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详细说明： 1、几何25 1.1 注意...................................................................................................................25 1.2 几何公式...........................................................................................................25 1.3 多边形...............................................................................................................27 1.4 多边形切割.......................................................................................................30 1.5 浮点函数......................................... ..................................................................31 1.6 面积...................................................................................................................36 1.7 球面...................................................................................................................37 1.8 三角形...............................................................................................................38 1.9 三维几何...........................................................................................................40 1.10 凸包...................................................................................................................47 1.11 网格...................................................................................................................49 1.12 圆.......................................................................................................................49 1.13 整数函数...........................................................................................................51 2、组合54 2.1 组合公式....................................................................................................................54 2.2 排列组合生成............................................................................................................54 2.3 生成gray 码.............................................................................................................. 56 2.4 置换(polya)................................................................................................................56 2.5 字典序全排列............................................................................................................57 2.6 字典序组合................................................................................................................57 3、结构58 3.1 并查集........................................................................................................................58 3.2 堆...............................................................................................................................59 3.3 线段树........................................................................................................................60 3.4 子段和........................................................................................................................65 3.5 子阵和........................................................................................................................65 4、数论66 4.1 阶乘最后非0 位........................................................................................................66 4.2 模线性方程组............................................................................................................67 4.3 素数............................................................................................................................68 4.4 欧拉函数....................................................................................................................69 5、数值计算70 5.1 定积分计算(Romberg)..............................................................................................70 5.2 多项式求根(牛顿法).................................................................................................72 5.3 周期性方程(追赶法).................................................................................................73 6、图论—NP 搜索74 6.1 最大团........................................................................................................................74 6.2 最大团(n<64)(faster).................................................................................................75 7、图论—连通性77 7.1 无向图关键点(dfs 邻接阵).......................................................................................77 7.2 无向图关键边(dfs 邻接阵).......................................................................................78 7.3 无向图的块(bfs 邻接阵)...........................................................................................79 7.4 无向图连通分支(dfs/bfs 邻接阵).............................................................................80 3 7.5 有向图强连通分支(dfs/bfs 邻接阵).........................................................................81 7.6 有向图最小点基(邻接阵).........................................................................................82 8、图论—匹配83 8.1 二分图最大匹配(hungary 邻接表).......................................................................... 83 8.2 二分图最大匹配(hungary 邻接阵).......................................................................... 84 8.3 二分图最大匹配(hungary 正向表).......................................................................... 84 8.4 二分图最佳匹配(kuhn_munkras 邻接阵).................................................................85 8.5 一般图匹配(邻接表).................................................................................................86 8.6 一般图匹配(邻接阵).................................................................................................87 8.7 一般图匹配(正向表).................................................................................................87 9、图论—网络流88 9.1 最大流(邻接阵).........................................................................................................88 9.2 上下界最大流(邻接阵).............................................................................................89 9.3 上下界最小流(邻接阵).............................................................................................90 9.4 最大流无流量(邻接阵).............................................................................................91 9.5 最小费用最大流(邻接阵).........................................................................................91 10、图论—应用92 10.1 欧拉回路(邻接阵)...................................................................................................92 10.2 树的前序表转化......................................................................................................93 10.3 树的优化算法..........................................................................................................94 10.4 拓扑排序(邻接阵)...................................................................................................95 10.5 最佳边割集..............................................................................................................96 10.6 最佳点割集..............................................................................................................97 10.7 最小边割集..............................................................................................................98 10.8 最小点割集..............................................................................................................99 10.9 最小路径覆盖........................................................................................................101 11、图论—支撑树101 11.1 最小生成树(kruskal 邻接表)................................................................................101 11.2 最小生成树(kruskal 正向表)................................................................................103 11.3 最小生成树(prim+binary_heap 邻接表)..............................................................104 11.4 最小生成树(prim+binary_heap 正向表)..............................................................105 11.5 最小生成树(prim+mapped_heap 邻接表)............................................................106 11.6 最小生成树(prim+mapped_heap 正向表)............................................................108 11.7 最小生成树(prim 邻接阵).................................................................................... 109 11.8 最小树形图(邻接阵).............................................................................................109 12、图论—最短路径111 12.1 最短路径(单源bellman_ford 邻接阵)................................................................. 111 12.2 最短路径(单源dijkstra+bfs 邻接表)....................................................................111 12.3 最短路径(单源dijkstra+bfs 正向表)....................................................................112 12.4 最短路径(单源dijkstra+binary_heap 邻接表).....................................................113 12.5 最短路径(单源dijkstra+binary_heap 正向表).....................................................114 12.6 最短路径(单源dijkstra+mapped_heap 邻接表).................................................. 115 12.7 最短路径(单源dijkstra+mapped_heap 正向表).................................................. 116 12.8 最短路径(单源dijkstra 邻接阵)...........................................................................117 4 12.9 最短路径(多源floyd_warshall 邻接阵)...............................................................118 13、应用118 13.1 Joseph 问题.............................................................................................................118 13.2 N 皇后构造解.........................................................................................................119 13.3 布尔母函数............................................................................................................120 13.4 第k 元素................................................................................................................120 13.5 幻方构造................................................................................................................121 13.6 模式匹配(kmp)......................................................................................................122 13.7 逆序对数................................................................................................................123 13.8 字符串最小表示................................................................................................... 123 13.9 最长公共单调子序列........................................................................................... 124 13.10 最长子序列..........................................................................................................125 13.11 最大子串匹配......................................................................................................126 13.12 最大子段和..........................................................................................................127 13.13 最大子阵和..........................................................................................................127 14 、其它 128 14.1 大数(只能处理正数).............................................................................................128 14.2 分数........................................................................................................................134 14.3 矩阵........................................................................................................................136 14.4 线性方程组............................................................................................................138 14.5 线性相关................................................................................................................140 14 ...展开收缩
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