LeetCode-in-Java

547. Number of Provinces

Medium

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]

Solution

import java.util.Arrays;

public class Solution {
    public int findCircleNum(int[][] arr) {
        int[] parent = new int[arr.length];
        Arrays.fill(parent, -1);
        int ans = 0;
        for (int i = 0; i < arr.length - 1; i++) {
            for (int j = i + 1; j < arr[i].length; j++) {
                if (arr[i][j] == 1) {
                    ans += union(i, j, parent);
                }
            }
        }
        return arr.length - ans;
    }

    private int union(int a, int b, int[] arr) {
        int ga = find(a, arr);
        int gb = find(b, arr);
        if (ga != gb) {
            arr[gb] = ga;
            return 1;
        }
        return 0;
    }

    private int find(int a, int[] arr) {
        if (arr[a] == -1) {
            return a;
        }
        arr[a] = find(arr[a], arr);
        return arr[a];
    }
}

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