poj 3041 Asteroids(二分图 *【矩阵实现】【最小点覆盖==最大匹配数】)

Asteroids

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 16379		Accepted: 8930

Description

Bessie wants to navigate her spaceship through a dangerous asteroid field in the shape of an N x N grid (1 <= N <= 500). The grid contains K asteroids (1 <= K <= 10,000), which are conveniently located at the lattice points of the grid.

Fortunately, Bessie has a powerful weapon that can vaporize all the
asteroids in any given row or column of the grid with a single shot.This
weapon is quite expensive, so she wishes to use it sparingly.Given the
location of all the asteroids in the field, find the minimum number of
shots Bessie needs to fire to eliminate all of the asteroids.

Input

* Line 1: Two integers N and K, separated by a single space.

* Lines 2..K+1: Each line contains two space-separated integers R
and C (1 <= R, C <= N) denoting the row and column coordinates of
an asteroid, respectively.

Output

* Line 1: The integer representing the minimum number of times Bessie must shoot.

Sample Input

3 4
1 1
1 3
2 2
3 2

Sample Output

2

Hint

INPUT DETAILS:
The following diagram represents the data, where "X" is an asteroid and "." is empty space:

X.X

.X.

.X.

OUTPUT DETAILS:

Bessie may fire across row 1 to destroy the asteroids at (1,1) and
(1,3), and then she may fire down column 2 to destroy the asteroids at
(2,2) and (3,2).

 

代码：

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <ctype.h>
#include <iostream>
#include <string>
#include <stack>
#include <queue>
#include <algorithm>
#define N 500+20
#define INF 0x3f3f3f3f
 
using namespace std;
int n, m;
int map[N][N];
int link[N];
bool vis[N];
 
bool match( int u )
{
	for(int i=1; i<=n; i++)
	{
		if(vis[i]==false && map[u][i]==1 )
		{
			vis[i]=true;
			if(link[i]==-1 || match(link[i]) )
			{
				link[i]=u;
				return true;
			}
		}
	}
	return false;
}
 
int main()
{
	int i, j, k;
	int u, v;
	scanf("%d %d", &n, &m);
	memset(map, 0, sizeof(map));
 
	for(i=0; i<m; i++ ){
		scanf("%d %d", &u, &v);
		map[u][v] = 1;
	}
	memset(link, -1, sizeof(link));
	int ans=0;
 
	for(int i=1; i<=n; i++)
	{
		memset(vis, false, sizeof(vis));
        if(match(i))
            ans++;
 
	}
	printf("%d\n", ans );
	return 0;
}