.2083em;",[188,13141],{}," 保证是可乘的。不同的计算次序需要的乘法次数不同。用动态规划算法求解最小乘法次数，动态转移方程如下：\n",[188,13144,13146,13328],{"className":13145},[191],[188,13147,13149],{"className":13148},[195],[197,13150,13151],{"xmlns":199},[201,13152,13153,13325],{},[204,13154,13155,13157,13159,13161,13163,13165,13167,13169,13171,13173],{},[207,13156,9361],{},[207,13158,27],{},[211,13160,9366],{"stretchy":213},[207,13162,6651],{},[211,13164,9371],{"stretchy":213},[211,13166,9366],{"stretchy":213},[207,13168,8087],{},[211,13170,9371],{"stretchy":213},[211,13172,2464],{},[204,13174,13175,13178],{},[211,13176,13177],{"fence":230},"{",[13179,13180,13184,13207],"mtable",{"rowspacing":13181,"columnalign":13182,"columnspacing":13183},"0.36em","left left","1em",[13185,13186,13187,13195],"mtr",{},[13188,13189,13190],"mtd",{},[13191,13192,13193],"mstyle",{"scriptlevel":8307,"displaystyle":213},[505,13194,8307],{},[13188,13196,13197],{},[13191,13198,13199],{"scriptlevel":8307,"displaystyle":213},[204,13200,13201,13203,13205],{},[207,13202,6651],{},[211,13204,2464],{},[207,13206,8087],{},[13185,13208,13209,13313],{},[13188,13210,13211],{},[13191,13212,13213],{"scriptlevel":8307,"displaystyle":213},[13191,13214,13215,13239,13241,13243,13245,13247,13249,13251,13253,13255,13257,13259,13261,13263,13265,13267,13269,13271,13273,13275,13277,13279,13281,13293,13296,13302,13304,13310],{"scriptlevel":8307,"displaystyle":230},[13216,13217,13218,13225],"munder",{},[204,13219,13220,13223],{},[207,13221,13222],{},"min",[211,13224,925],{},[204,13226,13227,13229,13232,13234,13237],{},[207,13228,6651],{},[211,13230,13231],{},"≤",[207,13233,4755],{},[211,13235,13236],{},"\u003C",[207,13238,8087],{},[211,13240,13177],{"stretchy":213},[207,13242,9361],{},[207,13244,27],{},[211,13246,9366],{"stretchy":213},[207,13248,6651],{},[211,13250,9371],{"stretchy":213},[211,13252,9366],{"stretchy":213},[207,13254,4755],{},[211,13256,9371],{"stretchy":213},[211,13258,516],{},[207,13260,9361],{},[207,13262,27],{},[211,13264,9366],{"stretchy":213},[207,13266,4755],{},[211,13268,516],{},[505,13270,4948],{},[211,13272,9371],{"stretchy":213},[211,13274,9366],{"stretchy":213},[207,13276,8087],{},[211,13278,9371],{"stretchy":213},[211,13280,516],{},[916,13282,13283,13285],{},[207,13284,27],{},[204,13286,13287,13289,13291],{},[207,13288,6651],{},[211,13290,4945],{},[505,13292,4948],{},[211,13294,13295],{},"⋅",[916,13297,13298,13300],{},[207,13299,27],{},[207,13301,4755],{},[211,13303,13295],{},[916,13305,13306,13308],{},[207,13307,27],{},[207,13309,8087],{},[211,13311,13312],{"stretchy":213},"}",[13188,13314,13315],{},[13191,13316,13317],{"scriptlevel":8307,"displaystyle":213},[204,13318,13319,13321,13323],{},[207,13320,6651],{},[211,13322,13236],{},[207,13324,8087],{},[222,13326,13327],{"encoding":224},"dp[i][j] = \\begin{cases} 0 & i=j \\\\ \\displaystyle\\min_{i \\le k \u003C j}\\{dp[i][k]+dp[k+1][j]+ p_{i-1} \\cdot p_{k} \\cdot p_{j}\\} & i\u003Cj \\end{cases}",[188,13329,13331,13370],{"className":13330,"ariaHidden":230},[229],[188,13332,13334,13337,13340,13343,13346,13349,13352,13355,13358,13361,13364,13367],{"className":13333},[234],[188,13335],{"className":13336,"style":239},[238],[188,13338,9361],{"className":13339},[243,244],[188,13341,27],{"className":13342},[243,244],[188,13344,9366],{"className":13345},[249],[188,13347,6651],{"className":13348},[243,244],[188,13350,9371],{"className":13351},[256],[188,13353,9366],{"className":13354},[249],[188,13356,8087],{"className":13357,"style":9476},[243,244],[188,13359,9371],{"className":13360},[256],[188,13362],{"className":13363,"style":2528},[584],[188,13365,2464],{"className":13366},[2532],[188,13368],{"className":13369,"style":2528},[584],[188,13371,13373,13377],{"className":13372},[234],[188,13374],{"className":13375,"style":13376},[238],"height:3.6em;vertical-align:-1.55em;",[188,13378,13380,13480,13909],{"className":13379},[9697],[188,13381,13383],{"className":13382},[249],[188,13384,13388],{"className":13385},[13386,13387],"delimsizing","mult",[188,13389,13391,13471],{"className":13390},[549,966],[188,13392,13394,13468],{"className":13393},[553],[188,13395,13398,13413,13432,13444,13456],{"className":13396,"style":13397},[557],"height:2.05em;",[188,13399,13401,13405],{"style":13400},"top:-2.5em;",[188,13402],{"className":13403,"style":13404},[565],"height:3.15em;",[188,13406,13410],{"className":13407},[13408,13409],"delimsizinginner","delim-size4",[188,13411,13412],{},"⎩",[188,13414,13416,13419],{"style":13415},"top:-2.492em;",[188,13417],{"className":13418,"style":13404},[565],[188,13420,13422],{"style":13421},"height:0.016em;width:0.8889em;",[7023,13423,13429],{"xmlns":7025,"width":13424,"height":13425,"style":13426,"viewBox":13427,"preserveAspectRatio":13428},"0.8889em","0.016em","width:0.8889em","0 0 888.89 16","xMinYMin",[7031,13430],{"d":13431},"M384 0 H504 V16 H384z M384 0 H504 V16 H384z",[188,13433,13435,13438],{"style":13434},"top:-3.15em;",[188,13436],{"className":13437,"style":13404},[565],[188,13439,13441],{"className":13440},[13408,13409],[188,13442,13443],{},"⎨",[188,13445,13447,13450],{"style":13446},"top:-4.292em;",[188,13448],{"className":13449,"style":13404},[565],[188,13451,13452],{"style":13421},[7023,13453,13454],{"xmlns":7025,"width":13424,"height":13425,"style":13426,"viewBox":13427,"preserveAspectRatio":13428},[7031,13455],{"d":13431},[188,13457,13459,13462],{"style":13458},"top:-4.3em;",[188,13460],{"className":13461,"style":13404},[565],[188,13463,13465],{"className":13464},[13408,13409],[188,13466,13467],{},"⎧",[188,13469,990],{"className":13470},[989],[188,13472,13474],{"className":13473},[553],[188,13475,13478],{"className":13476,"style":13477},[557],"height:1.55em;",[188,13479],{},[188,13481,13483],{"className":13482},[243],[188,13484,13486,13835,13840],{"className":13485},[13179],[188,13487,13490],{"className":13488},[13489],"col-align-l",[188,13491,13493,13826],{"className":13492},[549,966],[188,13494,13496,13823],{"className":13495},[553],[188,13497,13500,13513],{"className":13498,"style":13499},[557],"height:1.9181em;",[188,13501,13503,13507],{"style":13502},"top:-3.9181em;",[188,13504],{"className":13505,"style":13506},[565],"height:3.008em;",[188,13508,13510],{"className":13509},[243],[188,13511,8307],{"className":13512},[243],[188,13514,13516,13519],{"style":13515},"top:-2.4781em;",[188,13517],{"className":13518,"style":13506},[565],[188,13520,13522,13585,13588,13591,13594,13597,13600,13603,13606,13609,13612,13615,13618,13621,13624,13627,13630,13633,13636,13639,13642,13645,13648,13651,13654,13657,13660,13663,13666,13715,13718,13721,13724,13768,13771,13774,13777,13820],{"className":13521},[243],[188,13523,13526],{"className":13524},[951,13525],"op-limits",[188,13527,13529,13576],{"className":13528},[549,966],[188,13530,13532,13573],{"className":13531},[553],[188,13533,13536,13563],{"className":13534,"style":13535},[557],"height:0.6679em;",[188,13537,13539,13542],{"style":13538},"top:-2.3479em;margin-left:0em;",[188,13540],{"className":13541,"style":7003},[565],[188,13543,13545],{"className":13544},[570,571,572,573],[188,13546,13548,13551,13554,13557,13560],{"className":13547},[243,573],[188,13549,6651],{"className":13550},[243,244,573],[188,13552,13231],{"className":13553},[2532,573],[188,13555,4755],{"className":13556,"style":4807},[243,244,573],[188,13558,13236],{"className":13559},[2532,573],[188,13561,8087],{"className":13562,"style":9476},[243,244,573],[188,13564,13565,13568],{"style":6999},[188,13566],{"className":13567,"style":7003},[565],[188,13569,13570],{},[188,13571,13222],{"className":13572},[951],[188,13574,990],{"className":13575},[989],[188,13577,13579],{"className":13578},[553],[188,13580,13583],{"className":13581,"style":13582},[557],"height:0.8882em;",[188,13584],{},[188,13586,13177],{"className":13587},[249],[188,13589,9361],{"className":13590},[243,244],[188,13592,27],{"className":13593},[243,244],[188,13595,9366],{"className":13596},[249],[188,13598,6651],{"className":13599},[243,244],[188,13601,9371],{"className":13602},[256],[188,13604,9366],{"className":13605},[249],[188,13607,4755],{"className":13608,"style":4807},[243,244],[188,13610,9371],{"className":13611},[256],[188,13613],{"className":13614,"style":585},[584],[188,13616,516],{"className":13617},[589],[188,13619],{"className":13620,"style":585},[584],[188,13622,9361],{"className":13623},[243,244],[188,13625,27],{"className":13626},[243,244],[188,13628,9366],{"className":13629},[249],[188,13631,4755],{"className":13632,"style":4807},[243,244],[188,13634],{"className":13635,"style":585},[584],[188,13637,516],{"className":13638},[589],[188,13640],{"className":13641,"style":585},[584],[188,13643,4948],{"className":13644},[243],[188,13646,9371],{"className":13647},[256],[188,13649,9366],{"className":13650},[249],[188,13652,8087],{"className":13653,"style":9476},[243,244],[188,13655,9371],{"className":13656},[256],[188,13658],{"className":13659,"style":585},[584],[188,13661,516],{"className":13662},[589],[188,13664],{"className":13665,"style":585},[584],[188,13667,13669,13672],{"className":13668},[243],[188,13670,27],{"className":13671},[243,244],[188,13673,13675],{"className":13674},[545],[188,13676,13678,13707],{"className":13677},[549,966],[188,13679,13681,13704],{"className":13680},[553],[188,13682,13684],{"className":13683,"style":6684},[557],[188,13685,13686,13689],{"style":9621},[188,13687],{"className":13688,"style":566},[565],[188,13690,13692],{"className":13691},[570,571,572,573],[188,13693,13695,13698,13701],{"className":13694},[243,573],[188,13696,6651],{"className":13697},[243,244,573],[188,13699,4945],{"className":13700},[589,573],[188,13702,4948],{"className":13703},[243,573],[188,13705,990],{"className":13706},[989],[188,13708,13710],{"className":13709},[553],[188,13711,13713],{"className":13712,"style":13139},[557],[188,13714],{},[188,13716],{"className":13717,"styl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",[188,13918,13920,14019],{"className":13919},[191],[188,13921,13923],{"className":13922},[195],[197,13924,13925],{"xmlns":199},[201,13926,13927,14016],{},[204,13928,13929,13935,13937,13940,13942,13948,13950,13953,13955,13961,13963,13965,13967,13973,13975,13978,13980,13986,13988,13990,13992,13998,14000,14003,14005,14012,14014],{},[916,13930,13931,13933],{},[207,13932,27],{},[505,13934,8307],{},[211,13936,2464],{},[505,13938,13939],{},"5",[211,13941,8137],{"separator":230},[916,13943,13944,13946],{},[207,13945,27],{},[505,13947,4948],{},[211,13949,2464],{},[505,13951,13952],{},"10",[211,13954,8137],{"separator":230},[916,13956,13957,13959],{},[207,13958,27],{},[505,13960,507],{},[211,13962,2464],{},[505,13964,934],{},[211,13966,8137],{"separator":230},[916,13968,13969,13971],{},[207,13970,27],{},[505,13972,934],{},[211,13974,2464],{},[505,13976,13977],{},"12",[211,13979,8137],{"separator":230},[916,13981,13982,13984],{},[207,13983,27],{},[505,13985,4869],{},[211,13987,2464],{},[505,13989,13939],{},[211,13991,8137],{"separator":230},[916,13993,13994,13996],{},[207,13995,27],{},[505,13997,13939],{},[211,13999,2464],{},[505,14001,14002],{},"50",[211,14004,8137],{"separator":230},[916,14006,14007,14009],{},[207,14008,27],{},[505,14010,14011],{},"6",[211,14013,2464],{},[505,14015,14011],{},[222,14017,14018],{"encoding":224},"p_0=5, p_1=10, p_2=3, p_3=12, p_4=5, p_5=50, p_6=6",[188,14020,14022,14078,14142,14206,14270,14334,14398,14462],{"className":14021,"ariaHidden":230},[229],[188,14023,14025,14029,14069,14072,14075],{"className":14024},[234],[188,14026],{"className":14027,"style":14028},[238],"height:0.625em;vertical-align:-0.1944em;",[188,14030,14032,14035],{"className":14031},[243],[188,14033,27],{"className":14034},[243,244],[188,14036,14038],{"className":14037},[545],[188,14039,14041,14061],{"className":14040},[549,966],[188,14042,14044,14058],{"className":14043},[553],[188,14045,14047],{"className":14046,"style":9618},[557],[188,14048,14049,14052],{"style":9621},[188,14050],{"className":14051,"style":566},[565],[188,14053,14055],{"className":14054},[570,571,572,573],[188,14056,8307],{"className":14057},[243,573],[188,14059,990],{"className":14060},[989],[188,14062,14064],{"className":14063},[553],[188,14065,14067],{"className":14066,"style":6706},[557],[188,14068],{},[188,14070],{"className":14071,"style":2528},[584],[188,14073,2464],{"className":14074},[2532],[188,14076],{"className":14077,"style":2528},[584],[188,14079,14081,14084,14087,14090,14093,14133,14136,14139],{"className":14080},[234],[188,14082],{"className":14083,"style":8346},[238],[188,14085,13939],{"className":14086},[243],[188,14088,8137],{"className":14089},[8167],[188,14091],{"className":14092,"style":1003},[584],[188,14094,14096,14099],{"className":14095},[243],[188,14097,27],{"className":14098},[243,244],[188,14100,14102],{"className":14101},[545],[188,14103,14105,14125],{"className":14104},[549,966],[188,14106,14108,14122],{"className":14107},[553],[188,14109,14111],{"className":14110,"style":9618},[557],[188,14112,14113,14116],{"style":9621},[188,14114],{"className":14115,"style":566},[565],[188,14117,14119],{"className":14118},[570,571,572,573],[188,14120,4948],{"className":14121},[243,573],[188,14123,990],{"className":14124},[989],[188,14126,14128],{"className":14127},[553],[188,14129,14131],{"className":14130,"style":6706},[557],[188,14132],{},[188,14134],{"className":14135,"style":2528},[584],[188,14137,2464],{"className":14138},[2532],[188,14140],{"className":14141,"style":2528},[584],[188,14143,14145,14148,14151,14154,14157,14197,14200,14203],{"className":14144},[234],[188,14146],{"className":14147,"style":8346},[238],[188,14149,13952],{"className":14150},[243],[188,14152,8137],{"className":14153},[8167],[188,14155],{"className":14156,"style":1003},[584],[188,14158,14160,14163],{"className":14159},[243],[188,14161,27],{"className":14162},[243,244],[188,14164,14166],{"className":14165},[545],[188,14167,14169,14189],{"className":14168},[549,966],[188,14170,14172,14186],{"className":14171},[553],[188,14173,14175],{"className":14174,"style":9618},[557],[188,14176,14177,14180],{"style":9621},[188,14178],{"className":14179,"style":566},[565],[188,14181,14183],{"className":14182},[570,571,572,573],[188,14184,507],{"className":14185},[243,573],[188,14187,990],{"className":14188},[989],[188,14190,14192],{"className":14191},[553],[188,14193,14195],{"className":14194,"style":6706},[557],[188,14196],{},[188,14198],{"className":14199,"style":2528},[584],[188,14201,2464],{"className":14202},[2532],[188,14204],{"className":14205,"style":2528},[584],[188,14207,14209,14212,14215,14218,14221,14261,14264,14267],{"className":14208},[234],[188,14210],{"className":14211,"style":8346},[238],[188,14213,934],{"className":14214},[243],[188,14216,8137],{"className":14217},[8167],[188,14219],{"className":14220,"style":1003},[584],[188,14222,14224,14227],{"className":14223},[243],[188,14225,27],{"className":14226},[243,244],[188,14228,14230],{"className":14229},[545],[188,14231,14233,14253],{"className":14232},[549,966],[188,14234,14236,14250],{"className":14235},[553],[188,14237,14239],{"className":14238,"style":9618},[557],[188,14240,14241,14244],{"style":9621},[188,14242],{"className":14243,"style":566},[565],[188,14245,14247],{"className":14246},[570,571,572,573],[188,14248,934],{"className":14249},[243,573],[188,14251,990],{"className":14252},[989],[188,14254,14256],{"className":14255},[553],[188,14257,14259],{"className":14258,"style":6706},[557],[188,14260],{},[188,14262],{"className":14263,"style":2528},[584],[188,14265,2464],{"className":14266},[2532],[188,14268],{"className":14269,"style":2528},[584],[188,14271,14273,14276,14279,14282,14285,14325,14328,14331],{"className":14272},[234],[188,14274],{"className":14275,"style":8346},[238],[188,14277,13977],{"className":14278},[243],[188,14280,8137],{"className":14281},[8167],[188,14283],{"className":14284,"style":1003},[584],[188,14286,14288,14291],{"className":14287},[243],[188,14289,27],{"className":14290},[243,244],[188,14292,14294],{"className":14293},[545],[188,14295,14297,14317],{"className":14296},[549,966],[188,14298,14300,14314],{"className":14299},[553],[188,14301,14303],{"className":14302,"style":9618},[557],[188,14304,14305,14308],{"style":9621},[188,14306],{"className":14307,"style":566},[565],[188,14309,14311],{"className":14310},[570,571,572,573],[188,14312,4869],{"className":14313},[243,573],[188,14315,990],{"className":14316},[989],[188,14318,14320],{"className":14319},[553],[188,14321,14323],{"className":14322,"style":6706},[557],[188,14324],{},[188,14326],{"className":14327,"style":2528},[584],[188,14329,2464],{"className":14330},[2532],[188,14332],{"className":14333,"style":2528},[584],[188,14335,14337,14340,14343,14346,14349,14389,14392,14395],{"className":14336},[234],[188,14338],{"className":14339,"style":8346},[238],[188,14341,13939],{"className":14342},[243],[188,14344,8137],{"className":14345},[8167],[188,14347],{"className":14348,"style":1003},[584],[188,14350,14352,14355],{"className":14351},[243],[188,14353,27],{"className":14354},[243,244],[188,14356,14358],{"className":14357},[545],[188,14359,14361,14381],{"className":14360},[549,966],[188,14362,14364,14378],{"className":14363},[553],[188,14365,14367],{"className":14366,"style":9618},[557],[188,14368,14369,14372],{"style":9621},[188,14370],{"className":14371,"style":566},[565],[188,14373,14375],{"className":14374},[570,571,572,573],[188,14376,13939],{"className":14377},[243,573],[188,14379,990],{"className":14380},[989],[188,14382,14384],{"className":14383},[553],[188,14385,14387],{"className":14386,"style":6706},[557],[188,14388],{},[188,14390],{"className":14391,"style":2528},[584],[188,14393,2464],{"className":14394},[2532],[188,14396],{"className":14397,"style":2528},[584],[188,14399,14401,14404,14407,14410,14413,14453,14456,14459],{"className":14400},[234],[188,14402],{"className":14403,"style":8346},[238],[188,14405,14002],{"className":14406},[243],[188,14408,8137],{"className":14409},[8167],[188,14411],{"className":14412,"style":1003},[584],[188,14414,14416,14419],{"className":14415},[243],[188,14417,27],{"className":14418},[243,244],[188,14420,14422],{"className":14421},[545],[188,14423,14425,14445],{"className":14424},[549,966],[188,14426,14428,14442],{"className":14427},[553],[188,14429,14431],{"className":14430,"style":9618},[557],[188,14432,14433,14436],{"style":9621},[188,14434],{"className":14435,"style":566},[565],[188,14437,14439],{"className":14438},[570,571,572,573],[188,14440,14011],{"className":14441},[243,573],[188,14443,990],{"className":14444},[989],[188,14446,14448],{"className":14447},[553],[188,14449,14451],{"className":14450,"style":6706},[557],[188,14452],{},[188,14454],{"className":14455,"style":2528},[584],[188,14457,2464],{"className":14458},[2532],[188,14460],{"className":14461,"style":2528},[584],[188,14463,14465,14468],{"className":14464},[234],[188,14466],{"className":14467,"style":3213},[238],[188,14469,14011],{"className":14470},[243],[41,14472,14473,14541],{},[44,14474,14475,14476,14510,14511,14540],{},"给出动态规划数组 ",[188,14477,14479,14495],{"className":14478},[191],[188,14480,14482],{"className":14481},[195],[197,14483,14484],{"xmlns":199},[201,14485,14486,14492],{},[204,14487,14488,14490],{},[207,14489,9361],{},[207,14491,27],{},[222,14493,14494],{"encoding":224},"dp",[188,14496,14498],{"className":14497,"ariaHidden":230},[229],[188,14499,14501,14504,14507],{"className":14500},[234],[188,14502],{"className":14503,"style":10322},[238],[188,14505,9361],{"className":14506},[243,244],[188,14508,27],{"className":14509},[243,244]," 及矩阵连乘的断点数组 ",[188,14512,14514,14528],{"className":14513},[191],[188,14515,14517],{"className":14516},[195],[197,14518,14519],{"xmlns":199},[201,14520,14521,14526],{},[204,14522,14523],{},[207,14524,14525],{},"s",[222,14527,14525],{"encoding":224},[188,14529,14531],{"className":14530,"ariaHidden":230},[229],[188,14532,14534,14537],{"className":14533},[234],[188,14535],{"className":14536,"style":351},[238],[188,14538,14525],{"className":14539},[243,244],"。（8分）",[44,14542,14543],{},"写出最优的矩阵乘法运算顺序。（2分）",[22,14545,32],{"id":14546},"答案与深度解析-20",[27,14548,14549,14550,14601,14602,14741,14742,14811,14812,85],{},"这道题是动态规划中经典的“矩阵连乘问题”，计算量大，我们需要严谨地列表步步为营。",[188,14551,14553,14571],{"className":14552},[191],[188,14554,14556],{"className":14555},[195],[197,14557,14558],{"xmlns":199},[201,14559,14560,14568],{},[204,14561,14562,14564,14566],{},[207,14563,217],{},[211,14565,2464],{},[505,14567,14011],{},[222,14569,14570],{"encoding":224},"n=6",[188,14572,14574,14592],{"className":14573,"ariaHidden":230},[229],[188,14575,14577,14580,14583,14586,14589],{"className":14576},[234],[188,14578],{"className":14579,"style":351},[238],[188,14581,217],{"className":14582},[243,244],[188,14584],{"className":14585,"style":2528},[584],[188,14587,2464],{"className":14588},[2532],[188,14590],{"className":14591,"style":2528},[584],[188,14593,14595,14598],{"className":14594},[234],[188,14596],{"className":14597,"style":3213},[238],[188,14599,14011],{"className":14600},[243],"，即 6 个矩阵连乘。维度向量 ",[188,14603,14605,14651],{"className":14604},[191],[188,14606,14608],{"className":14607},[195],[197,14609,14610],{"xmlns":199},[201,14611,14612,14648],{},[204,14613,14614,14616,14618,14620,14622,14624,14626,14628,14630,14632,14634,14636,14638,14640,14642,14644,14646],{},[207,14615,27],{},[211,14617,2464],{},[211,14619,9366],{"stretchy":213},[505,14621,13939],{},[211,14623,8137],{"separator":230},[505,14625,13952],{},[211,14627,8137],{"separator":230},[505,14629,934],{},[211,14631,8137],{"separator":230},[505,14633,13977],{},[211,14635,8137],{"separator":230},[505,14637,13939],{},[211,14639,8137],{"separator":230},[505,14641,14002],{},[211,14643,8137],{"separator":230},[505,14645,14011],{},[211,14647,9371],{"stretchy":213},[222,14649,14650],{"encoding":224},"p = [5, 10, 3, 12, 5, 50, 6]",[188,14652,14654,14672],{"className":14653,"ariaHidden":230},[229],[188,14655,14657,14660,14663,14666,14669],{"className":14656},[234],[188,14658],{"className":14659,"style":14028},[238],[188,14661,27],{"className":14662},[243,244],[188,14664],{"className":14665,"style":2528},[584],[188,14667,2464],{"className":14668},[2532],[188,14670],{"className":14671,"style":2528},[584],[188,14673,14675,14678,14681,14684,14687,14690,14693,14696,14699,14702,14705,14708,14711,14714,14717,14720,14723,14726,14729,14732,14735,14738],{"className":14674},[234],[188,14676],{"className":14677,"style":239},[238],[188,14679,9366],{"className":14680},[249],[188,14682,13939],{"className":14683},[243],[188,14685,8137],{"className":14686},[8167],[188,14688],{"className":14689,"style":1003},[584],[188,14691,13952],{"className":14692},[243],[188,14694,8137],{"className":14695},[8167],[188,14697],{"className":14698,"style":1003},[584],[188,14700,934],{"className":14701},[243],[188,14703,8137],{"className":14704},[8167],[188,14706],{"className":14707,"style":1003},[584],[188,14709,13977],{"className":14710},[243],[188,14712,8137],{"className":14713},[8167],[188,14715],{"className":14716,"style":1003},[584],[188,14718,13939],{"className":14719},[243],[188,14721,8137],{"className":14722},[8167],[188,14724],{"className":14725,"style":1003},[584],[188,14727,14002],{"className":14728},[243],[188,14730,8137],{"className":14731},[8167],[188,14733],{"className":14734,"style":1003},[584],[188,14736,14011],{"className":14737},[243],[188,14739,9371],{"className":14740},[256],"。矩阵 ",[188,14743,14745,14762],{"className":14744},[191],[188,14746,14748],{"className":14747},[195],[197,14749,14750],{"xmlns":199},[201,14751,14752,14760],{},[204,14753,14754],{},[916,14755,14756,14758],{},[207,14757,12802],{},[207,14759,6651],{},[222,14761,13004],{"encoding":224},[188,14763,14765],{"className":14764,"ariaHidden":230},[229],[188,14766,14768,14771],{"className":14767},[234],[188,14769],{"className":14770,"style":13014},[238],[188,14772,14774,14777],{"className":14773},[243],[188,14775,12802],{"className":14776},[243,244],[188,14778,14780],{"className":14779},[545],[188,14781,14783,14803],{"className":14782},[549,966],[188,14784,14786,14800],{"className":14785},[553],[188,14787,14789],{"className":14788,"style":6684},[557],[188,14790,14791,14794],{"style":9621},[188,14792],{"className":14793,"style":566},[565],[188,14795,14797],{"className":14796},[570,571,572,573],[188,14798,6651],{"className":14799},[243,244,573],[188,14801,990],{"className":14802},[989],[188,14804,14806],{"className":14805},[553],[188,14807,14809],{"className":14808,"style":6706},[557],[188,14810],{}," 的维度是 ",[188,14813,14815,14847],{"className":14814},[191],[188,14816,14818],{"className":14817},[195],[197,14819,14820],{"xmlns":199},[201,14821,14822,14844],{},[204,14823,14824,14836,14838],{},[916,14825,14826,14828],{},[207,14827,27],{},[204,14829,14830,14832,14834],{},[207,14831,6651],{},[211,14833,4945],{},[505,14835,4948],{},[211,14837,4758],{},[916,14839,14840,14842],{},[207,14841,27],{},[207,14843,6651],{},[222,14845,14846],{"encoding":224},"p_{i-1} \\times p_i",[188,14848,14850,14915],{"className":14849,"ariaHidden":230},[229],[188,14851,14853,14857,14906,14909,14912],{"className":14852},[234],[188,14854],{"className":14855,"style":14856},[238],"height:0.7917em;vertical-align:-0.2083em;",[188,14858,14860,14863],{"className":14859},[243],[188,14861,27],{"className":14862},[243,244],[188,14864,14866],{"className":14865},[545],[188,14867,14869,14898],{"className":14868},[549,966],[188,14870,14872,14895],{"className":14871},[553],[188,14873,14875],{"className":14874,"style":6684},[557],[188,14876,14877,14880],{"style":9621},[188,14878],{"className":14879,"style":566},[565],[188,14881,14883],{"className":14882},[570,571,572,573],[188,14884,14886,14889,14892],{"className":14885},[243,573],[188,14887,6651],{"className":14888},[243,244,573],[188,14890,4945],{"className":14891},[589,573],[188,14893,4948],{"className":14894},[243,573],[188,14896,990],{"className":14897},[989],[188,14899,14901],{"className":14900},[553],[188,14902,14904],{"className":14903,"style":13139},[557],[188,14905],{},[188,14907],{"className":14908,"style":585},[584],[188,14910,4758],{"className":14911},[589],[188,14913],{"className":14914,"style":585},[584],[188,14916,14918,14921],{"className":14917},[234],[188,14919],{"className":14920,"style":14028},[238],[188,14922,14924,14927],{"className":14923},[243],[188,14925,27],{"className":14926},[243,244],[188,14928,14930],{"className":14929},[545],[188,14931,14933,14953],{"className":14932},[549,966],[188,14934,14936,14950],{"className":14935},[553],[188,14937,14939],{"className":14938,"style":6684},[557],[188,14940,14941,14944],{"style":9621},[188,14942],{"className":14943,"style":566},[565],[188,14945,14947],{"className":14946},[570,571,572,573],[188,14948,6651],{"className":14949},[243,244,573],[188,14951,990],{"className":14952},[989],[188,14954,14956],{"className":14955},[553],[188,14957,14959],{"className":14958,"style":6706},[557],[188,14960],{},[27,14962,14963,15028,15029,15032],{},[36,14964,14965,14966,14999,15000,11006],{},"1) 计算动态规划数组 ",[188,14967,14969,14984],{"className":14968},[191],[188,14970,14972],{"className":14971},[195],[197,14973,14974],{"xmlns":199},[201,14975,14976,14982],{},[204,14977,14978,14980],{},[207,14979,9361],{},[207,14981,27],{},[222,14983,14494],{"encoding":224},[188,14985,14987],{"className":14986,"ariaHidden":230},[229],[188,14988,14990,14993,14996],{"className":14989},[234],[188,14991],{"className":14992,"style":10322},[238],[188,14994,9361],{"className":14995},[243,244],[188,14997,27],{"className":14998},[243,244]," 和断点数组 ",[188,15001,15003,15016],{"className":15002},[191],[188,15004,15006],{"className":15005},[195],[197,15007,15008],{"xmlns":199},[201,15009,15010,15014],{},[204,15011,15012],{},[207,15013,14525],{},[222,15015,14525],{"encoding":224},[188,15017,15019],{"className":15018,"ariaHidden":230},[229],[188,15020,15022,15025],{"className":15021},[234],[188,15023],{"className":15024,"style":351},[238],[188,15026,14525],{"className":15027},[243,244],"\n填表的顺序是",[36,15030,15031],{},"按照链长（长度为 L）从小到大","进行填写，这样我们在计算较长的链时，它所依赖的短链数据已经算好了。",[68,15034,15035,15264,17623,19869,21982,23413],{},[44,15036,15037,15040,15041],{},[36,15038,15039],{},"长度 L = 1："," 即单一矩阵，不需要乘法。对角线全部为 0。