poj 1611 并查集学习 The suspects



The Suspects

Time Limit: 1000MS		Memory Limit: 20000K
Total Submissions: 32838		Accepted: 15919

Description

Severe acute respiratory syndrome (SARS), an atypical pneumonia of unknown aetiology, was recognized as a global threat in mid-March 2003. To minimize transmission to others, the best strategy is to separate the suspects from others. 
In the Not-Spreading-Your-Sickness University (NSYSU), there are many student groups. Students in the same group intercommunicate with each other frequently, and a student may join several groups. To prevent the possible transmissions of SARS, the NSYSU collects the member lists of all student groups, and makes the following rule in their standard operation procedure (SOP). 
Once a member in a group is a suspect, all members in the group are suspects. 
However, they find that it is not easy to identify all the suspects when a student is recognized as a suspect. Your job is to write a program which finds all the suspects.

Input

The input file contains several cases. Each test case begins with two integers n and m in a line, where n is the number of students, and m is the number of groups. You may assume that 0 < n <= 30000 and 0 <= m <= 500. Every student is numbered by a unique integer between 0 and n−1, and initially student 0 is recognized as a suspect in all the cases. This line is followed by m member lists of the groups, one line per group. Each line begins with an integer k by itself representing the number of members in the group. Following the number of members, there are k integers representing the students in this group. All the integers in a line are separated by at least one space. 
A case with n = 0 and m = 0 indicates the end of the input, and need not be processed.

Output

For each case, output the number of suspects in one line.

Sample Input

100 4
2 1 2
5 10 13 11 12 14
2 0 1
2 99 2
200 2
1 5
5 1 2 3 4 5
1 0
0 0

Sample Output

4
1
1

题意：SARS很容易传染，该题说有多组学生，每个组也会有新的同学加入，如果该组有一个同学感染了SARS，则认为这个组所有的同学均感染SARS。初始认为0号学生感染了SARS，求一共有多少学生感染了SARS。

思路：并查集的应用，将和0号学生相关的学生不断合并构成集合并不断更新集合人数数组num，通过查找0号学生的最顶层的人num数组所储存的该集合的人数，来求出和0号同学相关的感染SARS的人数。

若有错误或有更好的优化请大神们指正~

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;

const int Max=30001;
int p[Max];
int rank_s[Max];
int num[Max];


//集合初始化>>每一个元素点为一个孤立的集合
void make_set(int x)
{
	p[x]=x;
	rank_s[x]=0;
	num[x]=1;
}

//找x元素的祖先，也就是并查集那个讲解里的该门派的掌门人
int find_set(int x)
{
	int r;
	r=x;    //派r去找掌门人
	while(p[r]!=r)
	{
		r=p[r];
	}
	return r;
}

//两个集合合并
void union_set(int x,int y)
{
	x=find_set(x);
	y=find_set(y);
	if(x==y) return ;       //掌门人是自己
	if(rank_s[x]<rank_s[y])
	{
		p[x]=y;
		num[y]+=num[x];
	}
	else
	{
		p[y]=x;
		num[x]+=num[y];
		if(rank_s[x]==rank_s[y])
			rank_s[x]++;
	}
}

int main()
{
	int n,m,aa,x,r;
	while(scanf("%d%d",&n,&m)!=EOF)
	{
		if(n==0&&m==0) break;
		if(m==0)
		{
			cout<<"1"<<endl;
			continue;
		}
		for(int i=0;i<n;i++) make_set(i);
		for(int i=0;i<m;i++)
		{
			scanf("%d",&aa);
			scanf("%d",&x);
			for(int j=1;j<aa;j++)
			{
				scanf("%d",&r);
				union_set(x,r);
				x=r;
			}
		}
		x=find_set(0);

		cout<<num[x]<<endl;
	}
	return 0;
}