poj 2524 Ubiquitous Religions（并查集）

题目链接：http://poj.org/problem?id=2524

Ubiquitous Religions

Time Limit: 5000MS Memory Limit: 65536KTotal Submissions: 33619 Accepted: 16258

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 91 21 31 41 51 61 71 81 91 1010 42 34 54 85 80 0

Sample Output

Case 1: 1Case 2: 7

Hint

Huge input, scanf is recommended.

Source

Alberta Collegiate Programming Contest 2003.10.18

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题意：n个人，问了k对，每对有相同的宗教信仰，求最少的宗教信仰

解析：并查集，看最后有几个父节点

代码：

#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<queue>#include<cmath>#include<map>#include<vector>#include<stack>#define N 50009using namespace std;const int INF = 0x3f3f3f3f;int father[N];void init(int n){    for(int i = 1; i <= n; i++)        father[i] = i;}int dfs(int u){    return u == father[u] ? u : (father[u] = dfs(father[u]));}void unint(int u, int v){    int x = dfs(u);    int y = dfs(v);    if(x != y) father[x] = y;}int main(){    int u, v, cnt = 0, n, k;    while(scanf("%d%d", &n, &k), n + k)    {        init(n);        for(int i = 0; i < k; i++)        {            scanf("%d%d", &u, &v);            unint(u, v);        }        int ans = 0;        for(int i = 1; i <= n; i++)        {            if(father[i] == i) ans++;        }        printf("Case %d: %d\n", ++cnt, ans);    }    return 0;}