\n",[188,15042,15044,15116],{"className":15043},[191],[188,15045,15047],{"className":15046},[195],[197,15048,15049],{"xmlns":199},[201,15050,15051,15113],{},[204,15052,15053,15055,15057,15059,15061,15063,15065,15067,15069,15071,15073,15075,15077,15079,15081,15083,15085,15087,15089,15091,15093,15095,15097,15099,15101,15103,15105,15107,15109,15111],{},[207,15054,9361],{},[207,15056,27],{},[211,15058,9366],{"stretchy":213},[505,15060,4948],{},[211,15062,9371],{"stretchy":213},[211,15064,9366],{"stretchy":213},[505,15066,4948],{},[211,15068,9371],{"stretchy":213},[211,15070,2464],{},[207,15072,9361],{},[207,15074,27],{},[211,15076,9366],{"stretchy":213},[505,15078,507],{},[211,15080,9371],{"stretchy":213},[211,15082,9366],{"stretchy":213},[505,15084,507],{},[211,15086,9371],{"stretchy":213},[211,15088,2464],{},[211,15090,12318],{},[211,15092,2464],{},[207,15094,9361],{},[207,15096,27],{},[211,15098,9366],{"stretchy":213},[505,15100,14011],{},[211,15102,9371],{"stretchy":213},[211,15104,9366],{"stretchy":213},[505,15106,14011],{},[211,15108,9371],{"stretchy":213},[211,15110,2464],{},[505,15112,8307],{},[222,15114,15115],{"encoding":224},"dp[1][1] = dp[2][2] = \\dots = dp[6][6] = 0",[188,15117,15119,15158,15197,15216,15255],{"className":15118,"ariaHidden":230},[229],[188,15120,15122,15125,15128,15131,15134,15137,15140,15143,15146,15149,15152,15155],{"className":15121},[234],[188,15123],{"className":15124,"style":239},[238],[188,15126,9361],{"className":15127},[243,244],[188,15129,27],{"className":15130},[243,244],[188,15132,9366],{"className":15133},[249],[188,15135,4948],{"className":15136},[243],[188,15138,9371],{"className":15139},[256],[188,15141,9366],{"className":15142},[249],[188,15144,4948],{"className":15145},[243],[188,15147,9371],{"className":15148},[256],[188,15150],{"className":15151,"style":2528},[584],[188,15153,2464],{"className":15154},[2532],[188,15156],{"className":15157,"style":2528},[584],[188,15159,15161,15164,15167,15170,15173,15176,15179,15182,15185,15188,15191,15194],{"className":15160},[234],[188,15162],{"className":15163,"style":239},[238],[188,15165,9361],{"className":15166},[243,244],[188,15168,27],{"className":15169},[243,244],[188,15171,9366],{"className":15172},[249],[188,15174,507],{"className":15175},[243],[188,15177,9371],{"className":15178},[256],[188,15180,9366],{"className":15181},[249],[188,15183,507],{"className":15184},[243],[188,15186,9371],{"className":15187},[256],[188,15189],{"className":15190,"style":2528},[584],[188,15192,2464],{"className":15193},[2532],[188,15195],{"className":15196,"style":2528},[584],[188,15198,15200,15204,15207,15210,15213],{"className":15199},[234],[188,15201],{"className":15202,"style":15203},[238],"height:0.3669em;",[188,15205,12318],{"className":15206},[9697],[188,15208],{"className":15209,"style":2528},[584],[188,15211,2464],{"className":15212},[2532],[188,15214],{"className":15215,"style":2528},[584],[188,15217,15219,15222,15225,15228,15231,15234,15237,15240,15243,15246,15249,15252],{"className":15218},[234],[188,15220],{"className":15221,"style":239},[238],[188,15223,9361],{"className":15224},[243,244],[188,15226,27],{"className":15227},[243,244],[188,15229,9366],{"className":15230},[249],[188,15232,14011],{"className":15233},[243],[188,15235,9371],{"className":15236},[256],[188,15238,9366],{"className":15239},[249],[188,15241,14011],{"className":15242},[243],[188,15244,9371],{"className":15245},[256],[188,15247],{"className":15248,"style":2528},[584],[188,15250,2464],{"className":15251},[2532],[188,15253],{"className":15254,"style":2528},[584],[188,15256,15258,15261],{"className":15257},[234],[188,15259],{"className":15260,"style":3213},[238],[188,15262,8307],{"className":15263},[243],[44,15265,15266,15269,15270,15463,15464,15492,15493],{},[36,15267,15268],{},"长度 L = 2："," 两个相邻矩阵相乘，公式为 ",[188,15271,15273,15315],{"className":15272},[191],[188,15274,15276],{"className":15275},[195],[197,15277,15278],{"xmlns":199},[201,15279,15280,15312],{},[204,15281,15282,15294,15300],{},[916,15283,15284,15286],{},[207,15285,27],{},[204,15287,15288,15290,15292],{},[207,15289,6651],{},[211,15291,4945],{},[505,15293,4948],{},[916,15295,15296,15298],{},[207,15297,27],{},[207,15299,6651],{},[916,15301,15302,15304],{},[207,15303,27],{},[204,15305,15306,15308,15310],{},[207,15307,6651],{},[211,15309,516],{},[505,15311,4948],{},[222,15313,15314],{"encoding":224},"p_{i-1} p_i p_{i+1}",[188,15316,15318],{"className":15317,"ariaHidden":230},[229],[188,15319,15321,15325,15374,15414],{"className":15320},[234],[188,15322],{"className":15323,"style":15324},[238],"height:0.6389em;vertical-align:-0.2083em;",[188,15326,15328,15331],{"className":15327},[243],[188,15329,27],{"className":15330},[243,244],[188,15332,15334],{"className":15333},[545],[188,15335,15337,15366],{"className":15336},[549,966],[188,15338,15340,15363],{"className":15339},[553],[188,15341,15343],{"className":15342,"style":6684},[557],[188,15344,15345,15348],{"style":9621},[188,15346],{"className":15347,"style":566},[565],[188,15349,15351],{"className":15350},[570,571,572,573],[188,15352,15354,15357,15360],{"className":15353},[243,573],[188,15355,6651],{"className":15356},[243,244,573],[188,15358,4945],{"className":15359},[589,573],[188,15361,4948],{"className":15362},[243,573],[188,15364,990],{"className":15365},[989],[188,15367,15369],{"className":15368},[553],[188,15370,15372],{"className":15371,"style":13139},[557],[188,15373],{},[188,15375,15377,15380],{"className":15376},[243],[188,15378,27],{"className":15379},[243,244],[188,15381,15383],{"className":15382},[545],[188,15384,15386,15406],{"className":15385},[549,966],[188,15387,15389,15403],{"className":15388},[553],[188,15390,15392],{"className":15391,"style":6684},[557],[188,15393,15394,15397],{"style":9621},[188,15395],{"className":15396,"style":566},[565],[188,15398,15400],{"className":15399},[570,571,572,573],[188,15401,6651],{"className":15402},[243,244,573],[188,15404,990],{"className":15405},[989],[188,15407,15409],{"className":15408},[553],[188,15410,15412],{"className":15411,"style":6706},[557],[188,15413],{},[188,15415,15417,15420],{"className":15416},[243],[188,15418,27],{"className":15419},[243,244],[188,15421,15423],{"className":15422},[545],[188,15424,15426,15455],{"className":15425},[549,966],[188,15427,15429,15452],{"className":15428},[553],[188,15430,15432],{"className":15431,"style":6684},[557],[188,15433,15434,15437],{"style":9621},[188,15435],{"className":15436,"style":566},[565],[188,15438,15440],{"className":15439},[570,571,572,573],[188,15441,15443,15446,15449],{"className":15442},[243,573],[188,15444,6651],{"className":15445},[243,244,573],[188,15447,516],{"className":15448},[589,573],[188,15450,4948],{"className":15451},[243,573],[188,15453,990],{"className":15454},[989],[188,15456,15458],{"className":15457},[553],[188,15459,15461],{"className":15460,"style":13139},[557],[188,15462],{},"，没有别的断点选择，断点 ",[188,15465,15467,15480],{"className":15466},[191],[188,15468,15470],{"className":15469},[195],[197,15471,15472],{"xmlns":199},[201,15473,15474,15478],{},[204,15475,15476],{},[207,15477,14525],{},[222,15479,14525],{"encoding":224},[188,15481,15483],{"className":15482,"ariaHidden":230},[229],[188,15484,15486,15489],{"className":15485},[234],[188,15487],{"className":15488,"style":351},[238],[188,15490,14525],{"className":15491},[243,244]," 即为左矩阵下标。",[68,15494,15495,15922,16348,16773,17198],{},[44,15496,15497,15840,15841],{},[188,15498,15500,15569],{"className":15499},[191],[188,15501,15503],{"className":15502},[195],[197,15504,15505],{"xmlns":199},[201,15506,15507,15566],{},[204,15508,15509,15511,15513,15515,15517,15519,15521,15523,15525,15527,15533,15535,15541,15543,15549,15551,15553,15555,15557,15559,15561,15563],{},[207,15510,9361],{},[207,15512,27],{},[211,15514,9366],{"stretchy":213},[505,15516,4948],{},[211,15518,9371],{"stretchy":213},[211,15520,9366],{"stretchy":213},[505,15522,507],{},[211,15524,9371],{"stretchy":213},[211,15526,2464],{},[916,15528,15529,15531],{},[207,15530,27],{},[505,15532,8307],{},[211,15534,13295],{},[916,15536,15537,15539],{},[207,15538,27],{},[505,15540,4948],{},[211,15542,13295],{},[916,15544,15545,15547],{},[207,15546,27],{},[505,15548,507],{},[211,15550,2464],{},[505,15552,13939],{},[211,15554,4758],{},[505,15556,13952],{},[211,15558,4758],{},[505,15560,934],{},[211,15562,2464],{},[505,15564,15565],{},"150",[222,15567,15568],{"encoding":224},"dp[1][2] = p_0 \\cdot p_1 \\cdot p_2 = 5 \\times 10 \\times 3 = 150",[188,15570,15572,15611,15667,15722,15777,15795,15813,15831],{"className":15571,"ariaHidden":230},[229],[188,15573,15575,15578,15581,15584,15587,15590,15593,15596,15599,15602,15605,15608],{"className":15574},[234],[188,15576],{"className":15577,"style":239},[238],[188,15579,9361],{"className":15580},[243,244],[188,15582,27],{"className":15583},[243,244],[188,15585,9366],{"className":15586},[249],[188,15588,4948],{"className":15589},[243],[188,15591,9371],{"className":15592},[256],[188,15594,9366],{"className":15595},[249],[188,15597,507],{"className":15598},[243],[188,15600,9371],{"className":15601},[256],[188,15603],{"className":15604,"style":2528},[584],[188,15606,2464],{"className":15607},[2532],[188,15609],{"className":15610,"style":2528},[584],[188,15612,15614,15618,15658,15661,15664],{"className":15613},[234],[188,15615],{"className":15616,"style":15617},[238],"height:0.6389em;vertical-align:-0.1944em;",[188,15619,15621,15624],{"className":15620},[243],[188,15622,27],{"className":15623},[243,244],[188,15625,15627],{"className":15626},[545],[188,15628,15630,15650],{"className":15629},[549,966],[188,15631,15633,15647],{"className":15632},[553],[188,15634,15636],{"className":15635,"style":9618},[557],[188,15637,15638,15641],{"style":9621},[188,15639],{"className":15640,"style":566},[565],[188,15642,15644],{"className":15643},[570,571,572,573],[188,15645,8307],{"className":15646},[243,573],[188,15648,990],{"className":15649},[989],[188,15651,15653],{"className":15652},[553],[188,15654,15656],{"className":15655,"style":6706},[557],[188,15657],{},[188,15659],{"className":15660,"style":585},[584],[188,15662,13295],{"className":15663},[589],[188,15665],{"className":15666,"style":585},[584],[188,15668,15670,15673,15713,15716,15719],{"className":15669},[234],[188,15671],{"className":15672,"style":15617},[238],[188,15674,15676,15679],{"className":15675},[243],[188,15677,27],{"className":15678},[243,244],[188,15680,15682],{"className":15681},[545],[188,15683,15685,15705],{"className":15684},[549,966],[188,15686,15688,15702],{"className":15687},[553],[188,15689,15691],{"className":15690,"style":9618},[557],[188,15692,15693,15696],{"style":9621},[188,15694],{"className":15695,"style":566},[565],[188,15697,15699],{"className":15698},[570,571,572,573],[188,15700,4948],{"className":15701},[243,573],[188,15703,990],{"className":15704},[989],[188,15706,15708],{"className":15707},[553],[188,15709,15711],{"className":15710,"style":6706},[557],[188,15712],{},[188,15714],{"className":15715,"style":585},[584],[188,15717,13295],{"className":15718},[589],[188,15720],{"className":15721,"style":585},[584],[188,15723,15725,15728,15768,15771,15774],{"className":15724},[234],[188,15726],{"className":15727,"style":14028},[238],[188,15729,15731,15734],{"className":15730},[243],[188,15732,27],{"className":15733},[243,244],[188,15735,15737],{"className":15736},[545],[188,15738,15740,15760],{"className":15739},[549,966],[188,15741,15743,15757],{"className":15742},[553],[188,15744,15746],{"className":15745,"style":9618},[557],[188,15747,15748,15751],{"style":9621},[188,15749],{"className":15750,"style":566},[565],[188,15752,15754],{"className":15753},[570,571,572,573],[188,15755,507],{"className":15756},[243,573],[188,15758,990],{"className":15759},[989],[188,15761,15763],{"className":15762},[553],[188,15764,15766],{"className":15765,"style":6706},[557],[188,15767],{},[188,15769],{"className":15770,"style":2528},[584],[188,15772,2464],{"className":15773},[2532],[188,15775],{"className":15776,"style":2528},[584],[188,15778,15780,15783,15786,15789,15792],{"className":15779},[234],[188,15781],{"className":15782,"style":7545},[238],[188,15784,13939],{"className":15785},[243],[188,15787],{"className":15788,"style":585},[584],[188,15790,4758],{"className":15791},[589],[188,15793],{"className":15794,"style":585},[584],[188,15796,15798,15801,15804,15807,15810],{"className":15797},[234],[188,15799],{"className":15800,"style":7545},[238],[188,15802,13952],{"className":15803},[243],[188,15805],{"className":15806,"style":585},[584],[188,15808,4758],{"className":15809},[589],[188,15811],{"className":15812,"style":585},[584],[188,15814,15816,15819,15822,15825,15828],{"className":15815},[234],[188,15817],{"className":15818,"style":3213},[238],[188,15820,934],{"className":15821},[243],[188,15823],{"className":15824,"style":2528},[584],[188,15826,2464],{"className":15827},[2532],[188,15829],{"className":15830,"style":2528},[584],[188,15832,15834,15837],{"className":15833},[234],[188,15835],{"className":15836,"style":3213},[238],[188,15838,15565],{"className":15839},[243],"，断点 ",[188,15842,15844,15874],{"className":15843},[191],[188,15845,15847],{"className":15846},[195],[197,15848,15849],{"xmlns":199},[201,15850,15851,15871],{},[204,15852,15853,15855,15857,15859,15861,15863,15865,15867,15869],{},[207,15854,14525],{},[211,15856,9366],{"stretchy":213},[505,15858,4948],{},[211,15860,9371],{"stretchy":213},[211,15862,9366],{"stretchy":213},[505,15864,507],{},[211,15866,9371],{"stretchy":213},[211,15868,2464],{},[505,15870,4948],{},[222,15872,15873],{"encoding":224},"s[1][2]=1",[188,15875,15877,15913],{"className":15876,"ariaHidden":230},[229],[188,15878,15880,15883,15886,15889,15892,15895,15898,15901,15904,15907,15910],{"className":15879},[234],[188,15881],{"className":15882,"style":239},[238],[188,15884,14525],{"className":15885},[243,244],[188,15887,9366],{"className":15888},[249],[188,15890,4948],{"className":15891},[243],[188,15893,9371],{"className":15894},[256],[188,15896,9366],{"className":15897},[249],[188,15899,507],{"className":15900},[243],[188,15902,9371],{"className":15903},[256],[188,15905],{"className":15906,"style":2528},[584],[188,15908,2464],{"className":15909},[2532],[188,15911],{"className":15912,"style":2528},[584],[188,15914,15916,15919],{"className":15915},[234],[188,15917],{"className":15918,"style":3213},[238],[188,15920,4948],{"className":15921},[243],[44,15923,15924,16266,16267],{},[188,15925,15927,15996],{"className":15926},[191],[188,15928,15930],{"className":15929},[195],[197,15931,15932],{"xmlns":199},[201,15933,15934,15993],{},[204,15935,15936,15938,15940,15942,15944,15946,15948,15950,15952,15954,15960,15962,15968,15970,15976,15978,15980,15982,15984,15986,15988,15990],{},[207,15937,9361],{},[207,15939,27],{},[211,15941,9366],{"stretchy":213},[505,15943,507],{},[211,15945,9371],{"stretchy":213},[211,15947,9366],{"stretchy":213},[505,15949,934],{},[211,15951,9371],{"stretchy":213},[211,15953,2464],{},[916,15955,15956,15958],{},[207,15957,27],{},[505,15959,4948],{},[211,15961,13295],{},[916,15963,15964,15966],{},[207,15965,27],{},[505,15967,507],{},[211,15969,13295],{},[916,15971,15972,15974],{},[207,15973,27],{},[505,15975,934],{},[211,15977,2464],{},[505,15979,13952],{},[211,15981,4758],{},[505,15983,934],{},[211,15985,4758],{},[505,15987,13977],{},[211,15989,2464],{},[505,15991,15992],{},"360",[222,15994,15995],{"encoding":224},"dp[2][3] = p_1 \\cdot p_2 \\cdot p_3 = 10 \\times 3 \\times 12 = 360",[188,15997,15999,16038,16093,16148,16203,16221,16239,16257],{"className":15998,"ariaHidden":230},[229],[188,16000,16002,16005,16008,16011,16014,16017,16020,16023,16026,16029,16032,16035],{"className":16001},[234],[188,16003],{"className":16004,"style":239},[238],[188,16006,9361],{"className":16007},[243,244],[188,16009,27],{"className":16010},[243,244],[188,16012,9366],{"className":16013},[249],[188,16015,507],{"className":16016},[243],[188,16018,9371],{"className":16019},[256],[188,16021,9366],{"className":16022},[249],[188,16024,934],{"className":16025},[243],[188,16027,9371],{"className":16028},[256],[188,16030],{"className":16031,"style":2528},[584],[188,16033,2464],{"className":16034},[2532],[188,16036],{"className":16037,"style":2528},[584],[188,16039,16041,16044,16084,16087,16090],{"className":16040},[234],[188,16042],{"className":16043,"style":15617},[238],[188,16045,16047,16050],{"className":16046},[243],[188,16048,27],{"className":16049},[243,244],[188,16051,16053],{"className":16052},[545],[188,16054,16056,16076],{"className":16055},[549,966],[188,16057,16059,16073],{"className":16058},[553],[188,16060,16062],{"className":16061,"style":9618},[557],[188,16063,16064,16067],{"style":9621},[188,16065],{"className":16066,"style":566},[565],[188,16068,16070],{"className":16069},[570,571,572,573],[188,16071,4948],{"className":16072},[243,573],[188,16074,990],{"className":16075},[989],[188,16077,16079],{"className":16078},[553],[188,16080,16082],{"className":16081,"style":6706},[557],[188,16083],{},[188,16085],{"className":16086,"style":585},[584],[188,16088,13295],{"className":16089},[589],[188,16091],{"className":16092,"style":585},[584],[188,16094,16096,16099,16139,16142,16145],{"className":16095},[234],[188,16097],{"className":16098,"style":15617},[238],[188,16100,16102,16105],{"className":16101},[243],[188,16103,27],{"className":16104},[243,244],[188,16106,16108],{"className":16107},[545],[188,16109,16111,16131],{"className":16110},[549,966],[188,16112,16114,16128],{"className":16113},[553],[188,16115,16117],{"className":16116,"style":9618},[557],[188,16118,16119,16122],{"style":9621},[188,16120],{"className":16121,"style":566},[565],[188,16123,16125],{"className":16124},[570,571,572,573],[188,16126,507],{"className":16127},[243,573],[188,16129,990],{"className":16130},[989],[188,16132,16134],{"className":16133},[553],[188,16135,16137],{"className":16136,"style":6706},[557],[188,16138],{},[188,16140],{"className":16141,"style":585},[584],[188,16143,13295],{"className":16144},[589],[188,16146],{"className":16147,"style":585},[584],[188,16149,16151,16154,16194,16197,16200],{"className":16150},[234],[188,16152],{"className":16153,"style":14028},[238],[188,16155,16157,16160],{"className":16156},[243],[188,16158,27],{"className":16159},[243,244],[188,16161,16163],{"className":16162},[545],[188,16164,16166,16186],{"className":16165},[549,966],[188,16167,16169,16183],{"className":16168},[553],[188,16170,16172],{"className":16171,"style":9618},[557],[188,16173,16174,16177],{"style":9621},[188,16175],{"className":16176,"style":566},[565],[188,16178,16180],{"className":16179},[570,571,572,573],[188,16181,934],{"className":16182},[243,573],[188,16184,990],{"className":16185},[989],[188,16187,16189],{"className":16188},[553],[188,16190,16192],{"className":16191,"style":6706},[557],[188,16193],{},[188,16195],{"className":16196,"style":2528},[584],[188,16198,2464],{"className":16199},[2532],[188,16201],{"className":16202,"style":2528},[584],[188,16204,16206,16209,16212,16215,16218],{"className":16205},[234],[188,16207],{"className":16208,"style":7545},[238],[188,16210,13952],{"className":16211},[243],[188,16213],{"className":16214,"style":585},[584],[188,16216,4758],{"className":16217},[589],[188,16219],{"className":16220,"style":585},[584],[188,16222,16224,16227,16230,16233,16236],{"className":16223},[234],[188,16225],{"className":16226,"style":7545},[238],[188,16228,934],{"className":16229},[243],[188,16231],{"className":16232,"style":585},[584],[188,16234,4758],{"className":16235},[589],[188,16237],{"className":16238,"style":585},[584],[188,16240,16242,16245,16248,16251,16254],{"className":16241},[234],[188,16243],{"className":16244,"style":3213},[238],[188,16246,13977],{"className":16247},[243],[188,16249],{"className":16250,"style":2528},[584],[188,16252,2464],{"className":16253},[2532],[188,16255],{"className":16256,"style":2528},[584],[188,16258,16260,16263],{"className":16259},[234],[188,16261],{"className":16262,"style":3213},[238],[188,16264,15992],{"className":16265},[243],"，",[188,16268,16270,16300],{"className":16269},[191],[188,16271,16273],{"className":16272},[195],[197,16274,16275],{"xmlns":199},[201,16276,16277,16297],{},[204,16278,16279,16281,16283,16285,16287,16289,16291,16293,16295],{},[207,16280,14525],{},[211,16282,9366],{"stretchy":213},[505,16284,507],{},[211,16286,9371],{"stretchy":213},[211,16288,9366],{"stretchy":213},[505,16290,934],{},[211,16292,9371],{"stretchy":213},[211,16294,2464],{},[505,16296,507],{},[222,16298,16299],{"encoding":224},"s[2][3]=2",[188,16301,16303,16339],{"className":16302,"ariaHidden":230},[229],[188,16304,16306,16309,16312,16315,16318,16321,16324,16327,16330,16333,16336],{"className":16305},[234],[188,16307],{"className":16308,"style":239},[238],[188,16310,14525],{"className":16311},[243,244],[188,16313,9366],{"className":16314},[249],[188,16316,507],{"className":16317},[243],[188,16319,9371],{"className":16320},[256],[188,16322,9366],{"className":16323},[249],[188,16325,934],{"className":16326},[243],[188,16328,9371],{"className":16329},[256],[188,16331],{"className":16332,"style":2528},[584],[188,16334,2464],{"className":16335},[2532],[188,16337],{"className":16338,"style":2528},[584],[188,16340,16342,16345],{"className":16341},[234],[188,16343],{"className":16344,"style":3213},[238],[188,16346,507],{"className":16347},[243],[44,16349,16350,16266,16692],{},[188,16351,16353,16422],{"className":16352},[191],[188,16354,16356],{"className":16355},[195],[197,16357,16358],{"xmlns":199},[201,16359,16360,16419],{},[204,16361,16362,16364,16366,16368,16370,16372,16374,16376,16378,16380,16386,16388,16394,16396,16402,16404,16406,16408,16410,16412,16414,16416],{},[207,16363,9361],{},[207,16365,27],{},[211,16367,9366],{"stretchy":213},[505,16369,934],{},[211,16371,9371],{"stretchy":213},[211,16373,9366],{"stretchy":213},[505,16375,4869],{},[211,16377,9371],{"stretchy":213},[211,16379,2464],{},[916,16381,16382,16384],{},[207,16383,27],{},[505,16385,507],{},[211,16387,13295],{},[916,16389,16390,16392],{},[207,16391,27],{},[505,16393,934],{},[211,16395,13295],{},[916,16397,16398,16400],{},[207,16399,27],{},[505,16401,4869],{},[211,16403,2464],{},[505,16405,934],{},[211,16407,4758],{},[505,16409,13977],{},[211,16411,4758],{},[505,16413,13939],{},[211,16415,2464],{},[505,16417,16418],{},"180",[222,16420,16421],{"encoding":224},"dp[3][4] = p_2 \\cdot p_3 \\cdot p_4 = 3 \\times 12 \\times 5 = 180",[188,16423,16425,16464,16519,16574,16629,16647,16665,16683],{"className":16424,"ariaHidden":230},[229],[188,16426,16428,16431,16434,16437,16440,16443,16446,16449,16452,16455,16458,16461],{"className":16427},[234],[188,16429],{"className":16430,"style":239},[238],[188,16432,9361],{"className":16433},[243,244],[188,16435,27],{"className":16436},[243,244],[188,16438,9366],{"className":16439},[249],[188,16441,934],{"className":16442},[243],[188,16444,9371],{"className":16445},[256],[188,16447,9366],{"className":16448},[249],[188,16450,4869],{"className":16451},[243],[188,16453,9371],{"className":16454},[256],[188,16456],{"className":16457,"style":2528},[584],[188,16459,2464],{"className":16460},[2532],[188,16462],{"className":16463,"style":2528},[584],[188,16465,16467,16470,16510,16513,16516],{"className":16466},[234],[188,16468],{"className":16469,"style":15617},[238],[188,16471,16473,16476],{"className":16472},[243],[188,16474,27],{"className":16475},[243,244],[188,16477,16479],{"className":16478},[545],[188,16480,16482,16502],{"className":16481},[549,966],[188,16483,16485,16499],{"className":16484},[553],[188,16486,16488],{"className":16487,"style":9618},[557],[188,16489,16490,16493],{"style":9621},[188,16491],{"className":16492,"style":566},[565],[188,16494,16496],{"className":16495},[570,571,572,573],[188,16497,507],{"className":16498},[243,573],[188,16500,990],{"className":16501},[989],[188,16503,16505],{"className":16504},[553],[188,16506,16508],{"className":16507,"style":6706},[557],[188,16509],{},[188,16511],{"className":16512,"style":585},[584],[188,16514,13295],{"className":16515},[589],[188,16517],{"className":16518,"style":585},[584],[188,16520,16522,16525,16565,16568,16571],{"className":16521},[234],[188,16523],{"className":16524,"style":15617},[238],[188,16526,16528,16531],{"className":16527},[243],[188,16529,27],{"className":16530},[243,244],[188,16532,16534],{"className":16533},[545],[188,16535,16537,16557],{"className":16536},[549,966],[188,16538,16540,16554],{"className":16539},[553],[188,16541,16543],{"className":16542,"style":9618},[557],[188,16544,16545,16548],{"style":9621},[188,16546],{"className":16547,"style":566},[565],[188,16549,16551],{"className":16550},[570,571,572,573],[188,16552,934],{"className":16553},[243,573],[188,16555,990],{"className":16556},[989],[188,16558,16560],{"className":16559},[553],[188,16561,16563],{"className":16562,"style":6706},[557],[188,16564],{},[188,16566],{"className":16567,"style":585},[584],[188,16569,13295],{"className":16570},[589],[188,16572],{"className":16573,"style":585},[584],[188,16575,16577,16580,16620,16623,16626],{"className":16576},[234],[188,16578],{"className":16579,"style":14028},[238],[188,16581,16583,16586],{"className":16582},[243],[188,16584,27],{"className":16585},[243,244],[188,16587,16589],{"className":16588},[545],[188,16590,16592,16612],{"className":16591},[549,966],[188,16593,16595,16609],{"className":16594},[553],[188,16596,16598],{"className":16597,"style":9618},[557],[188,16599,16600,16603],{"style":9621},[188,16601],{"className":16602,"style":566},[565],[188,16604,16606],{"className":16605},[570,571,572,573],[188,16607,4869],{"className":16608},[243,573],[188,16610,990],{"className":16611},[989],[188,16613,16615],{"className":16614},[553],[188,16616,16618],{"className":16617,"style":6706},[557],[188,16619],{},[188,16621],{"className":16622,"style":2528},[584],[188,16624,2464],{"className":16625},[2532],[188,16627],{"className":16628,"style":2528},[584],[188,16630,16632,16635,16638,16641,16644],{"className":16631},[234],[188,16633],{"className":16634,"style":7545},[238],[188,16636,934],{"className":16637},[243],[188,16639],{"className":16640,"style":585},[584],[188,16642,4758],{"className":16643},[589],[188,16645],{"className":16646,"style":585},[584],[188,16648,16650,16653,16656,16659,16662],{"className":16649},[234],[188,16651],{"className":16652,"style":7545},[238],[188,16654,13977],{"className":16655},[243],[188,16657],{"className":16658,"style":585},[584],[188,16660,4758],{"className":16661},[589],[188,16663],{"className":16664,"style":585},[584],[188,16666,16668,16671,16674,16677,16680],{"className":16667},[234],[188,16669],{"className":16670,"style":3213},[238],[188,16672,13939],{"className":16673},[243],[188,16675],{"className":16676,"style":2528},[584],[188,16678,2464],{"className":16679},[2532],[188,16681],{"className":16682,"style":2528},[584],[188,16684,16686,16689],{"className":16685},[234],[188,16687],{"className":16688,"style":3213},[238],[188,16690,16418],{"className":16691},[243],[188,16693,16695,16725],{"className":16694},[191],[188,16696,16698],{"className":16697},[195],[197,16699,16700],{"xmlns":199},[201,16701,16702,16722],{},[204,16703,16704,16706,16708,16710,16712,16714,16716,16718,16720],{},[207,16705,14525],{},[211,16707,9366],{"stretchy":213},[505,16709,934],{},[211,16711,9371],{"stretchy":213},[211,16713,9366],{"stretchy":213},[505,16715,4869],{},[211,16717,9371],{"stretchy":213},[211,16719,2464],{},[505,16721,934],{},[222,16723,16724],{"encoding":224},"s[3][4]=3",[188,16726,16728,16764],{"className":16727,"ariaHidden":230},[229],[188,16729,16731,16734,16737,16740,16743,16746,16749,16752,16755,16758,16761],{"className":16730},[234],[188,16732],{"className":16733,"style":239},[238],[188,16735,14525],{"className":16736},[243,244],[188,16738,9366],{"className":16739},[249],[188,16741,934],{"className":16742},[243],[188,16744,9371],{"className":16745},[256],[188,16747,9366],{"className":16748},[249],[188,16750,4869],{"className":16751},[243],[188,16753,9371],{"className":16754},[256],[188,16756],{"className":16757,"style":2528},[584],[188,16759,2464],{"className":16760},[2532],[188,16762],{"className":16763,"style":2528},[584],[188,16765,16767,16770],{"className":16766},[234],[188,16768],{"className":16769,"style":3213},[238],[188,16771,934],{"className":16772},[243],[44,16774,16775,16266,17117],{},[188,16776,16778,16847],{"className":16777},[191],[188,16779,16781],{"className":16780},[195],[197,16782,16783],{"xmlns":199},[201,16784,16785,16844],{},[204,16786,16787,16789,16791,16793,16795,16797,16799,16801,16803,16805,16811,16813,16819,16821,16827,16829,16831,16833,16835,16837,16839,16841],{},[207,16788,9361],{},[207,16790,27],{},[211,16792,9366],{"stretchy":213},[505,16794,4869],{},[211,16796,9371],{"stretchy":213},[211,16798,9366],{"stretchy":213},[505,16800,13939],{},[211,16802,9371],{"stretchy":213},[211,16804,2464],{},[916,16806,16807,16809],{},[207,16808,27],{},[505,16810,934],{},[211,16812,13295],{},[916,16814,16815,16817],{},[207,16816,27],{},[505,16818,4869],{},[211,16820,13295],{},[916,16822,16823,16825],{},[207,16824,27],{},[505,16826,13939],{},[211,16828,2464],{},[505,16830,13977],{},[211,16832,4758],{},[505,16834,13939],{},[211,16836,4758],{},[505,16838,14002],{},[211,16840,2464],{},[505,16842,16843],{},"3000",[222,16845,16846],{"encoding":224},"dp[4][5] = p_3 \\cdot p_4 \\cdot p_5 = 12 \\times 5 \\times 50 = 3000",[188,16848,16850,16889,16944,16999,17054,17072,17090,17108],{"className":16849,"ariaHidden":230},[229],[188,16851,16853,16856,16859,16862,16865,16868,16871,16874,16877,16880,16883,16886],{"className":16852},[234],[188,16854],{"className":16855,"style":239},[238],[188,16857,9361],{"className":16858},[243,244],[188,16860,27],{"className":16861},[243,244],[188,16863,9366],{"className":16864},[249],[188,16866,4869],{"className":16867},[243],[188,16869,9371],{"className":16870},[256],[188,16872,9366],{"className":16873},[249],[188,16875,13939],{"className":16876},[243],[188,16878,9371],{"className":16879},[256],[188,16881],{"className":16882,"style":2528},[584],[188,16884,2464],{"className":16885},[2532],[188,16887],{"className":16888,"style":2528},[584],[188,16890,16892,16895,16935,16938,16941],{"className":16891},[234],[188,16893],{"className":16894,"style":15617},[238],[188,16896,16898,16901],{"className":16897},[243],[188,16899,27],{"className":16900},[243,244],[188,16902,16904],{"className":16903},[545],[188,16905,16907,16927],{"className":16906},[549,966],[188,16908,16910,16924],{"className":16909},[553],[188,16911,16913],{"className":16912,"style":9618},[557],[188,16914,16915,16918],{"style":9621},[188,16916],{"className":16917,"style":566},[565],[188,16919,16921],{"className":16920},[570,571,572,573],[188,16922,934],{"className":16923},[243,573],[188,16925,990],{"className":16926},[989],[188,16928,16930],{"className":16929},[553],[188,16931,16933],{"className":16932,"style":6706},[557],[188,16934],{},[188,16936],{"className":16937,"style":585},[584],[188,16939,13295],{"className":16940},[589],[188,16942],{"className":16943,"style":585},[584],[188,16945,16947,16950,16990,16993,16996],{"className":16946},[234],[188,16948],{"className":16949,"style":15617},[238],[188,16951,16953,16956],{"className":16952},[243],[188,16954,27],{"className":16955},[243,244],[188,16957,16959],{"className":16958},[545],[188,16960,16962,16982],{"className":16961},[549,966],[188,16963,16965,16979],{"className":16964},[553],[188,16966,16968],{"className":16967,"style":9618},[557],[188,16969,16970,16973],{"style":9621},[188,16971],{"className":16972,"style":566},[565],[188,16974,16976],{"className":16975},[570,571,572,573],[188,16977,4869],{"className":16978},[243,573],[188,16980,990],{"className":16981},[989],[188,16983,16985],{"className":16984},[553],[188,16986,16988],{"className":16987,"style":6706},[557],[188,16989],{},[188,16991],{"className":16992,"style":585},[584],[188,16994,13295],{"className":16995},[589],[188,16997],{"className":16998,"style":585},[584],[188,17000,17002,17005,17045,17048,17051],{"className":17001},[234],[188,17003],{"className":17004,"style":14028},[238],[188,17006,17008,17011],{"className":17007},[243],[188,17009,27],{"className":17010},[243,244],[188,17012,17014],{"className":17013},[545],[188,17015,17017,17037],{"className":17016},[549,966],[188,17018,17020,17034],{"className":17019},[553],[188,17021,17023],{"className":17022,"style":9618},[557],[188,17024,17025,17028],{"style":9621},[188,17026],{"className":17027,"style":566},[565],[188,17029,17031],{"className":17030},[570,571,572,573],[188,17032,13939],{"className":17033},[243,573],[188,17035,990],{"className":17036},[989],[188,17038,17040],{"className":17039},[553],[188,17041,17043],{"className":17042,"style":6706},[557],[188,17044],{},[188,17046],{"className":17047,"style":2528},[584],[188,17049,2464],{"className":17050},[2532],[188,17052],{"className":17053,"style":2528},[584],[188,17055,17057,17060,17063,17066,17069],{"className":17056},[234],[188,17058],{"className":17059,"style":7545},[238],[188,17061,13977],{"className":17062},[243],[188,17064],{"className":17065,"style":585},[584],[188,17067,4758],{"className":17068},[589],[188,17070],{"className":17071,"style":585},[584],[188,17073,17075,17078,17081,17084,17087],{"className":17074},[234],[188,17076],{"className":17077,"style":7545},[238],[188,17079,13939],{"className":17080},[243],[188,17082],{"className":17083,"style":585},[584],[188,17085,4758],{"className":17086},[589],[188,17088],{"className":17089,"style":585},[584],[188,17091,17093,17096,17099,17102,17105],{"className":17092},[234],[188,17094],{"className":17095,"style":3213},[238],[188,17097,14002],{"className":17098},[243],[188,17100],{"className":17101,"style":2528},[584],[188,17103,2464],{"className":17104},[2532],[188,17106],{"className":17107,"style":2528},[584],[188,17109,17111,17114],{"className":17110},[234],[188,17112],{"className":17113,"style":3213},[238],[188,17115,16843],{"className":17116},[243],[188,17118,17120,17150],{"className":17119},[191],[188,17121,17123],{"className":17122},[195],[197,17124,17125],{"xmlns":199},[201,17126,17127,17147],{},[204,17128,17129,17131,17133,17135,17137,17139,17141,17143,17145],{},[207,17130,14525],{},[211,17132,9366],{"stretchy":213},[505,17134,4869],{},[211,17136,9371],{"stretchy":213},[211,17138,9366],{"stretchy":213},[505,17140,13939],{},[211,17142,9371],{"stretchy":213},[211,17144,2464],{},[505,17146,4869],{},[222,17148,17149],{"encoding":224},"s[4][5]=4",[188,17151,17153,17189],{"className":17152,"ariaHidden":230},[229],[188,17154,17156,17159,17162,17165,17168,17171,17174,17177,17180,17183,17186],{"className":17155},[234],[188,17157],{"className":17158,"style":239},[238],[188,17160,14525],{"className":17161},[243,244],[188,17163,9366],{"className":17164},[249],[188,17166,4869],{"className":17167},[243],[188,17169,9371],{"className":17170},[256],[188,17172,9366],{"className":17173},[249],[188,17175,13939],{"className":17176},[243],[188,17178,9371],{"className":17179},[256],[188,17181],{"className":17182,"style":2528},[584],[188,17184,2464],{"className":17185},[2532],[188,17187],{"className":17188,"style":2528},[584],[188,17190,17192,17195],{"className":17191},[234],[188,17193],{"className":17194,"style":3213},[238],[188,17196,4869],{"className":17197},[243],[44,17199,17200,16266,17542],{},[188,17201,17203,17272],{"className":17202},[191],[188,17204,17206],{"className":17205},[195],[197,17207,17208],{"xmlns":199},[201,17209,17210,17269],{},[204,17211,17212,17214,17216,17218,17220,17222,17224,17226,17228,17230,17236,17238,17244,17246,17252,17254,17256,17258,17260,17262,17264,17266],{},[207,17213,9361],{},[207,17215,27],{},[211,17217,9366],{"stretchy":213},[505,17219,13939],{},[211,17221,9371],{"stretchy":213},[211,17223,9366],{"stretchy":213},[505,17225,14011],{},[211,17227,9371],{"stretchy":213},[211,17229,2464],{},[916,17231,17232,17234],{},[207,17233,27],{},[505,17235,4869],{},[211,17237,13295],{},[916,17239,17240,17242],{},[207,17241,27],{},[505,17243,13939],{},[211,17245,13295],{},[916,17247,17248,17250],{},[207,17249,27],{},[505,17251,14011],{},[211,17253,2464],{},[505,17255,13939],{},[211,17257,4758],{},[505,17259,14002],{},[211,17261,4758],{},[505,17263,14011],{},[211,17265,2464],{},[505,17267,17268],{},"1500",[222,17270,17271],{"encoding":224},"dp[5][6] = p_4 \\cdot p_5 \\cdot p_6 = 5 \\times 50 \\times 6 = 1500",[188,17273,17275,17314,17369,17424,17479,17497,17515,17533],{"className":17274,"ariaHidden":230},[229],[188,17276,17278,17281,17284,17287,17290,17293,17296,17299,17302,17305,17308,17311],{"className":17277},[234],[188,17279],{"className":17280,"style":239},[238],[188,17282,9361],{"className":17283},[243,244],[188,17285,27],{"className":17286},[243,244],[188,17288,9366],{"className":17289},[249],[188,17291,13939],{"className":17292},[243],[188,17294,9371],{"className":17295},[256],[188,17297,9366],{"className":17298},[249],[188,17300,14011],{"className":17301},[243],[188,17303,9371],{"className":17304},[256],[188,17306],{"className":17307,"style":2528},[584],[188,17309,2464],{"className":17310},[2532],[188,17312],{"className":17313,"style":2528},[584],[188,17315,17317,17320,17360,17363,17366],{"className":17316},[234],[188,17318],{"className":17319,"style":15617},[238],[188,17321,17323,17326],{"className":17322},[243],[188,17324,27],{"className":17325},[243,244],[188,17327,17329],{"className":17328},[545],[188,17330,17332,17352],{"className":17331},[549,966],[188,17333,17335,17349],{"className":17334},[553],[188,17336,17338],{"className":17337,"style":9618},[557],[188,17339,17340,17343],{"style":9621},[188,17341],{"className":17342,"style":566},[565],[188,17344,17346],{"className":17345},[570,571,572,573],[188,17347,4869],{"className":17348},[243,573],[188,17350,990],{"className":17351},[989],[188,17353,17355],{"className":17354},[553],[188,17356,17358],{"className":17357,"style":6706},[557],[188,17359],{},[188,17361],{"className":17362,"style":585},[584],[188,17364,13295],{"className":17365},[589],[188,17367],{"className":17368,"style":585},[584],[188,17370,17372,17375,17415,17418,17421],{"className":17371},[234],[188,17373],{"className":17374,"style":15617},[238],[188,17376,17378,17381],{"className":17377},[243],[188,17379,27],{"className":17380},[243,244],[188,17382,17384],{"className":17383},[545],[188,17385,17387,17407],{"className":17386},[549,966],[188,17388,17390,17404],{"className":17389},[553],[188,17391,17393],{"className":17392,"style":9618},[557],[188,17394,17395,17398],{"style":9621},[188,17396],{"className":17397,"style":566},[565],[188,17399,17401],{"className":17400},[570,571,572,573],[188,17402,13939],{"className":17403},[243,573],[188,17405,990],{"className":17406},[989],[188,17408,17410],{"className":17409},[553],[188,17411,17413],{"className":17412,"style":6706},[557],[188,17414],{},[188,17416],{"className":17417,"style":585},[584],[188,17419,13295],{"className":17420},[589],[188,17422],{"className":17423,"style":585},[584],[188,17425,17427,17430,17470,17473,17476],{"className":17426},[234],[188,17428],{"className":17429,"style":14028},[238],[188,17431,17433,17436],{"className":17432},[243],[188,17434,27],{"className":17435},[243,244],[188,17437,17439],{"className":17438},[545],[188,17440,17442,17462],{"className":17441},[549,966],[188,17443,17445,17459],{"className":17444},[553],[188,17446,17448],{"className":17447,"style":9618},[557],[188,17449,17450,17453],{"style":9621},[188,17451],{"className":17452,"style":566},[565],[188,17454,17456],{"className":17455},[570,571,572,573],[188,17457,14011],{"className":17458},[243,573],[188,17460,990],{"className":17461},[989],[188,17463,17465],{"className":17464},[553],[188,17466,17468],{"className":17467,"style":6706},[557],[188,17469],{},[188,17471],{"className":17472,"style":2528},[584],[188,17474,2464],{"className":17475},[2532],[188,17477],{"className":17478,"style":2528},[584],[188,17480,17482,17485,17488,17491,17494],{"className":17481},[234],[188,17483],{"className":17484,"style":7545},[238],[188,17486,13939],{"className":17487},[243],[188,17489],{"className":17490,"style":585},[584],[188,17492,4758],{"className":17493},[589],[188,17495],{"className":17496,"style":585},[584],[188,17498,17500,17503,17506,17509,17512],{"className":17499},[234],[188,17501],{"className":17502,"style":7545},[238],[188,17504,14002],{"className":17505},[243],[188,17507],{"className":17508,"style":585},[584],[188,17510,4758],{"className":17511},[589],[188,17513],{"className":17514,"style":585},[584],[188,17516,17518,17521,17524,17527,17530],{"className":17517},[234],[188,17519],{"className":17520,"style":3213},[238],[188,17522,14011],{"className":17523},[243],[188,17525],{"className":17526,"style":2528},[584],[188,17528,2464],{"className":17529},[2532],[188,17531],{"className":17532,"style":2528},[584],[188,17534,17536,17539],{"className":17535},[234],[188,17537],{"className":17538,"style":3213},[238],[188,17540,17268],{"className":17541},[243],[188,17543,17545,17575],{"className":17544},[191],[188,17546,17548],{"className":17547},[195],[197,17549,17550],{"xmlns":199},[201,17551,17552,17572],{},[204,17553,17554,17556,17558,17560,17562,17564,17566,17568,17570],{},[207,17555,14525],{},[211,17557,9366],{"stretchy":213},[505,17559,13939],{},[211,17561,9371],{"stretchy":213},[211,17563,9366],{"stretchy":213},[505,17565,14011],{},[211,17567,9371],{"stretchy":213},[211,17569,2464],{},[505,17571,13939],{},[222,17573,17574],{"encoding":224},"s[5][6]=5",[188,17576,17578,17614],{"className":17577,"ariaHidden":230},[229],[188,17579,17581,17584,17587,17590,17593,17596,17599,17602,17605,17608,17611],{"className":17580},[234],[188,17582],{"className":17583,"style":239},[238],[188,17585,14525],{"className":17586},[243,244],[188,17588,9366],{"className":17589},[249],[188,17591,13939],{"className":17592},[243],[188,17594,9371],{"className":17595},[256],[188,17597,9366],{"className":17598},[249],[188,17600,14011],{"className":17601},[243],[188,17603,9371],{"className":17604},[256],[188,17606],{"className":17607,"style":2528},[584],[188,17609,2464],{"className":17610},[2532],[188,17612],{"className":17613,"style":2528},[584],[188,17615,17617,17620],{"className":17616},[234],[188,17618],{"className":17619,"style":3213},[238],[188,17621,13939],{"className":17622},[243],[44,17624,17625,17628,17629,17657,17658],{},[36,17626,17627],{},"长度 L = 3："," 试探断点 ",[188,17630,17632,17645],{"className":17631},[191],[188,17633,17635],{"className":17634},[195],[197,17636,17637],{"xmlns":199},[201,17638,17639,17643],{},[204,17640,17641],{},[207,17642,4755],{},[222,17644,4755],{"encoding":224},[188,17646,17648],{"className":17647,"ariaHidden":230},[229],[188,17649,17651,17654],{"className":17650},[234],[188,17652],{"className":17653,"style":3248},[238],[188,17655,4755],{"className":17656,"style":4807},[243,244]," 取哪一边使得代价最小。",[68,17659,17660,18398,18887,19378],{},[44,17661,17662,18314,18315,16266,18317,85],{},[188,17663,17665,17865],{"className":17664},[191],[188,17666,17668],{"className":17667},[195],[197,17669,17670],{"xmlns":199},[201,17671,17672,17862],{},[204,17673,17674,17676,17678,17680,17682,17684,17686,17688,17690,17692,17694,17696],{},[207,17675,9361],{},[207,17677,27],{},[211,17679,9366],{"stretchy":213},[505,17681,4948],{},[211,17683,9371],{"stretchy":213},[211,17685,9366],{"stretchy":213},[505,17687,934],{},[211,17689,9371],{"stretchy":213},[211,17691,2464],{},[207,17693,13222],{},[211,17695,925],{},[204,17697,17698,17700],{},[211,17699,13177],{"fence":230},[13179,17701,17702,17783],{"rowspacing":13181,"columnalign":13182,"columnspacing":13183},[13185,17703,17704],{},[13188,17705,17706],{},[13191,17707,17708],{"scriptlevel":8307,"displaystyle":213},[204,17709,17710,17712,17714,17716,17719,17721,17723,17725,17727,17729,17731,17733,17735,17737,17739,17741,17743,17745,17747,17749,17751,17753,17755,17757,17759,17761,17763,17765,17767,17769,17771,17773,17775,17778,17780],{},[207,17711,4755],{},[211,17713,2464],{},[505,17715,4948],{},[211,17717,17718],{},":",[207,17720,9361],{},[207,17722,27],{},[211,17724,9366],{"stretchy":213},[505,17726,4948],{},[211,17728,9371],{"stretchy":213},[211,17730,9366],{"stretchy":213},[505,17732,4948],{},[211,17734,9371],{"stretchy":213},[211,17736,516],{},[207,17738,9361],{},[207,17740,27],{},[211,17742,9366],{"stretchy":213},[505,17744,507],{},[211,17746,9371],{"stretchy":213},[211,17748,9366],{"stretchy":213},[505,17750,934],{},[211,17752,9371],{"stretchy":213},[211,17754,516],{},[505,17756,13939],{},[211,17758,4758],{},[505,17760,13952],{},[211,17762,4758],{},[505,17764,13977],{},[211,17766,2464],{},[505,17768,8307],{},[211,17770,516],{},[505,17772,15992],{},[211,17774,516],{},[505,17776,17777],{},"600",[211,17779,2464],{},[505,17781,17782],{},"960",[13185,17784,17785],{},[13188,17786,17787],{},[13191,17788,17789],{"scriptlevel":8307,"displaystyle":213},[204,17790,17791,17793,17795,17797,17799,17801,17803,17805,17807,17809,17811,17813,17815,17817,17819,17821,17823,17825,17827,17829,17831,17833,17835,17837,17839,17841,17843,17845,17847,17849,17851,17853,17855,17857,17859],{},[207,17792,4755],{},[211,17794,2464],{},[505,17796,507],{},[211,17798,17718],{},[207,17800,9361],{},[207,17802,27],{},[211,17804,9366],{"stretchy":213},[505,17806,4948],{},[211,17808,9371],{"stretchy":213},[211,17810,9366],{"stretchy":213},[505,17812,507],{},[211,17814,9371],{"stretchy":213},[211,17816,516],{},[207,17818,9361],{},[207,17820,27],{},[211,17822,9366],{"stretchy":213},[505,17824,934],{},[211,17826,9371],{"stretchy":213},[211,17828,9366],{"stretchy":213},[505,17830,934],{},[211,17832,9371],{"stretchy":213},[211,17834,516],{},[505,17836,13939],{},[211,17838,4758],{},[505,17840,934],{},[211,17842,4758],{},[505,17844,13977],{},[211,17846,2464],{},[505,17848,15565],{},[211,17850,516],{},[505,17852,8307],{},[211,17854,516],{},[505,17856,16418],{},[211,17858,2464],{},[505,17860,17861],{},"330",[222,17863,17864],{"encoding":224},"dp[1][3] = \\min \\begin{cases} k=1: dp[1][1] + dp[2][3] + 5\\times 10\\times 12 = 0 + 360 + 600 = 960 \\\\ k=2: dp[1][2] + dp[3][3] + 5\\times 3\\times 12 = 150 + 0 + 180 = 330 \\end{cases}",[188,17866,17868,17907],{"className":17867,"ariaHidden":230},[229],[188,17869,17871,17874,17877,17880,17883,17886,17889,17892,17895,17898,17901,17904],{"className":17870},[234],[188,17872],{"className":17873,"style":239},[238],[188,17875,9361],{"className":17876},[243,244],[188,17878,27],{"className":17879},[243,244],[188,17881,9366],{"className":17882},[249],[188,17884,4948],{"className":17885},[243],[188,17887,9371],{"className":17888},[256],[188,17890,9366],{"className":17891},[249],[188,17893,934],{"className":17894},[243],[188,17896,9371],{"className":17897},[256],[188,17899],{"className":17900,"style":2528},[584],[188,17902,2464],{"className":17903},[2532],[188,17905],{"className":17906,"style":2528},[584],[188,17908,17910,17914,17917,17920],{"className":17909},[234],[188,17911],{"className":17912,"style":17913},[238],"height:3em;vertical-align:-1.25em;",[188,17915,13222],{"className":17916},[951],[188,17918],{"className":17919,"style":1003},[584],[188,17921,17923,17932,18311],{"className":17922},[9697],[188,17924,17928],{"className":17925,"style":17927},[249,17926],"delimcenter","top:0em;",[188,17929,13177],{"className":17930},[13386,17931],"size4",[188,17933,17935],{"className":17934},[243],[188,17936,17938],{"className":17937},[13179],[188,17939,17941],{"className":17940},[13489],[188,17942,17944,18302],{"className":17943},[549,966],[188,17945,17947,18299],{"className":17946},[553],[188,17948,17951,18125],{"className":17949,"style":17950},[557],"height:1.69em;",[188,17952,17954,17957],{"style":17953},"top:-3.69em;",[188,17955],{"className":17956,"style":13506},[565],[188,17958,17960,17963,17966,17969,17972,17975,17978,17981,17984,17987,17990,17993,17996,17999,18002,18005,18008,18011,18014,18017,18020,18023,18026,18029,18032,18035,18038,18041,18044,18047,18050,18053,18056,18059,18062,18065,18068,18071,18074,18077,18080,18083,18086,18089,18092,18095,18098,18101,18104,18107,18110,18113,18116,18119,18122],{"className":17959},[243],[188,17961,4755],{"className":17962,"style":4807},[243,244],[188,17964],{"className":17965,"style":2528},[584],[188,17967,2464],{"className":17968},[2532],[188,17970],{"className":17971,"style":2528},[584],[188,17973,4948],{"className":17974},[243],[188,17976],{"className":17977,"style":2528},[584],[188,17979,17718],{"className":17980},[2532],[188,17982],{"className":17983,"style":2528},[584],[188,17985,9361],{"className":17986},[243,244],[188,17988,27],{"className":17989},[243,244],[188,17991,9366],{"className":17992},[249],[188,17994,4948],{"className":17995},[243],[188,17997,9371],{"className":17998},[256],[188,18000,9366],{"className":18001},[249],[188,18003,4948],{"className":18004},[243],[188,18006,9371],{"className":18007},[256],[188,18009],{"className":18010,"style":585},[584],[188,18012,516],{"className":18013},[589],[188,18015],{"className":18016,"style":585},[584],[188,18018,9361],{"className":18019},[243,244],[188,18021,27],{"className":18022},[243,244],[188,18024,9366],{"className":18025},[249],[188,18027,507],{"className":18028},[243],[188,18030,9371],{"className":18031},[256],[188,18033,9366],{"className":18034},[249],[188,18036,934],{"className":18037},[243],[188,18039,9371],{"className":18040},[256],[188,18042],{"className":18043,"style":585},[584],[188,18045,516],{"className":18046},[589],[188,18048],{"className":18049,"style":585},[584],[188,18051,13939],{"className":18052},[243],[188,18054],{"className":18055,"style":585},[584],[188,18057,4758],{"className":18058},[589],[188,18060],{"className":18061,"style":585},[584],[188,18063,13952],{"className":18064},[243],[188,18066],{"className":18067,"style":585},[584],[188,18069,4758],{"className":18070},[589],[188,18072],{"className":18073,"style":585},[584],[188,18075,13977],{"className":18076},[243],[188,18078],{"className":18079,"style":2528},[584],[188,18081,2464],{"className":18082},[2532],[188,18084],{"className":18085,"style":2528},[584],[188,18087,8307],{"className":18088},[243],[188,18090],{"className":18091,"style":585},[584],[188,18093,516],{"className":18094},[589],[188,18096],{"className":18097,"style":585},[584],[188,18099,15992],{"className":18100},[243],[188,18102],{"className":18103,"style":585},[584],[188,18105,516],{"className":18106},[589],[188,18108],{"className":18109,"style":585},[584],[188,18111,17777],{"className":18112},[243],[188,18114],{"className":18115,"style":2528},[584],[188,18117,2464],{"className":18118},[2532],[188,18120],{"className":18121,"style":2528},[584],[188,18123,17782],{"className":18124},[243],[188,18126,18128,18131],{"style":18127},"top:-2.25em;",[188,18129],{"className":18130,"style":13506},[565],[188,18132,18134,18137,18140,18143,18146,18149,18152,18155,18158,18161,18164,18167,18170,18173,18176,18179,18182,18185,18188,18191,18194,18197,18200,18203,18206,18209,18212,18215,18218,18221,18224,18227,18230,18233,18236,18239,18242,18245,18248,18251,18254,18257,18260,18263,18266,18269,18272,18275,18278,18281,18284,18287,18290,18293,18296],{"className":18133},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",[36,18316,17861],{},[188,18318,18320,18350],{"className":18319},[191],[188,18321,18323],{"className":18322},[195],[197,18324,18325],{"xmlns":199},[201,18326,18327,18347],{},[204,18328,18329,18331,18333,18335,18337,18339,18341,18343,18345],{},[207,18330,14525],{},[211,18332,9366],{"stretchy":213},[505,18334,4948],{},[211,18336,9371],{"stretchy":213},[211,18338,9366],{"stretchy":213},[505,18340,934],{},[211,18342,9371],{"stretchy":213},[211,18344,2464],{},[505,18346,507],{},[222,18348,18349],{"encoding":224},"s[1][3]=2",[188,18351,18353,18389],{"className":18352,"ariaHidden":230},[229],[188,18354,18356,18359,18362,18365,18368,18371,18374,18377,18380,18383,18386],{"className":18355},[234],[188,18357],{"className":18358,"style":239},[238],[188,18360,14525],{"className":18361},[243,244],[188,18363,9366],{"className":18364},[249],[188,18366,4948],{"className":18367},[243],[188,18369,9371],{"className":18370},[256],[188,18372,9366],{"className":18373},[249],[188,18375,934],{"className":18376},[243],[188,18378,9371],{"className":18379},[256],[188,18381],{"className":18382,"style":2528},[584],[188,18384,2464],{"className":18385},[2532],[188,18387],{"className":18388,"style":2528},[584],[188,18390,18392,18395],{"className":18391},[234],[188,18393],{"className":18394,"style":3213},[238],[188,18396,507],{"className":18397},[243],[44,18399,18400,18314,18804,16266,18806,85],{},[188,18401,18403,18519],{"className":18402},[191],[188,18404,18406],{"className":18405},[195],[197,18407,18408],{"xmlns":199},[201,18409,18410,18516],{},[204,18411,18412,18414,18416,18418,18420,18422,18424,18426,18428,18430,18432,18434],{},[207,18413,9361],{},[207,18415,27],{},[211,18417,9366],{"stretchy":213},[505,18419,507],{},[211,18421,9371],{"stretchy":213},[211,18423,9366],{"stretchy":213},[505,18425,4869],{},[211,18427,9371],{"stretchy":213},[211,18429,2464],{},[207,18431,13222],{},[211,18433,925],{},[204,18435,18436,18438],{},[211,18437,13177],{"fence":230},[13179,18439,18440,18478],{"rowspacing":13181,"columnalign":13182,"columnspacing":13183},[13185,18441,18442],{},[13188,18443,18444],{},[13191,18445,18446],{"scriptlevel":8307,"displaystyle":213},[204,18447,18448,18450,18452,18454,18456,18458,18460,18462,18464,18466,18468,18470,18472,18474,18476],{},[207,18449,4755],{},[211,18451,2464],{},[505,18453,507],{},[211,18455,17718],{},[505,18457,8307],{},[211,18459,516],{},[505,18461,16418],{},[211,18463,516],{},[505,18465,13952],{},[211,18467,4758],{},[505,18469,934],{},[211,18471,4758],{},[505,18473,13939],{},[211,18475,2464],{},[505,18477,17861],{},[13185,18479,18480],{},[13188,18481,18482],{},[13191,18483,18484],{"scriptlevel":8307,"displaystyle":213},[204,18485,18486,18488,18490,18492,18494,18496,18498,18500,18502,18504,18506,18508,18510,18512,18514],{},[207,18487,4755],{},[211,18489,2464],{},[505,18491,934],{},[211,18493,17718],{},[505,18495,15992],{},[211,18497,516],{},[505,18499,8307],{},[211,18501,516],{},[505,18503,13952],{},[211,18505,4758],{},[505,18507,13977],{},[211,18509,4758],{},[505,18511,13939],{},[211,18513,2464],{},[505,18515,17782],{},[222,18517,18518],{"encoding":224},"dp[2][4] = \\min \\begin{cases} k=2: 0 + 180 + 10\\times 3\\times 5 = 330 \\\\ k=3: 360 + 0 + 10\\times 12\\times 5 = 960 \\end{cases}",[188,18520,18522,18561],{"className":18521,"ariaHidden":230},[229],[188,18523,18525,18528,18531,18534,18537,18540,18543,18546,18549,18552,18555,18558],{"className":18524},[234],[188,18526],{"className":18527,"style":239},[238],[188,18529,9361],{"className":18530},[243,244],[188,18532,27],{"className":18533},[243,244],[188,18535,9366],{"className":18536},[249],[188,18538,507],{"className":18539},[243],[188,18541,9371],{"className":18542},[256],[188,18544,9366],{"className":18545},[249],[188,18547,4869],{"className":18548},[243],[188,18550,9371],{"className":18551},[256],[188,18553],{"className":18554,"style":2528},[584],[188,18556,2464],{"className":18557},[2532],[188,18559],{"className":18560,"style":2528},[584],[188,18562,18564,18567,18570,18573],{"className":18563},[234],[188,18565],{"className":18566,"style":17913},[238],[188,18568,13222],{"className":18569},[951],[188,18571],{"className":18572,"style":1003},[584],[188,18574,18576,18582,18801],{"className":18575},[9697],[188,18577,18579],{"className":18578,"style":17927},[249,17926],[188,18580,13177],{"className":18581},[13386,17931],[188,18583,18585],{"className":18584},[243],[188,18586,18588],{"className":18587},[13179],[188,18589,18591],{"className":18590},[13489],[188,18592,18594,18793],{"className":18593},[549,966],[188,18595,18597,18790],{"className":18596},[553],[188,18598,18600,18695],{"className":18599,"style":17950},[557],[188,18601,18602,18605],{"style":17953},[188,18603],{"className":18604,"style":13506},[565],[188,18606,18608,18611,18614,18617,18620,18623,18626,18629,18632,18635,18638,18641,18644,18647,18650,18653,18656,18659,18662,18665,18668,18671,18674,18677,18680,18683,18686,18689,18692],{"className":18607},[243],[188,18609,4755],{"className":18610,"style":4807},[243,244],[188,18612],{"className":18613,"style":2528},[584],[188,18615,2464],{"className":18616},[2532],[188,18618],{"className":18619,"style":2528},[584],[188,18621,507],{"className":18622},[243],[188,18624],{"className":18625,"style":2528},[584],[188,18627,17718],{"className":18628},[2532],[188,18630],{"className":18631,"style":2528},[584],[188,18633,8307],{"className":18634},[243],[188,18636],{"className":18637,"style":585},[584],[188,18639,516],{"className":18640},[589],[188,18642],{"className":18643,"style":585},[584],[188,18645,16418],{"className":18646},[243],[188,18648],{"className":18649,"style":585},[584],[188,18651,516],{"className":18652},[589],[188,18654],{"className":18655,"style":585},[584],[188,18657,13952],{"className":18658},[243],[188,18660],{"className":18661,"style":585},[584],[188,18663,4758],{"className":18664},[589],[188,18666],{"className":18667,"style":585},[584],[188,18669,934],{"className":18670},[243],[188,18672],{"className":18673,"style":585},[584],[188,18675,4758],{"className":18676},[589],[188,18678],{"className":18679,"style":585},[584],[188,18681,13939],{"className":18682},[243],[188,18684],{"className":18685,"style":2528},[584],[188,18687,2464],{"className":18688},[2532],[188,18690],{"className":18691,"style":2528},[584],[188,18693,17861],{"className":18694},[243],[188,18696,18697,18700],{"style":18127},[188,18698],{"className":18699,"style":13506},[565],[188,18701,18703,18706,18709,18712,18715,18718,18721,18724,18727,18730,18733,18736,18739,18742,18745,18748,18751,18754,18757,18760,18763,18766,18769,18772,18775,18778,18781,18784,18787],{"className":18702},[243],[188,18704,4755],{"className":18705,"style":4807},[243,244],[188,18707],{"className":18708,"style":2528},[584],[188,18710,2464],{"className":18711},[2532],[188,18713],{"className":18714,"style":2528},[584],[188,18716,934],{"className":18717},[243],[188,18719],{"className":18720,"style":2528},[584],[188,18722,17718],{"className":18723},[2532],[188,18725],{"className":18726,"style":2528},[584],[188,18728,15992],{"className":18729},[243],[188,18731],{"className":18732,"style":585},[584],[188,18734,516],{"className":18735},[589],[188,18737],{"className":18738,"style":585},[584],[188,18740,8307],{"className":18741},[243],[188,18743],{"className":18744,"style":585},[584],[188,18746,516],{"className":18747},[589],[188,18749],{"className":18750,"style":585},[584],[188,18752,13952],{"className":18753},[243],[188,18755],{"className":18756,"style":585},[584],[188,18758,4758],{"className":18759},[589],[188,18761],{"className":18762,"style":585},[584],[188,18764,13977],{"className":18765},[243],[188,18767],{"className":18768,"style":585},[584],[188,18770,4758],{"className":18771},[589],[188,18773],{"className":18774,"style":585},[584],[188,18776,13939],{"className":18777},[243],[188,18779],{"className":18780,"style":2528},[584],[188,18782,2464],{"className":18783},[2532],[188,18785],{"className":18786,"style":2528},[584],[188,18788,17782],{"className":18789},[243],[188,18791,990],{"className":18792},[989],[188,18794,18796],{"className":18795},[553],[188,18797,18799],{"className":18798,"style":18308},[557],[188,18800],{},[188,18802],{"className":18803},[256,12583],[36,18805,17861],{},[188,18807,18809,18839],{"className":18808},[191],[188,18810,18812],{"className":18811},[195],[197,18813,18814],{"xmlns":199},[201,18815,18816,18836],{},[204,18817,18818,18820,18822,18824,18826,18828,18830,18832,18834],{},[207,18819,14525],{},[211,18821,9366],{"stretchy":213},[505,18823,507],{},[211,18825,9371],{"stretchy":213},[211,18827,9366],{"stretchy":213},[505,18829,4869],{},[211,18831,9371],{"stretchy":213},[211,18833,2464],{},[505,18835,507],{},[222,18837,18838],{"encoding":224},"s[2][4]=2",[188,18840,18842,18878],{"className":18841,"ariaHidden":230},[229],[188,18843,18845,18848,18851,18854,18857,18860,18863,18866,18869,18872,18875],{"className":18844},[234],[188,18846],{"className":18847,"style":239},[238],[188,18849,14525],{"className":18850},[243,244],[188,18852,9366],{"className":18853},[249],[188,18855,507],{"className":18856},[243],[188,18858,9371],{"className":18859},[256],[188,18861,9366],{"className":18862},[249],[188,18864,4869],{"className":18865},[243],[188,18867,9371],{"className":18868},[256],[188,18870],{"className":18871,"style":2528},[584],[188,18873,2464],{"className":18874},[2532],[188,18876],{"className":18877,"style":2528},[584],[188,18879,18881,18884],{"className":18880},[234],[188,18882],{"className":18883,"style":3213},[238],[188,18885,507],{"className":18886},[243],[44,18888,18889,18314,19295,16266,19297,85],{},[188,18890,18892,19010],{"className":18891},[191],[188,18893,18895],{"className":18894},[195],[197,18896,18897],{"xmlns":199},[201,18898,18899,19007],{},[204,18900,18901,18903,18905,18907,18909,18911,18913,18915,18917,18919,18921,18923],{},[207,18902,9361],{},[207,18904,27],{},[211,18906,9366],{"stretchy":213},[505,18908,934],{},[211,18910,9371],{"stretchy":213},[211,18912,9366],{"stretchy":213},[505,18914,13939],{},[211,18916,9371],{"stretchy":213},[211,18918,2464],{},[207,18920,13222],{},[211,18922,925],{},[204,18924,18925,18927],{},[211,18926,13177],{"fence":230},[13179,18928,18929,18968],{"rowspacing":13181,"columnalign":13182,"columnspacing":13183},[13185,18930,18931],{},[13188,18932,18933],{},[13191,18934,18935],{"scriptlevel":8307,"displaystyle":213},[204,18936,18937,18939,18941,18943,18945,18947,18949,18951,18953,18955,18957,18959,18961,18963,18965],{},[207,18938,4755],{},[211,18940,2464],{},[505,18942,934],{},[211,18944,17718],{},[505,18946,8307],{},[211,18948,516],{},[505,18950,16843],{},[211,18952,516],{},[505,18954,934],{},[211,18956,4758],{},[505,18958,13977],{},[211,18960,4758],{},[505,18962,14002],{},[211,18964,2464],{},[505,18966,18967],{},"4800",[13185,18969,18970],{},[13188,18971,18972],{},[13191,18973,18974],{"scriptlevel":8307,"displaystyle":213},[204,18975,18976,18978,18980,18982,18984,18986,18988,18990,18992,18994,18996,18998,19000,19002,19004],{},[207,18977,4755],{},[211,18979,2464],{},[505,18981,4869],{},[211,18983,17718],{},[505,18985,16418],{},[211,18987,516],{},[505,18989,8307],{},[211,18991,516],{},[505,18993,934],{},[211,18995,4758],{},[505,18997,13939],{},[211,18999,4758],{},[505,19001,14002],{},[211,19003,2464],{},[505,19005,19006],{},"930",[222,19008,19009],{"encoding":224},"dp[3][5] = \\min \\begin{cases} k=3: 0 + 3000 + 3\\times 12\\times 50 = 4800 \\\\ k=4: 180 + 0 + 3\\times 5\\times 50 = 930 \\end{cases}",[188,19011,19013,19052],{"className":19012,"ariaHidden":230},[229],[188,19014,19016,19019,19022,19025,19028,19031,19034,19037,19040,19043,19046,19049],{"className":19015},[234],[188,19017],{"className":19018,"style":239},[238],[188,19020,9361],{"className":19021},[243,244],[188,19023,27],{"className":19024},[243,244],[188,19026,9366],{"className":19027},[249],[188,19029,934],{"className":19030},[243],[188,19032,9371],{"className":19033},[256],[188,19035,9366],{"className":19036},[249],[188,19038,13939],{"className":19039},[243],[188,19041,9371],{"className":19042},[256],[188,19044],{"className":19045,"style":2528},[584],[188,19047,2464],{"className":19048},[2532],[188,19050],{"className":19051,"style":2528},[584],[188,19053,19055,19058,19061,19064],{"className":19054},[234],[188,19056],{"className":19057,"style":17913},[238],[188,19059,13222],{"className":19060},[951],[188,19062],{"className":19063,"style":1003},[584],[188,19065,19067,19073,19292],{"className":19066},[9697],[188,19068,19070],{"className":19069,"style":17927},[249,17926],[188,19071,13177],{"className":19072},[13386,17931],[188,19074,19076],{"className":19075},[243],[188,19077,19079],{"className":19078},[13179],[188,19080,19082],{"className":19081},[13489],[188,19083,19085,19284],{"className":19084},[549,966],[188,19086,19088,19281],{"className":19087},[553],[188,19089,19091,19186],{"className":19090,"style":17950},[557],[188,19092,19093,19096],{"style":17953},[188,19094],{"className":19095,"style":13506},[565],[188,19097,19099,19102,19105,19108,19111,19114,19117,19120,19123,19126,19129,19132,19135,19138,19141,19144,19147,19150,19153,19156,19159,19162,19165,19168,19171,19174,19177,19180,19183],{"className":19098},[243],[188,19100,4755],{"className":19101,"style":4807},[243,244],[188,19103],{"className":19104,"style":2528},[584],[188,19106,2464],{"className":19107},[2532],[188,19109],{"className":19110,"style":2528},[584],[188,19112,934],{"className":19113},[243],[188,19115],{"className":19116,"style":2528},[584],[188,19118,17718],{"className":19119},[2532],[188,19121],{"className":19122,"style":2528},[584],[188,19124,8307],{"className":19125},[243],[188,19127],{"className":19128,"style":585},[584],[188,19130,516],{"className":19131},[589],[188,19133],{"className":19134,"style":585},[584],[188,19136,16843],{"className":19137},[243],[188,19139],{"className":19140,"style":585},[584],[188,19142,516],{"className":19143},[589],[188,19145],{"className":19146,"style":585},[584],[188,19148,934],{"className":19149},[243],[188,19151],{"className":19152,"style":585},[584],[188,19154,4758],{"className":19155},[589],[188,19157],{"className":19158,"style":585},[584],[188,19160,13977],{"className":19161},[243],[188,19163],{"className":19164,"style":585},[584],[188,19166,4758],{"className":19167},[589],[188,19169],{"className":19170,"style":585},[584],[188,19172,14002],{"className":19173},[243],[188,19175],{"className":19176,"style":2528},[584],[188,19178,2464],{"className":19179},[2532],[188,19181],{"className":19182,"style":2528},[584],[188,19184,18967],{"className":19185},[243],[188,19187,19188,19191],{"style":18127},[188,19189],{"className":19190,"style":13506},[565],[188,19192,19194,19197,19200,19203,19206,19209,19212,19215,19218,19221,19224,19227,19230,19233,19236,19239,19242,19245,19248,19251,19254,19257,19260,19263,19266,19269,19272,19275,19278],{"className":19193},[243],[188,19195,4755],{"className":19196,"style":4807},[243,244],[188,19198],{"className":19199,"style":2528},[584],[188,19201,2464],{"className":19202},[2532],[188,19204],{"className":19205,"style":2528},[584],[188,19207,4869],{"className":19208},[243],[188,19210],{"className":19211,"style":2528},[584],[188,19213,17718],{"className":19214},[2532],[188,19216],{"className":19217,"style":2528},[584],[188,19219,16418],{"className":19220},[243],[188,19222],{"className":19223,"style":585},[584],[188,19225,516],{"className":19226},[589],[188,19228],{"className":19229,"style":585},[584],[188,19231,8307],{"className":19232},[243],[188,19234],{"className":19235,"style":585},[584],[188,19237,516],{"className":19238},[589],[188,19240],{"className":19241,"style":585},[584],[188,19243,934],{"className":19244},[243],[188,19246],{"className":19247,"style":585},[584],[188,19249,4758],{"className":19250},[589],[188,19252],{"className":19253,"style":585},[584],[188,19255,13939],{"className":19256},[243],[188,19258],{"className":19259,"style":585},[584],[188,19261,4758],{"className":19262},[589],[188,19264],{"className":19265,"style":585},[584],[188,19267,14002],{"className":19268},[243],[188,19270],{"className":19271,"style":2528},[584],[188,19273,2464],{"className":19274},[2532],[188,19276],{"className":19277,"style":2528},[584],[188,19279,19006],{"className":19280},[243],[188,19282,990],{"className":19283},[989],[188,19285,19287],{"className":19286},[553],[188,19288,19290],{"className":19289,"style":18308},[557],[188,19291],{},[188,19293],{"className":19294},[256,12583],[36,19296,19006],{},[188,19298,19300,19330],{"className":19299},[191],[188,19301,19303],{"className":19302},[195],[197,19304,19305],{"xmlns":199},[201,19306,19307,19327],{},[204,19308,19309,19311,19313,19315,19317,19319,19321,19323,19325],{},[207,19310,14525],{},[211,19312,9366],{"stretchy":213},[505,19314,934],{},[211,19316,9371],{"stretchy":213},[211,19318,9366],{"stretchy":213},[505,19320,13939],{},[211,19322,9371],{"stretchy":213},[211,19324,2464],{},[505,19326,4869],{},[222,19328,19329],{"encoding":224},"s[3][5]=4",[188,19331,19333,19369],{"className":19332,"ariaHidden":230},[229],[188,19334,19336,19339,19342,19345,19348,19351,19354,19357,19360,19363,19366],{"className":19335},[234],[188,19337],{"className":19338,"style":239},[238],[188,19340,14525],{"className":19341},[243,244],[188,19343,9366],{"className":19344},[249],[188,19346,934],{"className":19347},[243],[188,19349,9371],{"className":19350},[256],[188,19352,9366],{"className":19353},[249],[188,19355,13939],{"className":19356},[243],[188,19358,9371],{"className":19359},[256],[188,19361],{"className":19362,"style":2528},[584],[188,19364,2464],{"className":19365},[2532],[188,19367],{"className":19368,"style":2528},[584],[188,19370,19372,19375],{"className":19371},[234],[188,19373],{"className":19374,"style":3213},[238],[188,19376,4869],{"className":19377},[243],[44,19379,19380,18314,19786,16266,19788,85],{},[188,19381,19383,19501],{"className":19382},[191],[188,19384,19386],{"className":19385},[195],[197,19387,19388],{"xmlns":199},[201,19389,19390,19498],{},[204,19391,19392,19394,19396,19398,19400,19402,19404,19406,19408,19410,19412,19414],{},[207,19393,9361],{},[207,19395,27],{},[211,19397,9366],{"stretchy":213},[505,19399,4869],{},[211,19401,9371],{"stretchy":213},[211,19403,9366],{"stretchy":213},[505,19405,14011],{},[211,19407,9371],{"stretchy":213},[211,19409,2464],{},[207,19411,13222],{},[211,19413,925],{},[204,19415,19416,19418],{},[211,19417,13177],{"fence":230},[13179,19419,19420,19459],{"rowspacing":13181,"columnalign":13182,"columnspacing":13183},[13185,19421,19422],{},[13188,19423,19424],{},[13191,19425,19426],{"scriptlevel":8307,"displaystyle":213},[204,19427,19428,19430,19432,19434,19436,19438,19440,19442,19444,19446,19448,19450,19452,19454,19456],{},[207,19429,4755],{},[211,19431,2464],{},[505,19433,4869],{},[211,19435,17718],{},[505,19437,8307],{},[211,19439,516],{},[505,19441,17268],{},[211,19443,516],{},[505,19445,13977],{},[211,19447,4758],{},[505,19449,13939],{},[211,19451,4758],{},[505,19453,14011],{},[211,19455,2464],{},[505,19457,19458],{},"1860",[13185,19460,19461],{},[13188,19462,19463],{},[13191,19464,19465],{"scriptlevel":8307,"displaystyle":213},[204,19466,19467,19469,19471,19473,19475,19477,19479,19481,19483,19485,19487,19489,19491,19493,19495],{},[207,19468,4755],{},[211,19470,2464],{},[505,19472,13939],{},[211,19474,17718],{},[505,19476,16843],{},[211,19478,516],{},[505,19480,8307],{},[211,19482,516],{},[505,19484,13977],{},[211,19486,4758],{},[505,19488,14002],{},[211,19490,4758],{},[505,19492,14011],{},[211,19494,2464],{},[505,19496,19497],{},"6600",[222,19499,19500],{"encoding":224},"dp[4][6] = \\min \\begin{cases} k=4: 0 + 1500 + 12\\times 5\\times 6 = 1860 \\\\ k=5: 3000 + 0 + 12\\times 50\\times 6 = 6600 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L = 4：",[68,19875,19876,20588,21285],{},[44,19877,19878,18314,20505,16266,20507,85],{},[188,19879,19881,20038],{"className":19880},[191],[188,19882,19884],{"className":19883},[195],[197,19885,19886],{"xmlns":199},[201,19887,19888,20035],{},[204,19889,19890,19892,19894,19896,19898,19900,19902,19904,19906,19908,19910,19912],{},[207,19891,9361],{},[207,19893,27],{},[211,19895,9366],{"stretchy":213},[505,19897,4948],{},[211,19899,9371],{"stretchy":213},[211,19901,9366],{"stretchy":213},[505,19903,4869],{},[211,19905,9371],{"stretchy":213},[211,19907,2464],{},[207,19909,13222],{},[211,19911,925],{},[204,19913,19914,19916],{},[211,19915,13177],{"fence":230},[13179,19917,19918,19957,19996],{"rowspacing":13181,"columnalign":13182,"columnspacing":13183},[13185,19919,19920],{},[13188,19921,19922],{},[13191,19923,19924],{"scriptlevel":8307,"displaystyle":213},[204,19925,19926,19928,19930,19932,19934,19936,19938,19940,19942,19944,19946,19948,19950,19952,19954],{},[207,19927,4755],{},[211,19929,2464],{},[505,19931,4948],{},[211,19933,17718],{},[505,19935,8307],{},[211,19937,516],{},[505,19939,17861],{},[211,19941,516],{},[505,19943,13939],{},[211,19945,4758],{},[505,19947,13952],{},[211,19949,4758],{},[505,19951,13939],{},[211,19953,2464],{},[505,19955,19956],{},"580",[13185,19958,19959],{},[13188,19960,19961],{},[13191,19962,19963],{"scriptlevel":8307,"displaystyle":213},[204,19964,19965,19967,19969,19971,19973,19975,19977,19979,19981,19983,19985,19987,19989,19991,19993],{},[207,19966,4755],{},[211,19968,2464],{},[505,19970,507],{},[211,19972,17718],{},[505,19974,15565],{},[211,19976,516],{},[505,19978,16418],{},[211,19980,516],{},[505,19982,13939],{},[211,19984,4758],{},[505,19986,934],{},[211,19988,4758],{},[505,19990,13939],{},[211,19992,2464],{},[505,19994,19995],{},"405",[13185,19997,19998],{},[13188,19999,20000],{},[13191,20001,20002],{"scriptlevel":8307,"displaystyle":213},[204,20003,20004,20006,20008,20010,20012,20014,20016,20018,20020,20022,20024,20026,20028,20030,20032],{},[207,20005,4755],{},[211,20007,2464],{},[505,20009,934],{},[211,20011,17718],{},[505,20013,17861],{},[211,20015,516],{},[505,20017,8307],{},[211,20019,516],{},[505,20021,13939],{},[211,20023,4758],{},[505,20025,13977],{},[211,20027,4758],{},[505,20029,13939],{},[211,20031,2464],{},[505,20033,20034],{},"630",[222,20036,20037],{"encoding":224},"dp[1][4] = \\min \\begin{cases} k=1: 0 + 330 + 5\\times 10\\times 5 = 580 \\\\ k=2: 150 + 180 + 5\\times 3\\times 5 = 405 \\\\ k=3: 330 + 0 + 5\\times 12\\times 5 = 630 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= \\min \\begin{cases} k=2: 0 + 930 + 10\\times 3\\times 50 = 2430 \\\\ k=3: 360 + 3000 + 10\\times 12\\times 50 = 9360 \\\\ k=4: 330 + 0 + 10\\times 5\\times 50 = 2830 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= \\min \\begin{cases} k=3: 0 + 1860 + 3\\times 12\\times 6 = 2076 \\\\ k=4: 180 + 1500 + 3\\times 5\\times 6 = 1770 \\\\ k=5: 930 + 0 + 3\\times 50\\times 6 = 1830 \\end{cases}",[188,21448,21450,21489],{"className":21449,"ariaHidden":230},[229],[188,21451,21453,21456,21459,21462,21465,21468,21471,21474,21477,21480,21483,21486],{"className":21452},[234],[188,21454],{"className":21455,"style":239},[238],[188,21457,9361],{"className":21458},[243,244],[188,21460,27],{"className":21461},[243,244],[188,21463,9366],{"className":21464},[249],[188,21466,934],{"className":21467},[243],[188,21469,9371],{"className":21470},[256],[188,21472,9366],{"className":21473},[249],[188,21475,14011],{"className":21476},[243],[188,21478,9371],{"className":21479},[256],[188,21481],{"className":21482,"style":2528},[584],[188,21484,2464],{"className":21485},[2532],[188,21487],{"className":21488,"style":2528},[584],[188,21490,21492,21495,21498,21501],{"className":21491},[234],[188,21493],{"className":21494,"style":20086},[238],[188,21496,13222],{"className":21497},[951],[188,21499],{"className":21500,"style":1003},[584],[188,21502,21504,21582,21896],{"className":21503},[9697],[188,21505,21507],{"className":21506},[249],[188,21508,21510],{"className":21509},[13386,13387],[188,21511,21513,21574],{"className":21512},[549,966],[188,21514,21516,21571],{"className":21515},[553],[188,21517,21519,21529,21540,21550,21561],{"className":21518,"style":20111},[557],[188,21520,21521,21524],{"style":20114},[188,21522],{"className":21523,"style":13404},[565],[188,21525,21527],{"className":21526},[13408,13409],[188,21528,13412],{},[188,21530,21531,21534],{"style":20125},[188,21532],{"className":21533,"style":13404},[565],[188,21535,21536],{"style":20131},[7023,21537,21538],{"xmlns":7025,"width":13424,"height":20134,"style":13426,"viewBox":20135,"preserveAspectRatio":13428},[7031,21539],{"d":20138},[188,21541,21542,21545],{"style":13434},[188,21543],{"className":21544,"style":13404},[565],[188,21546,21548],{"className":21547},[13408,13409],[188,21549,13443],{},[188,21551,21552,21555],{"style":13446},[188,21553],{"className":21554,"style":13404},[565],[188,21556,21557],{"style":20131},[7023,21558,21559],{"xmlns":7025,"width":13424,"height":20134,"style":13426,"viewBox":20135,"preserveAspectRatio":13428},[7031,21560],{"d":20138},[188,21562,21563,21566],{"style":20162},[188,21564],{"className":21565,"style":13404},[565],[188,21567,21569],{"className":21568},[13408,13409],[188,21570,13467],{},[188,21572,990],{"className":21573},[989],[188,21575,21577],{"className":21576},[553],[188,21578,21580],{"className":21579,"style":20180},[557],[188,21581],{},[188,21583,21585],{"className":21584},[243],[188,21586,21588],{"className":21587},[13179],[188,21589,21591],{"className":21590},[13489],[188,21592,21594,21888],{"className":21593},[549,966],[188,21595,21597,21885],{"className":21596},[553],[188,21598,21600,21695,21790],{"className":21599,"style":20201},[557],[188,21601,21602,21605],{"style":20204},[188,21603],{"className":21604,"style":13506},[565],[188,21606,21608,21611,21614,21617,21620,21623,21626,21629,21632,21635,21638,21641,21644,21647,21650,21653,21656,21659,21662,21665,21668,21671,21674,21677,21680,21683,21686,21689,21692],{"className":21607},[243],[188,21609,4755],{"className":21610,"style":4807},[243,244],[188,21612],{"className":21613,"style":2528},[584],[188,21615,2464],{"className":21616},[2532],[188,21618],{"className":21619,"style":2528},[584],[188,21621,934],{"className":21622},[243],[188,21624],{"className":21625,"style":2528},[584],[188,21627,17718],{"className":21628},[2532],[188,21630],{"className":21631,"style":2528},[584],[188,21633,8307],{"className":21634},[243],[188,21636],{"className":21637,"style":585},[584],[188,21639,516],{"className":21640},[589],[188,21642],{"className":21643,"style":585},[584],[188,21645,19458],{"className":21646},[243],[188,21648],{"className":21649,"style":585},[584],[188,21651,516],{"className":21652},[589],[188,21654],{"className":21655,"style":585},[584],[188,21657,934],{"className":21658},[243],[188,21660],{"className":21661,"style":585},[584],[188,21663,4758],{"className":21664},[589],[188,21666],{"className":21667,"style":585},[584],[188,21669,13977],{"className":21670},[243],[188,21672],{"className":21673,"style":585},[584],[188,21675,4758],{"className":21676},[589],[188,21678],{"className":21679,"style":585},[584],[188,21681,14011],{"className":21682},[243],[188,21684],{"className":21685,"style":2528},[584],[188,21687,2464],{"className":21688},[2532],[188,21690],{"className":21691,"style":2528},[584],[188,21693,21365],{"className":21694},[243],[188,21696,21697,21700],{"style":20300},[188,21698],{"className":21699,"style":13506},[565],[188,21701,21703,21706,21709,21712,21715,21718,21721,21724,21727,21730,21733,21736,21739,21742,21745,21748,21751,21754,21757,21760,21763,21766,21769,21772,21775,21778,21781,21784,21787],{"className":21702},[243],[188,21704,4755],{"className":21705,"style":4807},[243,244],[188,21707],{"className":21708,"style":2528},[584],[188,21710,2464],{"className":21711},[2532],[188,21713],{"className":21714,"style":2528},[584],[188,21716,4869],{"cl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L = 5：",[68,21988,21989,22708],{},[44,21990,21991,18314,22625,16266,22627,85],{},[188,21992,21994,22160],{"className":21993},[191],[188,21995,21997],{"className":21996},[195],[197,21998,21999],{"xmlns":199},[201,22000,22001,22157],{},[204,22002,22003,22005,22007,22009,22011,22013,22015,22017,22019,22021,22023,22025],{},[207,22004,9361],{},[207,22006,27],{},[211,22008,9366],{"stretchy":213},[505,22010,4948],{},[211,22012,9371],{"stretchy":213},[211,22014,9366],{"stretchy":213},[505,22016,13939],{},[211,22018,9371],{"stretchy":213},[211,22020,2464],{},[207,22022,13222],{},[211,22024,925],{},[204,22026,22027,22029],{},[211,22028,13177],{"fence":230},[13179,22030,22031,22063,22094,22125],{"rowspacing":13181,"columnalign":13182,"columnspacing":13183},[13185,22032,22033],{},[13188,22034,22035],{},[13191,22036,22037],{"scriptlevel":8307,"displaystyle":213},[204,22038,22039,22041,22043,22045,22047,22049,22051,22053,22055,22058,22060],{},[207,22040,4755],{},[211,22042,2464],{},[505,22044,4948],{},[211,22046,17718],{},[505,22048,8307],{},[211,22050,516],{},[505,22052,20668],{},[211,22054,516],{},[505,22056,22057],{},"2500",[211,22059,2464],{},[505,22061,22062],{},"4930",[13185,22064,22065],{},[13188,22066,22067],{},[13191,22068,22069],{"scriptlevel":8307,"displaystyle":213},[204,22070,22071,22073,22075,22077,22079,22081,22083,22085,22087,22090,22092],{},[207,22072,4755],{},[211,22074,2464],{},[505,22076,507],{},[211,22078,17718],{},[505,22080,15565],{},[211,22082,516],{},[505,22084,19006],{},[211,22086,516],{},[505,22088,22089],{},"750",[211,22091,2464],{},[505,22093,21443],{},[13185,22095,22096],{},[13188,22097,22098],{},[13191,22099,22100],{"scriptlevel":8307,"displaystyle":213},[204,22101,22102,22104,22106,22108,22110,22112,22114,22116,22118,22120,22122],{},[207,22103,4755],{},[211,22105,2464],{},[505,22107,934],{},[211,22109,17718],{},[505,22111,17861],{},[211,22113,516],{},[505,22115,16843],{},[211,22117,516],{},[505,22119,16843],{},[211,22121,2464],{},[505,22123,22124],{},"6330",[13185,22126,22127],{},[13188,22128,22129],{},[13191,22130,22131],{"scriptlevel":8307,"displaystyle":213},[204,22132,22133,22135,22137,22139,22141,22143,22145,22147,22149,22152,22154],{},[207,22134,4755],{},[211,22136,2464],{},[505,22138,4869],{},[211,22140,17718],{},[505,22142,19995],{},[211,22144,516],{},[505,22146,8307],{},[211,22148,516],{},[505,22150,22151],{},"1250",[211,22153,2464],{},[505,22155,22156],{},"1655",[222,22158,22159],{"encoding":224},"dp[1][5] = \\min \\begin{cases} k=1: 0 + 2430 + 2500 = 4930 \\\\ k=2: 150 + 930 + 750 = 1830 \\\\ k=3: 330 + 3000 + 3000 = 6330 \\\\ k=4: 405 + 0 + 1250 = 1655 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= \\min \\begin{cases} k=2: 0 + 1770 + 180 = 1950 \\\\ k=3: 360 + 1860 + 720 = 2940 \\\\ k=4: 330 + 1500 + 300 = 2130 \\\\ k=5: 2430 + 0 + 3000 = 5430 \\end{cases}",[188,22880,22882,22921],{"className":22881,"ariaHidden":230},[229],[188,22883,22885,22888,22891,22894,22897,22900,22903,22906,22909,22912,22915,22918],{"className":22884},[234],[188,22886],{"className":22887,"style":239},[238],[188,22889,9361],{"className":22890},[243,244],[188,22892,27],{"className":22893},[243,244],[188,22895,9366],{"className":22896},[249],[188,22898,507],{"className":22899},[243],[188,22901,9371],{"className":22902},[256],[188,22904,9366],{"className":22905},[249],[188,22907,14011],{"className":22908},[243],[188,22910,9371],{"className":22911},[256],[188,22913],{"className":22914,"style":2528},[584],[188,22916,2464],{"className":22917},[2532],[188,22919],{"className":22920,"style":2528},[584],[188,22922,22924,22927,22930,22933],{"className":22923},[234],[188,22925],{"className":22926,"style":22208},[238],[188,22928,13222],{"className":22929},[951],[188,22931],{"className":22932,"style":1003},[584],[188,22934,22936,23014,23327],{"className":22935},[9697],[188,22937,22939],{"className":22938},[249],[188,22940,22942],{"className":22941},[13386,13387],[188,22943,22945,23006],{"className":22944},[549,966],[188,22946,22948,23003],{"className":22947},[553],[188,22949,22951,22961,22972,22982,22993],{"className":22950,"style":22233},[557],[188,22952,22953,22956],{"style":22236},[188,22954],{"className":22955,"style":13404},[565],[188,22957,22959],{"className":22958},[13408,13409],[188,22960,13412],{},[188,22962,22963,22966],{"style":22247},[188,22964],{"className":22965,"style":13404},[565],[188,22967,22968],{"style":22253},[7023,22969,22970],{"xmlns":7025,"width":13424,"height":22256,"style":13426,"viewBox":22257,"preserveAspectRatio":13428},[7031,22971],{"d":22260},[188,22973,22974,22977],{"style":13434},[188,22975],{"className":22976,"style":13404},[565],[188,22978,22980],{"className":22979},[13408,13409],[188,22981,13443],{},[188,22983,22984,22987],{"style":13446},[188,22985],{"className":22986,"style":13404},[565],[188,22988,22989],{"style":22253},[7023,22990,22991],{"xmlns":7025,"width":13424,"height":22256,"style":13426,"viewBox":22257,"preserveAspectRatio":13428},[7031,22992],{"d":22260},[188,22994,22995,22998],{"style":22284},[188,22996],{"className":22997,"style":13404},[565],[188,22999,23001],{"className":23000},[13408,13409],[188,23002,13467],{},[188,23004,990],{"className":23005},[989],[188,23007,23009],{"className":23008},[553],[188,23010,23012],{"className":23011,"style":22302},[557],[188,23013],{},[188,23015,23017],{"className":23016},[243],[188,23018,23020],{"className":23019},[13179],[188,23021,23023],{"className":23022},[13489],[188,23024,23026,23319],{"className":23025},[549,966],[188,23027,23029,23316],{"className":23028},[553],[188,23030,23032,23103,23174,23245],{"className":23031,"style":22323},[557],[188,23033,23034,23037],{"style":22326},[188,23035],{"className":23036,"style":13506},[565],[188,23038,23040,23043,23046,23049,23052,23055,23058,23061,23064,23067,23070,23073,23076,23079,23082,23085,23088,23091,23094,23097,23100],{"className":23039},[243],[188,23041,4755],{"className":23042,"style":4807},[243,244],[188,23044],{"className":23045,"style":2528},[584],[188,23047,2464],{"className":23048},[2532],[188,23050],{"className":23051,"style":2528},[584],[188,23053,507],{"className":23054},[243],[188,23056],{"className":23057,"style":2528},[584],[188,23059,17718],{"className":23060},[2532],[188,23062],{"className":23063,"style":2528},[584],[188,23065,8307],{"className":23066},[243],[188,23068],{"className":23069,"style":585},[584],[188,23071,516],{"className":23072},[589],[188,23074],{"className":23075,"style":585},[584],[188,23077,21404],{"className":23078},[243],[188,23080],{"className":23081,"style":585},[584],[188,23083,516],{"className":23084},[589],[188,23086],{"className":23087,"style":585},[584],[188,23089,16418],{"className":23090},[243],[188,23092],{"className":23093,"style":2528},[584],[188,23095,2464],{"className":23096},[2532],[188,23098],{"className":23099,"style":2528},[584],[188,23101,22780],{"className":23102},[243],[188,23104,23105,23108],{"style":17953},[188,23106],{"className":23107,"style":13506},[565],[188,23109,23111,23114,23117,23120,23123,23126,23129,23132,23135,23138,23141,23144,23147,23150,23153,23156,23159,23162,23165,23168,23171],{"className":23110},[243],[188,23112,4755],{"className":23113,"style":4807},[243,244],[188,23115],{"className":23116,"style":2528},[584],[188,23118,2464],{"className":23119},[2532],[188,23121],{"className":23122,"style":2528},[584],[188,23124,934],{"className":23125},[243],[188,23127],{"className":23128,"style":2528},[584],[188,23130,17718],{"className":23131},[2532],[188,23133],{"className":23134,"style":2528},[584],[188,23136,15992],{"className":23137},[243],[188,23139],{"className":23140,"style":585},[584],[188,23142,516],{"className":23143},[589],[188,23145],{"className":23146,"style":585},[584],[188,23148,19458],{"className":23149},[243],[188,23151],{"className":23152,"style":585},[584],[188,23154,516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L = 6（全局最终解）：",[68,23419,23420],{},[44,23421,23422,18314,24317,16266,24319,85],{},[188,23423,23425,23660],{"className":23424},[191],[188,23426,23428],{"className":23427},[195],[197,23429,23430],{"xmlns":199},[201,23431,23432,23657],{},[204,23433,23434,23436,23438,23440,23442,23444,23446,23448,23450,23452,23454,23456],{},[207,23435,9361],{},[207,23437,27],{},[211,23439,9366],{"stretchy":213},[505,23441,4948],{},[211,23443,9371],{"stretchy":213},[211,23445,9366],{"stretchy":213},[505,23447,14011],{},[211,23449,9371],{"stretchy":213},[211,23451,2464],{},[207,23453,13222],{},[211,23455,925],{},[204,23457,23458,23460],{},[211,23459,13177],{"fence":230},[13179,23461,23462,23501,23540,23579,23618],{"rowspacing":13181,"columnalign":13182,"columnspacing":13183},[13185,23463,23464],{},[13188,23465,23466],{},[13191,23467,23468],{"scriptlevel":8307,"displaystyle":213},[204,23469,23470,23472,23474,23476,23478,23480,23482,23484,23486,23488,23490,23492,23494,23496,23498],{},[207,23471,4755],{},[211,23473,2464],{},[505,23475,4948],{},[211,23477,17718],{},[505,23479,8307],{},[211,23481,516],{},[505,23483,22780],{},[211,23485,516],{},[505,23487,13939],{},[211,23489,4758],{},[505,23491,13952],{},[211,23493,4758],{},[505,23495,14011],{},[211,23497,2464],{},[505,23499,23500],{},"2250",[13185,23502,23503],{},[13188,23504,23505],{},[13191,23506,23507],{"scriptlevel":8307,"displaystyle":213},[204,23508,23509,23511,23513,23515,23517,23519,23521,23523,23525,23527,23529,23531,23533,23535,23537],{},[207,23510,4755],{},[211,23512,2464],{},[505,23514,507],{},[211,23516,17718],{},[505,23518,15565],{},[211,23520,516],{},[505,23522,21404],{},[211,23524,516],{},[505,23526,13939],{},[211,23528,4758],{},[505,23530,934],{},[211,23532,4758],{},[505,23534,14011],{},[211,23536,2464],{},[505,23538,23539],{},"2010",[13185,23541,23542],{},[13188,23543,23544],{},[13191,23545,23546],{"scriptlevel":8307,"displaystyle":213},[204,23547,23548,23550,23552,23554,23556,23558,23560,23562,23564,23566,23568,23570,23572,23574,23576],{},[207,23549,4755],{},[211,23551,2464],{},[505,23553,934],{},[211,23555,17718],{},[505,23557,17861],{},[211,23559,516],{},[505,23561,19458],{},[211,23563,516],{},[505,23565,13939],{},[211,23567,4758],{},[505,23569,13977],{},[211,23571,4758],{},[505,23573,14011],{},[211,23575,2464],{},[505,23577,23578],{},"2550",[13185,23580,23581],{},[13188,23582,23583],{},[13191,23584,23585],{"scriptlevel":8307,"displaystyle":213},[204,23586,23587,23589,23591,23593,23595,23597,23599,23601,23603,23605,23607,23609,23611,23613,23615],{},[207,23588,4755],{},[211,23590,2464],{},[505,23592,4869],{},[211,23594,17718],{},[505,23596,19995],{},[211,23598,516],{},[505,23600,17268],{},[211,23602,516],{},[505,23604,13939],{},[211,23606,4758],{},[505,23608,13939],{},[211,23610,4758],{},[505,23612,14011],{},[211,23614,2464],{},[505,23616,23617],{},"2055",[13185,23619,23620],{},[13188,23621,23622],{},[13191,23623,23624],{"scriptlevel":8307,"displaystyle":213},[204,23625,23626,23628,23630,23632,23634,23636,23638,23640,23642,23644,23646,23648,23650,23652,23654],{},[207,23627,4755],{},[211,23629,2464],{},[505,23631,13939],{},[211,23633,17718],{},[505,23635,22156],{},[211,23637,516],{},[505,23639,8307],{},[211,23641,516],{},[505,23643,13939],{},[211,23645,4758],{},[505,23647,14002],{},[211,23649,4758],{},[505,23651,14011],{},[211,23653,2464],{},[505,23655,23656],{},"3155",[222,23658,23659],{"encoding":224},"dp[1][6] = \\min \\begin{cases} k=1: 0 + 1950 + 5\\times 10\\times 6 = 2250 \\\\ k=2: 150 + 1770 + 5\\times 3\\times 6 = 2010 \\\\ k=3: 330 + 1860 + 5\\times 12\\times 6 = 2550 \\\\ k=4: 405 + 1500 + 5\\times 5\\times 6 = 2055 \\\\ k=5: 1655 + 0 + 5\\times 50\\times 6 = 3155 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(s=4)",[24535,24554,24555],{"align":24476},[36,24556,24557],{},"2010 (s=2)",[24471,24559,24560,24564,24567,24569,24572,24574,24577],{},[24535,24561,24562],{"align":24476},[36,24563,507],{},[24535,24565,24566],{"align":24476},"-",[24535,24568,8307],{"align":24476},[24535,24570,24571],{"align":24476},"360 (s=2)",[24535,24573,24546],{"align":24476},[24535,24575,24576],{"align":24476},"2430 (s=2)",[24535,24578,24579],{"align":24476},"1950 (s=2)",[24471,24581,24582,24586,24588,24590,24592,24595,24598],{},[24535,24583,24584],{"align":24476},[36,24585,934],{},[24535,24587,24566],{"align":24476},[24535,24589,24566],{"align":24476},[24535,24591,8307],{"align":24476},[24535,24593,24594],{"align":24476},"180 (s=3)",[24535,24596,24597],{"align":24476},"930 (s=4)",[24535,24599,24600],{"align":24476},"1770 (s=4)",[24471,24602,24603,24607,24609,24611,24613,24615,24618],{},[24535,24604,24605],{"align":24476},[36,24606,4869],{},[24535,24608,24566],{"align":24476},[24535,24610,24566],{"align":24476},[24535,24612,24566],{"align":24476},[24535,24614,8307],{"align":24476},[24535,24616,24617],{"align":24476},"3000 (s=4)",[24535,24619,24620],{"align":24476},"1860 (s=4)",[24471,24622,24623,24627,24629,24631,24633,24635,24637],{},[24535,24624,24625],{"align":24476},[36,24626,13939],{},[24535,24628,24566],{"align":24476},[24535,24630,24566],{"align":24476},[24535,24632,24566],{"align":24476},[24535,24634,24566],{"align":24476},[24535,24636,8307],{"align":24476},[24535,24638,24639],{"align":24476},"1500 (s=5)",[24471,24641,24642,24646,24648,24650,24652,24654,24656],{},[24535,24643,24644],{"align":24476},[36,24645,14011],{},[24535,24647,24566],{"align":24476},[24535,24649,24566],{"align":24476},[24535,24651,24566],{"align":24476},[24535,24653,24566],{"align":24476},[24535,24655,24566],{"align":24476},[24535,24657,8307],{"align":24476},[27,24659,24660,24663,24664,24692],{},[36,24661,24662],{},"2) 最优的矩阵乘法运算顺序：","\n我们利用求出的断点数组 ",[188,24665,24667,24680],{"className":24666},[191],[188,24668,24670],{"className":24669},[195],[197,24671,24672],{"xmlns":199},[201,24673,24674,24678],{},[204,24675,24676],{},[207,24677,14525],{},[222,24679,14525],{"encoding":224},[188,24681,24683],{"className":24682,"ariaHidden":230},[229],[188,24684,24686,24689],{"className":24685},[234],[188,24687],{"className":24688,"style":351},[238],[188,24690,14525],{"className":24691},[243,244],"，从大范围不断往里拆解。",[68,24694,24695,25124,25253,25590],{},[44,24696,24697,24698,24779,24780,11026,24906,85],{},"全局范围是 1 到 6，查表得知 ",[188,24699,24701,24731],{"className":24700},[191],[188,24702,24704],{"className":24703},[195],[197,24705,24706],{"xmlns":199},[201,24707,24708,24728],{},[204,24709,24710,24712,24714,24716,24718,24720,24722,24724,24726],{},[207,24711,14525],{},[211,24713,9366],{"stretchy":213},[505,24715,4948],{},[211,24717,9371],{"stretchy":213},[211,24719,9366],{"stretchy":213},[505,24721,14011],{},[211,24723,9371],{"stretchy":213},[211,24725,2464],{},[505,24727,507],{},[222,24729,24730],{"encoding":224},"s[1][6] = 2",[188,24732,24734,24770],{"className":24733,"ariaHidden":230},[229],[188,24735,24737,24740,24743,24746,24749,24752,24755,24758,24761,24764,24767],{"className":24736},[234],[188,24738],{"className":24739,"style":239},[238],[188,24741,14525],{"className":24742},[243,244],[188,24744,9366],{"className":24745},[249],[188,24747,4948],{"className":24748},[243],[188,24750,9371],{"className":24751},[256],[188,24753,9366],{"className":24754},[249],[188,24756,14011],{"className":24757},[243],[188,24759,9371],{"className":24760},[256],[188,24762],{"className":24763,"style":2528},[584],[188,24765,2464],{"className":24766},[2532],[188,24768],{"className":24769,"style":2528},[584],[188,24771,24773,24776],{"className":24772},[234],[188,24774],{"className":24775,"style":3213},[238],[188,24777,507],{"className":24778},[243],"。说明第一刀切在第2个矩阵后。整体结构分为 ",[188,24781,24783,24811],{"className":24782},[191],[188,24784,24786],{"className":24785},[195],[197,24787,24788],{"xmlns":199},[201,24789,24790,24808],{},[204,24791,24792,24794,24800,24806],{},[211,24793,214],{"stretchy":213},[916,24795,24796,24798],{},[207,24797,12802],{},[505,24799,4948],{},[916,24801,24802,24804],{},[207,24803,12802],{},[505,24805,507],{},[211,24807,220],{"stretchy":213},[222,24809,24810],{"encoding":224},"(A_1 A_2)",[188,24812,24814],{"className":24813,"ariaHidden":230},[229],[188,24815,24817,24820,24823,24863,24903],{"className":24816},[234],[188,24818],{"className":24819,"style":239},[238],[188,24821,214],{"className":24822},[249],[188,24824,24826,24829],{"className":24825},[243],[188,24827,12802],{"className":24828},[243,244],[188,24830,24832],{"className":24831},[545],[188,24833,24835,24855],{"className":24834},[549,966],[188,24836,24838,24852],{"className":24837},[553],[188,24839,24841],{"className":24840,"style":9618},[557],[188,24842,24843,24846],{"style":9621},[188,24844],{"className":24845,"style":566},[565],[188,24847,24849],{"className":24848},[570,571,572,573],[188,24850,4948],{"className":24851},[243,573],[188,24853,990],{"className":24854},[989],[188,24856,24858],{"className":24857},[553],[188,24859,24861],{"className":24860,"style":6706},[557],[188,24862],{},[188,24864,24866,24869],{"className":24865},[243],[188,24867,12802],{"className":24868},[243,244],[188,24870,24872],{"className":24871},[545],[188,24873,24875,24895],{"className":24874},[549,966],[188,24876,24878,24892],{"className":24877},[553],[188,24879,24881],{"className":24880,"style":9618},[557],[188,24882,24883,24886],{"style":9621},[188,24884],{"className":24885,"style":566},[565],[188,24887,24889],{"className":24888},[570,571,572,573],[188,24890,507],{"className":24891},[243,573],[188,24893,990],{"className":24894},[989],[188,24896,24898],{"className":24897},[553],[188,24899,24901],{"className":24900,"style":6706},[557],[188,24902],{},[188,24904,220],{"className":24905},[256],[188,24907,24909,24949],{"className":24908},[191],[188,24910,24912],{"className":24911},[195],[197,24913,24914],{"xmlns":199},[201,24915,24916,24946],{},[204,24917,24918,24920,24926,24932,24938,24944],{},[211,24919,214],{"stretchy":213},[916,24921,24922,24924],{},[207,24923,12802],{},[505,24925,934],{},[916,24927,24928,24930],{},[207,24929,12802],{},[505,24931,4869],{},[916,24933,24934,24936],{},[207,24935,12802],{},[505,24937,13939],{},[916,24939,24940,24942],{},[207,24941,12802],{},[505,24943,14011],{},[211,24945,220],{"stretchy":213},[222,24947,24948],{"encoding":224},"(A_3 A_4 A_5 A_6)",[188,24950,24952],{"className":24951,"ariaHidden":230},[229],[188,24953,24955,24958,24961,25001,25041,25081,25121],{"className":24954},[234],[188,24956],{"className":24957,"style":239},[238],[188,24959,214],{"className":24960},[249],[188,24962,24964,24967],{"className":24963},[243],[188,24965,12802],{"className":24966},[243,244],[188,24968,24970],{"className":24969},[545],[188,24971,24973,24993],{"className":24972},[549,966],[188,24974,24976,24990],{"className":24975},[553],[188,24977,24979],{"className":24978,"style":9618},[557],[188,24980,24981,24984],{"style":9621},[188,24982],{"className":24983,"style":566},[565],[188,24985,24987],{"className":24986},[570,571,572,573],[188,24988,934],{"className":24989},[243,573],[188,24991,990],{"className":24992},[989],[188,24994,24996],{"className":24995},[553],[188,24997,24999],{"className":24998,"style":6706},[557],[188,25000],{},[188,25002,25004,25007],{"className":25003},[243],[188,25005,12802],{"className":25006},[243,244],[188,25008,25010],{"className":25009},[545],[188,25011,25013,25033],{"className":25012},[549,966],[188,25014,25016,25030],{"className":25015},[553],[188,25017,25019],{"className":25018,"style":9618},[557],[188,25020,25021,25024],{"style":9621},[188,25022],{"className":25023,"style":566},[565],[188,25025,25027],{"className":25026},[570,571,572,573],[188,25028,4869],{"className":25029},[243,573],[188,25031,990],{"className":25032},[989],[188,25034,25036],{"className":25035},[553],[188,25037,25039],{"className":25038,"style":6706},[557],[188,25040],{},[188,25042,25044,25047],{"className":25043},[243],[188,25045,12802],{"className":25046},[243,244],[188,25048,25050],{"className":25049},[545],[188,25051,25053,25073],{"className":25052},[549,966],[188,25054,25056,25070],{"className":25055},[553],[188,25057,25059],{"className":25058,"style":9618},[557],[188,25060,25061,25064],{"style":9621},[188,25062],{"className":25063,"style":566},[565],[188,25065,25067],{"className":25066},[570,571,572,573],[188,25068,13939],{"className":25069},[243,573],[188,25071,990],{"className":25072},[989],[188,25074,25076],{"className":25075},[553],[188,25077,25079],{"className":25078,"style":6706},[557],[188,25080],{},[188,25082,25084,25087],{"className":25083},[243],[188,25085,12802],{"className":25086},[243,244],[188,25088,25090],{"className":25089},[545],[188,25091,25093,25113],{"className":25092},[549,966],[188,25094,25096,25110],{"className":25095},[553],[188,25097,25099],{"className":25098,"style":9618},[557],[188,25100,25101,25104],{"style":9621},[188,25102],{"className":25103,"style":566},[565],[188,25105,25107],{"className":25106},[570,571,572,573],[188,25108,14011],{"className":25109},[243,573],[188,25111,990],{"className":25112},[989],[188,25114,25116],{"className":25115},[553],[188,25117,25119],{"className":25118,"style":6706},[557],[188,25120],{},[188,25122,220],{"className":25123},[256],[44,25125,25126,25127,25252],{},"对于左半边 ",[188,25128,25130,25157],{"className":25129},[191],[188,25131,25133],{"className":25132},[195],[197,25134,25135],{"xmlns":199},[201,25136,25137,25155],{},[204,25138,25139,25141,25147,25153],{},[211,25140,214],{"stretchy":213},[916,25142,25143,25145],{},[207,25144,12802],{},[505,25146,4948],{},[916,25148,25149,25151],{},[207,25150,12802],{},[505,25152,507],{},[211,25154,220],{"stretchy":213},[222,25156,24810],{"encoding":224},[188,25158,25160],{"className":25159,"ariaHidden":230},[229],[188,25161,25163,25166,25169,25209,25249],{"className":25162},[234],[188,25164],{"className":25165,"style":239},[238],[188,25167,214],{"className":25168},[249],[188,25170,25172,25175],{"className":25171},[243],[188,25173,12802],{"className":25174},[243,244],[188,25176,25178],{"className":25177},[545],[188,25179,25181,25201],{"className":25180},[549,966],[188,25182,25184,25198],{"className":25183},[553],[188,25185,25187],{"className":25186,"style":9618},[557],[188,25188,25189,25192],{"style":9621},[188,25190],{"className":25191,"style":566},[565],[188,25193,25195],{"className":25194},[570,571,572,573],[188,25196,4948],{"className":25197},[243,573],[188,25199,990],{"className":25200},[989],[188,25202,25204],{"className":25203},[553],[188,25205,25207],{"className":25206,"style":6706},[557],[188,25208],{},[188,25210,25212,25215],{"className":25211},[243],[188,25213,12802],{"className":25214},[243,244],[188,25216,25218],{"className":25217},[545],[188,25219,25221,25241],{"className":25220},[549,966],[188,25222,25224,25238],{"className":25223},[553],[188,25225,25227],{"className":25226,"style":9618},[557],[188,25228,25229,25232],{"style":9621},[188,25230],{"className":25231,"style":566},[565],[188,25233,25235],{"className":25234},[570,571,572,573],[188,25236,507],{"className":25237},[243,573],[188,25239,990],{"className":25240},[989],[188,25242,25244],{"className":25243},[553],[188,25245,25247],{"className":25246,"style":6706},[557],[188,25248],{},[188,25250,220],{"className":25251},[256],"，毫无疑问就是直接相乘。",[44,25254,25255,25256,25337,25338,11026,25464,85],{},"对于右半边范围 3 到 6，查表得知 ",[188,25257,25259,25289],{"className":25258},[191],[188,25260,25262],{"className":25261},[195],[197,25263,25264],{"xmlns":199},[201,25265,25266,25286],{},[204,25267,25268,25270,25272,25274,25276,25278,25280,25282,25284],{},[207,25269,14525],{},[211,25271,9366],{"stretchy":213},[505,25273,934],{},[211,25275,9371],{"stretchy":213},[211,25277,9366],{"stretchy":213},[505,25279,14011],{},[211,25281,9371],{"stretchy":213},[211,25283,2464],{},[505,25285,4869],{},[222,25287,25288],{"encoding":224},"s[3][6] = 4",[188,25290,25292,25328],{"className":25291,"ariaHidden":230},[229],[188,25293,25295,25298,25301,25304,25307,25310,25313,25316,25319,25322,25325],{"className":25294},[234],[188,25296],{"className":25297,"style":239},[238],[188,25299,14525],{"className":25300},[243,244],[188,25302,9366],{"className":25303},[249],[188,25305,934],{"className":25306},[243],[188,25308,9371],{"className":25309},[256],[188,25311,9366],{"className":25312},[249],[188,25314,14011],{"className":25315},[243],[188,25317,9371],{"className":25318},[256],[188,25320],{"className":25321,"style":2528},[584],[188,25323,2464],{"className":25324},[2532],[188,25326],{"className":25327,"style":2528},[584],[188,25329,25331,25334],{"className":25330},[234],[188,25332],{"className":25333,"style":3213},[238],[188,25335,4869],{"className":25336},[243],"。