【HDU3549】

(http://www.elijahqi.win/2017/07/11/%E3%80%90hdu3549%E3%80%91/)
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

题解：好像名字就叫网络流问题 于是用了两种方法试试
dinic：

#include<cstdio>
#include<cstring>
int S,T,map[20][20],f[20],data[20],n,m,t;
int min(int x,int y){
    return x<y?x:y;
}
bool bfs(){
    memset(f,-1,sizeof(f));
    int op=0,cl=1;data[1]=S;f[1]=0;
    bool flag=false;
    while (op<cl){
        op++;int u=data[op];
        for (int v=1;v<=T;++v){
            if (map[u][v]!=0&&f[v]==-1){
                f[v]=f[u]+1;data[++cl]=v;
                if (v==T) {
                    flag=true;
                }
            }
        }
    }
    return flag;
}
int dfs(int u,int s){
    if (u==T) return s;
    int ss=s;
    for (int v=1;v<=n;++v){
        if (map[u][v]!=0&&f[v]==f[u]+1){
            int x=dfs(v,min(map[u][v],s));
            s-=x;
            map[u][v]-=x;
            map[v][u]+=x;
            if (s==0) return ss;
        }
    }
    return ss-s;
}
int main(){
    freopen("hdu3549.in","r",stdin);
    freopen("hdu3549.out","w",stdout);
    scanf("%d",&t);
    int tmpp=t;
    while (t--){
        scanf("%d%d",&n,&m);
        memset(map,0,sizeof(map));
        for (int i=1;i<=m;++i){
            int x,y,c;
            scanf("%d%d%d",&x,&y,&c);
            map[x][y]+=c;
        }
        S=1;T=n;
        int ans=0,maxlong=0x7fffffff;
        while (bfs()){
            int x=dfs(S,maxlong);
            ans+=x;
        }
        printf("Case %d: %d\n",tmpp-t,ans);
    }
    return 0;
}

sap

#include<cstdio>
#include<cstring>
int S,T,t,n,m,map[20][20],h[20],f[20];
int min(int x,int y){
    return x<y?x:y;
}
int sap(int u,int ss){
    if (u==T) return ss;
    int temp=ss;
    int tmp=T-1;
    for (int v=1;v<=n;++v){
        if (map[u][v]!=0){
            if (h[u]==h[v]+1){
                int x=sap(v,min(map[u][v],ss));
                ss-=x;
                map[u][v]-=x;
                map[v][u]+=x;
                if (ss==0) return temp; 
            }
            if (h[v]<tmp) tmp=h[v];
        }

    }
    if (temp==ss){
        f[h[u]]--;
        if (f[h[u]]==0) h[1]=n;
        h[u]=tmp+1;
        f[h[u]]++;
    }
    return temp-ss;
}
int main(){
    freopen("hdu3549.in","r",stdin);
    freopen("hdu3549.out","w",stdout);
    scanf("%d",&t);
    int tmpp=t;
    while (t--){
        scanf("%d%d",&n,&m);
        memset(map,0,sizeof(map));
        for (int i=1;i<=m;++i){
            int x,y,c;
            scanf("%d%d%d",&x,&y,&c);
            map[x][y]+=c;
        }
        S=1;T=n;
        memset(h,0,sizeof(h));memset(f,0,sizeof(f));
        f[0]=n;
        int ans=0;
        while (h[S]<n){
            int x=sap(S,0x7fffffff);
            ans+=x;
        }
        printf("Case %d: %d\n",tmpp-t,ans);
    }
    return 0;
}