0547 - Number of Provinces

0547 - Number of Provinces

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.

Examples

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

Java Solution (Depth First Search)

class Solution {
    public int findCircleNum(int[][] isConnected) {
        int[] visited = new int[isConnected.length];
        
        int result = 0;
        
        for(int i = 0; i < isConnected.length; i++) {
            if(visited[i] == 0){
                dfs(isConnected, visited, i);
                result++;
            }
        }
        return result;
    }
    
    private void dfs(int[][] isConnected, int[] visited, int i) {
        for(int j = 0; j < isConnected.length; j++) {
            if(isConnected[i][j] == 1 && visited[j] == 0) {
                visited[j] = 1;
                dfs(isConnected, visited, j);
            }
        }
    }
}