# Flow Problem

Time Limit: 5000/5000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others) Total Submission(s): 8203    Accepted Submission(s): 3817

Problem Description

Network flow is a well-known difficult problem for ACMers. Given a graph, your task is to find out the maximum flow for the weighted directed graph.

Input

The first line of input contains an integer T, denoting the number of test cases. For each test case, the first line contains two integers N and M, denoting the number of vertexes and edges in the graph. (2 <= N <= 15, 0 <= M <= 1000) Next M lines, each line contains three integers X, Y and C, there is an edge from X to Y and the capacity of it is C. (1 <= X, Y <= N, 1 <= C <= 1000)

Output

For each test cases, you should output the maximum flow from source 1 to sink N.

Sample Input

2 3 2 1 2 1 2 3 1 3 3 1 2 1 2 3 1 1 3 1

Sample Output

Case 1: 1 Case 2: 2

Author

HyperHexagon

Source

``` 1 #include<cstdio>
2 #include<cstring>
3 #include<iostream>
4 #include<queue>
5 using namespace std;
6 const int inf=0x3f3f3f3f;
7 int mat[30][30];
8 int dist[31];
9 int n,m;
10 int min(int a,int b)
11 {
12 return a<b?a:b;
13 }
14 bool bfs(int st,int to){
15     memset(dist,-1,sizeof(dist));
16     queue<int>q;
17     q.push(st);
18     dist[st]=0;
19     int t;
20     while(!q.empty()){
21        t=q.front();
22        q.pop();
23     for(int i=1;i<=n;i++){
24         if(dist[i]<0&&mat[t][i]>0){
25             dist[i]=dist[t]+1;
26             if(i==to)return 1;
27             q.push(i);
28         }
29     }
30     }
31   return 0;
32 }
33 int dfs(int st,int to,int flow)
34 {
35     int tem;
36     if(st==to||flow==0) return flow;
37     for(int i=1;i<=n;i++){
38       if((dist[i]==dist[st]+1)&&mat[st][i]>0&&(tem=dfs(i,to,min(mat[st][i],flow))))
39       {
40           mat[st][i]-=tem;
41           mat[i][st]+=tem;
42           return tem;
43       }
44     }
45   return 0;
46 }
47 int Dinic(int st,int en)
48 {
49     int ans=0;
50     while(bfs(st,en))
51         ans+=dfs(st,en,inf);
52    return ans;
53 }
54 int main(){
55   int cas,i,a,b,c;
56   scanf("%d",&cas);
57   for(i=1;i<=cas;i++){
58       scanf("%d%d",&n,&m);
59       memset(mat,0,sizeof(mat));
60      while(m--){
61        scanf("%d%d%d",&a,&b,&c);
62        mat[a][b]+=c;
63      }
64    printf("Case %d: %d\n",i,Dinic(1,n));
65   }
66   return 0;
67 }```

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