Number of Provinces

Description

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.

Example 1:

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

Example 2:

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

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]

Code

Union and Find

• Union By Rank and Path Compression in Union-Find Algorithm Time Complexity: $O(n)$, Space Complexity: $O(n)$

class Solution {
    int res;
    unordered_map<int, int> f;
public:
    int findCircleNum(vector<vector<int>>& isConnected) {
        res = isConnected.size();
        for(int i = 0; i < isConnected.size(); i++) {
            for(int j = 0; j < isConnected[i].size(); j++) {
                if(isConnected[i][j] == 1) {
                    uni(i, j);
                }
            }
        }
        return res;
    }
 
    int find(int x) {
        if(!f.count(x)) {
            f[x] = x;
        }
        if(f[x] != x) {
            f[x] = find(f[x]);
        }
        return f[x];
    }
 
    void uni(int x, int y) {
        x = find(x), y = find(y);
        if(x != y) {
            res--;
            f[x] = y;
        }
    }
};

Source

• Number of Provinces - LeetCode