POJ2446_Chessboard(二分图最大匹配)

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解题报告

http://blog.csdn.net/juncoder/article/details/38172083

题目传送门

题意：

M×N的矩阵，k个点被标记，用2×1的木板最多可以放置多少个。

思路：

把标记的格子除外，链接相邻的两个格子，然后最大匹配出来的是二分图的两倍。

c++TLE了，G++1700+过了，理论上匈牙利算法的时间复杂度是n^3，就应该超时，可能数据弱吧。

还有一种建图方式就是建成二分图，将矩阵中的点奇偶分。

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
int n,m,k,mmap[2050][2050],edge[2050][2050],pre[2050],vis[2050],kk;
int dx[]= {1,-1,0,0};
int dy[]= {0,0,1,-1};
int dfs(int x)
{for(int i=1; i<=kk; i++) {if(!vis[i]&&edge[x][i]) {vis[i]=1;if(pre[i]==-1||dfs(pre[i])) {pre[i]=x;return 1;}}}return 0;
}
int main()
{int i,j,a,b;while(~scanf("%d%d%d",&m,&n,&k)) {memset(mmap,0,sizeof(mmap));memset(pre,-1,sizeof(pre));memset(edge,0,sizeof(edge));for(i=1; i<=k; i++) {scanf("%d%d",&b,&a);mmap[a][b]=-1;}if(n*m%2!=k%2) {printf("NO\n");continue;}kk=0;for(i=1; i<=m; i++) {for(j=1; j<=n; j++) {if(!mmap[i][j])mmap[i][j]=++kk;}}if(kk%2!=0) {printf("NO\n");continue;}int l=0;for(i=1; i<=m; i++) {for(j=1; j<=n; j++) {if(mmap[i][j]!=-1)for(l=0; l<4; l++) {int x=i+dx[l];int y=j+dy[l];if(x>=1&&x<=m&&y>=1&&y<=n&&mmap[x][y]!=-1) {edge[mmap[i][j]][mmap[x][y]]=1;}}}}int ans=0;for(i=1; i<=kk; i++) {memset(vis,0,sizeof(vis));ans+=dfs(i);}if(ans==kk)printf("YES\n");else printf("NO\n");}return 0;
}

Chessboard

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 13140		Accepted: 4105

Description

Alice and Bob often play games on chessboard. One day, Alice draws a board with size M * N. She wants Bob to use a lot of cards with size 1 * 2 to cover the board. However, she thinks it too easy to bob, so she makes some holes on the board (as shown in the figure below).

We call a grid, which doesn’t contain a hole, a normal grid. Bob has to follow the rules below:
1. Any normal grid should be covered with exactly one card.
2. One card should cover exactly 2 normal adjacent grids.

Some examples are given in the figures below:

A VALID solution.

An invalid solution, because the hole of red color is covered with a card.

An invalid solution, because there exists a grid, which is not covered.
Your task is to help Bob to decide whether or not the chessboard can be covered according to the rules above.

Input

There are 3 integers in the first line: m, n, k (0 < m, n <= 32, 0 <= K < m * n), the number of rows, column and holes. In the next k lines, there is a pair of integers (x, y) in each line, which represents a hole in the y-th row, the x-th column.

Output

If the board can be covered, output "YES". Otherwise, output "NO".

Sample Input