PAT 甲级 1107 Social Clusters (30分)（并查集）

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 (≤), 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:

K​i​​: h​i​​[1] h​i​​[2] ... h​i​​[K​i​​]

where K​i​​ (>) is the number of hobbies, and [ 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:

8
3: 2 7 10
1: 4
2: 5 3
1: 4
1: 3
1: 4
4: 6 8 1 5
1: 4

 

Sample Output:

3
4 3 1

 

题意：

有n个人，每个人喜欢k个活动，如果两个人有任意一个活动相同，就称为他们处于同一个社交网络。求这n个人一共形成了多少个社交网络。

题解：

并查集。通过vector是按兴趣爱好分类，再遍历vector将同一爱好的人合并。最后用a数组统计聚类个数及类别里的个数。

AC代码：

#include<bits/stdc++.h>
using namespace std;
vector<int>v[1005];
int n;
int a[1005];
int p=0;
int fa[1005];
int find(int x){
    if(x==fa[x]) return x;
    return fa[x]=find(fa[x]);
}
void unio(int x,int y){
    int yy=find(y);
    int xx=find(x);
    if(xx!=yy){
        fa[yy]=xx;
    }
} 
bool cmp(int x,int y){
    return x>y;
}
int main(){
    cin>>n;
    for(int i=1;i<=n;i++){
        fa[i]=i;
        char s;
        int m;
        cin>>m>>s;
        for(int j=1;j<=m;j++){
            int x;
            cin>>x;
            v[x].push_back(i);
        }
    }
    memset(a,0,sizeof(a));
    for(int i=1;i<=1000;i++){
        if(v[i].size()>0){
            int x=v[i].at(0);
            for(int j=1;j<v[i].size();j++){
                unio(x,v[i].at(j));//相同爱好合并 
            }            
        }
    }
    for(int i=1;i<=n;i++){//统计聚类个数 
        a[find(i)]++;
    }
    sort(a+1,a+1+1000,cmp);
    for(int i=1;i<=1000;i++){
        if(a[i]>0){
            p++;
        }
    }
    cout<<p<<endl;
    for(int i=1;i<=p;i++){
        cout<<a[i];
        if(i!=p) cout<<" ";
    }
    return 0;
}