题目抽象：给你m条边u,v,c。 n个定点，源点1，汇点n.求最大流。 最好的入门题，各种算法都可以拿来练习
（1）： 一般增广路算法 ford()
1 #include <iostream> 2 #include <cstdio> 3 #include <cstring> 4 #include <cmath> 5 #include <algorithm> 6 #include <string> 7 #include <vector> 8 #include <set> 9 #include <map> 10 #include <stack> 11 #include <queue> 12 #include <sstream> 13 #include <iomanip> 14 using namespace std; 15 typedef long long LL; 16 const int INF = 0x4fffffff; 17 const double EXP = 1e-5; 18 const int MS = 10005; 19 const int SIZE = 10005; 20 21 struct edge 22 { 23 int c, f; 24 }edges[MS][MS]; 25 26 int n, m; 27 28 int flag[MS]; 29 int pre[MS]; 30 int alpha[MS]; 31 32 int que[SIZE]; 33 34 int u; 35 int qs, qe; 36 int i, j; 37 38 void ford() 39 { 40 while (1) 41 { 42 // label method 43 memset(flag, 0xff, sizeof(flag)); 44 memset(pre, 0xff, sizeof(pre)); 45 memset(alpha, 0xff, sizeof(alpha)); 46 flag[1] = 0; 47 pre[1] = 0; 48 alpha[1] = INF; 49 qs = qe = 0; 50 que[qe++] = 1; 51 52 while (qs < qe&&flag[n ] == -1) 53 { 54 u = que[qs++]; 55 for (int i = 1; i <= n; i++) 56 { 57 if (flag[i] == -1) 58 { 59 if (edges[u][i].c >0&&edges[u][i].f < edges[u][i].c) 60 { 61 flag[i] = 0; pre[i] = u; 62 alpha[i] = min(alpha[u], edges[u][i].c - edges[u][i].f); 63 que[qe++] = i; 64 } 65 else if (edges[i][u].c>0&&edges[i][u].f>0) 66 { 67 flag[i] = 0; pre[i] = -u; 68 alpha[i] = min(alpha[u], edges[i][u].f); 69 que[qe++] = i; 70 } 71 } 72 } 73 flag[u] = 1; 74 } // END OF WHILE 75 if (flag[n ] == -1 || alpha[n ] == 0) 76 break; // END OF WHILE 77 78 int k1 = n , k2 = abs(pre[k1]); 79 int a = alpha[n ]; 80 while (1) 81 { 82 if (edges[k2][k1].c>0) //用f是否==INF来判断正向 83 edges[k2][k1].f += a; 84 else 85 edges[k1][k2].f -= a; 86 if (k2 == 1) 87 break; 88 k1 = k2; 89 k2 = abs(pre[k1]); 90 } // END OF WHILE 91 } // END OF WHILE 92 93 int max_flow = 0; 94 for (int i = 1; i <=n; i++) 95 { 96 for (int j = 1; j <=n; j++) 97 { 98 if (i == 1 && edges[i][j].f >0) 99 max_flow += edges[i][j].f; 100 // if (edges[i][j].f > 0) 101 // printf("%d-->%d: %d ", i, j, edges[i][j].f); 102 } 103 } 104 printf("%d ", max_flow); 105 } 106 107 int main() 108 { 109 int u, v, c, f; 110 while(scanf("%d%d",&m,&n)!=EOF) 111 { 112 for (int i = 0; i <= n; i++) 113 for (int j = 0; j <= n; j++) 114 // edges[i][j].c = edges[i][j].f = INF; 115 edges[i][j].c=edges[i][j].f=0; 116 for (int i = 0; i < m; i++) 117 { 118 //scanf("%d%d%d%d", &u, &v, &c, &f); 119 scanf("%d%d%d",&u,&v,&c); // 这里是零流 120 edges[u][v].c +=c; // 可能有重边 121 // edges[u][v].f = f; 122 } 123 ford(); 124 } 125 return 0; 126 }
(2): dinic()
1 #include <iostream> 2 #include <cstdio> 3 #include <cstring> 4 #include <cmath> 5 #include <algorithm> 6 #include <string> 7 #include <vector> 8 #include <stack> 9 #include <queue> 10 #include <set> 11 #include <map> 12 #include <list> 13 #include <iomanip> 14 #include <cstdlib> 15 #include <sstream> 16 using namespace std; 17 typedef long long LL; 18 const int INF=0x5fffffff; 19 const double EXP=1e-6; 20 const int MS=1005; 21 22 int edges[MS][MS]; 23 int level[MS]; 24 int que[MS],qs,qe; 25 int n,m,ans; 26 27 int BFS() // BFS求level 28 { 29 memset(level,0xff,sizeof(level)); 30 level[1]=0; 31 qs=qe=0; 32 que[qe++]=1; 33 while(qs<qe) 34 { 35 int u=que[qs++]; 36 for(int v=1;v<=n;v++) 37 { 38 if(level[v]<0&&edges[u][v]>0) 39 { 40 level[v]=level[u]+1; 41 que[qe++]=v; 42 } 43 } 44 } 45 if(level[n]>0) // 汇点在残留网络中，存在增广路 46 return 1; 47 else 48 return 0; 49 } 50 51 int DFS(int u,int minv) 52 { 53 if(u==n) 54 return minv; 55 int t; 56 for(int v=1;v<=n;v++) 57 if(edges[u][v]>0&&level[v]==level[u]+1&&(t=DFS(v,min(minv,edges[u][v])))) 58 { 59 edges[u][v]-=t; 60 edges[v][u]+=t; 61 return t; 62 } 63 return 0; 64 } 65 66 int main() 67 { 68 int u,v,c; 69 while(scanf("%d%d",&m,&n)!=EOF) 70 { 71 memset(edges,0,sizeof(edges)); 72 for(int i=1;i<=m;i++) 73 { 74 scanf("%d%d%d",&u,&v,&c); 75 edges[u][v]+=c; 76 } 77 ans=0; 78 int t; 79 // DINIC() 80 while(BFS()) //还存在增广路 81 { 82 while(t=DFS(1,INF)) //DFS找出残留网络中的所有增广路 83 { 84 ans+=t; 85 } 86 } 87 printf("%d ",ans); 88 } 89 return 0; 90 }