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详细说明： 1、 几何...........................................................................................................................1 1.1 注意...................................................................................................................1 1.2 几何公式...........................................................................................................1 1.3 多边形..................................................................................... ..........................3 1.4 多边形切割.......................................................................................................6 1.5 浮点函数...........................................................................................................7 1.6 面积.................................................................................................................12 1.7 球面.................................................................................................................13 1.8 三角形.............................................................................................................14 1.9 三维几何.........................................................................................................16 1.10 凸包.................................................................................................................23 1.11 网格.................................................................................................................25 1.12 圆.....................................................................................................................25 1.13 整数函数.........................................................................................................27 2、 组合.................................................................................................................30 2.1 组合公式..................................................................................................................30 2.2 排列组合生成..........................................................................................................30 2.3 生成gray 码.............................................................................................................32 2.4 置换(polya) ..............................................................................................................32 2.5 字典序全排列..........................................................................................................33 2.6 字典序组合..............................................................................................................33 3、............... 结构 34 3.1 并查集......................................................................................................................34 3.2 堆..............................................................................................................................35 3.3 线段树......................................................................................................................36 3.4 子段和......................................................................................................................41 3.5 子阵和......................................................................................................................41 4、..数论 42 4.1 阶乘最后非0 位......................................................................................................42 4.2 模线性方程组..........................................................................................................43 4.3 素数..........................................................................................................................44 4.4 欧拉函数...................................................................... 5、 数值计算.................................................................................................................46 5.1 定积分计算(Romberg) ............................................................................................46 5.2 多项式求根(牛顿法) ...............................................................................................48 5.3 周期性方程(追赶法) ...............................................................................................49 6、......... 图论—NP 搜索 50 6.1 最大团......................................................................................................................50 6.2 最大团(n<64)(faster) ...............................................................................................51 7、 图论—连通性 53 7.1 无向图关键点(dfs 邻接阵) .....................................................................................53 7.2 无向图关键边(dfs 邻接阵) .....................................................................................54 7.3 无向图的块(bfs 邻接阵) .........................................................................................55 7.4 无向图连通分支(dfs/bfs 邻接阵) ...........................................................................56 7.5 有向图强连通分支(dfs/bfs 邻接阵) .......................................................................57 7.6 有向图最小点基(邻接阵) .......................................................................................58 8、....... 图论—匹配 59 8.1 二分图最大匹配(hungary 邻接表) .........................................................................59 8.2 二分图最大匹配(hungary 邻接阵) .........................................................................60 8.3 二分图最大匹配(hungary 正向表) .........................................................................60 8.4 二分图最佳匹配(kuhn_munkras 邻接阵) ...............................................................61 8.5 一般图匹配(邻接表) ...............................................................................................62 8.6 一般图匹配(邻接阵) ...............................................................................................63 8.7 一般图匹配(正向表) ...............................................................................................63 9、....... 图论—网络流 64 9.1 最大流(邻接阵).......................................................................................................64 9.2 上下界最大流(邻接阵) ...........................................................................................65 9.3 上下界最小流(邻接阵) ...........................................................................................66 9.4 最大流无流量(邻接阵) ...........................................................................................67 9.5 最小费用最大流(邻接阵) .......................................................................................67 10、....... 图论—应用 68 10.1 欧拉回路(邻接阵).................................................................................................68 10.2 树的前序表转化....................................................................................................69 10.3 树的优化算法........................................................................................................70 10.4 拓扑排序(邻接阵).................................................................................................71 10.5 最佳边割集............................................................................................................72 10.6 最佳点割集............................................................................................................73 10.7 最小边割集............................................................................................................74 10.8 最小点割集....................................................................... 10.9 最小路径覆盖........................................................................................................77 11、......... 图论—支撑树 77 11.1 最小生成树(kruskal 邻接表).................................................................................77 11.2 最小生成树(kruskal 正向表).................................................................................79 11.3 最小生成树(prim+binary_heap 邻接表)...............................................................80 11.4 最小生成树(prim+binary_heap 正向表)...............................................................81 11.5 最小生成树(prim+mapped_heap 邻接表) ............................................. .......... ...展开收缩
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