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一．数论.......................................................................................................................... 4

1.阶乘最后非零位 ..................................................................................................... 4

2. 模线性方程(组) ..................................................................................................... 4

3. 素数表.................................................................................................................. 6

4. 素数随机判定(miller_rabin).................................................................................... 6

5. 质因数分解........................................................................................................... 7

6. 最大公约数欧拉函数............................................................................................. 8

二．图论_匹配 ................................................................................................................. 9

1. 二分图最大匹配(hungary 邻接表形式).................................................................... 9

2. 二分图最大匹配(hungary 邻接表形式,邻接阵接口) ............................................... 10

3. 二分图最大匹配(hungary 邻接阵形式).................................................................. 10

4. 二分图最大匹配(hungary 正向表形式)...................................................................11

5. 二分图最佳匹配(kuhn_munkras 邻接阵形式) .........................................................11

6. 一般图匹配(邻接表形式) ..................................................................................... 12

7. 一般图匹配(邻接表形式,邻接阵接口)................................................................... 13

8. 一般图匹配(邻接阵形式) ..................................................................................... 14

9. 一般图匹配(正向表形式) ..................................................................................... 15

三．图论_生成树 ........................................................................................................... 16

1. 最小生成树(kruskal 邻接表形式).......................................................................... 16

2. 最小生成树(kruskal 正向表形式).......................................................................... 17

3. 最小生成树(prim+binary_heap 邻接表形式) .......................................................... 19

4. 最小生成树(prim+binary_heap 正向表形式) .......................................................... 20

5. 最小生成树(prim+mapped_heap 邻接表形式) ........................................................ 21

6. 最小生成树(prim+mapped_heap 正向表形式) ........................................................ 22

7. 最小生成树(prim 邻接阵形式) ............................................................................. 23

8. 最小树形图(邻接阵形式) ..................................................................................... 24

四．图论_网络流 ........................................................................................................... 25

1. 上下界最大流(邻接表形式) ................................................................................. 25

2. 上下界最大流(邻接阵形式) ................................................................................. 26

3. 上下界最小流(邻接表形式) ................................................................................. 27

4. 上下界最小流(邻接阵形式) ................................................................................. 29

5. 最大流(邻接表形式) ............................................................................................ 30

6. 最大流(邻接表形式,邻接阵接口).......................................................................... 31

7. 最大流(邻接阵形式) ............................................................................................ 32

8. 最大流无流量(邻接阵形式) ................................................................................. 32

9. 最小费用最大流(邻接阵形式) .............................................................................. 33

五. 图论_最短路径......................................................................................................... 34

1. 最短路径(单源 bellman_ford 邻接阵形式) ............................................................. 34

2. 最短路径(单源 dijkstra_bfs 邻接表形式) ............................................................... 35

3. 最短路径(单源 dijkstra_bfs 正向表形式) ............................................................... 35

4. 最短路径(单源 dijkstra+binary_heap 邻接表形式) .................................................. 36

5. 最短路径(单源 dijkstra+binary_heap 正向表形式) .................................................. 37

6. 最短路径(单源 dijkstra+mapped_heap 邻接表形式)................................................ 38

7. 最短路径(单源 dijkstra+mapped_heap 正向表形式)................................................ 39

8. 最短路径(单源 dijkstra 邻接阵形式) ..................................................................... 40

9. 最短路径(多源 floyd_warshall 邻接阵形式)........................................................... 40

六. 图论_连通性 ............................................................................................................ 41

1. 无向图关键边(dfs 邻接阵形式) ............................................................................ 41

2. 无向图关键点(dfs 邻接阵形式) ............................................................................ 42

3. 无向图块(bfs 邻接阵形式) ................................................................................... 43

4. 无向图连通分支(bfs 邻接阵形式)......................................................................... 43

5. 无向图连通分支(dfs 邻接阵形式)......................................................................... 44

6. 有向图强连通分支(bfs 邻接阵形式) ..................................................................... 44

7. 有向图强连通分支(dfs 邻接阵形式) ..................................................................... 45

8. 有向图最小点基(邻接阵形式) .............................................................................. 46

七. 图论_应用................................................................................................................ 46

1.欧拉回路(邻接阵形式) .......................................................................................... 46

2. 前序表转化......................................................................................................... 47

3. 树的优化算法 ..................................................................................................... 48

4. 拓扑排序(邻接阵形式)......................................................................................... 49

5. 最佳边割集......................................................................................................... 50

6. 最佳顶点割集 ..................................................................................................... 51

7. 最小边割集......................................................................................................... 52

8. 最小顶点割集 ..................................................................................................... 53

9. 最小路径覆盖 ..................................................................................................... 55

八. 图论_NP 搜索 .......................................................................................................... 55

1. 最大团(n 小于 64)(faster) ..................................................................................... 55

2. 最大团................................................................................................................ 58

九. 组合 ........................................................................................................................ 59

1. 排列组合生成 ..................................................................................................... 59

2. 生成 gray 码 ........................................................................................................ 60

3. 置换(polya) ......................................................................................................... 61

4. 字典序全排列 ..................................................................................................... 61

5. 字典序组合......................................................................................................... 62

6. 组合公式 ............................................................................................................ 62

十. 数值计算 ................................................................................................................. 63

1. 定积分计算(Romberg) ......................................................................................... 63

2. 多项式求根(牛顿法) ............................................................................................ 64

3. 周期性方程(追赶法) ............................................................................................ 66

十一. 几何 ..................................................................................................................... 67

1. 多边形................................................................................................................ 67

2. 多边形切割......................................................................................................... 70

3. 浮点函数 ............................................................................................................ 71

4. 几何公式 ............................................................................................................ 76

5. 面积 ................................................................................................................... 78

6. 球面 ................................................................................................................... 79

7. 三角形................................................................................................................ 79

8. 三维几何 ............................................................................................................ 81

9. 凸包(graham) ...................................................................................................... 89

10. 网格(pick) ......................................................................................................... 91

11. 圆 ..................................................................................................................... 92

12. 整数函数 .......................................................................................................... 94

13. 注意 ................................................................................................................. 96

十二. 结构 ..................................................................................................................... 97

1. 并查集................................................................................................................ 97

2. 并查集扩展(friend_enemy) ................................................................................... 98

3. 堆(binary) ........................................................................................................... 98

4. 堆(mapped) ......................................................................................................... 99

5. 矩形切割 ............................................................................................................ 99

6. 线段树...............................................................................................................100

7. 线段树扩展........................................................................................................102

8. 线段树应用........................................................................................................105

9. 子段和...............................................................................................................105

10. 子阵和 .............................................................................................................105

十三. 其他 ....................................................................................................................106

1. 分数 ..................................................................................................................106

2. 矩阵 ..................................................................................................................108

3. 日期 .................................................................................................................. 110

4. 线性方程组(gauss).............................................................................................. 111

5. 线性相关 ........................................................................................................... 113

十四. 应用 .................................................................................................................... 114

1. joseph ................................................................................................................. 114

2. N 皇后构造解 ..................................................................................................... 115

3. 布尔母函数........................................................................................................ 115

4. 第 k 元素 ........................................................................................................... 116

5. 幻方构造 ........................................................................................................... 116

6. 模式匹配(kmp)................................................................................................... 118

7. 逆序对数 ........................................................................................................... 118

8. 字符串最小表示................................................................................................. 119

9. 最长公共单调子序列.......................................................................................... 119

10. 最长子序列 ......................................................................................................120

11. 最大子串匹配...................................................................................................121

12. 最大子段和 ......................................................................................................122

13. 最大子阵和 ......................................................................................................123

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