技術標籤：leetcode每日一題202101leetcode並查集

Problem

There are n cities. Some of them are connected, while some are not. If city a is connected directly with city b, and city b is connected directly with city c, then city a is connected indirectly with city c.

A province is a group of directly or indirectly connected cities and no other cities outside of the group.

You are given an n x n matrix isConnected where isConnected[i][j] = 1 if the ith city and the jth city are directly connected, and isConnected[i][j] = 0 otherwise.

Return the total number of provinces.

Constraints:

• 1 <= n <= 200
• n == isConnected.length
• n == isConnected[i].length
• isConnected[i][j] is 1 or 0.
• isConnected[i][i] == 1
• isConnected[i][j] == isConnected[j][i]

Example1

Input: isConnected = [[1,1,0],[1,1,0],[0,0,1]]
Output: 2

Example2

Input: isConnected = [[1,0,0],[0,1,0],[0,0,1]]
Output: 3

Solution

class Solution {
public:
    vector<int> p;

    int find(int x) {
        if (p[x] != x) p[x] =
 
 find(p[x]);
        return p[x];
    }

    int findCircleNum(vector<vector<int>>& M) {
        int n = M.size();
        for (int i = 0; i < n; i ++ ) p.push_back(i);

        int cnt = n;
        for (int i = 0; i < n; i ++ )
            for (int j = 0; j < n; j ++ )
                if (M[i][j] && find(i) != find(j)) {
                    p[find(i)] = find(j);
                    cnt -- ;
                }

        return cnt;
    }
};