POJ题目1719 Shooting Contest（二分图）

Shooting Contest

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 4048 Accepted: 1479 Special Judge

Description

Welcome to the Annual Byteland Shooting Contest. Each competitor will shoot to a target which is a rectangular grid. The target consists of r*c squares located in r rows and c columns. The squares are coloured white or black. There are exactly two white squares and r-2 black squares in each column. Rows are consecutively labelled 1,..,r from top to bottom and columns are labelled 1,..,c from left to right. The shooter has c shots. 

A volley of c shots is correct if exactly one white square is hit in each column and there is no row without white square being hit. Help the shooter to find a correct volley of hits if such a volley exists. 
Example 
Consider the following target: 

Volley of hits at white squares in rows 2, 3, 1, 4 in consecutive columns 1, 2, 3, 4 is correct. 
Write a program that: verifies whether any correct volley of hits exists and if so, finds one of them.

Input

The first line of the input contains the number of data blocks x, 1 <= x <= 5. The following lines constitute x blocks. The first block starts in the second line of the input file; each next block starts directly after the previous one. 

The first line of each block contains two integers r and c separated by a single space, 2 <= r <= c <= 1000. These are the numbers of rows and columns, respectively. Each of the next c lines in the block contains two integers separated by a single space. The integers in the input line i + 1 in the block, 1 <= i <= c, are labels of rows with white squares in the i-th column. 

Output

For the i-th block, 1 <= i <= x, your program should write to the i-th line of the standard output either a sequence of c row labels (separated by single spaces) forming a correct volley of hits at white squares in consecutive columns 1, 2, ..., c, or one word NO if such a volley does not exists.

Sample Input

24 42 43 41 31 45 51 52 43 42 42 3

Sample Output

2 3 1 4NO

Source

CEOI 1997

题意：给定一个矩阵，每列有两个白点，其他都是黑点，现在要求每列选一个白点，使得每一行至少包含一个白点被选中

思路：二分图匹配，白点的位置行列建边，然后跑匹配，如果匹配数不等于行数，就是是无解，然后输出方案的时候注意，如果有位置是没匹配的，说明这个位置是多余的，但是还是要任意选一个白点来输出

ac代码

#include<stdio.h>#include<string.h>#include<vector>#include<iostream>using namespace std;int r,c;vector<int>vt[1010];int save[1010],link[1010],vis[1010];void init(){int i;for(i=0;i<=r;i++){vt[i].clear();}}int dfs(int x){int i,j;for(i=0;i<vt[x].size();i++){int v=vt[x][i];if(!vis[v]){vis[v]=1;if(link[v]==-1||dfs(link[v])){link[v]=x;return 1;}}}return 0;}int main(){int t;scanf("%d",&t);while(t--){int i;scanf("%d%d",&r,&c);init();for(i=1;i<=c;i++){int x,y;scanf("%d%d",&x,&y);vt[x].push_back(i);vt[y].push_back(i);save[i]=y;}memset(link,-1,sizeof(link));int ans=0;for(i=1;i<=r;i++){memset(vis,0,sizeof(vis));if(dfs(i))ans++;}if(r!=ans){printf("NO\n");continue;}for(i=1;i<=c;i++){if(i==1)printf("%d",link[i]==-1?save[i]:link[i]);elseprintf(" %d",link[i]==-1?save[i]:link[i]);}printf("\n");}}