poj 3041 Asteroids (二分匹配)
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题目链接:http://poj.org/problem?id=3041
Asteroids
Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 22020 Accepted: 11942
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.
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.
* 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).
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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题意:给一个n*n的矩阵,然后给出k个 ‘x’ 障碍,可以用枪去射击这些障碍,每次射击可以消除一行或者一列的障碍,求最少的射击次数
解析:单纯的二分匹配,不知道的可以百度下二分匹配相关算法,比如匈牙利算法
代码:
#include<iostream>#include<algorithm>#include<cstdio>#include<cstring>#include<cmath>#define N 509using namespace std;int mp[N][N], used[N], f[N];int n;bool dfs(int u){ for(int i = 1; i <= n; i++) { if(!used[i] && mp[u][i]) { used[i] = 1; if(f[i] == -1 || dfs(f[i])) { f[i] = u; return true; } } } return false;}int main(){ int x, y, k; scanf("%d%d", &n, &k); memset(mp, 0, sizeof(mp)); memset(f, -1, sizeof(f)); for(int i = 1; i <= k; i++) { scanf("%d%d", &x, &y); mp[x][y] = 1; } int ans = 0; for(int i = 1; i <= n; i++) { memset(used, 0, sizeof(used)); ans += dfs(i); } printf("%d\n", ans); return 0;}
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