1107 Social Clusters

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：

　　根据每个人的爱好，将不同的人划分为不同的社交圈。一个人可能有多种爱好，因此一个人可以把几种不同的圈子归并到一个大的圈子里。

思路：

　　将爱好当做节点，一个人将不同的爱好归并到一个子集中，有相同爱好的人，也会把此人的其他爱好归并到这个子集中。我们可以让祖先结点的序号最小，一次来保证祖先结点只有一个。

Code：

#include <bits/stdc++.h>

using namespace std;

int fa[1005];

int findFather(int x) {
    int a = x;
    while (x != fa[x]) x = fa[x];
    while (a != fa[a]) {
        int z = a;
        a = fa[a];
        fa[z] = x;
    }
    return x;
}

void Union(int x, int y) {
    int faX = findFather(x);
    int faY = findFather(y);
    if (faX > faY)
        fa[faX] = faY;
    else
        fa[faY] = faX;
}

int main() {
    int n, k;
    cin >> n;
    getchar();
    int num;
    vector<int> people;
    for (int i = 0; i < 1005; ++i) fa[i] = i;
    for (int i = 0; i < n; ++i) {
        string temp, dummy;
        getline(cin, temp);
        int pos = temp.find(':');
        int len = stoi(temp.substr(0, pos));
        dummy = temp.substr(pos + 2);
        vector<int> hobbies;
        string str = "";
        for (int j = 0; j <= dummy.size(); ++j) {
            if (dummy[j] == ' ' || dummy[j] == '') {
                hobbies.push_back(stoi(str));
                str = "";
            } else {
                str += dummy[j];
            }
        }
        for (int j = 1; j < hobbies.size(); ++j) {
            Union(hobbies[0], hobbies[j]);
        }
        people.push_back(hobbies[0]);
    }
    map<int, int> mp;
    for (int i = 0; i < n; ++i) {
        int r = findFather(people[i]);
        mp[r]++;
    }
    vector<int> ans;
    for (auto it : mp) ans.push_back(it.second);
    sort(ans.begin(), ans.end(), greater<int>());
    cout << ans.size() << endl;
    cout << ans[0];
    for (int i = 1; i < ans.size(); ++i) cout << " " << ans[i];
    cout << endl;
    return 0;
}