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POJ训练计划3041_Asteroids(二分图/最小点覆盖=最大匹配)

2024-07-14 01:54:45   225人阅读

解题报告

题意：

给出NxN的矩阵，有M个点是障碍

每次只能删除一行或者一列，最少删除多少次才能清除障碍

思路：

把行和列看作两个集合结点，把障碍看作集合结点的连线，这样就转化成求用最少的点来消灭边，也就是最小点覆盖。

在二分图中：（n个结点，且没有孤立的点）

最小点覆盖=最大匹配

最大点独立=结点数-最大匹配

#include <queue>
#include <vector>
#include <cstdio>
#include <cstring>
#include <iostream>
#define N 510
using namespace std;
int mmap[N+N][N+N],n,k,vis[N+N],pre[N+N];
int dfs(int x)
{
    int i;
    for(i=n+1; i<=n+n; i++) {
        if(!vis[i]&&mmap[x][i]) {
            vis[i]=1;
            if(pre[i]==-1||dfs(pre[i])) {
                pre[i]=x;
                return 1;
            }
        }
    }
    return 0;
}
int main()
{
    int i,j,x,y;
    while(cin>>n>>k) {
        memset(mmap,0,sizeof(mmap));
        memset(pre,-1,sizeof(pre));
        for(i=0; i<k; i++) {
            cin>>x>>y;
            mmap[x][n+y]=1;
        }
        int ans=0;
        for(i=1; i<=n; i++) {
            memset(vis,0,sizeof(vis));
            ans+=dfs(i);
        }
        cout<<ans<<endl;
    }
}

Asteroids
Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 14694 Accepted: 8016

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).

Source

USACO 2005 November Gold


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