POJ3041 Asteroids (最小顶点覆盖)

Asteroids

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 22298 Accepted: 12084

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 41 11 32 23 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

思路：题目要求的是用最少的子弹来消灭所有的行星，所以问题就可以转化成为最小顶点覆盖。

#include <cstdio>#include <vector>#include <cstring>using namespace std;int n,k,vis[505],link[505];vector<int>p[505];int find(int u){for(int i = 0; i < p[u].size(); i ++){int v = p[u][i];if(!vis[v]){vis[v] = 1;if(link[v] == -1 || find(link[v])){link[v] = u;return 1;}}}return 0;}int main(){while(~scanf("%d%d",&n,&k)){for(int i = 0; i <= n; i ++){p[i].clear();}int a,b;for(int i = 0; i < k; i ++){scanf("%d%d",&a,&b);p[a].push_back(b);}memset(link,-1,sizeof(link));int cnt = 0;for(int i = 1; i <= n; i ++){memset(vis,0,sizeof(vis));if(find(i))cnt ++;}printf("%d\n",cnt);}return 0;}