POJ 2524 Ubiquitous Religions

Ubiquitous Religions

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 20668		Accepted: 10153

Description

There are so many different religions in the world today that it is difficult to keep track of them all. You are interested in finding out how many different religions students in your university believe in. 

You know that there are n students in your university (0 < n <= 50000). It is infeasible for you to ask every student their religious beliefs. Furthermore, many students are not comfortable expressing their beliefs. One way to avoid these problems is to ask m (0 <= m <= n(n-1)/2) pairs of students and ask them whether they believe in the same religion (e.g. they may know if they both attend the same church). From this data, you may not know what each person believes in, but you can get an idea of the upper bound of how many different religions can be possibly represented on campus. You may assume that each student subscribes to at most one religion.

Input

The input consists of a number of cases. Each case starts with a line specifying the integers n and m. The next m lines each consists of two integers i and j, specifying that students i and j believe in the same religion. The students are numbered 1 to n. The end of input is specified by a line in which n = m = 0.

Output

For each test case, print on a single line the case number (starting with 1) followed by the maximum number of different religions that the students in the university believe in.

Sample Input

10 9
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
10 4
2 3
4 5
4 8
5 8
0 0

Sample Output

Case 1: 1
Case 2: 7
題目大意：輸入n,m表明有n個幫派，下面輸入m行x,y，表明學生x,y同一個幫派，問總共有多少個幫派。
解題方法：並查集，每次輸入x,y時若是發現他們不一樣幫派，則n減一，而後合併。

#include <stdio.h>

typedef struct
{
    int parent;
    int rank;
}UFSTree;

UFSTree Student[50005];

void MakeSet(int n)
{
    for (int i = 0; i <= n; i++)
    {
        Student[i].parent = i;
        Student[i].rank = 0;
    }
}

int FindSet(int x)
{
    if (x != Student[x].parent)
    {
        return FindSet(Student[x].parent);
    }
    else
    {
        return x;
    }
}

void UnionSet(int x, int y)
{
    x = FindSet(x);
    y = FindSet(y);
    if (Student[x].rank > Student[y].rank)
    {
        Student[y].parent = x;
    }
    else
    {
        Student[x].parent = y;
        if (Student[x].rank == Student[y].rank)
        {
            Student[y].rank++;
        }
    }
}

int main()
{
    int m, n, x, y, nCase = 0;
    while(scanf("%d%d", &n, &m) != EOF && n != 0 && m != 0)
    {
        MakeSet(n);
        for (int i = 0; i < m; i++)
        {
            scanf("%d%d", &x, &y);
            if (FindSet(x) != FindSet(y))
            {
                n--;
                UnionSet(x, y);
            }
        }
        printf("Case %d: %d\n", ++nCase, n);
    }
    return 0;
}