说明这一刀切在第4个矩阵后。结构变为 ",[188,25339,25341,25369],{"className":25340},[191],[188,25342,25344],{"className":25343},[195],[197,25345,25346],{"xmlns":199},[201,25347,25348,25366],{},[204,25349,25350,25352,25358,25364],{},[211,25351,214],{"stretchy":213},[916,25353,25354,25356],{},[207,25355,12802],{},[505,25357,934],{},[916,25359,25360,25362],{},[207,25361,12802],{},[505,25363,4869],{},[211,25365,220],{"stretchy":213},[222,25367,25368],{"encoding":224},"(A_3 A_4)",[188,25370,25372],{"className":25371,"ariaHidden":230},[229],[188,25373,25375,25378,25381,25421,25461],{"className":25374},[234],[188,25376],{"className":25377,"style":239},[238],[188,25379,214],{"className":25380},[249],[188,25382,25384,25387],{"className":25383},[243],[188,25385,12802],{"className":25386},[243,244],[188,25388,25390],{"className":25389},[545],[188,25391,25393,25413],{"className":25392},[549,966],[188,25394,25396,25410],{"className":25395},[553],[188,25397,25399],{"className":25398,"style":9618},[557],[188,25400,25401,25404],{"style":9621},[188,25402],{"className":25403,"style":566},[565],[188,25405,25407],{"className":25406},[570,571,572,573],[188,25408,934],{"className":25409},[243,573],[188,25411,990],{"className":25412},[989],[188,25414,25416],{"className":25415},[553],[188,25417,25419],{"className":25418,"style":6706},[557],[188,25420],{},[188,25422,25424,25427],{"className":25423},[243],[188,25425,12802],{"className":25426},[243,244],[188,25428,25430],{"className":25429},[545],[188,25431,25433,25453],{"className":25432},[549,966],[188,25434,25436,25450],{"className":25435},[553],[188,25437,25439],{"className":25438,"style":9618},[557],[188,25440,25441,25444],{"style":9621},[188,25442],{"className":25443,"style":566},[565],[188,25445,25447],{"className":25446},[570,571,572,573],[188,25448,4869],{"className":25449},[243,573],[188,25451,990],{"className":25452},[989],[188,25454,25456],{"className":25455},[553],[188,25457,25459],{"className":25458,"style":6706},[557],[188,25460],{},[188,25462,220],{"className":25463},[256],[188,25465,25467,25495],{"className":25466},[191],[188,25468,25470],{"className":25469},[195],[197,25471,25472],{"xmlns":199},[201,25473,25474,25492],{},[204,25475,25476,25478,25484,25490],{},[211,25477,214],{"stretchy":213},[916,25479,25480,25482],{},[207,25481,12802],{},[505,25483,13939],{},[916,25485,25486,25488],{},[207,25487,12802],{},[505,25489,14011],{},[211,25491,220],{"stretchy":213},[222,25493,25494],{"encoding":224},"(A_5 A_6)",[188,25496,25498],{"className":25497,"ariaHidden":230},[229],[188,25499,25501,25504,25507,25547,25587],{"className":25500},[234],[188,25502],{"className":25503,"style":239},[238],[188,25505,214],{"className":25506},[249],[188,25508,25510,25513],{"className":25509},[243],[188,25511,12802],{"className":25512},[243,244],[188,25514,25516],{"className":25515},[545],[188,25517,25519,25539],{"className":25518},[549,966],[188,25520,25522,25536],{"className":25521},[553],[188,25523,25525],{"className":25524,"style":9618},[557],[188,25526,25527,25530],{"style":9621},[188,25528],{"className":25529,"style":566},[565],[188,25531,25533],{"className":25532},[570,571,572,573],[188,25534,13939],{"className":25535},[243,573],[188,25537,990],{"className":25538},[989],[188,25540,25542],{"className":25541},[553],[188,25543,25545],{"className":25544,"style":6706},[557],[188,25546],{},[188,25548,25550,25553],{"className":25549},[243],[188,25551,12802],{"className":25552},[243,244],[188,25554,25556],{"className":25555},[545],[188,25557,25559,25579],{"className":25558},[549,966],[188,25560,25562,25576],{"className":25561},[553],[188,25563,25565],{"className":25564,"style":9618},[557],[188,25566,25567,25570],{"style":9621},[188,25568],{"className":25569,"style":566},[565],[188,25571,25573],{"className":25572},[570,571,572,573],[188,25574,14011],{"className":25575},[243,573],[188,25577,990],{"className":25578},[989],[188,25580,25582],{"className":25581},[553],[188,25583,25585],{"className":25584,"style":6706},[557],[188,25586],{},[188,25588,220],{"className":25589},[256],[44,25591,25592,25593],{},"合并所有括号。最终的最优运算顺序（加括号方式）为：\n",[36,25594,25595],{},[188,25596,25598,25662],{"className":25597},[191],[188,25599,25601],{"className":25600},[195],[197,25602,25603],{"xmlns":199},[201,25604,25605,25659],{},[204,25606,25607,25609,25615,25621,25623,25625,25627,25633,25639,25641,25643,25649,25655,25657],{},[211,25608,214],{"stretchy":213},[916,25610,25611,25613],{},[207,25612,12802],{},[505,25614,4948],{},[916,25616,25617,25619],{},[207,25618,12802],{},[505,25620,507],{},[211,25622,220],{"stretchy":213},[211,25624,214],{"stretchy":213},[211,25626,214],{"stretchy":213},[916,25628,25629,25631],{},[207,25630,12802],{},[505,25632,934],{},[916,25634,25635,25637],{},[207,25636,12802],{},[505,25638,4869],{},[211,25640,220],{"stretchy":213},[211,25642,214],{"stretchy":213},[916,25644,25645,25647],{},[207,25646,12802],{},[505,25648,13939],{},[916,25650,25651,25653],{},[207,25652,12802],{},[505,25654,14011],{},[211,25656,220],{"stretchy":213},[211,25658,220],{"stretchy":213},[222,25660,25661],{"encoding":224},"(A_1 A_2)((A_3 A_4)(A_5 A_6))",[188,25663,25665],{"className":25664,"ariaHidden":230},[229],[188,25666,25668,25671,25674,25714,25754,25757,25761,25801,25841,25844,25847,25887,25927],{"className":25667},[234],[188,25669],{"className":25670,"style":239},[238],[188,25672,214],{"className":25673},[249],[188,25675,25677,25680],{"className":25676},[243],[188,25678,12802],{"className":25679},[243,244],[188,25681,25683],{"className":25682},[545],[188,25684,25686,25706],{"className":25685},[549,966],[188,25687,25689,25703],{"className":25688},[553],[188,25690,25692],{"className":25691,"style":9618},[557],[188,25693,25694,25697],{"style":9621},[188,25695],{"className":25696,"style":566},[565],[188,25698,25700],{"className":25699},[570,571,572,573],[188,25701,4948],{"className":25702},[243,573],[188,25704,990],{"className":25705},[989],[188,25707,25709],{"className":25708},[553],[188,25710,25712],{"className":25711,"style":6706},[557],[188,25713],{},[188,25715,25717,25720],{"className":25716},[243],[188,25718,12802],{"className":25719},[243,244],[188,25721,25723],{"className":25722},[545],[188,25724,25726,25746],{"className":25725},[549,966],[188,25727,25729,25743],{"className":25728},[553],[188,25730,25732],{"className":25731,"style":9618},[557],[188,25733,25734,25737],{"style":9621},[188,25735],{"className":25736,"style":566},[565],[188,25738,25740],{"className":25739},[570,571,572,573],[188,25741,507],{"className":25742},[243,573],[188,25744,990],{"className":25745},[989],[188,25747,25749],{"className":25748},[553],[188,25750,25752],{"className":25751,"style":6706},[557],[188,25753],{},[188,25755,220],{"className":25756},[256],[188,25758,25760],{"className":25759},[249],"((",[188,25762,25764,25767],{"className":25763},[243],[188,25765,12802],{"className":25766},[243,244],[188,25768,25770],{"className":25769},[545],[188,25771,25773,25793],{"className":25772},[549,966],[188,25774,25776,25790],{"className":25775},[553],[188,25777,25779],{"className":25778,"style":9618},[557],[188,25780,25781,25784],{"style":9621},[188,25782],{"className":25783,"style":566},[565],[188,25785,25787],{"className":25786},[570,571,572,573],[188,25788,934],{"className":25789},[243,573],[188,25791,990],{"className":25792},[989],[188,25794,25796],{"className":25795},[553],[188,25797,25799],{"className":25798,"style":6706},[557],[188,25800],{},[188,25802,25804,25807],{"className":25803},[243],[188,25805,12802],{"className":25806},[243,244],[188,25808,25810],{"className":25809},[545],[188,25811,25813,25833],{"className":25812},[549,966],[188,25814,25816,25830],{"className":25815},[553],[188,25817,25819],{"className":25818,"style":9618},[557],[188,25820,25821,25824],{"style":9621},[188,25822],{"className":25823,"style":566},[565],[188,25825,25827],{"className":25826},[570,571,572,573],[188,25828,4869],{"className":25829},[243,573],[188,25831,990],{"className":25832},[989],[188,25834,25836],{"className":25835},[553],[188,25837,25839],{"className":25838,"style":6706},[557],[188,25840],{},[188,25842,220],{"className":25843},[256],[188,25845,214],{"className":25846},[249],[188,25848,25850,25853],{"className":25849},[243],[188,25851,12802],{"className":25852},[243,244],[188,25854,25856],{"className":25855},[545],[188,25857,25859,25879],{"className":25858},[549,966],[188,25860,25862,25876],{"className":25861},[553],[188,25863,25865],{"className":25864,"style":9618},[557],[188,25866,25867,25870],{"style":9621},[188,25868],{"className":25869,"style":566},[565],[188,25871,25873],{"className":25872},[570,571,572,573],[188,25874,13939],{"className":25875},[243,573],[188,25877,990],{"className":25878},[989],[188,25880,25882],{"className":25881},[553],[188,25883,25885],{"className":25884,"style":6706},[557],[188,25886],{},[188,25888,25890,25893],{"className":25889},[243],[188,25891,12802],{"className":25892},[243,244],[188,25894,25896],{"className":25895},[545],[188,25897,25899,25919],{"className":25898},[549,966],[188,25900,25902,25916],{"className":25901},[553],[188,25903,25905],{"className":25904,"style":9618},[557],[188,25906,25907,25910],{"style":9621},[188,25908],{"className":25909,"style":566},[565],[188,25911,25913],{"className":25912},[570,571,572,573],[188,25914,14011],{"className":25915},[243,573],[188,25917,990],{"className":25918},[989],[188,25920,25922],{"className":25921},[553],[188,25923,25925],{"className":25924,"style":6706},[557],[188,25926],{},[188,25928,4624],{"className":25929},[256],[14,25931],{},[22,25933,263],{"id":25934},"_3-题目内容-3",[27,25936,25937,25938,25966,25967,26038,26039,10490],{},"在操作系统的单机作业调度问题中，",[188,25939,25941,25954],{"className":25940},[191],[188,25942,25944],{"className":25943},[195],[197,25945,25946],{"xmlns":199},[201,25947,25948,25952],{},[204,25949,25950],{},[207,25951,217],{},[222,25953,217],{"encoding":224},[188,25955,25957],{"className":25956,"ariaHidden":230},[229],[188,25958,25960,25963],{"className":25959},[234],[188,25961],{"className":25962,"style":351},[238],[188,25964,217],{"className":25965},[243,244]," 个作业同时提交给系统，每个作业需要 CPU 处理的时间分别为 ",[188,25968,25970,25988],{"className":25969},[191],[188,25971,25973],{"className":25972},[195],[197,25974,25975],{"xmlns":199},[201,25976,25977,25985],{},[204,25978,25979],{},[916,25980,25981,25983],{},[207,25982,7855],{},[207,25984,6651],{},[222,25986,25987],{"encoding":224},"t_i",[188,25989,25991],{"className":25990,"ariaHidden":230},[229],[188,25992,25994,25998],{"className":25993},[234],[188,25995],{"className":25996,"style":25997},[238],"height:0.7651em;vertical-align:-0.15em;",[188,25999,26001,26004],{"className":26000},[243],[188,26002,7855],{"className":26003},[243,244],[188,26005,26007],{"className":26006},[545],[188,26008,26010,26030],{"className":26009},[549,966],[188,26011,26013,26027],{"className":26012},[553],[188,26014,26016],{"className":26015,"style":6684},[557],[188,26017,26018,26021],{"style":9621},[188,26019],{"className":26020,"style":566},[565],[188,26022,26024],{"className":26023},[570,571,572,573],[188,26025,6651],{"className":26026},[243,244,573],[188,26028,990],{"className":26029},[989],[188,26031,26033],{"className":26032},[553],[188,26034,26036],{"className":26035,"style":6706},[557],[188,26037],{},"（",[188,26040,26042,26064],{"className":26041},[191],[188,26043,26045],{"className":26044},[195],[197,26046,26047],{"xmlns":199},[201,26048,26049,26061],{},[204,26050,26051,26053,26055,26057,26059],{},[505,26052,4948],{},[211,26054,13231],{},[207,26056,6651],{},[211,26058,13231],{},[207,26060,217],{},[222,26062,26063],{"encoding":224},"1 \\le i \\le n",[188,26065,26067,26086,26105],{"className":26066,"ariaHidden":230},[229],[188,26068,26070,26074,26077,26080,26083],{"className":26069},[234],[188,26071],{"className":26072,"style":26073},[238],"height:0.7804em;vertical-align:-0.136em;",[188,26075,4948],{"className":26076},[243],[188,26078],{"className":26079,"style":2528},[584],[188,26081,13231],{"className":26082},[2532],[188,26084],{"className":26085,"style":2528},[584],[188,26087,26089,26093,26096,26099,26102],{"className":26088},[234],[188,26090],{"className":26091,"style":26092},[238],"height:0.7955em;vertical-align:-0.136em;",[188,26094,6651],{"className":26095},[243,244],[188,26097],{"className":26098,"style":2528},[584],[188,26100,13231],{"className":26101},[2532],[188,26103],{"className":26104,"style":2528},[584],[188,26106,26108,26111],{"className":26107},[234],[188,26109],{"className":26110,"style":351},[238],[188,26112,217],{"className":26113},[243,244],[41,26115,26116,26119],{},[44,26117,26118],{},"请设计一种贪心策略对作业进行调度，使得所有作业的平均等待时间最短。（5分）",[44,26120,26121],{},"证明该贪心策略满足贪心选择和最优子结构性质。（5分）",[22,26123,32],{"id":26124},"答案与深度解析-21",[27,26126,26127],{},[36,26128,26129],{},"1) 贪心策略设计：",[68,26131,26132,26237],{},[44,26133,26134,26137,26138,26166,26167,26236],{},[36,26135,26136],{},"策略（短作业优先，SJF）："," 将这 ",[188,26139,26141,26154],{"className":26140},[191],[188,26142,26144],{"className":26143},[195],[197,26145,26146],{"xmlns":199},[201,26147,26148,26152],{},[204,26149,26150],{},[207,26151,217],{},[222,26153,217],{"encoding":224},[188,26155,26157],{"className":26156,"ariaHidden":230},[229],[188,26158,26160,26163],{"className":26159},[234],[188,26161],{"className":26162,"style":351},[238],[188,26164,217],{"className":26165},[243,244]," 个作业按照它们所需 CPU 处理时间 ",[188,26168,26170,26187],{"className":26169},[191],[188,26171,26173],{"className":26172},[195],[197,26174,26175],{"xmlns":199},[201,26176,26177,26185],{},[204,26178,26179],{},[916,26180,26181,26183],{},[207,26182,7855],{},[207,26184,6651],{},[222,26186,25987],{"encoding":224},[188,26188,26190],{"className":26189,"ariaHidden":230},[229],[188,26191,26193,26196],{"className":26192},[234],[188,26194],{"className":26195,"style":25997},[238],[188,26197,26199,26202],{"className":26198},[243],[188,26200,7855],{"className":26201},[243,244],[188,26203,26205],{"className":26204},[545],[188,26206,26208,26228],{"className":26207},[549,966],[188,26209,26211,26225],{"className":26210},[553],[188,26212,26214],{"className":26213,"style":6684},[557],[188,26215,26216,26219],{"style":9621},[188,26217],{"className":26218,"style":566},[565],[188,26220,26222],{"className":26221},[570,571,572,573],[188,26223,6651],{"className":26224},[243,244,573],[188,26226,990],{"className":26227},[989],[188,26229,26231],{"className":26230},[553],[188,26232,26234],{"className":26233,"style":6706},[557],[188,26235],{}," 进行**从小到大（升序）**排序，然后依次调度执行。",[44,26238,26239,26242],{},[36,26240,26241],{},"零基础理解："," 想象去银行排队办业务，如果你办业务只需要 1 分钟，而前面站了一个需要办 1 小时的人，你是不是会觉得极其绝望（等待时间巨长）？为了让大家的总体体验最好（平均等待时间最短），银行正确的做法是让办事快的人先办。",[27,26244,26245,26248,26249,26320,26321,26391,26392,26525,26526,27034,27035,27104,27105,27155,27156,27104,27226,27277,27278,27632,27633,27661],{},[36,26246,26247],{},"2) 数学严格证明：","\n在进行证明之前，我们要先梳理一个公式：\n假设调度顺序已经是 ",[188,26250,26252,26278],{"className":26251},[191],[188,26253,26255],{"className":26254},[195],[197,26256,26257],{"xmlns":199},[201,26258,26259,26275],{},[204,26260,26261,26263,26265,26267,26269,26271,26273],{},[505,26262,4948],{},[211,26264,8137],{"separator":230},[505,26266,507],{},[211,26268,8137],{"separator":230},[211,26270,9574],{},[211,26272,8137],{"separator":230},[207,26274,217],{},[222,26276,26277],{"encoding":224},"1, 2, \\dots, n",[188,26279,26281],{"className":26280,"ariaHidden":230},[229],[188,26282,26284,26287,26290,26293,26296,26299,26302,26305,26308,26311,26314,26317],{"className":26283},[234],[188,26285],{"className":26286,"style":8346},[238],[188,26288,4948],{"className":26289},[243],[188,26291,8137],{"className":26292},[8167],[188,26294],{"className":26295,"style":1003},[584],[188,26297,507],{"className":26298},[243],[188,26300,8137],{"className":26301},[8167],[188,26303],{"className":26304,"style":1003},[584],[188,26306,9574],{"className":26307},[9697],[188,26309],{"className":26310,"style":1003},[584],[188,26312,8137],{"className":26313},[8167],[188,26315],{"className":26316,"style":1003},[584],[188,26318,217],{"className":26319},[243,244],"。\n第 1 个作业无需等待，等待时间为 0。\n第 2 个作业需等待第 1 个作业执行完毕，等待时间为 ",[188,26322,26324,26342],{"className":26323},[191],[188,26325,26327],{"className":26326},[195],[197,26328,26329],{"xmlns":199},[201,26330,26331,26339],{},[204,26332,26333],{},[916,26334,26335,26337],{},[207,26336,7855],{},[505,26338,4948],{},[222,26340,26341],{"encoding":224},"t_1",[188,26343,26345],{"className":26344,"ariaHidden":230},[229],[188,26346,26348,26351],{"className":26347},[234],[188,26349],{"className":26350,"style":25997},[238],[188,26352,26354,26357],{"className":26353},[243],[188,26355,7855],{"className":26356},[243,244],[188,26358,26360],{"className":26359},[545],[188,26361,26363,26383],{"className":26362},[549,966],[188,26364,26366,26380],{"className":26365},[553],[188,26367,26369],{"className":26368,"style":9618},[557],[188,26370,26371,26374],{"style":9621},[188,26372],{"className":26373,"style":566},[565],[188,26375,26377],{"className":26376},[570,571,572,573],[188,26378,4948],{"className":26379},[243,573],[188,26381,990],{"className":26382},[989],[188,26384,26386],{"className":26385},[553],[188,26387,26389],{"className":26388,"style":6706},[557],[188,26390],{},"。\n第 3 个作业需等待前两个作业执行完，等待时间为 ",[188,26393,26395,26421],{"className":26394},[191],[188,26396,26398],{"className":26397},[195],[197,26399,26400],{"xmlns":199},[201,26401,26402,26418],{},[204,26403,26404,26410,26412],{},[916,26405,26406,26408],{},[207,26407,7855],{},[505,26409,4948],{},[211,26411,516],{},[916,26413,26414,26416],{},[207,26415,7855],{},[505,26417,507],{},[222,26419,26420],{"encoding":224},"t_1 + t_2",[188,26422,26424,26479],{"className":26423,"ariaHidden":230},[229],[188,26425,26427,26430,26470,26473,26476],{"className":26426},[234],[188,26428],{"className":26429,"style":25997},[238],[188,26431,26433,26436],{"className":26432},[243],[188,26434,7855],{"className":26435},[243,244],[188,26437,26439],{"className":26438},[545],[188,26440,26442,26462],{"className":26441},[549,966],[188,26443,26445,26459],{"className":26444},[553],[188,26446,26448],{"className":26447,"style":9618},[557],[188,26449,26450,26453],{"style":9621},[188,26451],{"className":26452,"style":566},[565],[188,26454,26456],{"className":26455},[570,571,572,573],[188,26457,4948],{"className":26458},[243,573],[188,26460,990],{"className":26461},[989],[188,26463,26465],{"className":26464},[553],[188,26466,26468],{"className":26467,"style":6706},[557],[188,26469],{},[188,26471],{"className":26472,"style":585},[584],[188,26474,516],{"className":26475},[589],[188,26477],{"className":26478,"style":585},[584],[188,26480,26482,26485],{"className":26481},[234],[188,26483],{"className":26484,"style":25997},[238],[188,26486,26488,26491],{"className":26487},[243],[188,26489,7855],{"className":26490},[243,244],[188,26492,26494],{"className":26493},[545],[188,26495,26497,26517],{"className":26496},[549,966],[188,26498,26500,26514],{"className":26499},[553],[188,26501,26503],{"className":26502,"style":9618},[557],[188,26504,26505,26508],{"style":9621},[188,26506],{"className":26507,"style":566},[565],[188,26509,26511],{"className":26510},[570,571,572,573],[188,26512,507],{"className":26513},[243,573],[188,26515,990],{"className":26516},[989],[188,26518,26520],{"className":26519},[553],[188,26521,26523],{"className":26522,"style":6706},[557],[188,26524],{},"。\n...\n总等待时间 ",[188,26527,26529,26617],{"className":26528},[191],[188,26530,26532],{"className":26531},[195],[197,26533,26534],{"xmlns":199},[201,26535,26536,26614],{},[204,26537,26538,26540,26542,26544,26546,26552,26554,26556,26562,26564,26570,26572,26574,26576,26578,26580,26586,26588,26594,26596,26598,26600,26612],{},[207,26539,2455],{},[211,26541,2464],{},[505,26543,8307],{},[211,26545,516],{},[916,26547,26548,26550],{},[207,26549,7855],{},[505,26551,4948],{},[211,26553,516],{},[211,26555,214],{"stretchy":213},[916,26557,26558,26560],{},[207,26559,7855],{},[505,26561,4948],{},[211,26563,516],{},[916,26565,26566,26568],{},[207,26567,7855],{},[505,26569,507],{},[211,26571,220],{"stretchy":213},[211,26573,516],{},[211,26575,12318],{},[211,26577,516],{},[211,26579,214],{"stretchy":213},[916,26581,26582,26584],{},[207,26583,7855],{},[505,26585,4948],{},[211,26587,516],{},[916,26589,26590,26592],{},[207,26591,7855],{},[505,26593,507],{},[211,26595,516],{},[211,26597,12318],{},[211,26599,516],{},[916,26601,26602,26604],{},[207,26603,7855],{},[204,26605,26606,26608,26610],{},[207,26607,217],{},[211,26609,4945],{},[505,26611,4948],{},[211,26613,220],{"stretchy":213},[222,26615,26616],{"encoding":224},"T = 0 + t_1 + (t_1 + t_2) + \\dots + (t_1 + t_2 + \\dots + t_{n-1})",[188,26618,26620,26638,26656,26711,26769,26827,26845,26903,26958,26976],{"className":26619,"ariaHidden":230},[229],[188,26621,26623,26626,26629,26632,26635],{"className":26622},[234],[188,26624],{"className":26625,"style":1693},[238],[188,26627,2455],{"className":26628,"style":2515},[243,244],[188,26630],{"className":26631,"style":2528},[584],[188,26633,2464],{"className":26634},[2532],[188,26636],{"className":26637,"style":2528},[584],[188,26639,26641,26644,26647,26650,26653],{"className":26640},[234],[188,26642],{"className":26643,"style":7545},[238],[188,26645,8307],{"className":26646},[243],[188,26648],{"className":26649,"style":585},[584],[188,26651,516],{"className":26652},[589],[188,26654],{"className":26655,"style":585},[584],[188,26657,26659,26662,26702,26705,26708],{"className":26658},[234],[188,26660],{"className":26661,"style":25997},[238],[188,26663,26665,26668],{"className":26664},[243],[188,26666,7855],{"className":26667},[243,244],[188,26669,26671],{"className":26670},[545],[188,26672,26674,26694],{"className":26673},[549,966],[188,26675,26677,26691],{"className":26676},[553],[188,26678,26680],{"className":26679,"style":9618},[557],[188,26681,26682,26685],{"style":9621},[188,26683],{"className":26684,"style":566},[565],[188,26686,26688],{"className":26687},[570,571,572,573],[188,26689,4948],{"className":26690},[243,573],[188,26692,990],{"className":26693},[989],[188,26695,26697],{"className":26696},[553],[188,26698,26700],{"className":26699,"style":6706},[557],[188,26701],{},[188,26703],{"className":26704,"style":585},[584],[188,26706,516],{"className":26707},[589],[188,26709],{"className":26710,"style":585},[584],[188,26712,26714,26717,26720,26760,26763,26766],{"className":26713},[234],[188,26715],{"className":26716,"style":239},[238],[188,26718,214],{"className":26719},[249],[188,26721,26723,26726],{"className":26722},[243],[188,26724,7855],{"className":26725},[243,244],[188,26727,26729],{"className":26728},[545],[188,26730,26732,26752],{"className":26731},[549,966],[188,26733,26735,26749],{"className":26734},[553],[188,26736,26738],{"className":26737,"style":9618},[557],[188,26739,26740,26743],{"style":9621},[188,26741],{"className":26742,"style":566},[565],[188,26744,26746],{"className":26745},[570,571,572,573],[188,26747,4948],{"className":26748},[243,573],[188,26750,990],{"className":26751},[989],[188,26753,26755],{"className":26754},[553],[188,26756,26758],{"className":26757,"style":6706},[557],[188,26759],{},[188,26761],{"className":26762,"style":585},[584],[188,26764,516],{"className":26765},[589],[188,26767],{"className":26768,"style":585},[584],[188,26770,26772,26775,26815,26818,26821,26824],{"className":26771},[234],[188,26773],{"className":26774,"style":239},[238],[188,26776,26778,26781],{"className":26777},[243],[188,26779,7855],{"className":26780},[243,244],[188,26782,26784],{"className":26783},[545],[188,26785,26787,26807],{"className":26786},[549,966],[188,26788,26790,26804],{"className":26789},[553],[188,26791,26793],{"className":26792,"style":9618},[557],[188,26794,26795,26798],{"style":9621},[188,26796],{"className":26797,"style":566},[565],[188,26799,26801],{"className":26800},[570,571,572,573],[188,26802,507],{"className":26803},[243,573],[188,26805,990],{"className":26806},[989],[188,26808,26810],{"className":26809},[553],[188,26811,26813],{"className":26812,"style":6706},[557],[188,26814],{},[188,26816,220],{"className":26817},[256],[188,26819],{"className":26820,"style":585},[584],[188,26822,516],{"className":26823},[589],[188,26825],{"className":26826,"style":585},[584],[188,26828,26830,26833,26836,26839,26842],{"className":26829},[234],[188,26831],{"className":26832,"style":8822},[238],[188,26834,12318],{"className":26835},[9697],[188,26837],{"className":26838,"style":585},[584],[188,26840,516],{"className":26841},[589],[188,26843],{"className":26844,"style":585},[584],[188,26846,26848,26851,26854,26894,26897,26900],{"className":26847},[234],[188,26849],{"className":26850,"style":239},[238],[188,26852,214],{"className":26853},[249],[188,26855,26857,26860],{"className":26856},[243],[188,26858,7855],{"className":26859},[243,244],[188,26861,26863],{"className":26862},[545],[188,26864,26866,26886],{"className":26865},[549,966],[188,26867,26869,26883],{"className":26868},[553],[188,26870,26872],{"className":26871,"style":9618},[557],[188,26873,26874,26877],{"style":9621},[188,26875],{"className":26876,"style":566},[565],[188,26878,26880],{"className":26879},[570,571,572,573],[188,26881,4948],{"className":26882},[243,573],[188,26884,990],{"className":26885},[989],[188,26887,26889],{"className":26888},[553],[188,26890,26892],{"className":26891,"style":6706},[557],[188,26893],{},[188,26895],{"className":26896,"style":585},[584],[188,26898,516],{"className":26899},[589],[188,26901],{"className":26902,"style":585},[584],[188,26904,26906,26909,26949,26952,26955],{"className":26905},[234],[188,26907],{"className":26908,"style":25997},[238],[188,26910,26912,26915],{"className":26911},[243],[188,26913,7855],{"className":26914},[243,244],[188,26916,26918],{"className":26917},[545],[188,26919,26921,26941],{"className":26920},[549,966],[188,26922,26924,26938],{"className":26923},[553],[188,26925,26927],{"className":26926,"style":9618},[557],[188,26928,26929,26932],{"style":9621},[188,26930],{"className":26931,"style":566},[565],[188,26933,26935],{"className":26934},[570,571,572,573],[188,26936,507],{"className":26937},[243,573],[188,26939,990],{"className":26940},[989],[188,26942,26944],{"className":26943},[553],[188,26945,26947],{"className":26946,"style":6706},[557],[188,26948],{},[188,26950],{"className":26951,"style":585},[584],[188,26953,516],{"className":26954},[589],[188,26956],{"className":26957,"style":585},[584],[188,26959,26961,26964,26967,26970,26973],{"className":26960},[234],[188,26962],{"className":26963,"style":8822},[238],[188,26965,12318],{"className":26966},[9697],[188,26968],{"className":26969,"style":585},[584],[188,26971,516],{"className":26972},[589],[188,26974],{"className":26975,"style":585},[584],[188,26977,26979,26982,27031],{"className":26978},[234],[188,26980],{"className":26981,"style":239},[238],[188,26983,26985,26988],{"className":26984},[243],[188,26986,7855],{"className":26987},[243,244],[188,26989,26991],{"className":26990},[545],[188,26992,26994,27023],{"className":26993},[549,966],[188,26995,26997,27020],{"className":26996},[553],[188,26998,27000],{"className":26999,"style":9618},[557],[188,27001,27002,27005],{"style":9621},[188,27003],{"className":27004,"style":566},[565],[188,27006,27008],{"className":27007},[570,571,572,573],[188,27009,27011,27014,27017],{"className":27010},[243,573],[188,27012,217],{"className":27013},[243,244,573],[188,27015,4945],{"className":27016},[589,573],[188,27018,4948],{"className":27019},[243,573],[188,27021,990],{"className":27022},[989],[188,27024,27026],{"className":27025},[553],[188,27027,27029],{"className":27028,"style":13139},[557],[188,27030],{},[188,27032,220],{"className":27033},[256],"。