POJ 3692 Kindergarten(最大独立集)

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题意：已知班级有g个女孩和b个男孩，所有女生之间都相互认识，所有男生之间也相互认识，给出m对关系表示哪个女孩与哪个男孩认识。现在要选择一些学生来组成一个团，使得里面所有人都认识，求此团最大人数。

思路：任意两个同学之间要么认识,要么不认识.现在我们根据所有同学之间的不认识关系来建图.为什么呢？因为二分图匹配的时候左边和右边的点是独立的没有边的，如果我们按照同学间认识关系来建图，那么左边的点互相都有边，右边的点也互相都有边，那么就有问题了。

假设女生在左边点集,男生在右边点集.那么左边点集的内部肯定没边,右边点集同样没边. 对于女生i与男生j不认识的话,就连一条左边i与右边j的无向边. 这个图肯定是二分图.

然后我们现在要在这个图中选择最多的点,使得所选点集合中任意两个点都不存在边.(不存在边,那么就是任意两点都相互认识.其实就是该图的最大独立集).

由于最大独立集 = n(图节点总数)-最小覆盖数=n-最大匹配数. 所以我们只要求最大匹配数即可.

#include<cstdio>#include<cstring>#include<vector>using namespace std;const int maxn=500+10;struct Max_Match{    int n,m;    int g[maxn][maxn];    bool vis[maxn];    int left[maxn];    void init(int n,int m)    {        this->n=n;        this->m=m;        for (int i = 1;i<=n;i++)for (int j = 1;j<=m;j++)g[i][j]=1;        memset(left,-1,sizeof(left));    }    bool match(int u)    {        for(int v=1;v<=m;v++)        {            if(g[u][v] && !vis[v])            {                vis[v]=true;                if(left[v]==-1 || match(left[v]))                {                    left[v]=u;                    return true;                }            }        }        return false;    }    int solve()    {        int ans=0;        for(int i=1;i<=n;i++)        {            memset(vis,0,sizeof(vis));            if(match(i)) ans++;        }        return ans;    }}MM;int T;int cas = 1;int main(){    int g,b,m;while (scanf("%d%d%d",&g,&b,&m) && g+b+m){MM.init(g,b);for (int i = 1;i<=m;i++){int u,v;scanf("%d%d",&u,&v);MM.g[u][v]=0;}printf("Case %d: %d\n",cas++,g+b-MM.solve());}    return 0;}

Description

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.

Input

The 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.

Output

For 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

2 3 31 11 22 32 3 51 11 22 12 22 30 0 0

Sample Output

Case 1: 3Case 2: 4

0 0