POJ 2524 Ubiquitous Religions

POJ 2524 Ubiquitous Religions

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
Hint
Huge input, scanf is recommended.

题意：
一个学校的学生信仰宗教的最大种类数。已知学生总数及同一信仰的两个学生编号。

分析：
并查集的简单应用，将同一信仰的两个学生合并。求得共有多少个分组，未提及的学生自成一组，算得最大种类数。

#include<cstdio>
#include <iostream>
#include<cstring>
#include<algorithm>
#define N 50005 
using namespace std;

int u[N],rank[N], m, n;

int find(int x)
{
    if(x != u[x])
    {
        u[x] = find(u[x]);
    }
    return u[x];
}
void mix(int a, int b)
{
    a = find(a);
    b = find(b);
    if (a == b)
        return ;
    if (rank[a] > rank[b])
    {
        u[b] = a;
    }
    else
    {
        u[a] = b;
        if (rank[a] == rank[b])
        {
            rank[a]++;
        }
    }
}

int main()
{
#ifndef ONLINE_JUDGE
    freopen("1.txt", "r", stdin);
#endif
    int a, b, i, j, ans, count = 0;
    while(scanf("%d%d", &n, &m), n)
    {
        for(i = 1; i <= n; i++)
        {
            u[i] = i;
            rank[i] = 1;
        }
        for(i = 0; i < m; i++)
        {
            scanf("%d%d", &a, &b);
            mix(a, b);
        }
        cout << "Case " << ++count << ": ";
        ans = 0;
        for(i = 1; i <= n; i++)
        {
            if (i == u[i])
            {
                ans++;
            }
        }
        cout << ans << endl;
    }

    return 0;
}