poj 2542

 题意：给定多组（x，y），x和y的信仰相同，估计信仰的数量

 解法：并查集，初始化ans为总人数，当添加一对（x，y）后，判断，如果已经是一组了，不做，如果不是，ans-1.

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/*
*This file is about union set operations.
*and the program is c-style,you can transfer it to
*cpp-style.
*you can copy,re-write,sell this program but no need to
*let me know this.but you need copy this comment to your
*program's header comment.
*hujian nankai university
*2016/5/26
*/

#define UNION_SET_MAX_SIZE 1024*50 //the size of union.

//the parent array
int parent[UNION_SET_MAX_SIZE];

//the height of the union tree
int rank[UNION_SET_MAX_SIZE];

//the size of union
int union_size=0;

//the ans
int ans=0,n,m;

//initialze the union set
void init_set(int s)
{
int i;
for(i=0;i<=s;i++){
parent[i]=i;
rank[i]=0;
}
}

//find the root of this tree
int find_set(int x){
if(x==parent[x]){
return x;
}else{
return parent[x]=find_set(parent[x]);
}
}

//union x and y is the root of each tree
void union_set(int x,int y)
{
x=find_set(x);
y=find_set(y);
if(x==y) return;//same tree

//x and y have same religions
ans--;

if(rank[x]<rank[y]){
//the height x<height y
//then,let the y as the root
parent[x]=y;
}else{
parent[y]=x;
if(rank[x]==rank[y]){
rank[x]++;
}
}
}

//judge if the x and y is the same tree
bool same_set(int x,int y)
{
return find_set(x)==find_set(y);
}

int main()
{
int i,x,y,j=1;
while(scanf("%d%d",&n,&m)){
if((n+m)==0) break;
init_set(n);
ans=n;
for(i=0;i<m;i++){
scanf("%d%d",&x,&y);
union_set(x,y);
}
printf("Case %d: %d\n",j++,ans);
}
return 0;
}