PAT A1107 2019.08.30 【并查集】

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本文探讨了如何使用并查集算法解决社交网络中寻找具有相同兴趣爱好群体的问题，通过实例输入输出展示了算法的具体应用。

1107 Social Clusters (30 分)

When register on a social network, you are always asked to specify your hobbies in order to find some potential friends with the same hobbies. A social cluster is a set of people who have some of their hobbies in common. You are supposed to find all the clusters.

Input Specification:

Each input file contains one test case. For each test case, the first line contains a positive integer N (≤1000), the total number of people in a social network. Hence the people are numbered from 1 to N. Then N lines follow, each gives the hobby list of a person in the format:

Ki: hi[1] hi[2] ... hi[Ki]

where Ki (>0) is the number of hobbies, and hi[j] is the index of the j-th hobby, which is an integer in [1, 1000].

Output Specification:

For each case, print in one line the total number of clusters in the network. Then in the second line, print the numbers of people in the clusters in non-increasing order. The numbers must be separated by exactly one space, and there must be no extra space at the end of the line.

Sample Input:

Sample Output:

3
4 3 1

思路分析

并查集基本操作：初始化、寻根（路径压缩）、合并

寻根函数采用递归的方法比较好记忆

下面是copy的柳神的代码，自己想出来的17分，还是要看思路

#include<cstdio>
#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
vector<int>father,isRoot;

int findFather(int x)
{
	if(x==father[x])return x;
	else return findFather(father[x]);
} 

void merge(int a,int b)
{
	int faA=findFather(a);
	int faB=findFather(b);
	if(faA!=faB)father[faA]=faB;
}

bool cmp(int a,int b)
{
	return a>b;
}

int main()
{
	int n,k,t,cnt=0;
	int course[1001]={0};
	cin>>n;
	father.resize(n+1);
	isRoot.resize(n+1);//以i为根的人数为 isRoot(i) 
	for(int i=1;i<=n;i++)father[i]=i;
	for(int i=1;i<=n;i++)
	{
		scanf("%d:",&k);
		for(int j=0;j<k;j++)
		{
			cin>>t;
			if(course[t]==0)course[t]=i;
			merge(i,findFather(course[t]));
		}
	}
	
	for(int i=1;i<=n;i++)
	  isRoot[findFather(i)]++;
	for(int i=1;i<=n;i++)
	  if(isRoot[i]!=0)cnt++;
	
	cout<<cnt<<endl;
	
	sort(isRoot.begin(),isRoot.end(),cmp);
	for(int i=0;i<cnt;i++)
	{
		cout<<isRoot[i];
		if(i!=cnt-1)cout<<" ";
	}
	
}