POJ 3041 Asteroids

2022-11-06 09:05:17

最小点覆盖数==最大匹配数

Asteroids

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 12678		Accepted: 6904

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

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).

Source

USACO 2005 November Gold

#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>

using namespace std;

int N,P,from[1000];
vector<int> g[1000];
bool use[1000];

bool match(int u)
{
    for(int i=0;i<g.size();i++)
    {
        if(!use[g])
        {
            use[g]=true;
            if(!from[g]||match(from[g]))
            {
                from[g]=u;
                return true;
            }
        }
    }
    return false;
}

int hungary()
{
    int ret=0;
    memset(from,0,sizeof(from));
    for(int i=1;i<=N;i++)
    {
        memset(use,0,sizeof(use));
        if(match(i)) ret++;
    }
    return ret;
}

int main()
{
    while(scanf("%d%d",&N,&P)!=EOF)
    {
        memset(g,0,sizeof(g));
        for(int i=1;i<=P;i++)
        {
            int a,b;
            scanf("%d%d",&a,&b);
            g[a].push_back(b);
        }
        printf("%d\n",hungary());
    }
    return 0;
}

* This source code was highlighted by YcdoiT. ( style: Vs )

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