Flow Problem

Time Limit: 5000/5000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 11405    Accepted Submission(s):
5418

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

刚开始看不是太理解  解析会后续更新

#include<stdio.h>
#include<string.h>
#include<stack>
#include<queue>
#include<vector>
#include<algorithm>
#define INF 0x7fffff
#define MAX 2100
using namespace std;
int ans,head[MAX];
int n,m;
int dis[MAX],vis[MAX];
int cur[MAX];
struct node
{
	int beg,end,cap,flow,next;
}edge[MAX];
void init()
{
	ans=0;
	memset(head,-1,sizeof(head));
}
void add(int u,int v,int w)
{
	edge[ans].beg=u;
	edge[ans].end=v;
	edge[ans].cap=w;
	edge[ans].flow=0;
	edge[ans].next=head[u];
	head[u]=ans++;
}
void getmap()
{
	int i,a,b,c;
	while(m--)
	{
		scanf("%d%d%d",&a,&b,&c);
		add(a,b,c);
		add(b,a,0);
	}
}
int bfs(int start,int over)
{
	int i,v;
	memset(dis,-1,sizeof(dis));
	memset(vis,0,sizeof(vis));
    queue<int>q;
    while(!q.empty())
        q.pop();
    q.push(start);
    vis[start]=1;
    dis[start]=0;
    while(!q.empty())
    {
    	int u=q.front();
    	q.pop();
    	for(i=head[u];i!=-1;i=edge[i].next)
    	{
    	    v=edge[i].end;
			if(!vis[v]&&edge[i].cap>edge[i].flow)
			{
				vis[v]=1;
				dis[v]=dis[u]+1;
				if(v==over)
				    return 1;
				q.push(v);
			}
    	}
    }
    return 0;
}
int dfs(int x,int a,int over)
{
	if(x==over||a==0)
	    return a;
	int flow=0,f;
	for(int& i=cur[x];i!=-1;i=edge[i].next)
	{
		if(dis[x]+1==dis[edge[i].end]&&(f=dfs(edge[i].end,min(a,edge[i].cap-edge[i].flow),over))>0)
		{
			edge[i].flow+=f;
			edge[i^1].flow-=f;
			flow+=f;
			a-=f;
			if(a==0) break;
		}
	}
	return flow;
}
int maxflow(int start,int over)
{
	int flow=0;
	while(bfs(start,over))
	{
		memcpy(cur,head,sizeof(head));
		flow+=dfs(start,INF,over);
	}
	return flow;
}
int main()
{
	int t,k,j,i;
	scanf("%d",&t);
	k=1;
	while(t--)
	{
		scanf("%d%d",&n,&m);
		init();
		getmap();
		printf("Case %d: ",k++);
		printf("%d\n",maxflow(1,n));
	}
	return 0;
}