路徑壓縮 tro not lines () using number rest targe

題目鏈接：

http://poj.org/problem?id=2524

Ubiquitous Religions

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 39369		Accepted: 18782

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. 分析： 裸的並查集（我覺得叫查並集更好） 代碼如下：

#include<stdio.h>
#include<iostream>
using namespace std;
#define max_v 50005
int pa[max_v];//pa[x] 表示x的父節點
int rk[max_v];//rk[x] 表示以x為根結點的樹的高度
int n,ans;
void make_set(int x)
{
    pa[x]=x;
    rk[x]=0;//一開始每個節點的父節點都是自己
}
int find_set(int x)//帶路徑壓縮的查找
{
    if(x!=pa[x])
        pa[x]=find_set(pa[x]);
    return pa[x];
}
void union_set(int x,int y)
{
    x=find_set(x);//找到x的根結點
    y=find_set(y);
    if(x==y)//根結點相同 同一棵樹
        return ;
    ans--;
    if(rk[x]>rk[y])
    {
        pa[y]=x;
    }else
    {
        pa[x]=y;
        if(rk[x]==rk[y])
            rk[y]++;
    }
}
int main()
{
    int n,m,j=0;
    while(~scanf("%d %d",&n,&m))
    {
        if(m+n==0)
            break;
        for(int i=1;i<=n;i++)
        {
            make_set(i);
        }
        ans=n;
        for(int i=0;i<m;i++)
        {
            int x,y;
            scanf("%d %d",&x,&y);
            union_set(x,y);
        }
        printf("Case %d: %d\n",++j,ans);
    }
    return 0;
}

　　

POJ 2524 獨一無二的宗教（裸並查集）