HDU 3549 Flow Problem 网络流 EK

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

23 21 2 12 3 13 31 2 12 3 11 3 1

 

Sample Output

Case 1: 1Case 2: 2

 

Author

HyperHexagon

 

Source

HyperHexagon's Summer Gift (Original tasks)

就是网络流的裸题。

这回练一下EK。。说实话EK真的好懂又好写。。

就是不停广搜找增广路，找到之后流量都减一遍，直到找不到增广路就好了。

可惜O(V*E^2)有局限。。稀疏图真的不错的。

其实这题也可以用EK做：poj1273

#include<cstdio>#include<cstring>#include<cmath>#include<algorithm>#define N 1005using namespace std;int n,m;bool visit[N];int map[N][N];int Q[N],pre[N];bool EdKa(int src,int des,int n){    int v,i,head,tail;    memset(visit,0,sizeof(visit));    head=tail=0;    Q[tail++]=src;    visit[src]=true;    while (head!=tail)    {        v=Q[head++];        for (i=1;i<=n;i++)            if (!visit[i] && map[v][i])            {                Q[tail++]=i;                visit[i]=true;                pre[i]=v;                if (i==des)    return true;            }    }    return false;}int maxflow(int src,int des,int n){    int i,_min,sum=0;    while (true)    {        if (!EdKa(src,des,n))            return sum;        _min=(1<<30);        i=des;        while (i!=src)        {            if (_min>map[pre[i]][i])                _min=map[pre[i]][i];            i=pre[i];        }        i=des;        while (i!=src)        {            map[pre[i]][i]-=_min;            map[i][pre[i]]+=_min;            i=pre[i];        }        sum+=_min;    }}int main(){    int T,cas;    scanf("%d",&T);    for (cas=1;cas<=T;cas++)    {        memset(map,0,sizeof(map));        int x,y,z,j;        scanf("%d%d",&n,&m);        for (j=1;j<=m;j++)        {            scanf("%d%d%d",&x,&y,&z);            map[x][y]+=z;        }        printf("Case %d: %d\n",cas,maxflow(1,n,n));    }}