POJ_2594_最小路径覆盖

Treasure Exploration

Description

Have you ever read any book about treasure exploration? Have you ever see any film about treasure exploration? Have you ever explored treasure? If you never have such experiences, you would never know what fun treasure exploring brings to you. 
Recently, a company named EUC (Exploring the Unknown Company) plan to explore an unknown place on Mars, which is considered full of treasure. For fast development of technology and bad environment for human beings, EUC sends some robots to explore the treasure. 
To make it easy, we use a graph, which is formed by N points (these N points are numbered from 1 to N), to represent the places to be explored. And some points are connected by one-way road, which means that, through the road, a robot can only move from one end to the other end, but cannot move back. For some unknown reasons, there is no circle in this graph. The robots can be sent to any point from Earth by rockets. After landing, the robot can visit some points through the roads, and it can choose some points, which are on its roads, to explore. You should notice that the roads of two different robots may contain some same point. 
For financial reason, EUC wants to use minimal number of robots to explore all the points on Mars. 
As an ICPCer, who has excellent programming skill, can your help EUC?

Input

The input will consist of several test cases. For each test case, two integers N (1 <= N <= 500) and M (0 <= M <= 5000) are given in the first line, indicating the number of points and the number of one-way roads in the graph respectively. Each of the following M lines contains two different integers A and B, indicating there is a one-way from A to B (0 < A, B <= N). The input is terminated by a single line with two zeros.

Output

For each test of the input, print a line containing the least robots needed.

Sample Input

1 0
2 1
1 2
2 0
0 0

Sample Output

1
1
2

最小路径覆盖。此题点可重，先用floyd求其传递闭包。最小路径覆盖=点数-最大匹配数个人感觉有向图和无向图有些许不同，关键在于理解匈牙利算法的过程。（无向图的最大匹配是匈牙利算法求得结果的一半）

#include<iostream>
#include<cstring>
#include<queue>
#include<cstdio>
#include<map>
using namespace std;

int mapp[505][505];
int link[505];
int vis[505];
int cnt=1,m,n;

void floyd()
{
    for(int k=1; k<=n; k++)
        for(int i=1; i<=n; i++)
        {
            if(mapp[i][k])
                for(int j=1; j<n; j++)
                    if(mapp[k][j])
                        mapp[i][j]=1;
        }
}

bool dfs(int x)
{
    for(int i=1; i<=n; i++)
        if(mapp[x][i]&&!vis[i])
        {
            vis[i]=1;
            if(link[i]==-1||dfs(link[i]))
            {
                link[i]=x;
                return true;
            }
        }
    return false;
}

int ans;
void solve()
{
    memset(link,-1,sizeof(link));
    for(int i=1; i<=n; i++)
    {
        memset(vis,0,sizeof(vis));
        if(dfs(i))
            ans++;
    }
}

int main()
{
    while(scanf("%d%d",&n,&m)!=EOF&&n+m)
    {
        memset(mapp,0,sizeof(mapp));
        for(int i=0; i<m; i++)
        {
            int x,y;
            scanf("%d%d",&x,&y);
            mapp[x][y]=1;
        }
        floyd();
        ans=0;
        solve();
        printf("%d\n",n-ans);
    }
    return 0;
}