\n稍微整理一下同类项，我们发现 ",[188,27036,27038,27055],{"className":27037},[191],[188,27039,27041],{"className":27040},[195],[197,27042,27043],{"xmlns":199},[201,27044,27045,27053],{},[204,27046,27047],{},[916,27048,27049,27051],{},[207,27050,7855],{},[505,27052,4948],{},[222,27054,26341],{"encoding":224},[188,27056,27058],{"className":27057,"ariaHidden":230},[229],[188,27059,27061,27064],{"className":27060},[234],[188,27062],{"className":27063,"style":25997},[238],[188,27065,27067,27070],{"className":27066},[243],[188,27068,7855],{"className":27069},[243,244],[188,27071,27073],{"className":27072},[545],[188,27074,27076,27096],{"className":27075},[549,966],[188,27077,27079,27093],{"className":27078},[553],[188,27080,27082],{"className":27081,"style":9618},[557],[188,27083,27084,27087],{"style":9621},[188,27085],{"className":27086,"style":566},[565],[188,27088,27090],{"className":27089},[570,571,572,573],[188,27091,4948],{"className":27092},[243,573],[188,27094,990],{"className":27095},[989],[188,27097,27099],{"className":27098},[553],[188,27100,27102],{"className":27101,"style":6706},[557],[188,27103],{}," 累加了 ",[188,27106,27108,27125],{"className":27107},[191],[188,27109,27111],{"className":27110},[195],[197,27112,27113],{"xmlns":199},[201,27114,27115,27123],{},[204,27116,27117,27119,27121],{},[207,27118,217],{},[211,27120,4945],{},[505,27122,4948],{},[222,27124,11536],{"encoding":224},[188,27126,27128,27146],{"className":27127,"ariaHidden":230},[229],[188,27129,27131,27134,27137,27140,27143],{"className":27130},[234],[188,27132],{"className":27133,"style":8822},[238],[188,27135,217],{"className":27136},[243,244],[188,27138],{"className":27139,"style":585},[584],[188,27141,4945],{"className":27142},[589],[188,27144],{"className":27145,"style":585},[584],[188,27147,27149,27152],{"className":27148},[234],[188,27150],{"className":27151,"style":3213},[238],[188,27153,4948],{"className":27154},[243]," 次，",[188,27157,27159,27177],{"className":27158},[191],[188,27160,27162],{"className":27161},[195],[197,27163,27164],{"xmlns":199},[201,27165,27166,27174],{},[204,27167,27168],{},[916,27169,27170,27172],{},[207,27171,7855],{},[505,27173,507],{},[222,27175,27176],{"encoding":224},"t_2",[188,27178,27180],{"className":27179,"ariaHidden":230},[229],[188,27181,27183,27186],{"className":27182},[234],[188,27184],{"className":27185,"style":25997},[238],[188,27187,27189,27192],{"className":27188},[243],[188,27190,7855],{"className":27191},[243,244],[188,27193,27195],{"className":27194},[545],[188,27196,27198,27218],{"className":27197},[549,966],[188,27199,27201,27215],{"className":27200},[553],[188,27202,27204],{"className":27203,"style":9618},[557],[188,27205,27206,27209],{"style":9621},[188,27207],{"className":27208,"style":566},[565],[188,27210,27212],{"className":27211},[570,571,572,573],[188,27213,507],{"className":27214},[243,573],[188,27216,990],{"className":27217},[989],[188,27219,27221],{"className":27220},[553],[188,27222,27224],{"className":27223,"style":6706},[557],[188,27225],{},[188,27227,27229,27247],{"className":27228},[191],[188,27230,27232],{"className":27231},[195],[197,27233,27234],{"xmlns":199},[201,27235,27236,27244],{},[204,27237,27238,27240,27242],{},[207,27239,217],{},[211,27241,4945],{},[505,27243,507],{},[222,27245,27246],{"encoding":224},"n-2",[188,27248,27250,27268],{"className":27249,"ariaHidden":230},[229],[188,27251,27253,27256,27259,27262,27265],{"className":27252},[234],[188,27254],{"className":27255,"style":8822},[238],[188,27257,217],{"className":27258},[243,244],[188,27260],{"className":27261,"style":585},[584],[188,27263,4945],{"className":27264},[589],[188,27266],{"className":27267,"style":585},[584],[188,27269,27271,27274],{"className":27270},[234],[188,27272],{"className":27273,"style":3213},[238],[188,27275,507],{"className":27276},[243]," 次……\n所以，总等待时间 ",[36,27279,27280],{},[188,27281,27283,27355],{"className":27282},[191],[188,27284,27286],{"className":27285},[195],[197,27287,27288],{"xmlns":199},[201,27289,27290,27352],{},[204,27291,27292,27294,27296,27298,27300,27302,27304,27306,27312,27314,27316,27318,27320,27322,27324,27330,27332,27334,27336,27338,27340],{},[207,27293,2455],{},[211,27295,2464],{},[211,27297,214],{"stretchy":213},[207,27299,217],{},[211,27301,4945],{},[505,27303,4948],{},[211,27305,220],{"stretchy":213},[916,27307,27308,27310],{},[207,27309,7855],{},[505,27311,4948],{},[211,27313,516],{},[211,27315,214],{"stretchy":213},[207,27317,217],{},[211,27319,4945],{},[505,27321,507],{},[211,27323,220],{"stretchy":213},[916,27325,27326,27328],{},[207,27327,7855],{},[505,27329,507],{},[211,27331,516],{},[211,27333,12318],{},[211,27335,516],{},[505,27337,4948],{},[211,27339,13295],{},[916,27341,27342,27344],{},[207,27343,7855],{},[204,27345,27346,27348,27350],{},[207,27347,217],{},[211,27349,4945],{},[505,27351,4948],{},[222,27353,27354],{"encoding":224},"T = (n-1)t_1 + (n-2)t_2 + \\dots + 1 \\cdot t_{n-1}",[188,27356,27358,27376,27397,27458,27479,27540,27558,27576],{"className":27357,"ariaHidden":230},[229],[188,27359,27361,27364,27367,27370,27373],{"className":27360},[234],[188,27362],{"className":27363,"style":1693},[238],[188,27365,2455],{"className":27366,"style":2515},[243,244],[188,27368],{"className":27369,"style":2528},[584],[188,27371,2464],{"className":27372},[2532],[188,27374],{"className":27375,"style":2528},[584],[188,27377,27379,27382,27385,27388,27391,27394],{"className":27378},[234],[188,27380],{"className":27381,"style":239},[238],[188,27383,214],{"className":27384},[249],[188,27386,217],{"className":27387},[243,244],[188,27389],{"className":27390,"style":585},[584],[188,27392,4945],{"className":27393},[589],[188,27395],{"className":27396,"style":585},[584],[188,27398,27400,27403,27406,27409,27449,27452,27455],{"className":27399},[234],[188,27401],{"className":27402,"style":239},[238],[188,27404,4948],{"className":27405},[243],[188,27407,220],{"className":27408},[256],[188,27410,27412,27415],{"className":27411},[243],[188,27413,7855],{"className":27414},[243,244],[188,27416,27418],{"className":27417},[545],[188,27419,27421,27441],{"className":27420},[549,966],[188,27422,27424,27438],{"className":27423},[553],[188,27425,27427],{"className":27426,"style":9618},[557],[188,27428,27429,27432],{"style":9621},[188,27430],{"className":27431,"style":566},[565],[188,27433,27435],{"className":27434},[570,571,572,573],[188,27436,4948],{"className":27437},[243,573],[188,27439,990],{"className":27440},[989],[188,27442,27444],{"className":27443},[553],[188,27445,27447],{"className":27446,"style":6706},[557],[188,27448],{},[188,27450],{"className":27451,"style":585},[584],[188,27453,516],{"className":27454},[589],[188,27456],{"className":27457,"style":585},[584],[188,27459,27461,27464,27467,27470,27473,27476],{"className":27460},[234],[188,27462],{"className":27463,"style":239},[238],[188,27465,214],{"className":27466},[249],[188,27468,217],{"className":27469},[243,244],[188,27471],{"className":27472,"style":585},[584],[188,27474,4945],{"className":27475},[589],[188,27477],{"className":27478,"style":585},[584],[188,27480,27482,27485,27488,27491,27531,27534,27537],{"className":27481},[234],[188,27483],{"className":27484,"style":239},[238],[188,27486,507],{"className":27487},[243],[188,27489,220],{"className":27490},[256],[188,27492,27494,27497],{"className":27493},[243],[188,27495,7855],{"className":27496},[243,244],[188,27498,27500],{"className":27499},[545],[188,27501,27503,27523],{"className":27502},[549,966],[188,27504,27506,27520],{"className":27505},[553],[188,27507,27509],{"className":27508,"style":9618},[557],[188,27510,27511,27514],{"style":9621},[188,27512],{"className":27513,"style":566},[565],[188,27515,27517],{"className":27516},[570,571,572,573],[188,27518,507],{"className":27519},[243,573],[188,27521,990],{"className":27522},[989],[188,27524,27526],{"className":27525},[553],[188,27527,27529],{"className":27528,"style":6706},[557],[188,27530],{},[188,27532],{"className":27533,"style":585},[584],[188,27535,516],{"className":27536},[589],[188,27538],{"className":27539,"style":585},[584],[188,27541,27543,27546,27549,27552,27555],{"className":27542},[234],[188,27544],{"className":27545,"style":8822},[238],[188,27547,12318],{"className":27548},[9697],[188,27550],{"className":27551,"style":585},[584],[188,27553,516],{"className":27554},[589],[188,27556],{"className":27557,"style":585},[584],[188,27559,27561,27564,27567,27570,27573],{"className":27560},[234],[188,27562],{"className":27563,"style":3213},[238],[188,27565,4948],{"className":27566},[243],[188,27568],{"className":27569,"style":585},[584],[188,27571,13295],{"className":27572},[589],[188,27574],{"className":27575,"style":585},[584],[188,27577,27579,27583],{"className":27578},[234],[188,27580],{"className":27581,"style":27582},[238],"height:0.8234em;vertical-align:-0.2083em;",[188,27584,27586,27589],{"className":27585},[243],[188,27587,7855],{"className":27588},[243,244],[188,27590,27592],{"className":27591},[545],[188,27593,27595,27624],{"className":27594},[549,966],[188,27596,27598,27621],{"className":27597},[553],[188,27599,27601],{"className":27600,"style":9618},[557],[188,27602,27603,27606],{"style":9621},[188,27604],{"className":27605,"style":566},[565],[188,27607,27609],{"className":27608},[570,571,572,573],[188,27610,27612,27615,27618],{"className":27611},[243,573],[188,27613,217],{"className":27614},[243,244,573],[188,27616,4945],{"className":27617},[589,573],[188,27619,4948],{"className":27620},[243,573],[188,27622,990],{"className":27623},[989],[188,27625,27627],{"className":27626},[553],[188,27628,27630],{"className":27629,"style":13139},[557],[188,27631],{},"。\n要使得“平均等待时间最短”，就等同于使得“总等待时间 ",[188,27634,27636,27649],{"className":27635},[191],[188,27637,27639],{"className":27638},[195],[197,27640,27641],{"xmlns":199},[201,27642,27643,27647],{},[204,27644,27645],{},[207,27646,2455],{},[222,27648,2455],{"encoding":224},[188,27650,27652],{"className":27651,"ariaHidden":230},[229],[188,27653,27655,27658],{"className":27654},[234],[188,27656],{"className":27657,"style":1693},[238],[188,27659,2455],{"className":27660,"style":2515},[243,244]," 最小”。",[68,27663,27664,29137],{},[44,27665,27666,27669,27670,27698,27699,27727,27728,27756,27757,27785,27786,27920,27921,27949,27950,28011,28012,28073,28074,28102,28103,28131,28132,28748,28749,28801,28802,3805,28934,29136],{},[36,27667,27668],{},"贪心选择性质证明（运用交换论证法）：","\n假设我们的短作业优先策略产生的升序排列不是最优的。这意味着存在某个最优调度方案，在这个方案中，必定存在“逆序对”——也就是说，存在排在前面的某个作业 ",[188,27671,27673,27686],{"className":27672},[191],[188,27674,27676],{"className":27675},[195],[197,27677,27678],{"xmlns":199},[201,27679,27680,27684],{},[204,27681,27682],{},[207,27683,6651],{},[222,27685,6651],{"encoding":224},[188,27687,27689],{"className":27688,"ariaHidden":230},[229],[188,27690,27692,27695],{"className":27691},[234],[188,27693],{"className":27694,"style":9506},[238],[188,27696,6651],{"className":27697},[243,244],"，其处理时间比排在后面的作业 ",[188,27700,27702,27715],{"className":27701},[191],[188,27703,27705],{"className":27704},[195],[197,27706,27707],{"xmlns":199},[201,27708,27709,27713],{},[204,27710,27711],{},[207,27712,8087],{},[222,27714,8087],{"encoding":224},[188,27716,27718],{"className":27717,"ariaHidden":230},[229],[188,27719,27721,27724],{"className":27720},[234],[188,27722],{"className":27723,"style":9776},[238],[188,27725,8087],{"className":27726,"style":9476},[243,244]," 更长（即存在某个排列次序使得靠前的位置 ",[188,27729,27731,27744],{"className":27730},[191],[188,27732,27734],{"className":27733},[195],[197,27735,27736],{"xmlns":199},[201,27737,27738,27742],{},[204,27739,27740],{},[207,27741,7859],{},[222,27743,7859],{"encoding":224},[188,27745,27747],{"className":27746,"ariaHidden":230},[229],[188,27748,27750,27753],{"className":27749},[234],[188,27751],{"className":27752,"style":351},[238],[188,27754,7859],{"className":27755},[243,244]," 和靠后的位置 ",[188,27758,27760,27773],{"className":27759},[191],[188,27761,27763],{"className":27762},[195],[197,27764,27765],{"xmlns":199},[201,27766,27767,27771],{},[204,27768,27769],{},[207,27770,9827],{},[222,27772,9827],{"encoding":224},[188,27774,27776],{"className":27775,"ariaHidden":230},[229],[188,27777,27779,27782],{"className":27778},[234],[188,27780],{"className":27781,"style":14028},[238],[188,27783,9827],{"className":27784,"style":355},[243,244]," 满足 ",[188,27787,27789,27815],{"className":27788},[191],[188,27790,27792],{"className":27791},[195],[197,27793,27794],{"xmlns":199},[201,27795,27796,27812],{},[204,27797,27798,27804,27806],{},[916,27799,27800,27802],{},[207,27801,7855],{},[207,27803,7859],{},[211,27805,3724],{},[916,27807,27808,27810],{},[207,27809,7855],{},[207,27811,9827],{},[222,27813,27814],{"encoding":224},"t_x > t_y",[188,27816,27818,27873],{"className":27817,"ariaHidden":230},[229],[188,27819,27821,27824,27864,27867,27870],{"className":27820},[234],[188,27822],{"className":27823,"style":25997},[238],[188,27825,27827,27830],{"className":27826},[243],[188,27828,7855],{"className":27829},[243,244],[188,27831,27833],{"className":27832},[545],[188,27834,27836,27856],{"className":27835},[549,966],[188,27837,27839,27853],{"className":27838},[553],[188,27840,27842],{"className":27841,"style":12960},[557],[188,27843,27844,27847],{"style":9621},[188,27845],{"className":27846,"style":566},[565],[188,27848,27850],{"className":27849},[570,571,572,573],[188,27851,7859],{"className":27852},[243,244,573],[188,27854,990],{"className":27855},[989],[188,27857,27859],{"className":27858},[553],[188,27860,27862],{"className":27861,"style":6706},[557],[188,27863],{},[188,27865],{"className":27866,"style":2528},[584],[188,27868,3724],{"className":27869},[2532],[188,27871],{"className":27872,"style":2528},[584],[188,27874,27876,27880],{"className":27875},[234],[188,27877],{"className":27878,"style":27879},[238],"height:0.9012em;vertical-align:-0.2861em;",[188,27881,27883,27886],{"className":27882},[243],[188,27884,7855],{"className":27885},[243,244],[188,27887,27889],{"className":27888},[545],[188,27890,27892,27912],{"className":27891},[549,966],[188,27893,27895,27909],{"className":27894},[553],[188,27896,27898],{"className":27897,"style":12960},[557],[188,27899,27900,27903],{"style":9621},[188,27901],{"className":27902,"style":566},[565],[188,27904,27906],{"className":27905},[570,571,572,573],[188,27907,9827],{"className":27908,"style":355},[243,244,573],[188,27910,990],{"className":27911},[989],[188,27913,27915],{"className":27914},[553],[188,27916,27918],{"className":27917,"style":10011},[557],[188,27919],{},"）。\n在刚才推导的公式 ",[188,27922,27924,27937],{"className":27923},[191],[188,27925,27927],{"className":27926},[195],[197,27928,27929],{"xmlns":199},[201,27930,27931,27935],{},[204,27932,27933],{},[207,27934,2455],{},[222,27936,2455],{"encoding":224},[188,27938,27940],{"className":27939,"ariaHidden":230},[229],[188,27941,27943,27946],{"className":27942},[234],[188,27944],{"className":27945,"style":1693},[238],[188,27947,2455],{"className":27948,"style":2515},[243,244]," 中，越排在前面的作业，它乘以的权重系数越大（",[188,27951,27953,27975],{"className":27952},[191],[188,27954,27956],{"className":27955},[195],[197,27957,27958],{"xmlns":199},[201,27959,27960,27972],{},[204,27961,27962,27964,27966,27968,27970],{},[211,27963,214],{"stretchy":213},[207,27965,217],{},[211,27967,4945],{},[207,27969,7859],{},[211,27971,220],{"stretchy":213},[222,27973,27974],{"encoding":224},"(n-x)",[188,27976,27978,27999],{"className":27977,"ariaHidden":230},[229],[188,27979,27981,27984,27987,27990,27993,27996],{"className":27980},[234],[188,27982],{"className":27983,"style":239},[238],[188,27985,214],{"className":27986},[249],[188,27988,217],{"className":27989},[243,244],[188,27991],{"className":27992,"style":585},[584],[188,27994,4945],{"className":27995},[589],[188,27997],{"className":27998,"style":585},[584],[188,28000,28002,28005,28008],{"className":28001},[234],[188,28003],{"className":28004,"style":239},[238],[188,28006,7859],{"className":28007},[243,244],[188,28009,220],{"className":28010},[256]," 大于 ",[188,28013,28015,28037],{"className":28014},[191],[188,28016,28018],{"className":28017},[195],[197,28019,28020],{"xmlns":199},[201,28021,28022,28034],{},[204,28023,28024,28026,28028,28030,28032],{},[211,28025,214],{"stretchy":213},[207,28027,217],{},[211,28029,4945],{},[207,28031,9827],{},[211,28033,220],{"stretchy":213},[222,28035,28036],{"encoding":224},"(n-y)",[188,28038,28040,28061],{"className":28039,"ariaHidden":230},[229],[188,28041,28043,28046,28049,28052,28055,28058],{"className":28042},[234],[188,28044],{"className":28045,"style":239},[238],[188,28047,214],{"className":28048},[249],[188,28050,217],{"className":28051},[243,244],[188,28053],{"className":28054,"style":585},[584],[188,28056,4945],{"className":28057},[589],[188,28059],{"className":28060,"style":585},[584],[188,28062,28064,28067,28070],{"className":28063},[234],[188,28065],{"className":28066,"style":239},[238],[188,28068,9827],{"className":28069,"style":355},[243,244],[188,28071,220],{"className":28072},[256],"）。\n如果我们将这个耗时较长的作业 ",[188,28075,28077,28090],{"className":28076},[191],[188,28078,28080],{"className":28079},[195],[197,28081,28082],{"xmlns":199},[201,28083,28084,28088],{},[204,28085,28086],{},[207,28087,7859],{},[222,28089,7859],{"encoding":224},[188,28091,28093],{"className":28092,"ariaHidden":230},[229],[188,28094,28096,28099],{"className":28095},[234],[188,28097],{"className":28098,"style":351},[238],[188,28100,7859],{"className":28101},[243,244]," 与耗时较短的作业 ",[188,28104,28106,28119],{"className":28105},[191],[188,28107,28109],{"className":28108},[195],[197,28110,28111],{"xmlns":199},[201,28112,28113,28117],{},[204,28114,28115],{},[207,28116,9827],{},[222,28118,9827],{"encoding":224},[188,28120,28122],{"className":28121,"ariaHidden":230},[229],[188,28123,28125,28128],{"className":28124},[234],[188,28126],{"className":28127,"style":14028},[238],[188,28129,9827],{"className":28130,"style":355},[243,244]," 交换位置。\n新的总耗时相比旧的总耗时，变化量为：",[188,28133,28135,28258],{"className":28134},[191],[188,28136,28138],{"className":28137},[195],[197,28139,28140],{"xmlns":199},[201,28141,28142,28255],{},[204,28143,28144,28147,28149,28151,28153,28155,28157,28159,28161,28167,28169,28171,28173,28175,28177,28179,28185,28187,28189,28191,28193,28195,28197,28199,28205,28207,28209,28211,28213,28215,28217,28223,28225,28227,28229,28231,28233,28235,28237,28239,28245,28247,28253],{},[207,28145,28146],{"mathvariant":510},"Δ",[207,28148,2455],{},[211,28150,2464],{},[211,28152,214],{"stretchy":213},[207,28154,217],{},[211,28156,4945],{},[207,28158,7859],{},[211,28160,220],{"stretchy":213},[916,28162,28163,28165],{},[207,28164,7855],{},[207,28166,9827],{},[211,28168,516],{},[211,28170,214],{"stretchy":213},[207,28172,217],{},[211,28174,4945],{},[207,28176,9827],{},[211,28178,220],{"stretchy":213},[916,28180,28181,28183],{},[207,28182,7855],{},[207,28184,7859],{},[211,28186,4945],{},[211,28188,9366],{"stretchy":213},[211,28190,214],{"stretchy":213},[207,28192,217],{},[211,28194,4945],{},[207,28196,7859],{},[211,28198,220],{"stretchy":213},[916,28200,28201,28203],{},[207,28202,7855],{},[207,28204,7859],{},[211,28206,516],{},[211,28208,214],{"stretchy":213},[207,28210,217],{},[211,28212,4945],{},[207,28214,9827],{},[211,28216,220],{"stretchy":213},[916,28218,28219,28221],{},[207,28220,7855],{},[207,28222,9827],{},[211,28224,9371],{"stretchy":213},[211,28226,2464],{},[211,28228,214],{"stretchy":213},[207,28230,9827],{},[211,28232,4945],{},[207,28234,7859],{},[211,28236,220],{"stretchy":213},[211,28238,214],{"stretchy":213},[916,28240,28241,28243],{},[207,28242,7855],{},[207,28244,7859],{},[211,28246,4945],{},[916,28248,28249,28251],{},[207,28250,7855],{},[207,28252,9827],{},[211,28254,220],{"stretchy":213},[222,28256,28257],{"encoding":224},"\\Delta T = (n-x)t_y + (n-y)t_x - [ (n-x)t_x + (n-y)t_y ] = (y-x)(t_x - t_y)",[188,28259,28261,28282,28303,28364,28385,28446,28468,28529,28550,28614,28635,28699],{"className":28260,"ariaHidden":230},[229],[188,28262,28264,28267,28270,28273,28276,28279],{"className":28263},[234],[188,28265],{"className":28266,"style":1693},[238],[188,28268,28146],{"className":28269},[243],[188,28271,2455],{"className":28272,"style":2515},[243,244],[188,28274],{"className":28275,"style":2528},[584],[188,28277,2464],{"className":28278},[2532],[188,28280],{"className":28281,"style":2528},[584],[188,28283,28285,28288,28291,28294,28297,28300],{"className":28284},[234],[188,28286],{"className":28287,"style":239},[238],[188,28289,214],{"className":28290},[249],[188,28292,217],{"className":28293},[243,244],[188,28295],{"className":28296,"style":585},[584],[188,28298,4945],{"className":28299},[589],[188,28301],{"className":28302,"style":585},[584],[188,28304,28306,28309,28312,28315,28355,28358,28361],{"className":28305},[234],[188,28307],{"className":28308,"style":9864},[238],[188,28310,7859],{"className":28311},[243,244],[188,28313,220],{"className":28314},[256],[188,28316,28318,28321],{"className":28317},[243],[188,28319,7855],{"className":28320},[243,244],[188,28322,28324],{"className":28323},[545],[188,28325,28327,28347],{"className":28326},[549,966],[188,28328,28330,28344],{"className":28329},[553],[188,28331,28333],{"className":28332,"style":12960},[557],[188,28334,28335,28338],{"style":9621},[188,28336],{"className":28337,"style":566},[565],[188,28339,28341],{"className":28340},[570,571,572,573],[188,28342,9827],{"className":28343,"style":355},[243,244,573],[188,28345,990],{"className":28346},[989],[188,28348,28350],{"className":28349},[553],[188,28351,28353],{"className":28352,"style":10011},[557],[188,28354],{},[188,28356],{"className":28357,"style":585},[584],[188,28359,516],{"className":28360},[589],[188,28362],{"className":28363,"style":585},[584],[188,28365,28367,28370,28373,28376,28379,28382],{"className":28366},[234],[188,28368],{"className":28369,"style":239},[238],[188,28371,214],{"className":28372},[249],[188,28374,217],{"className":28375},[243,244],[188,28377],{"className":28378,"style":585},[584],[188,28380,4945],{"className":28381},[589],[188,28383],{"className":28384,"style":585},[584],[188,28386,28388,28391,28394,28397,28437,28440,28443],{"className":28387},[234],[188,28389],{"className":28390,"style":239},[238],[188,28392,9827],{"className":28393,"style":355},[243,244],[188,28395,220],{"className":28396},[256],[188,28398,28400,28403],{"className":28399},[243],[188,28401,7855],{"className":28402},[243,244],[188,28404,28406],{"className":28405},[545],[188,28407,28409,28429],{"className":28408},[549,966],[188,28410,28412,28426],{"className":28411},[553],[188,28413,28415],{"className":28414,"style":12960},[557],[188,28416,28417,28420],{"style":9621},[188,28418],{"className":28419,"style":566},[565],[188,28421,28423],{"className":28422},[570,571,572,573],[188,28424,7859],{"className":28425},[243,244,573],[188,28427,990],{"className":28428},[989],[188,28430,28432],{"className":28431},[553],[188,28433,28435],{"className":28434,"style":6706},[557],[188,28436],{},[188,28438],{"className":28439,"style":585},[584],[188,28441,4945],{"className":28442},[589],[188,28444],{"className":28445,"style":585},[584],[188,28447,28449,28452,28456,28459,28462,28465],{"className":28448},[234],[188,28450],{"className":28451,"style":239},[238],[188,28453,28455],{"className":28454},[249],"[(",[188,28457,217],{"className":28458},[243,244],[188,28460],{"className":28461,"style":585},[584],[188,28463,4945],{"className":28464},[589],[188,28466],{"className":28467,"style":585},[584],[188,28469,28471,28474,28477,28480,28520,28523,28526],{"className":28470},[234],[188,28472],{"className":28473,"style":239},[238],[188,28475,7859],{"className":28476},[243,244],[188,28478,220],{"className":28479},[256],[188,28481,28483,28486],{"className":28482},[243],[188,28484,7855],{"className":28485},[243,244],[188,28487,28489],{"className":28488},[545],[188,28490,28492,28512],{"className":28491},[549,966],[188,28493,28495,28509],{"className":28494},[553],[188,28496,28498],{"className":28497,"style":12960},[557],[188,28499,28500,28503],{"style":9621},[188,28501],{"className":28502,"style":566},[565],[188,28504,28506],{"className":28505},[570,571,572,573],[188,28507,7859],{"className":28508},[243,244,573],[188,28510,990],{"className":28511},[989],[188,28513,28515],{"className":28514},[553],[188,28516,28518],{"className":28517,"style":6706},[557],[188,28519],{},[188,28521],{"className":28522,"style":585},[584],[188,28524,516],{"className":28525},[589],[188,28527],{"className":28528,"style":585},[584],[188,28530,28532,28535,28538,28541,28544,28547],{"className":28531},[234],[188,28533],{"className":28534,"style":239},[238],[188,28536,214],{"className":28537},[249],[188,28539,217],{"className":28540},[243,244],[188,28542],{"className":28543,"style":585},[584],[188,28545,4945],{"className":28546},[589],[188,28548],{"className":28549,"style":585},[584],[188,28551,28553,28556,28559,28562,28602,28605,28608,28611],{"className":28552},[234],[188,28554],{"className":28555,"style":9864},[238],[188,28557,9827],{"className":28558,"style":355},[243,244],[188,28560,220],{"className":28561},[256],[188,28563,28565,28568],{"className":28564},[243],[188,28566,7855],{"className":28567},[243,244],[188,28569,28571],{"className":28570},[545],[188,28572,28574,28594],{"className":28573},[549,966],[188,28575,28577,28591],{"className":28576},[553],[188,28578,28580],{"className":28579,"style":12960},[557],[188,28581,28582,28585],{"style":9621},[188,28583],{"className":28584,"style":566},[565],[188,28586,28588],{"className":28587},[570,571,572,573],[188,28589,9827],{"className":28590,"style":355},[243,244,573],[188,28592,990],{"className":28593},[989],[188,28595,28597],{"className":28596},[553],[188,28598,28600],{"className":28599,"style":10011},[557],[188,28601],{},[188,28603,9371],{"className":28604},[256],[188,28606],{"className":28607,"style":2528},[584],[188,28609,2464],{"className":28610},[2532],[188,28612],{"className":28613,"style":2528},[584],[188,28615,28617,28620,28623,28626,28629,28632],{"className":28616},[234],[188,28618],{"className":28619,"style":239},[238],[188,28621,214],{"className":28622},[249],[188,28624,9827],{"className":28625,"style":355},[243,244],[188,28627],{"className":28628,"style":585},[584],[188,28630,4945],{"className":28631},[589],[188,28633],{"className":28634,"style":585},[584],[188,28636,28638,28641,28644,28647,28650,28690,28693,28696],{"className":28637},[234],[188,28639],{"className":28640,"style":239},[238],[188,28642,7859],{"className":28643},[243,244],[188,28645,220],{"className":28646},[256],[188,28648,214],{"className":28649},[249],[188,28651,28653,28656],{"className":28652},[243],[188,28654,7855],{"className":28655},[243,244],[188,28657,28659],{"className":28658},[545],[188,28660,28662,28682],{"className":28661},[549,966],[188,28663,28665,28679],{"className":28664},[553],[188,28666,28668],{"className":28667,"style":12960},[557],[188,28669,28670,28673],{"style":9621},[188,28671],{"className":28672,"style":566},[565],[188,28674,28676],{"className":28675},[570,571,572,573],[188,28677,7859],{"className":28678},[243,244,573],[188,28680,990],{"className":28681},[989],[188,28683,28685],{"className":28684},[553],[188,28686,28688],{"className":28687,"style":6706},[557],[188,28689],{},[188,28691],{"className":28692,"style":585},[584],[188,28694,4945],{"className":28695},[589],[188,28697],{"className":28698,"style":585},[584],[188,28700,28702,28705,28745],{"className":28701},[234],[188,28703],{"className":28704,"style":9864},[238],[188,28706,28708,28711],{"className":28707},[243],[188,28709,7855],{"className":28710},[243,244],[188,28712,28714],{"className":28713},[545],[188,28715,28717,28737],{"className":28716},[549,966],[188,28718,28720,28734],{"className":28719},[553],[188,28721,28723],{"className":28722,"style":12960},[557],[188,28724,28725,28728],{"style":9621},[188,28726],{"className":28727,"style":566},[565],[188,28729,28731],{"className":28730},[570,571,572,573],[188,28732,9827],{"className":28733,"style":355},[243,244,573],[188,28735,990],{"className":28736},[989],[188,28738,28740],{"className":28739},[553],[188,28741,28743],{"className":28742,"style":10011},[557],[188,28744],{},[188,28746,220],{"className":28747},[256],"。\n因为 ",[188,28750,28752,28770],{"className":28751},[191],[188,28753,28755],{"className":28754},[195],[197,28756,28757],{"xmlns":199},[201,28758,28759,28767],{},[204,28760,28761,28763,28765],{},[207,28762,9827],{},[211,28764,3724],{},[207,28766,7859],{},[222,28768,28769],{"encoding":224},"y > x",[188,28771,28773,28792],{"className":28772,"ariaHidden":230},[229],[188,28774,28776,28780,28783,28786,28789],{"className":28775},[234],[188,28777],{"className":28778,"style":28779},[238],"height:0.7335em;vertical-align:-0.1944em;",[188,28781,9827],{"className":28782,"style":355},[243,244],[188,28784],{"className":28785,"style":2528},[584],[188,28787,3724],{"className":28788},[2532],[188,28790],{"className":28791,"style":2528},[584],[188,28793,28795,28798],{"className":28794},[234],[188,28796],{"className":28797,"style":351},[238],[188,28799,7859],{"className":28800},[243,244]," 且 ",[188,28803,28805,28830],{"className":28804},[191],[188,28806,28808],{"className":28807},[195],[197,28809,28810],{"xmlns":199},[201,28811,28812,28828],{},[204,28813,28814,28820,28822],{},[916,28815,28816,28818],{},[207,28817,7855],{},[207,28819,7859],{},[211,28821,3724],{},[916,28823,28824,28826],{},[207,28825,7855],{},[207,28827,9827],{},[222,28829,27814],{"encoding":224},[188,28831,28833,28888],{"className":28832,"ariaHidden":230},[229],[188,28834,28836,28839,28879,28882,28885],{"className":28835},[234],[188,28837],{"className":28838,"style":25997},[238],[188,28840,28842,28845],{"className":28841},[243],[188,28843,7855],{"className":28844},[243,244],[188,28846,28848],{"className":28847},[545],[188,28849,28851,28871],{"className":28850},[549,966],[188,28852,28854,28868],{"className":28853},[553],[188,28855,28857],{"className":28856,"style":12960},[557],[188,28858,28859,28862],{"style":9621},[188,28860],{"className":28861,"style":566},[565],[188,28863,28865],{"className":28864},[570,571,572,573],[188,28866,7859],{"className":28867},[243,244,573],[188,28869,990],{"className":28870},[989],[188,28872,28874],{"className":28873},[553],[188,28875,28877],{"className":28876,"style":6706},[557],[188,28878],{},[188,28880],{"className":28881,"style":2528},[584],[188,28883,3724],{"className":28884},[2532],[188,28886],{"className":28887,"style":2528},[584],[188,28889,28891,28894],{"className":28890},[234],[188,28892],{"className":28893,"style":27879},[238],[188,28895,28897,28900],{"className":28896},[243],[188,28898,7855],{"className":28899},[243,244],[188,28901,28903],{"className":28902},[545],[188,28904,28906,28926],{"className":28905},[549,966],[188,28907,28909,28923],{"className":28908},[553],[188,28910,28912],{"className":28911,"style":12960},[557],[188,28913,28914,28917],{"style":9621},[188,28915],{"className":28916,"style":566},[565],[188,28918,28920],{"className":28919},[570,571,572,573],[188,28921,9827],{"className":28922,"style":355},[243,244,573],[188,28924,990],{"className":28925},[989],[188,28927,28929],{"className":28928},[553],[188,28930,28932],{"className":28931,"style":10011},[557],[188,28933],{},[188,28935,28937,28981],{"className":28936},[191],[188,28938,28940],{"className":28939},[195],[197,28941,28942],{"xmlns":199},[201,28943,28944,28978],{},[204,28945,28946,28948,28950,28952,28954,28956,28958,28964,28966,28972,28974,28976],{},[211,28947,214],{"stretchy":213},[207,28949,9827],{},[211,28951,4945],{},[207,28953,7859],{},[211,28955,220],{"stretchy":213},[211,28957,214],{"stretchy":213},[916,28959,28960,28962],{},[207,28961,7855],{},[207,28963,7859],{},[211,28965,4945],{},[916,28967,28968,28970],{},[207,28969,7855],{},[207,28971,9827],{},[211,28973,220],{"stretchy":213},[211,28975,3724],{},[505,28977,8307],{},[222,28979,28980],{"encoding":224},"(y-x)(t_x - t_y) > 0",[188,28982,28984,29005,29069,29127],{"className":28983,"ariaHidden":230},[229],[188,28985,28987,28990,28993,28996,28999,29002],{"className":28986},[234],[188,28988],{"className":28989,"style":239},[238],[188,28991,214],{"className":28992},[249],[188,28994,9827],{"className":28995,"style":355},[243,244],[188,28997],{"className":28998,"style":585},[584],[188,29000,4945],{"className":29001},[589],[188,29003],{"className":29004,"style":585},[584],[188,29006,29008,29011,29014,29017,29020,29060,29063,29066],{"className":29007},[234],[188,29009],{"className":29010,"style":239},[238],[188,29012,7859],{"className":29013},[243,244],[188,29015,220],{"className":29016},[256],[188,29018,214],{"className":29019},[249],[188,29021,29023,29026],{"className":29022},[243],[188,29024,7855],{"className":29025},[243,244],[188,29027,29029],{"className":29028},[545],[188,29030,29032,29052],{"className":29031},[549,966],[188,29033,29035,29049],{"className":29034},[553],[188,29036,29038],{"className":29037,"style":12960},[557],[188,29039,29040,29043],{"style":9621},[188,29041],{"className":29042,"style":566},[565],[188,29044,29046],{"className":29045},[570,571,572,573],[188,29047,7859],{"className":29048},[243,244,573],[188,29050,990],{"className":29051},[989],[188,29053,29055],{"className":29054},[553],[188,29056,29058],{"className":29057,"style":6706},[557],[188,29059],{},[188,29061],{"className":29062,"style":585},[584],[188,29064,4945],{"className":29065},[589],[188,29067],{"className":29068,"style":585},[584],[188,29070,29072,29075,29115,29118,29121,29124],{"className":29071},[234],[188,29073],{"className":29074,"style":9864},[238],[188,29076,29078,29081],{"className":29077},[243],[188,29079,7855],{"className":29080},[243,244],[188,29082,29084],{"className":29083},[545],[188,29085,29087,29107],{"className":29086},[549,966],[188,29088,29090,29104],{"className":29089},[553],[188,29091,29093],{"className":29092,"style":12960},[557],[188,29094,29095,29098],{"style":9621},[188,29096],{"className":29097,"style":566},[565],[188,29099,29101],{"className":29100},[570,571,572,573],[188,29102,9827],{"className":29103,"style":355},[243,244,573],[188,29105,990],{"className":29106},[989],[188,29108,29110],{"className":29109},[553],[188,29111,29113],{"className":29112,"style":10011},[557],[188,29114],{},[188,29116,220],{"className":29117},[256],[188,29119],{"className":29120,"style":2528},[584],[188,29122,3724],{"className":29123},[2532],[188,29125],{"className":29126,"style":2528},[584],[188,29128,29130,29133],{"className":29129},[234],[188,29131],{"className":29132,"style":3213},[238],[188,29134,8307],{"className":29135},[243],"。