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【POJ - 3041】Asteroids (二分图,最小点覆盖)

發布時間:2023/12/10 编程问答 31 豆豆
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題干:

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).

題目大意:

在N*N的0和1組成的格子,一次操作可以將一行或一列的1全部變成0,問至少要進行多少次操作才能將所有的1全部變成0.

解題報告:

? ? 套路建圖方式、、、裸的最小點覆蓋、、

AC代碼:

#include<cstdio> #include<iostream> #include<algorithm> #include<queue> #include<map> #include<vector> #include<set> #include<string> #include<cmath> #include<cstring> #define ll long long #define pb push_back #define pm make_pair #define fi first #define se second using namespace std; const int MAX = 2e5 + 5; vector<int> vv[MAX]; int nxt[MAX]; bool used[MAX]; int n,k; bool find(int x) {int up = vv[x].size();for(int i = 0; i<up; i++) {int v = vv[x][i];if(used[v] == 1) continue;used[v] = 1;if(nxt[v] == -1 || find(nxt[v])) {nxt[v] = x;return 1;}}return 0; } int match() {int sum = 0;for(int i = 1; i<=n; i++) {memset(used,0,sizeof used);if(find(i)) sum++;}return sum; } int main() {cin>>n>>k;memset(nxt,-1,sizeof nxt);for(int i = 1; i<=k; i++) {int x,y;scanf("%d%d",&x,&y);vv[x].pb(y);}printf("%d\n",match());return 0 ;}

?

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