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547. 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**.

Example 1:

img

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

Example 2:

img

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:

UnionFind

class Solution {
    public int findCircleNum(int[][] isConnected) {
        int n = isConnected.length;
        UnionFind uf = new UnionFind(n);

        int result = 0;

        for (int i = 0; i < n; i++){
            for (int j = i + 1; j < n; j++){
                if (isConnected[i][j] == 1){
                    uf.union(i, j); // TC: O(n)
                }
            }
        }

        for (int i = 0; i < n; i++){
            if (uf.find(i) == i){ // TC: O(n)
                result++;
            }
        }


        return result;



    }
}

class UnionFind{
    int[] root;
    public UnionFind(int size){
        root = new int[size];
        for (int i = 0; i < size; i++){
            root[i] = i;
        }

    }

    public int find(int x){
        if (x == root[x]){
            return x;
        }

        return root[x] = find(root[x]);
    }



    public void union(int x, int y){ // TC: O(n)
        int rootX = find(x);
        int rootY = find(y);
        if (rootX != rootY){
            root[rootY] = rootX; // let X be dad
        }
    }

    public boolean connected(int x, int y){
        return find(x) == find(y);
    }
}


// TC: O(n^2)
// SC: O(n)