HDU 2458 Kindergarten 二分匹配

最新推荐文章于 2021-08-04 15:15:41 发布

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本文探讨了一个经典的组合优化问题——最大团问题，并通过一个具体的案例来展示如何使用二分匹配算法解决该问题。文章提供了完整的源代码，介绍了输入格式、算法实现细节及输出样例。

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In a kindergarten, there are a lot of kids. All girls of the kids know each other and all boys also know each other. In addition to that, some girls and boys know each other. Now the teachers want to pick some kids to play a game, which need that all players know each other. You are to help to find maximum number of kids the teacher can pick.

InputThe input consists of multiple test cases. Each test case starts with a line containing three integers
G, B (1 ≤ G, B ≤ 200) and M (0 ≤ M ≤ G × B), which is the number of girls, the number of boys and
the number of pairs of girl and boy who know each other, respectively.
Each of the following M lines contains two integers X and Y (1 ≤ X≤ G,1 ≤ Y ≤ B), which indicates that girl X and boy Y know each other.
The girls are numbered from 1 to G and the boys are numbered from 1 to B.

The last test case is followed by a line containing three zeros.OutputFor each test case, print a line containing the test case number( beginning with 1) followed by a integer which is the maximum number of kids the teacher can pick.Sample Input

Sample Output

Case 1: 3
Case 2: 4

题意：n个男生和m个女生存在k条关系，找出这些关系中的最大团，输出团的大小。

思路：二分匹配模板题，人数总和减去最大匹配即可。

#include<stdio.h>
#include<string.h>
int s[300][300];
int a[300],next[300];
int m,n;
int add(int x)
{
	int i,j;
	for(i=1;i<=n;i++)
	{
		if(s[x][i]==0&&next[i]==0)
		{
			next[i]=1;
			if(a[i]==0||add(a[i]))
			{
				a[i]=x;
				return 1;
			}
		}
	}
	return 0;
}
int main()
{
	int i,j,k,t,u,v;
	int z=1;
	while(scanf("%d%d%d",&m,&n,&t)!=EOF)
	{
		if(m+n+t==0)
			break;
		memset(s,0,sizeof(s));
		memset(a,0,sizeof(a));
		for(i=1;i<=t;i++)
		{
			scanf("%d%d",&u,&v);
			s[u][v]=1;
		}
		int sum=0;
		for(i=1;i<=m;i++)
		{
			memset(next,0,sizeof(next));
			if(add(i)==1)
				sum++;
		}
	/*	for(i=1;i<=n;i++)
		{
			printf("%d  ",a[i]);
		}*/
		printf("Case %d: ",z++);
		printf("%d\n",m+n-sum);
	}
	return 0;
}