并查集。

#include<cstdio>
#include<cstring>
using namespace std;
const int maxn = 55555;
int fa[maxn];
int vis[maxn];
int n,m,t;
void init(){
    for(int i = 0; i < n; i++) {fa[i] = i;}
    memset(vis,0,sizeof(vis));
}
int find_father(int u){
    return fa[u] == u ? u : fa[u] = find_father(fa[u]);
}
int main(){
    int Case = 1;
    while(scanf("%d%d",&n,&m)){
        if(!m && !n) break;
        init();
        for(int i = 0; i < m; i++){
            int x,y;
            scanf("%d%d",&x,&y);
            int fx = find_father(x);
            int fy = find_father(y);
            fa[fx] = fy;
        }
        int cnt = 0;
        for(int i = 1; i <= n; i++){
            int t = find_father(i);
            if(!vis[t]){
                vis[t] = 1;
                cnt ++;
            }
        }
        printf("Case %d: %d\n",Case++,cnt);
    }
    return 0;
}

【POJ-2524】Ubiquitous Religions（并查集）