\n这意味着交换后总等待时间减小了。这与它原本是“最优方案”相矛盾。\n因此，按照时间升序排列（贪心选择）必定包含在最优解中。",[44,29138,29139,29142,29143,29193,29194,29637,29638,29688,29689,29739,29740,29768],{},[36,29140,29141],{},"最优子结构性质证明：","\n假设我们按照贪心策略选出了耗时最短的作业 1。剩下的问题变成了：如何调度余下的 ",[188,29144,29146,29163],{"className":29145},[191],[188,29147,29149],{"className":29148},[195],[197,29150,29151],{"xmlns":199},[201,29152,29153,29161],{},[204,29154,29155,29157,29159],{},[207,29156,217],{},[211,29158,4945],{},[505,29160,4948],{},[222,29162,11536],{"encoding":224},[188,29164,29166,29184],{"className":29165,"ariaHidden":230},[229],[188,29167,29169,29172,29175,29178,29181],{"className":29168},[234],[188,29170],{"className":29171,"style":8822},[238],[188,29173,217],{"className":29174},[243,244],[188,29176],{"className":29177,"style":585},[584],[188,29179,4945],{"className":29180},[589],[188,29182],{"className":29183,"style":585},[584],[188,29185,29187,29190],{"className":29186},[234],[188,29188],{"className":29189,"style":3213},[238],[188,29191,4948],{"className":29192},[243]," 个作业使得总等待时间最小。\n根据公式推导 ",[188,29195,29197,29285],{"className":29196},[191],[188,29198,29200],{"className":29199},[195],[197,29201,29202],{"xmlns":199},[201,29203,29204,29282],{},[204,29205,29206,29208,29210,29212,29214,29216,29218,29220,29226,29228,29230,29232,29234,29236,29238,29240,29246,29248,29250,29252,29254,29256,29258,29264,29266,29268,29270,29272,29274,29280],{},[207,29207,2455],{},[211,29209,2464],{},[211,29211,214],{"stretchy":213},[207,29213,217],{},[211,29215,4945],{},[505,29217,4948],{},[211,29219,220],{"stretchy":213},[916,29221,29222,29224],{},[207,29223,7855],{},[505,29225,4948],{},[211,29227,516],{},[211,29229,9366],{"stretchy":213},[211,29231,214],{"stretchy":213},[207,29233,217],{},[211,29235,4945],{},[505,29237,507],{},[211,29239,220],{"stretchy":213},[916,29241,29242,29244],{},[207,29243,7855],{},[505,29245,507],{},[211,29247,516],{},[211,29249,214],{"stretchy":213},[207,29251,217],{},[211,29253,4945],{},[505,29255,934],{},[211,29257,220],{"stretchy":213},[916,29259,29260,29262],{},[207,29261,7855],{},[505,29263,934],{},[211,29265,516],{},[211,29267,12318],{},[211,29269,516],{},[505,29271,4948],{},[211,29273,13295],{},[916,29275,29276,29278],{},[207,29277,7855],{},[207,29279,217],{},[211,29281,9371],{"stretchy":213},[222,29283,29284],{"encoding":224},"T = (n-1)t_1 + [ (n-2)t_2 + (n-3)t_3 + \\dots + 1 \\cdot t_n ]",[188,29286,29288,29306,29327,29388,29409,29470,29491,29552,29570,29588],{"className":29287,"ariaHidden":230},[229],[188,29289,29291,29294,29297,29300,29303],{"className":29290},[234],[188,29292],{"className":29293,"style":1693},[238],[188,29295,2455],{"className":29296,"style":2515},[243,244],[188,29298],{"className":29299,"style":2528},[584],[188,29301,2464],{"className":29302},[2532],[188,29304],{"className":29305,"style":2528},[584],[188,29307,29309,29312,29315,29318,29321,29324],{"className":29308},[234],[188,29310],{"className":29311,"style":239},[238],[188,29313,214],{"className":29314},[249],[188,29316,217],{"className":29317},[243,244],[188,29319],{"className":29320,"style":585},[584],[188,29322,4945],{"className":29323},[589],[188,29325],{"className":29326,"style":585},[584],[188,29328,29330,29333,29336,29339,29379,29382,29385],{"className":29329},[234],[188,29331],{"className":29332,"style":239},[238],[188,29334,4948],{"className":29335},[243],[188,29337,220],{"className":29338},[256],[188,29340,29342,29345],{"className":29341},[243],[188,29343,7855],{"className":29344},[243,244],[188,29346,29348],{"className":29347},[545],[188,29349,29351,29371],{"className":29350},[549,966],[188,29352,29354,29368],{"className":29353},[553],[188,29355,29357],{"className":29356,"style":9618},[557],[188,29358,29359,29362],{"style":9621},[188,29360],{"className":29361,"style":566},[565],[188,29363,29365],{"className":29364},[570,571,572,573],[188,29366,4948],{"className":29367},[243,573],[188,29369,990],{"className":29370},[989],[188,29372,29374],{"className":29373},[553],[188,29375,29377],{"className":29376,"style":6706},[557],[188,29378],{},[188,29380],{"className":29381,"style":585},[584],[188,29383,516],{"className":29384},[589],[188,29386],{"className":29387,"style":585},[584],[188,29389,29391,29394,29397,29400,29403,29406],{"className":29390},[234],[188,29392],{"className":29393,"style":239},[238],[188,29395,28455],{"className":29396},[249],[188,29398,217],{"className":29399},[243,244],[188,29401],{"className":29402,"style":585},[584],[188,29404,4945],{"className":29405},[589],[188,29407],{"className":29408,"style":585},[584],[188,29410,29412,29415,29418,29421,29461,29464,29467],{"className":29411},[234],[188,29413],{"className":29414,"style":239},[238],[188,29416,507],{"className":29417},[243],[188,29419,220],{"className":29420},[256],[188,29422,29424,29427],{"className":29423},[243],[188,29425,7855],{"className":29426},[243,244],[188,29428,29430],{"className":29429},[545],[188,29431,29433,29453],{"className":29432},[549,966],[188,29434,29436,29450],{"className":29435},[553],[188,29437,29439],{"className":29438,"style":9618},[557],[188,29440,29441,29444],{"style":9621},[188,29442],{"className":29443,"style":566},[565],[188,29445,29447],{"className":29446},[570,571,572,573],[188,29448,507],{"className":29449},[243,573],[188,29451,990],{"className":29452},[989],[188,29454,29456],{"className":29455},[553],[188,29457,29459],{"className":29458,"style":6706},[557],[188,29460],{},[188,29462],{"className":29463,"style":585},[584],[188,29465,516],{"className":29466},[589],[188,29468],{"className":29469,"style":585},[584],[188,29471,29473,29476,29479,29482,29485,29488],{"className":29472},[234],[188,29474],{"className":29475,"style":239},[238],[188,29477,214],{"className":29478},[249],[188,29480,217],{"className":29481},[243,244],[188,29483],{"className":29484,"style":585},[584],[188,29486,4945],{"className":29487},[589],[188,29489],{"className":29490,"style":585},[584],[188,29492,29494,29497,29500,29503,29543,29546,29549],{"className":29493},[234],[188,29495],{"className":29496,"style":239},[238],[188,29498,934],{"className":29499},[243],[188,29501,220],{"className":29502},[256],[188,29504,29506,29509],{"className":29505},[243],[188,29507,7855],{"className":29508},[243,244],[188,29510,29512],{"className":29511},[545],[188,29513,29515,29535],{"className":29514},[549,966],[188,29516,29518,29532],{"className":29517},[553],[188,29519,29521],{"className":29520,"style":9618},[557],[188,29522,29523,29526],{"style":9621},[188,29524],{"className":29525,"style":566},[565],[188,29527,29529],{"className":29528},[570,571,572,573],[188,29530,934],{"className":29531},[243,573],[188,29533,990],{"className":29534},[989],[188,29536,29538],{"className":29537},[553],[188,29539,29541],{"className":29540,"style":6706},[557],[188,29542],{},[188,29544],{"className":29545,"style":585},[584],[188,29547,516],{"className":29548},[589],[188,29550],{"className":29551,"style":585},[584],[188,29553,29555,29558,29561,29564,29567],{"className":29554},[234],[188,29556],{"className":29557,"style":8822},[238],[188,29559,12318],{"className":29560},[9697],[188,29562],{"className":29563,"style":585},[584],[188,29565,516],{"className":29566},[589],[188,29568],{"className":29569,"style":585},[584],[188,29571,29573,29576,29579,29582,29585],{"className":29572},[234],[188,29574],{"className":29575,"style":3213},[238],[188,29577,4948],{"className":29578},[243],[188,29580],{"className":29581,"style":585},[584],[188,29583,13295],{"className":29584},[589],[188,29586],{"className":29587,"style":585},[584],[188,29589,29591,29594,29634],{"className":29590},[234],[188,29592],{"className":29593,"style":239},[238],[188,29595,29597,29600],{"className":29596},[243],[188,29598,7855],{"className":29599},[243,244],[188,29601,29603],{"className":29602},[545],[188,29604,29606,29626],{"className":29605},[549,966],[188,29607,29609,29623],{"className":29608},[553],[188,29610,29612],{"className":29611,"style":12960},[557],[188,29613,29614,29617],{"style":9621},[188,29615],{"className":29616,"style":566},[565],[188,29618,29620],{"className":29619},[570,571,572,573],[188,29621,217],{"className":29622},[243,244,573],[188,29624,990],{"className":29625},[989],[188,29627,29629],{"className":29628},[553],[188,29630,29632],{"className":29631,"style":6706},[557],[188,29633],{},[188,29635,9371],{"className":29636},[256],"。\n方括号内的部分，恰恰就是完全等价于剩下的 ",[188,29639,29641,29658],{"className":29640},[191],[188,29642,29644],{"className":29643},[195],[197,29645,29646],{"xmlns":199},[201,29647,29648,29656],{},[204,29649,29650,29652,29654],{},[207,29651,217],{},[211,29653,4945],{},[505,29655,4948],{},[222,29657,11536],{"encoding":224},[188,29659,29661,29679],{"className":29660,"ariaHidden":230},[229],[188,29662,29664,29667,29670,29673,29676],{"className":29663},[234],[188,29665],{"className":29666,"style":8822},[238],[188,29668,217],{"className":29669},[243,244],[188,29671],{"className":29672,"style":585},[584],[188,29674,4945],{"className":29675},[589],[188,29677],{"className":29678,"style":585},[584],[188,29680,29682,29685],{"className":29681},[234],[188,29683],{"className":29684,"style":3213},[238],[188,29686,4948],{"className":29687},[243]," 个作业独立调度的总等待时间模型（只是常数项权重集体偏移）。\n如果这剩下的 ",[188,29690,29692,29709],{"className":29691},[191],[188,29693,29695],{"className":29694},[195],[197,29696,29697],{"xmlns":199},[201,29698,29699,29707],{},[204,29700,29701,29703,29705],{},[207,29702,217],{},[211,29704,4945],{},[505,29706,4948],{},[222,29708,11536],{"encoding":224},[188,29710,29712,29730],{"className":29711,"ariaHidden":230},[229],[188,29713,29715,29718,29721,29724,29727],{"className":29714},[234],[188,29716],{"className":29717,"style":8822},[238],[188,29719,217],{"className":29720},[243,244],[188,29722],{"className":29723,"style":585},[584],[188,29725,4945],{"className":29726},[589],[188,29728],{"className":29729,"style":585},[584],[188,29731,29733,29736],{"className":29732},[234],[188,29734],{"className":29735,"style":3213},[238],[188,29737,4948],{"className":29738},[243]," 个作业没有按照使方括号内总和最小的方式去排列，那么必定存在另一个排列能让方括号内的值更小，进而导致整体 ",[188,29741,29743,29756],{"className":29742},[191],[188,29744,29746],{"className":29745},[195],[197,29747,29748],{"xmlns":199},[201,29749,29750,29754],{},[204,29751,29752],{},[207,29753,2455],{},[222,29755,2455],{"encoding":224},[188,29757,29759],{"className":29758,"ariaHidden":230},[229],[188,29760,29762,29765],{"className":29761},[234],[188,29763],{"className":29764,"style":1693},[238],[188,29766,2455],{"className":29767,"style":2515},[243,244]," 更小，这与原问题的最优性矛盾。\n因此，原问题的最优解包含了子问题的最优解，满足最优子结构性质。",[14,29770],{},[17,29772,29774],{"id":29773},"五算法设计每题10分共20分","五、算法设计（每题10分，共20分）",[22,29776,25],{"id":29777},"_1-题目内容-4",[27,29779,29780],{},"设计递归算法求一个不带头节点的单链表长度。",[41,29782,29783,29786],{},[44,29784,29785],{},"编写该算法。（5分）",[44,29787,29788],{},"分析所涉及的算法的时间和空间复杂度。（5分）",[22,29790,32],{"id":29791},"答案与深度解析-22",[27,29793,29794],{},[36,29795,29796],{},"1) 算法代码（C\u002FC++语言表示）：",[7746,29798,29800],{"className":7748,"code":29799,"language":7750,"meta":7751,"style":7751},"\u002F\u002F 假设链表节点结构体定义如下：\n\u002F\u002F struct Node {\n\u002F\u002F     int data;\n\u002F\u002F     struct Node* next;\n\u002F\u002F };\n\nint getListLength(struct Node* head) {\n    \u002F\u002F 基线条件：如果指针为空，说明走到了链表尽头（或本身是空链表），长度为0\n    if (head == NULL) {\n        return 0;\n    }\n    \u002F\u002F 递归思想：当前链表的总长度 = 当前这 1 个节点 + 后续链表的长度\n    return 1 + getListLength(head->next);\n}\n",[7457,29801,29802,29807,29812,29817,29822,29827,29833,29838,29843,29848,29853,29857,29862,29867],{"__ignoreMap":7751},[188,29803,29804],{"class":7756,"line":7757},[188,29805,29806],{},"\u002F\u002F 假设链表节点结构体定义如下：\n",[188,29808,29809],{"class":7756,"line":7763},[188,29810,29811],{},"\u002F\u002F struct Node {\n",[188,29813,29814],{"class":7756,"line":7769},[188,29815,29816],{},"\u002F\u002F     int data;\n",[188,29818,29819],{"class":7756,"line":7775},[188,29820,29821],{},"\u002F\u002F     struct Node* next;\n",[188,29823,29824],{"class":7756,"line":7781},[188,29825,29826],{},"\u002F\u002F };\n",[188,29828,29829],{"class":7756,"line":7787},[188,29830,29832],{"emptyLinePlaceholder":29831},true,"\n",[188,29834,29835],{"class":7756,"line":7793},[188,29836,29837],{},"int getListLength(struct Node* head) {\n",[188,29839,29840],{"class":7756,"line":7799},[188,29841,29842],{},"    \u002F\u002F 基线条件：如果指针为空，说明走到了链表尽头（或本身是空链表），长度为0\n",[188,29844,29845],{"class":7756,"line":7805},[188,29846,29847],{},"    if (head == NULL) {\n",[188,29849,29850],{"class":7756,"line":7811},[188,29851,29852],{},"        return 0;\n",[188,29854,29855],{"class":7756,"line":7817},[188,29856,10891],{},[188,29858,29859],{"class":7756,"line":7823},[188,29860,29861],{},"    \u002F\u002F 递归思想：当前链表的总长度 = 当前这 1 个节点 + 后续链表的长度\n",[188,29863,29864],{"class":7756,"line":7829},[188,29865,29866],{},"    return 1 + getListLength(head->next);\n",[188,29868,29869],{"class":7756,"line":10894},[188,29870,7832],{},[27,29872,29873],{},[36,29874,29875],{},"2) 复杂度分析：",[68,29877,29878,30058],{},[44,29879,29880,29882,29883,29886,29887,29915,29916,29967,29968,30012,30013,85],{},[36,29881,7106],{}," 该递归算法会从链表的首节点依次一直走到链表的末尾 ",[7457,29884,29885],{},"NULL","。如果链表长度为 ",[188,29888,29890,29903],{"className":29889},[191],[188,29891,29893],{"className":29892},[195],[197,29894,29895],{"xmlns":199},[201,29896,29897,29901],{},[204,29898,29899],{},[207,29900,217],{},[222,29902,217],{"encoding":224},[188,29904,29906],{"className":29905,"ariaHidden":230},[229],[188,29907,29909,29912],{"className":29908},[234],[188,29910],{"className":29911,"style":351},[238],[188,29913,217],{"className":29914},[243,244],"，函数就会被调用执行 ",[188,29917,29919,29937],{"className":29918},[191],[188,29920,29922],{"className":29921},[195],[197,29923,29924],{"xmlns":199},[201,29925,29926,29934],{},[204,29927,29928,29930,29932],{},[207,29929,217],{},[211,29931,516],{},[505,29933,4948],{},[222,29935,29936],{"encoding":224},"n+1",[188,29938,29940,29958],{"className":29939,"ariaHidden":230},[229],[188,29941,29943,29946,29949,29952,29955],{"className":29942},[234],[188,29944],{"className":29945,"style":8822},[238],[188,29947,217],{"className":29948},[243,244],[188,29950],{"className":29951,"style":585},[584],[188,29953,516],{"className":29954},[589],[188,29956],{"className":29957,"style":585},[584],[188,29959,29961,29964],{"className":29960},[234],[188,29962],{"className":29963,"style":3213},[238],[188,29965,4948],{"className":29966},[243]," 次。每一次函数调用内部只做了简单的指针判空与加法运算，耗时为 ",[188,29969,29971,29991],{"className":29970},[191],[188,29972,29974],{"className":29973},[195],[197,29975,29976],{"xmlns":199},[201,29977,29978,29988],{},[204,29979,29980,29982,29984,29986],{},[207,29981,209],{},[211,29983,214],{"stretchy":213},[505,29985,4948],{},[211,29987,220],{"stretchy":213},[222,29989,29990],{"encoding":224},"O(1)",[188,29992,29994],{"className":29993,"ariaHidden":230},[229],[188,29995,29997,30000,30003,30006,30009],{"className":29996},[234],[188,29998],{"className":29999,"style":239},[238],[188,30001,209],{"className":30002,"style":245},[243,244],[188,30004,214],{"className":30005},[249],[188,30007,4948],{"className":30008},[243],[188,30010,220],{"className":30011},[256],"。因此总时间复杂度为 ",[36,30014,30015],{},[188,30016,30018,30037],{"className":30017},[191],[188,30019,30021],{"className":30020},[195],[197,30022,30023],{"xmlns":199},[201,30024,30025,30035],{},[204,30026,30027,30029,30031,30033],{},[207,30028,209],{},[211,30030,214],{"stretchy":213},[207,30032,217],{},[211,30034,220],{"stretchy":213},[222,30036,225],{"encoding":224},[188,30038,30040],{"className":30039,"ariaHidden":230},[229],[188,30041,30043,30046,30049,30052,30055],{"className":30042},[234],[188,30044],{"className":30045,"style":239},[238],[188,30047,209],{"className":30048,"style":245},[243,244],[188,30050,214],{"className":30051},[249],[188,30053,217],{"className":30054},[243,244],[188,30056,220],{"className":30057},[256],[44,30059,30060,30063,30064,30067,30068,30096,30097,30147,30148,30198,30199,85],{},[36,30061,30062],{},"空间复杂度分析："," 这一点极其容易被忽略。虽然代码里没有动态分配数组，但是",[36,30065,30066],{},"系统执行递归是需要开辟“调用栈”的","。每次函数调用，系统要保存局部变量、返回地址等信息到栈帧中。链表长度为 ",[188,30069,30071,30084],{"className":30070},[191],[188,30072,30074],{"className":30073},[195],[197,30075,30076],{"xmlns":199},[201,30077,30078,30082],{},[204,30079,30080],{},[207,30081,217],{},[222,30083,217],{"encoding":224},[188,30085,30087],{"className":30086,"ariaHidden":230},[229],[188,30088,30090,30093],{"className":30089},[234],[188,30091],{"className":30092,"style":351},[238],[188,30094,217],{"className":30095},[243,244],"，递归就会深入 ",[188,30098,30100,30117],{"className":30099},[191],[188,30101,30103],{"className":30102},[195],[197,30104,30105],{"xmlns":199},[201,30106,30107,30115],{},[204,30108,30109,30111,30113],{},[207,30110,217],{},[211,30112,516],{},[505,30114,4948],{},[222,30116,29936],{"encoding":224},[188,30118,30120,30138],{"className":30119,"ariaHidden":230},[229],[188,30121,30123,30126,30129,30132,30135],{"className":30122},[234],[188,30124],{"className":30125,"style":8822},[238],[188,30127,217],{"className":30128},[243,244],[188,30130],{"className":30131,"style":585},[584],[188,30133,516],{"className":30134},[589],[188,30136],{"className":30137,"style":585},[584],[188,30139,30141,30144],{"className":30140},[234],[188,30142],{"className":30143,"style":3213},[238],[188,30145,4948],{"className":30146},[243]," 层，栈的最大深度就是 ",[188,30149,30151,30168],{"className":30150},[191],[188,30152,30154],{"className":30153},[195],[197,30155,30156],{"xmlns":199},[201,30157,30158,30166],{},[204,30159,30160,30162,30164],{},[207,30161,217],{},[211,30163,516],{},[505,30165,4948],{},[222,30167,29936],{"encoding":224},[188,30169,30171,30189],{"className":30170,"ariaHidden":230},[229],[188,30172,30174,30177,30180,30183,30186],{"className":30173},[234],[188,30175],{"className":30176,"style":8822},[238],[188,30178,217],{"className":30179},[243,244],[188,30181],{"className":30182,"style":585},[584],[188,30184,516],{"className":30185},[589],[188,30187],{"className":30188,"style":585},[584],[188,30190,30192,30195],{"className":30191},[234],[188,30193],{"className":30194,"style":3213},[238],[188,30196,4948],{"className":30197},[243],"。因此，空间复杂度同样为 ",[36,30200,30201],{},[188,30202,30204,30223],{"className":30203},[191],[188,30205,30207],{"className":30206},[195],[197,30208,30209],{"xmlns":199},[201,30210,30211,30221],{},[204,30212,30213,30215,30217,30219],{},[207,30214,209],{},[211,30216,214],{"stretchy":213},[207,30218,217],{},[211,30220,220],{"stretchy":213},[222,30222,225],{"encoding":224},[188,30224,30226],{"className":30225,"ariaHidden":230},[229],[188,30227,30229,30232,30235,30238,30241],{"className":30228},[234],[188,30230],{"className":30231,"style":239},[238],[188,30233,209],{"className":30234,"style":245},[243,244],[188,30236,214],{"className":30237},[249],[188,30239,217],{"className":30240},[243,244],[188,30242,220],{"className":30243},[256],[14,30245],{},[22,30247,97],{"id":30248},"_2-题目内容-4",[27,30250,30251,30252,11026,30280,30310,30311,11026,30339,30367,30368,30396,30397,30425],{},"利用动态规划法设计算法求两个字符串 ",[188,30253,30255,30268],{"className":30254},[191],[188,30256,30258],{"className":30257},[195],[197,30259,30260],{"xmlns":199},[201,30261,30262,30266],{},[204,30263,30264],{},[207,30265,12802],{},[222,30267,12802],{"encoding":224},[188,30269,30271],{"className":30270,"ariaHidden":230},[229],[188,30272,30274,30277],{"className":30273},[234],[188,30275],{"className":30276,"style":1693},[238],[188,30278,12802],{"className":30279},[243,244],[188,30281,30283,30297],{"className":30282},[191],[188,30284,30286],{"className":30285},[195],[197,30287,30288],{"xmlns":199},[201,30289,30290,30295],{},[204,30291,30292],{},[207,30293,30294],{},"B",[222,30296,30294],{"encoding":224},[188,30298,30300],{"className":30299,"ariaHidden":230},[229],[188,30301,30303,30306],{"className":30302},[234],[188,30304],{"className":30305,"style":1693},[238],[188,30307,30294],{"className":30308,"style":30309},[243,244],"margin-right:0.0502em;"," 的编辑距离。设 ",[188,30312,30314,30327],{"className":30313},[191],[188,30315,30317],{"className":30316},[195],[197,30318,30319],{"xmlns":199},[201,30320,30321,30325],{},[204,30322,30323],{},[207,30324,12802],{},[222,30326,12802],{"encoding":224},[188,30328,30330],{"className":30329,"ariaHidden":230},[229],[188,30331,30333,30336],{"className":30332},[234],[188,30334],{"className":30335,"style":1693},[238],[188,30337,12802],{"className":30338},[243,244],[188,30340,30342,30355],{"className":30341},[191],[188,30343,30345],{"className":30344},[195],[197,30346,30347],{"xmlns":199},[201,30348,30349,30353],{},[204,30350,30351],{},[207,30352,30294],{},[222,30354,30294],{"encoding":224},[188,30356,30358],{"className":30357,"ariaHidden":230},[229],[188,30359,30361,30364],{"className":30360},[234],[188,30362],{"className":30363,"style":1693},[238],[188,30365,30294],{"className":30366,"style":30309},[243,244]," 是两个字符串。所谓的编辑距离即将字符串 ",[188,30369,30371,30384],{"className":30370},[191],[188,30372,30374],{"className":30373},[195],[197,30375,30376],{"xmlns":199},[201,30377,30378,30382],{},[204,30379,30380],{},[207,30381,12802],{},[222,30383,12802],{"encoding":224},[188,30385,30387],{"className":30386,"ariaHidden":230},[229],[188,30388,30390,30393],{"className":30389},[234],[188,30391],{"className":30392,"style":1693},[238],[188,30394,12802],{"className":30395},[243,244]," 转换成字符串 ",[188,30398,30400,30413],{"className":30399},[191],[188,30401,30403],{"className":30402},[195],[197,30404,30405],{"xmlns":199},[201,30406,30407,30411],{},[204,30408,30409],{},[207,30410,30294],{},[222,30412,30294],{"encoding":224},[188,30414,30416],{"className":30415,"ariaHidden":230},[229],[188,30417,30419,30422],{"className":30418},[234],[188,30420],{"className":30421,"style":1693},[238],[188,30423,30294],{"className":30424,"style":30309},[243,244]," 所经历的最少编辑操作次数。编辑操作共有 3 种：(1) 删除一个字符 delete；(2) 插入一个字符 insert；(3) 将一个字符替换另一个字符 replace。",[41,30427,30428,30610],{},[44,30429,30430,30431,30494,30495,30523,30524,30552,30553,30523,30581,30609],{},"设计动态规划数组 ",[188,30432,30434,30461],{"className":30433},[191],[188,30435,30437],{"className":30436},[195],[197,30438,30439],{"xmlns":199},[201,30440,30441,30459],{},[204,30442,30443,30445,30447,30449,30451,30453,30455,30457],{},[207,30444,9361],{},[207,30446,27],{},[211,30448,9366],{"stretchy":213},[207,30450,6651],{},[211,30452,9371],{"stretchy":213},[211,30454,9366],{"stretchy":213},[207,30456,8087],{},[211,30458,9371],{"stretchy":213},[222,30460,9445],{"encoding":224},[188,30462,30464],{"className":30463,"ariaHidden":230},[229],[188,30465,30467,30470,30473,30476,30479,30482,30485,30488,30491],{"className":30466},[234],[188,30468],{"className":30469,"style":239},[238],[188,30471,9361],{"className":30472},[243,244],[188,30474,27],{"className":30475},[243,244],[188,30477,9366],{"className":30478},[249],[188,30480,6651],{"className":30481},[243,244],[188,30483,9371],{"className":30484},[256],[188,30486,9366],{"className":30487},[249],[188,30489,8087],{"className":30490,"style":9476},[243,244],[188,30492,9371],{"className":30493},[256],"（将长度为 ",[188,30496,30498,30511],{"className":30497},[191],[188,30499,30501],{"className":30500},[195],[197,30502,30503],{"xmlns":199},[201,30504,30505,30509],{},[204,30506,30507],{},[207,30508,6651],{},[222,30510,6651],{"encoding":224},[188,30512,30514],{"className":30513,"ariaHidden":230},[229],[188,30515,30517,30520],{"className":30516},[234],[188,30518],{"className":30519,"style":9506},[238],[188,30521,6651],{"className":30522},[243,244]," 的字符串 ",[188,30525,30527,30540],{"className":30526},[191],[188,30528,30530],{"className":30529},[195],[197,30531,30532],{"xmlns":199},[201,30533,30534,30538],{},[204,30535,30536],{},[207,30537,12802],{},[222,30539,12802],{"encoding":224},[188,30541,30543],{"className":30542,"ariaHidden":230},[229],[188,30544,30546,30549],{"className":30545},[234],[188,30547],{"className":30548,"style":1693},[238],[188,30550,12802],{"className":30551},[243,244]," 转换成长度为 ",[188,30554,30556,30569],{"className":30555},[191],[188,30557,30559],{"className":30558},[195],[197,30560,30561],{"xmlns":199},[201,30562,30563,30567],{},[204,30564,30565],{},[207,30566,8087],{},[222,30568,8087],{"encoding":224},[188,30570,30572],{"className":30571,"ariaHidden":230},[229],[188,30573,30575,30578],{"className":30574},[234],[188,30576],{"className":30577,"style":9776},[238],[188,30579,8087],{"className":30580,"style":9476},[243,244],[188,30582,30584,30597],{"className":30583},[191],[188,30585,30587],{"className":30586},[195],[197,30588,30589],{"xmlns":199},[201,30590,30591,30595],{},[204,30592,30593],{},[207,30594,30294],{},[222,30596,30294],{"encoding":224},[188,30598,30600],{"className":30599,"ariaHidden":230},[229],[188,30601,30603,30606],{"className":30602},[234],[188,30604],{"className":30605,"style":1693},[238],[188,30607,30294],{"className":30608,"style":30309},[243,244]," 的最少编辑操作次数）并给出其动态转移方程。（5分）",[44,30611,29785],{},[22,30613,32],{"id":30614},"答案与深度解析-23",[27,30616,30617],{},"这是一道经典的“莱文斯坦距离（Levenshtein Distance）”算法设计题。我们一步步从基础进行设计：",[27,30619,30620],{},[36,30621,30622],{},"1) DP 数组设计与动态转移方程推导：",[68,30624,30625,30748,31507,31749],{},[44,30626,30627,8007,30630,30632,30633,30661,30662,30690,30691,30661,30719,30747],{},[36,30628,30629],{},"数组定义：",[7457,30631,9445],{}," 表示将字符串 ",[188,30634,30636,30649],{"className":30635},[191],[188,30637,30639],{"className":30638},[195],[197,30640,30641],{"xmlns":199},[201,30642,30643,30647],{},[204,30644,30645],{},[207,30646,12802],{},[222,30648,12802],{"encoding":224},[188,30650,30652],{"className":30651,"ariaHidden":230},[229],[188,30653,30655,30658],{"className":30654},[234],[188,30656],{"className":30657,"style":1693},[238],[188,30659,12802],{"className":30660},[243,244]," 的前 ",[188,30663,30665,30678],{"className":30664},[191],[188,30666,30668],{"className":30667},[195],[197,30669,30670],{"xmlns":199},[201,30671,30672,30676],{},[204,30673,30674],{},[207,30675,6651],{},[222,30677,6651],{"encoding":224},[188,30679,30681],{"className":30680,"ariaHidden":230},[229],[188,30682,30684,30687],{"className":30683},[234],[188,30685],{"className":30686,"style":9506},[238],[188,30688,6651],{"className":30689},[243,244]," 个字符转换成字符串 ",[188,30692,30694,30707],{"className":30693},[191],[188,30695,30697],{"className":30696},[195],[197,30698,30699],{"xmlns":199},[201,30700,30701,30705],{},[204,30702,30703],{},[207,30704,30294],{},[222,30706,30294],{"encoding":224},[188,30708,30710],{"className":30709,"ariaHidden":230},[229],[188,30711,30713,30716],{"className":30712},[234],[188,30714],{"className":30715,"style":1693},[238],[188,30717,30294],{"className":30718,"style":30309},[243,244],[188,30720,30722,30735],{"className":30721},[191],[188,30723,30725],{"className":30724},[195],[197,30726,30727],{"xmlns":199},[201,30728,30729,30733],{},[204,30730,30731],{},[207,30732,8087],{},[222,30734,8087],{"encoding":224},[188,30736,30738],{"className":30737,"ariaHidden":230},[229],[188,30739,30741,30744],{"className":30740},[234],[188,30742],{"className":30743,"style":9776},[238],[188,30745,8087],{"className":30746,"style":9476},[243,244]," 个字符所需的最少编辑次数。",[44,30749,30750,30753,30754,30782,30783,30811,30812,30815,30816,30782,30844,30811,30872,30875,30876],{},[36,30751,30752],{},"核心逻辑（从零理解为什么这么转移）：","\n比较 ",[188,30755,30757,30770],{"className":30756},[191],[188,30758,30760],{"className":30759},[195],[197,30761,30762],{"xmlns":199},[201,30763,30764,30768],{},[204,30765,30766],{},[207,30767,12802],{},[222,30769,12802],{"encoding":224},[188,30771,30773],{"className":30772,"ariaHidden":230},[229],[188,30774,30776,30779],{"className":30775},[234],[188,30777],{"className":30778,"style":1693},[238],[188,30780,12802],{"className":30781},[243,244]," 的第 ",[188,30784,30786,30799],{"className":30785},[191],[188,30787,30789],{"className":30788},[195],[197,30790,30791],{"xmlns":199},[201,30792,30793,30797],{},[204,30794,30795],{},[207,30796,6651],{},[222,30798,6651],{"encoding":224},[188,30800,30802],{"className":30801,"ariaHidden":230},[229],[188,30803,30805,30808],{"className":30804},[234],[188,30806],{"className":30807,"style":9506},[238],[188,30809,6651],{"className":30810},[243,244]," 个字符（",[7457,30813,30814],{},"A[i-1]","）和 ",[188,30817,30819,30832],{"className":30818},[191],[188,30820,30822],{"className":30821},[195],[197,30823,30824],{"xmlns":199},[201,30825,30826,30830],{},[204,30827,30828],{},[207,30829,30294],{},[222,30831,30294],{"encoding":224},[188,30833,30835],{"className":30834,"ariaHidden":230},[229],[188,30836,30838,30841],{"className":30837},[234],[188,30839],{"className":30840,"style":1693},[238],[188,30842,30294],{"className":30843,"style":30309},[243,244],[188,30845,30847,30860],{"className":30846},[191],[188,30848,30850],{"className":30849},[195],[197,30851,30852],{"xmlns":199},[201,30853,30854,30858],{},[204,30855,30856],{},[207,30857,8087],{},[222,30859,8087],{"encoding":224},[188,30861,30863],{"className":30862,"ariaHidden":230},[229],[188,30864,30866,30869],{"className":30865},[234],[188,30867],{"className":30868,"style":9776},[238],[188,30870,8087],{"className":30871,"style":9476},[243,244],[7457,30873,30874],{},"B[j-1]","）：\n",[68,30877,30878,30890],{},[44,30879,30880,30886,30887],{},[36,30881,30882,30883,24463],{},"情况一：两者相等（",[7457,30884,30885],{},"A[i-1] == B[j-1]","。