poj2446_二分图

POJ 2446  二分图的最大匹配 匈牙利算法

Chessboard

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 14350		Accepted: 4471

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

4 3 2
2 1
3 3

Sample Output

YES

题意：用2*1的木板覆盖给定的棋盘（棋盘中有墙），木板不能重叠，问是否能全部覆盖
思路：奇偶建二分图，把棋盘涂成黑白相间，每个黑格和4个白格相邻，每个白格和四个黑格相邻，黑格移入U,白格移入V，求最大匹配，由于每个匹配对应两个结点，若最大匹配*2等于总结点数说明成功覆盖

/* poj2446 141ms  */
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<vector>

using namespace std;

const int maxn=1200;

int N,M,K;
int uN,vN;
vector<int> G[maxn];
int link[maxn];
bool vis[maxn];
int ch[maxn][maxn];
int dx[]={-1,1,0,0};
int dy[]={0,0,-1,1};

bool dfs(int u)
{
    for(int i=0;i<G[u].size();i++){
        int v=G[u][i];
        if(!vis[v]){
            vis[v]=1;
            if(link[v]==-1||dfs(link[v])){
                link[v]=u;
                return true;
            }
        }
    }
    return false;
}

int hungary()
{
    int res=0;
    memset(link,-1,sizeof(link));
    for(int u=1;u<=uN;u++){
        memset(vis,0,sizeof(vis));
        if(dfs(u)) res++;
    }
    return res;
}

int main()
{
    cin>>N>>M>>K;
    for(int i=1;i<=N*M;i++) G[i].clear();
    memset(ch,-1,sizeof(ch));
    uN=vN=0;
    while(K--){
        int i,j;
        scanf("%d%d",&j,&i);
        ch[i][j]=0;
    }
    for(int i=1;i<=N;i++){
        for(int j=1;j<=M;j++){
            if(ch[i][j]){
                if((i+j)%2) ch[i][j]=++uN;
                else ch[i][j]=++vN;
            }
        }
    }
    for(int i=1;i<=N;i++){
        for(int j=1;j<=M;j++){
            if(ch[i][j]&&ch[i][j]!=-1&&(i+j)%2){
                for(int k=0;k<4;k++){
                    int x=i+dx[k],y=j+dy[k];
                    if(ch[x][y]&&ch[x][y]!=-1) G[ch[i][j]].push_back(ch[x][y]);
                }
            }
        }
    }
    int match=hungary();
    if(match*2==uN+vN) cout<<"YES"<<endl;
    else cout<<"NO"<<endl;
    return 0;
}