最大匹配-HDOJ 2458 Kindergarten

HDOJ 2458 Kindergarten
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 3

1 1

1 2

2 3

2 3 5

1 1

1 2

2 1

2 2

2 3

0 0 0

Sample Output

Case 1: 3

Case 2: 4


大意：幼儿园里一群小朋友，男生彼此都认识，女生彼此都认识，一些男女生相互认识。求最大的集合，在这个集合里任意两人都认识。

分析：图论，求最大的连通分量中顶点个数。此题可以对原图取反（i,j不认识，置edge[i][j]=true），便成了二部图，所求问题转化为求最大独立集。

二部图的独立集：该集合中任意两点不相邻接。

独立集中顶点个数=总顶点数-最大匹配中边的数目。