运气好，最后一个字符不用作任何处理。当前所需的编辑距离与它们都不包含各自最后一个字符时的距离一模一样。\n即：",[7457,30888,30889],{},"dp[i][j] = dp[i-1][j-1]",[44,30891,30892,30898,30899],{},[36,30893,30894,30895,24463],{},"情况二：两者不等（",[7457,30896,30897],{},"A[i-1] != B[j-1]","。既然最后一个字符匹配不上，我们就必须得动手实施三种操作之一，实施任意一次操作代价都为 1：\n",[68,30900,30901,31128,31301],{},[44,30902,30903,30906,30907,30935,30936,30964,30965,30661,30993,31045,31046,30661,31074,31125,31126,85],{},[36,30904,30905],{},"如果执行“替换”："," 我们把 ",[188,30908,30910,30923],{"className":30909},[191],[188,30911,30913],{"className":30912},[195],[197,30914,30915],{"xmlns":199},[201,30916,30917,30921],{},[204,30918,30919],{},[207,30920,12802],{},[222,30922,12802],{"encoding":224},[188,30924,30926],{"className":30925,"ariaHidden":230},[229],[188,30927,30929,30932],{"className":30928},[234],[188,30930],{"className":30931,"style":1693},[238],[188,30933,12802],{"className":30934},[243,244]," 的最后一个字符强制替换成 ",[188,30937,30939,30952],{"className":30938},[191],[188,30940,30942],{"className":30941},[195],[197,30943,30944],{"xmlns":199},[201,30945,30946,30950],{},[204,30947,30948],{},[207,30949,30294],{},[222,30951,30294],{"encoding":224},[188,30953,30955],{"className":30954,"ariaHidden":230},[229],[188,30956,30958,30961],{"className":30957},[234],[188,30959],{"className":30960,"style":1693},[238],[188,30962,30294],{"className":30963,"style":30309},[243,244]," 的最后一个字符。替换完成后，这两者的末尾对齐了。那么之前的任务就是把 ",[188,30966,30968,30981],{"className":30967},[191],[188,30969,30971],{"className":30970},[195],[197,30972,30973],{"xmlns":199},[201,30974,30975,30979],{},[204,30976,30977],{},[207,30978,12802],{},[222,30980,12802],{"encoding":224},[188,30982,30984],{"className":30983,"ariaHidden":230},[229],[188,30985,30987,30990],{"className":30986},[234],[188,30988],{"className":30989,"style":1693},[238],[188,30991,12802],{"className":30992},[243,244],[188,30994,30996,31014],{"className":30995},[191],[188,30997,30999],{"className":30998},[195],[197,31000,31001],{"xmlns":199},[201,31002,31003,31011],{},[204,31004,31005,31007,31009],{},[207,31006,6651],{},[211,31008,4945],{},[505,31010,4948],{},[222,31012,31013],{"encoding":224},"i-1",[188,31015,31017,31036],{"className":31016,"ariaHidden":230},[229],[188,31018,31020,31024,31027,31030,31033],{"className":31019},[234],[188,31021],{"className":31022,"style":31023},[238],"height:0.7429em;vertical-align:-0.0833em;",[188,31025,6651],{"className":31026},[243,244],[188,31028],{"className":31029,"style":585},[584],[188,31031,4945],{"className":31032},[589],[188,31034],{"className":31035,"style":585},[584],[188,31037,31039,31042],{"className":31038},[234],[188,31040],{"className":31041,"style":3213},[238],[188,31043,4948],{"className":31044},[243]," 变成 ",[188,31047,31049,31062],{"className":31048},[191],[188,31050,31052],{"className":31051},[195],[197,31053,31054],{"xmlns":199},[201,31055,31056,31060],{},[204,31057,31058],{},[207,31059,30294],{},[222,31061,30294],{"encoding":224},[188,31063,31065],{"className":31064,"ariaHidden":230},[229],[188,31066,31068,31071],{"className":31067},[234],[188,31069],{"className":31070,"style":1693},[238],[188,31072,30294],{"className":31073,"style":30309},[243,244],[188,31075,31077,31095],{"className":31076},[191],[188,31078,31080],{"className":31079},[195],[197,31081,31082],{"xmlns":199},[201,31083,31084,31092],{},[204,31085,31086,31088,31090],{},[207,31087,8087],{},[211,31089,4945],{},[505,31091,4948],{},[222,31093,31094],{"encoding":224},"j-1",[188,31096,31098,31116],{"className":31097,"ariaHidden":230},[229],[188,31099,31101,31104,31107,31110,31113],{"className":31100},[234],[188,31102],{"className":31103,"style":9776},[238],[188,31105,8087],{"className":31106,"style":9476},[243,244],[188,31108],{"className":31109,"style":585},[584],[188,31111,4945],{"className":31112},[589],[188,31114],{"className":31115,"style":585},[584],[188,31117,31119,31122],{"className":31118},[234],[188,31120],{"className":31121,"style":3213},[238],[188,31123,4948],{"className":31124},[243],"。此时代价为：",[7457,31127,10467],{},[44,31129,31130,30906,31133,31161,31162,30661,31190,31240,31241,30661,31269,31297,31298,85],{},[36,31131,31132],{},"如果执行“删除”：",[188,31134,31136,31149],{"className":31135},[191],[188,31137,31139],{"className":31138},[195],[197,31140,31141],{"xmlns":199},[201,31142,31143,31147],{},[204,31144,31145],{},[207,31146,12802],{},[222,31148,12802],{"encoding":224},[188,31150,31152],{"className":31151,"ariaHidden":230},[229],[188,31153,31155,31158],{"className":31154},[234],[188,31156],{"className":31157,"style":1693},[238],[188,31159,12802],{"className":31160},[243,244]," 的最后一个字符删掉。这就指望 ",[188,31163,31165,31178],{"className":31164},[191],[188,31166,31168],{"className":31167},[195],[197,31169,31170],{"xmlns":199},[201,31171,31172,31176],{},[204,31173,31174],{},[207,31175,12802],{},[222,31177,12802],{"encoding":224},[188,31179,31181],{"className":31180,"ariaHidden":230},[229],[188,31182,31184,31187],{"className":31183},[234],[188,31185],{"className":31186,"style":1693},[238],[188,31188,12802],{"className":31189},[243,244],[188,31191,31193,31210],{"className":31192},[191],[188,31194,31196],{"className":31195},[195],[197,31197,31198],{"xmlns":199},[201,31199,31200,31208],{},[204,31201,31202,31204,31206],{},[207,31203,6651],{},[211,31205,4945],{},[505,31207,4948],{},[222,31209,31013],{"encoding":224},[188,31211,31213,31231],{"className":31212,"ariaHidden":230},[229],[188,31214,31216,31219,31222,31225,31228],{"className":31215},[234],[188,31217],{"className":31218,"style":31023},[238],[188,31220,6651],{"className":31221},[243,244],[188,31223],{"className":31224,"style":585},[584],[188,31226,4945],{"className":31227},[589],[188,31229],{"className":31230,"style":585},[584],[188,31232,31234,31237],{"className":31233},[234],[188,31235],{"className":31236,"style":3213},[238],[188,31238,4948],{"className":31239},[243]," 个字符自己能够变幻成 ",[188,31242,31244,31257],{"className":31243},[191],[188,31245,31247],{"className":31246},[195],[197,31248,31249],{"xmlns":199},[201,31250,31251,31255],{},[204,31252,31253],{},[207,31254,30294],{},[222,31256,30294],{"encoding":224},[188,31258,31260],{"className":31259,"ariaHidden":230},[229],[188,31261,31263,31266],{"className":31262},[234],[188,31264],{"className":31265,"style":1693},[238],[188,31267,30294],{"className":31268,"style":30309},[243,244],[188,31270,31272,31285],{"className":31271},[191],[188,31273,31275],{"className":31274},[195],[197,31276,31277],{"xmlns":199},[201,31278,31279,31283],{},[204,31280,31281],{},[207,31282,8087],{},[222,31284,8087],{"encoding":224},[188,31286,31288],{"className":31287,"ariaHidden":230},[229],[188,31289,31291,31294],{"className":31290},[234],[188,31292],{"className":31293,"style":9776},[238],[188,31295,8087],{"className":31296,"style":9476},[243,244]," 个字符。此时代价为：",[7457,31299,31300],{},"dp[i-1][j] + 1",[44,31302,31303,31306,31307,31335,31336,31364,31365,30661,31393,31421,31422,30661,31450,31297,31500,31503,31504,85],{},[36,31304,31305],{},"如果执行“插入”："," 我们在 ",[188,31308,31310,31323],{"className":31309},[191],[188,31311,31313],{"className":31312},[195],[197,31314,31315],{"xmlns":199},[201,31316,31317,31321],{},[204,31318,31319],{},[207,31320,12802],{},[222,31322,12802],{"encoding":224},[188,31324,31326],{"className":31325,"ariaHidden":230},[229],[188,31327,31329,31332],{"className":31328},[234],[188,31330],{"className":31331,"style":1693},[238],[188,31333,12802],{"className":31334},[243,244]," 的末尾无中生有地插入一个与 ",[188,31337,31339,31352],{"className":31338},[191],[188,31340,31342],{"className":31341},[195],[197,31343,31344],{"xmlns":199},[201,31345,31346,31350],{},[204,31347,31348],{},[207,31349,30294],{},[222,31351,30294],{"encoding":224},[188,31353,31355],{"className":31354,"ariaHidden":230},[229],[188,31356,31358,31361],{"className":31357},[234],[188,31359],{"className":31360,"style":1693},[238],[188,31362,30294],{"className":31363,"style":30309},[243,244]," 末尾一样的字符。末尾对齐后，我们需要将 ",[188,31366,31368,31381],{"className":31367},[191],[188,31369,31371],{"className":31370},[195],[197,31372,31373],{"xmlns":199},[201,31374,31375,31379],{},[204,31376,31377],{},[207,31378,12802],{},[222,31380,12802],{"encoding":224},[188,31382,31384],{"className":31383,"ariaHidden":230},[229],[188,31385,31387,31390],{"className":31386},[234],[188,31388],{"className":31389,"style":1693},[238],[188,31391,12802],{"className":31392},[243,244],[188,31394,31396,31409],{"className":31395},[191],[188,31397,31399],{"className":31398},[195],[197,31400,31401],{"xmlns":199},[201,31402,31403,31407],{},[204,31404,31405],{},[207,31406,6651],{},[222,31408,6651],{"encoding":224},[188,31410,31412],{"className":31411,"ariaHidden":230},[229],[188,31413,31415,31418],{"className":31414},[234],[188,31416],{"className":31417,"style":9506},[238],[188,31419,6651],{"className":31420},[243,244]," 个字符变幻成 ",[188,31423,31425,31438],{"className":31424},[191],[188,31426,31428],{"className":31427},[195],[197,31429,31430],{"xmlns":199},[201,31431,31432,31436],{},[204,31433,31434],{},[207,31435,30294],{},[222,31437,30294],{"encoding":224},[188,31439,31441],{"className":31440,"ariaHidden":230},[229],[188,31442,31444,31447],{"className":31443},[234],[188,31445],{"className":31446,"style":1693},[238],[188,31448,30294],{"className":31449,"style":30309},[243,244],[188,31451,31453,31470],{"className":31452},[191],[188,31454,31456],{"className":31455},[195],[197,31457,31458],{"xmlns":199},[201,31459,31460,31468],{},[204,31461,31462,31464,31466],{},[207,31463,8087],{},[211,31465,4945],{},[505,31467,4948],{},[222,31469,31094],{"encoding":224},[188,31471,31473,31491],{"className":31472,"ariaHidden":230},[229],[188,31474,31476,31479,31482,31485,31488],{"className":31475},[234],[188,31477],{"className":31478,"style":9776},[238],[188,31480,8087],{"className":31481,"style":9476},[243,244],[188,31483],{"className":31484,"style":585},[584],[188,31486,4945],{"className":31487},[589],[188,31489],{"className":31490,"style":585},[584],[188,31492,31494,31497],{"className":31493},[234],[188,31495],{"className":31496,"style":3213},[238],[188,31498,4948],{"className":31499},[243],[7457,31501,31502],{},"dp[i][j-1] + 1","。\n我们需要从中选择花费最小的一条路径：",[7457,31505,31506],{},"min(替换代价, 删除代价, 插入代价)",[44,31508,31509,31512,31513,31541,31542,31570,31571,31599,31600,31628,31629,31632,31633,31541,31661,31570,31689,31717,31718,31628,31746,85],{},[36,31510,31511],{},"边界条件：","\n如果 ",[188,31514,31516,31529],{"className":31515},[191],[188,31517,31519],{"className":31518},[195],[197,31520,31521],{"xmlns":199},[201,31522,31523,31527],{},[204,31524,31525],{},[207,31526,12802],{},[222,31528,12802],{"encoding":224},[188,31530,31532],{"className":31531,"ariaHidden":230},[229],[188,31533,31535,31538],{"className":31534},[234],[188,31536],{"className":31537,"style":1693},[238],[188,31539,12802],{"className":31540},[243,244]," 长度为 0，",[188,31543,31545,31558],{"className":31544},[191],[188,31546,31548],{"className":31547},[195],[197,31549,31550],{"xmlns":199},[201,31551,31552,31556],{},[204,31553,31554],{},[207,31555,30294],{},[222,31557,30294],{"encoding":224},[188,31559,31561],{"className":31560,"ariaHidden":230},[229],[188,31562,31564,31567],{"className":31563},[234],[188,31565],{"className":31566,"style":1693},[238],[188,31568,30294],{"className":31569,"style":30309},[243,244]," 长度为 ",[188,31572,31574,31587],{"className":31573},[191],[188,31575,31577],{"className":31576},[195],[197,31578,31579],{"xmlns":199},[201,31580,31581,31585],{},[204,31582,31583],{},[207,31584,8087],{},[222,31586,8087],{"encoding":224},[188,31588,31590],{"className":31589,"ariaHidden":230},[229],[188,31591,31593,31596],{"className":31592},[234],[188,31594],{"className":31595,"style":9776},[238],[188,31597,8087],{"className":31598,"style":9476},[243,244],"，要想转变过去，只能无脑插入 ",[188,31601,31603,31616],{"className":31602},[191],[188,31604,31606],{"className":31605},[195],[197,31607,31608],{"xmlns":199},[201,31609,31610,31614],{},[204,31611,31612],{},[207,31613,8087],{},[222,31615,8087],{"encoding":224},[188,31617,31619],{"className":31618,"ariaHidden":230},[229],[188,31620,31622,31625],{"className":31621},[234],[188,31623],{"className":31624,"style":9776},[238],[188,31626,8087],{"className":31627,"style":9476},[243,244]," 次。",[7457,31630,31631],{},"dp[0][j] = j","。\n如果 ",[188,31634,31636,31649],{"className":31635},[191],[188,31637,31639],{"className":31638},[195],[197,31640,31641],{"xmlns":199},[201,31642,31643,31647],{},[204,31644,31645],{},[207,31646,30294],{},[222,31648,30294],{"encoding":224},[188,31650,31652],{"className":31651,"ariaHidden":230},[229],[188,31653,31655,31658],{"className":31654},[234],[188,31656],{"className":31657,"style":1693},[238],[188,31659,30294],{"className":31660,"style":30309},[243,244],[188,31662,31664,31677],{"className":31663},[191],[188,31665,31667],{"className":31666},[195],[197,31668,31669],{"xmlns":199},[201,31670,31671,31675],{},[204,31672,31673],{},[207,31674,12802],{},[222,31676,12802],{"encoding":224},[188,31678,31680],{"className":31679,"ariaHidden":230},[229],[188,31681,31683,31686],{"className":31682},[234],[188,31684],{"className":31685,"style":1693},[238],[188,31687,12802],{"className":31688},[243,244],[188,31690,31692,31705],{"className":31691},[191],[188,31693,31695],{"className":31694},[195],[197,31696,31697],{"xmlns":199},[201,31698,31699,31703],{},[204,31700,31701],{},[207,31702,6651],{},[222,31704,6651],{"encoding":224},[188,31706,31708],{"className":31707,"ariaHidden":230},[229],[188,31709,31711,31714],{"className":31710},[234],[188,31712],{"className":31713,"style":9506},[238],[188,31715,6651],{"className":31716},[243,244],"，要想转变过去，只能无脑删除 ",[188,31719,31721,31734],{"className":31720},[191],[188,31722,31724],{"className":31723},[195],[197,31725,31726],{"xmlns":199},[201,31727,31728,31732],{},[204,31729,31730],{},[207,31731,6651],{},[222,31733,6651],{"encoding":224},[188,31735,31737],{"className":31736,"ariaHidden":230},[229],[188,31738,31740,31743],{"className":31739},[234],[188,31741],{"className":31742,"style":9506},[238],[188,31744,6651],{"className":31745},[243,244],[7457,31747,31748],{},"dp[i][0] = i",[44,31750,31751,31754],{},[36,31752,31753],{},"严谨的动态转移方程：",[188,31755,31757,32017],{"className":31756},[191],[188,31758,31760],{"className":31759},[195],[197,31761,31762],{"xmlns":199},[201,31763,31764,32014],{},[204,31765,31766,31768,31770,31772,31774,31776,31778,31780,31782,31784],{},[207,31767,9361],{},[207,31769,27],{},[211,31771,9366],{"stretchy":213},[207,31773,6651],{},[211,31775,9371],{"stretchy":213},[211,31777,9366],{"stretchy":213},[207,31779,8087],{},[211,31781,9371],{"stretchy":213},[211,31783,2464],{},[204,31785,31786,31788],{},[211,31787,13177],{"fence":230},[13179,31789,31790,31810,31830,31894],{"rowspacing":13181,"columnalign":13182,"columnspacing":13183},[13185,31791,31792,31798],{},[13188,31793,31794],{},[13191,31795,31796],{"scriptlevel":8307,"displaystyle":213},[207,31797,6651],{},[13188,31799,31800],{},[13191,31801,31802],{"scriptlevel":8307,"displaystyle":213},[204,31803,31804,31806,31808],{},[207,31805,8087],{},[211,31807,2464],{},[505,31809,8307],{},[13185,31811,31812,31818],{},[13188,31813,31814],{},[13191,31815,31816],{"scriptlevel":8307,"displaystyle":213},[207,31817,8087],{},[13188,31819,31820],{},[13191,31821,31822],{"scriptlevel":8307,"displaystyle":213},[204,31823,31824,31826,31828],{},[207,31825,6651],{},[211,31827,2464],{},[505,31829,8307],{},[13185,31831,31832,31862],{},[13188,31833,31834],{},[13191,31835,31836],{"scriptlevel":8307,"displaystyle":213},[204,31837,31838,31840,31842,31844,31846,31848,31850,31852,31854,31856,31858,31860],{},[207,31839,9361],{},[207,31841,27],{},[211,31843,9366],{"stretchy":213},[207,31845,6651],{},[211,31847,4945],{},[505,31849,4948],{},[211,31851,9371],{"stretchy":213},[211,31853,9366],{"stretchy":213},[207,31855,8087],{},[211,31857,4945],{},[505,31859,4948],{},[211,31861,9371],{"stretchy":213},[13188,31863,31864],{},[13191,31865,31866],{"scriptlevel":8307,"displaystyle":213},[204,31867,31868,31870,31872,31874,31876,31878,31880,31882,31884,31886,31888,31890,31892],{},[207,31869,12802],{},[211,31871,9366],{"stretchy":213},[207,31873,6651],{},[211,31875,4945],{},[505,31877,4948],{},[211,31879,9371],{"stretchy":213},[211,31881,2464],{},[207,31883,30294],{},[211,31885,9366],{"stretchy":213},[207,31887,8087],{},[211,31889,4945],{},[505,31891,4948],{},[211,31893,9371],{"stretchy":213},[13185,31895,31896,31982],{},[13188,31897,31898],{},[13191,31899,31900],{"scriptlevel":8307,"displaystyle":213},[204,31901,31902,31904,31906,31908,31910,31912,31914,31916,31918,31920,31922,31924,31926,31928,31930,31932,31934,31936,31938,31940,31942,31944,31946,31948,31950,31952,31954,31956,31958,31960,31962,31964,31966,31968,31970,31972,31974,31976,31978,31980],{},[207,31903,13222],{},[211,31905,925],{},[211,31907,214],{"stretchy":213},[207,31909,9361],{},[207,31911,27],{},[211,31913,9366],{"stretchy":213},[207,31915,6651],{},[211,31917,4945],{},[505,31919,4948],{},[211,31921,9371],{"stretchy":213},[211,31923,9366],{"stretchy":213},[207,31925,8087],{},[211,31927,4945],{},[505,31929,4948],{},[211,31931,9371],{"stretchy":213},[211,31933,8137],{"separator":230},[207,31935,9361],{},[207,31937,27],{},[211,31939,9366],{"stretchy":213},[207,31941,6651],{},[211,31943,4945],{},[505,31945,4948],{},[211,31947,9371],{"stretchy":213},[211,31949,9366],{"stretchy":213},[207,31951,8087],{},[211,31953,9371],{"stretchy":213},[211,31955,8137],{"separator":230},[207,31957,9361],{},[207,31959,27],{},[211,31961,9366],{"stretchy":213},[207,31963,6651],{},[211,31965,9371],{"stretchy":213},[211,31967,9366],{"stretchy":213},[207,31969,8087],{},[211,31971,4945],{},[505,31973,4948],{},[211,31975,9371],{"stretchy":213},[211,31977,220],{"stretchy":213},[211,31979,516],{},[505,31981,4948],{},[13188,31983,31984],{},[13191,31985,31986],{"scriptlevel":8307,"displaystyle":213},[204,31987,31988,31990,31992,31994,31996,31998,32000,32002,32004,32006,32008,32010,32012],{},[207,31989,12802],{},[211,31991,9366],{"stretchy":213},[207,31993,6651],{},[211,31995,4945],{},[505,31997,4948],{},[211,31999,9371],{"stretchy":213},[211,32001,10243],{"mathvariant":510},[207,32003,30294],{},[211,32005,9366],{"stretchy":213},[207,32007,8087],{},[211,32009,4945],{},[505,32011,4948],{},[211,32013,9371],{"stretchy":213},[222,32015,32016],{"encoding":224},"dp[i][j] = \\begin{cases} i & j = 0 \\\\ j & i = 0 \\\\ dp[i-1][j-1] & A[i-1] = B[j-1] \\\\ \\min(dp[i-1][j-1], dp[i-1][j], dp[i][j-1]) + 1 & A[i-1] \\neq B[j-1] \\end{cases}",[188,32018,32020,32059],{"className":32019,"ariaHidden":230},[229],[188,32021,32023,32026,32029,32032,32035,32038,32041,32044,32047,32050,32053,32056],{"className":32022},[234],[188,32024],{"className":32025,"style":239},[238],[188,32027,9361],{"className":32028},[243,244],[188,32030,27],{"className":32031},[243,244],[188,32033,9366],{"className":32034},[249],[188,32036,6651],{"className":32037},[243,244],[188,32039,9371],{"className":32040},[256],[188,32042,9366],{"className":32043},[249],[188,32045,8087],{"className":32046,"style":9476},[243,244],[188,32048,9371],{"className":32049},[256],[188,32051],{"className":32052,"style":2528},[584],[188,32054,2464],{"className":32055},[2532],[188,32057],{"className":32058,"style":2528},[584],[188,32060,32062,32065],{"className":32061},[234],[188,32063],{"className":32064,"style":22208},[238],[188,32066,32068,32146,32647],{"className":32067},[9697],[188,32069,32071],{"className":32070},[249],[188,32072,32074],{"className":32073},[13386,13387],[188,32075,32077,32138],{"className":32076},[549,966],[188,32078,32080,32135],{"className":32079},[553],[188,32081,32083,32093,32104,32114,32125],{"className":32082,"style":22233},[557],[188,32084,32085,32088],{"style":22236},[188,32086],{"className":32087,"style":13404},[565],[188,32089,32091],{"className":32090},[13408,13409],[188,32092,13412],{},[188,32094,32095,32098],{"style":22247},[188,32096],{"className":32097,"style":13404},[565],[188,32099,32100],{"style":22253},[7023,32101,32102],{"xmlns":7025,"width":13424,"height":22256,"style":13426,"viewBox":22257,"preserveAspectRatio":13428},[7031,32103],{"d":22260},[188,32105,32106,32109],{"style":13434},[188,32107],{"className":32108,"style":13404},[565],[188,32110,32112],{"className":32111},[13408,13409],[188,32113,13443],{},[188,32115,32116,32119],{"style":13446},[188,32117],{"className":32118,"style":13404},[565],[188,32120,32121],{"style":22253},[7023,32122,32123],{"xmlns":7025,"width":13424,"height":22256,"style":13426,"viewBox":22257,"preserveAspectRatio":13428},[7031,32124],{"d":22260},[188,32126,32127,32130],{"style":22284},[188,32128],{"className":32129,"style":13404},[565],[188,32131,32133],{"className":32132},[13408,13409],[188,32134,13467],{},[188,32136,990],{"className":32137},[989],[188,32139,32141],{"className":32140},[553],[188,32142,32144],{"className":32143,"style":22302},[557],[188,32145],{},[188,32147,32149],{"className":32148},[243],[188,32150,32152,32412,32415],{"className":32151},[13179],[188,32153,32155],{"className":32154},[13489],[188,32156,32158,32404],{"className":32157},[549,966],[188,32159,32161,32401],{"className":32160},[553],[188,32162,32164,32175,32186,32242],{"className":32163,"style":22323},[557],[188,32165,32166,32169],{"style":22326},[188,32167],{"className":32168,"style":13506},[565],[188,32170,32172],{"className":32171},[243],[188,32173,6651],{"className":32174},[243,244],[188,32176,32177,32180],{"style":17953},[188,32178],{"className":32179,"style":13506},[565],[188,32181,32183],{"className":32182},[243],[188,32184,8087],{"className":32185,"style":9476},[243,244],[188,32187,32188,32191],{"style":18127},[188,32189],{"className":32190,"style":13506},[565],[188,32192,32194,32197,32200,32203,32206,32209,32212,32215,32218,32221,32224,32227,32230,32233,32236,32239],{"className":32193},[243],[188,32195,9361],{"className":32196},[243,244],[188,32198,27],{"className":32199},[243,244],[188,32201,9366],{"className":32202},[249],[188,32204,6651],{"className":32205},[243,244],[188,32207],{"className":32208,"style":585},[584],[188,32210,4945],{"className":32211},[589],[188,32213],{"className":32214,"style":585},[584],[188,32216,4948],{"className":32217},[243],[188,32219,9371],{"className":32220},[256],[188,32222,9366],{"className":32223},[249],[188,32225,8087],{"className":32226,"style":9476},[243,244],[188,32228],{"className":32229,"style":585},[584],[188,32231,4945],{"className":32232},[589],[188,32234],{"className":32235,"style":585},[584],[188,32237,4948],{"className":32238},[243],[188,32240,9371],{"className":32241},[256],[188,32243,32244,32247],{"style":22540},[188,32245],{"className":32246,"style":13506},[565],[188,32248,32250,32253,32256,32259,32262,32265,32268,32271,32274,32277,32280,32283,32286,32289,32292,32295,32298,32301,32304,32307,32310,32313,32316,32319,32322,32325,32328,32331,32334,32337,32340,32343,32346,32349,32352,32355,32358,32361,32364,32367,32370,32373,32376,32379,32382,32385,32389,32392,32395,32398],{"className":32249},[243],[188,32251,13222],{"className":32252},[951],[188,32254,214],{"className":32255},[249],[188,32257,9361],{"className":32258},[243,244],[188,32260,27],{"className":32261},[243,244],[188,32263,9366],{"className":32264},[249],[188,32266,6651],{"className":32267},[243,244],[188,32269],{"className":32270,"style":585},[584],[188,32272,4945],{"className":32273},[589],[188,32275],{"className":32276,"style":585},[584],[188,32278,4948],{"className":32279},[243],[188,32281,9371],{"className":32282},[256],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82],{"className":32581},[243,10310],[188,32583,32585],{"className":32584},[10314],[188,32586,32588,32591,32600],{"className":32587},[10318],[188,32589],{"className":32590,"style":10322},[238],[188,32592,32594],{"className":32593},[10326],[188,32595,32597],{"className":32596},[243],[188,32598,10333],{"className":32599},[2532],[188,32601],{"className":32602},[10337],[188,32604],{"className":32605},[584,10341],[188,32607,2464],{"className":32608},[2532],[188,32610],{"className":32611,"style":2528},[584],[188,32613,30294],{"className":32614,"style":30309},[243,244],[188,32616,9366],{"className":32617},[249],[188,32619,8087],{"className":32620,"style":9476},[243,244],[188,32622],{"className":32623,"style":585},[584],[188,32625,4945],{"className":32626},[589],[188,32628],{"className":32629,"style":585},[584],[188,32631,4948],{"className":32632},[243],[188,32634,9371],{"className":32635},[256],[188,32637,990],{"className":32638},[989],[188,32640,32642],{"className":32641},[553],[188,32643,32645],{"className":32644,"style":22619},[557],[188,32646],{},[188,32648],{"className":32649},[256,12583],[27,32651,32652],{},[36,32653,32654],{},"2) 算法代码（C\u002FC++实现）：",[7746,32656,32658],{"className":7748,"code":32657,"language":7750,"meta":7751,"style":7751},"#include \u003Ciostream>\n#include \u003Cstring>\n#include \u003Cvector>\n#include \u003Calgorithm>\n\nusing namespace std;\n\n\u002F\u002F 获取三个数中最小值的辅助函数\nint getMin(int a, int b, int c) {\n    return min(min(a, b), c);\n}\n\nint minDistance(string A, string B) {\n    int m = A.length();\n    int n = B.length();\n    \n    \u002F\u002F 创建二维动态规划数组，并初始化全为 0\n    \u002F\u002F 注意数组维度是 (m+1) x (n+1)，因为我们要容纳前缀长度为0（空串）的情况\n    vector\u003Cvector\u003Cint>> dp(m + 1, vector\u003Cint>(n + 1, 0));\n    \n    \u002F\u002F 初始化边界条件\n    for (int i = 0; i \u003C= m; i++) {\n        dp[i][0] = i; \u002F\u002F B为空串，A必须不断执行删除\n    }\n    for (int j = 0; j \u003C= n; j++) {\n        dp[0][j] = j; \u002F\u002F A为空串，A必须不断执行插入\n    }\n    \n    \u002F\u002F 使用状态转移方程逐行填表\n    for (int i = 1; i \u003C= m; i++) {\n        for (int j = 1; j \u003C= n; j++) {\n            \u002F\u002F 注意：第 i 个字符在字符串中的索引是 i-1\n            if (A[i - 1] == B[j - 1]) {\n                dp[i][j] = dp[i - 1][j - 1]; \u002F\u002F 字符相同，无需操作代价\n            } else {\n                dp[i][j] = 1 + getMin(\n                    dp[i - 1][j - 1], \u002F\u002F 替换 (Replace)\n                    dp[i - 1][j],     \u002F\u002F 删除 (Delete)\n                    dp[i][j - 1]      \u002F\u002F 插入 (Insert)\n                );\n            }\n        }\n    }\n    \n    \u002F\u002F 表格右下角的值即为全局最小操作次数\n    return dp[m][n];\n}\n",[7457,32659,32660,32665,32670,32675,32680,32684,32689,32693,32698,32703,32708,32712,32716,32721,32726,32732,32738,32744,32750,32756,32761,32767,32773,32779,32784,32790,32796,32801,32806,32812,32818,32824,32830,32836,32842,32848,32854,32860,32866,32872,32878,32884,32889,32894,32899,32905,32911],{"__ignoreMap":7751},[188,32661,32662],{"class":7756,"line":7757},[188,32663,32664],{},"#include \u003Ciostream>\n",[188,32666,32667],{"class":7756,"line":7763},[188,32668,32669],{},"#include \u003Cstring>\n",[188,32671,32672],{"class":7756,"line":7769},[188,32673,32674],{},"#include \u003Cvector>\n",[188,32676,32677],{"class":7756,"line":7775},[188,32678,32679],{},"#include \u003Calgorithm>\n",[188,32681,32682],{"class":7756,"line":7781},[188,32683,29832],{"emptyLinePlaceholder":29831},[188,32685,32686],{"class":7756,"line":7787},[188,32687,32688],{},"using namespace std;\n",[188,32690,32691],{"class":7756,"line":7793},[188,32692,29832],{"emptyLinePlaceholder":29831},[188,32694,32695],{"class":7756,"line":7799},[188,32696,32697],{},"\u002F\u002F 获取三个数中最小值的辅助函数\n",[188,32699,32700],{"class":7756,"line":7805},[188,32701,32702],{},"int getMin(int a, int b, int c) {\n",[188,32704,32705],{"class":7756,"line":7811},[188,32706,32707],{},"    return min(min(a, b), c);\n",[188,32709,32710],{"class":7756,"line":7817},[188,32711,7832],{},[188,32713,32714],{"class":7756,"line":7823},[188,32715,29832],{"emptyLinePlaceholder":29831},[188,32717,32718],{"class":7756,"line":7829},[188,32719,32720],{},"int minDistance(string A, string B) {\n",[188,32722,32723],{"class":7756,"line":10894},[188,32724,32725],{},"    int m = A.length();\n",[188,32727,32729],{"class":7756,"line":32728},15,[188,32730,32731],{},"    int n = B.length();\n",[188,32733,32735],{"class":7756,"line":32734},16,[188,32736,32737],{},"    \n",[188,32739,32741],{"class":7756,"line":32740},17,[188,32742,32743],{},"    \u002F\u002F 创建二维动态规划数组，并初始化全为 0\n",[188,32745,32747],{"class":7756,"line":32746},18,[188,32748,32749],{},"    \u002F\u002F 注意数组维度是 (m+1) x (n+1)，因为我们要容纳前缀长度为0（空串）的情况\n",[188,32751,32753],{"class":7756,"line":32752},19,[188,32754,32755],{},"    vector\u003Cvector\u003Cint>> dp(m + 1, vector\u003Cint>(n + 1, 0));\n",[188,32757,32759],{"class":7756,"line":32758},20,[188,32760,32737],{},[188,32762,32764],{"class":7756,"line":32763},21,[188,32765,32766],{},"    \u002F\u002F 初始化边界条件\n",[188,32768,32770],{"class":7756,"line":32769},22,[188,32771,32772],{},"    for (int i = 0; i \u003C= m; i++) {\n",[188,32774,32776],{"class":7756,"line":32775},23,[188,32777,32778],{},"        dp[i][0] = i; \u002F\u002F B为空串，A必须不断执行删除\n",[188,32780,32782],{"class":7756,"line":32781},24,[188,32783,10891],{},[188,32785,32787],{"class":7756,"line":32786},25,[188,32788,32789],{},"    for (int j = 0; j \u003C= n; j++) {\n",[188,32791,32793],{"class":7756,"line":32792},26,[188,32794,32795],{},"        dp[0][j] = j; \u002F\u002F A为空串，A必须不断执行插入\n",[188,32797,32799],{"class":7756,"line":32798},27,[188,32800,10891],{},[188,32802,32804],{"class":7756,"line":32803},28,[188,32805,32737],{},[188,32807,32809],{"class":7756,"line":32808},29,[188,32810,32811],{},"    \u002F\u002F 使用状态转移方程逐行填表\n",[188,32813,32815],{"class":7756,"line":32814},30,[188,32816,32817],{},"    for (int i = 1; i \u003C= m; i++) {\n",[188,32819,32821],{"class":7756,"line":32820},31,[188,32822,32823],{},"        for (int j = 1; j \u003C= n; j++) {\n",[188,32825,32827],{"class":7756,"line":32826},32,[188,32828,32829],{},"            \u002F\u002F 注意：第 i 个字符在字符串中的索引是 i-1\n",[188,32831,32833],{"class":7756,"line":32832},33,[188,32834,32835],{},"            if (A[i - 1] == B[j - 1]) {\n",[188,32837,32839],{"class":7756,"line":32838},34,[188,32840,32841],{},"                dp[i][j] = dp[i - 1][j - 1]; \u002F\u002F 字符相同，无需操作代价\n",[188,32843,32845],{"class":7756,"line":32844},35,[188,32846,32847],{},"            } else {\n",[188,32849,32851],{"class":7756,"line":32850},36,[188,32852,32853],{},"                dp[i][j] = 1 + getMin(\n",[188,32855,32857],{"class":7756,"line":32856},37,[188,32858,32859],{},"                    dp[i - 1][j - 1], \u002F\u002F 替换 (Replace)\n",[188,32861,32863],{"class":7756,"line":32862},38,[188,32864,32865],{},"                    dp[i - 1][j],     \u002F\u002F 删除 (Delete)\n",[188,32867,32869],{"class":7756,"line":32868},39,[188,32870,32871],{},"                    dp[i][j - 1]      \u002F\u002F 插入 (Insert)\n",[188,32873,32875],{"class":7756,"line":32874},40,[188,32876,32877],{},"                );\n",[188,32879,32881],{"class":7756,"line":32880},41,[188,32882,32883],{},"            }\n",[188,32885,32887],{"class":7756,"line":32886},42,[188,32888,7826],{},[188,32890,32892],{"class":7756,"line":32891},43,[188,32893,10891],{},[188,32895,32897],{"class":7756,"line":32896},44,[188,32898,32737],{},[188,32900,32902],{"class":7756,"line":32901},45,[188,32903,32904],{},"    \u002F\u002F 表格右下角的值即为全局最小操作次数\n",[188,32906,32908],{"class":7756,"line":32907},46,[188,32909,32910],{},"    return dp[m][n];\n",[188,32912,32914],{"class":7756,"line":32913},47,[188,32915,7832],{},[32917,32918,32919],"style",{},"html .default 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