LeetCode-in-Java

1319. Number of Operations to Make Network Connected

Medium

There are n computers numbered from 0 to n - 1 connected by ethernet cables connections forming a network where connections[i] = [a_i, b_i] represents a connection between computers a_i and b_i. Any computer can reach any other computer directly or indirectly through the network.

You are given an initial computer network connections. You can extract certain cables between two directly connected computers, and place them between any pair of disconnected computers to make them directly connected.

Return the minimum number of times you need to do this in order to make all the computers connected. If it is not possible, return -1.

Example 1:

Input: n = 4, connections = [[0,1],[0,2],[1,2]]

Output: 1

Explanation: Remove cable between computer 1 and 2 and place between computers 1 and 3.

Example 2:

Input: n = 6, connections = [[0,1],[0,2],[0,3],[1,2],[1,3]]

Output: 2

Example 3:

Input: n = 6, connections = [[0,1],[0,2],[0,3],[1,2]]

Output: -1

Explanation: There are not enough cables.

Constraints:

1 <= n <= 10⁵
1 <= connections.length <= min(n * (n - 1) / 2, 10⁵)
connections[i].length == 2
0 <= a_i, b_i < n
a_i != b_i
There are no repeated connections.
No two computers are connected by more than one cable.

Solution

import java.util.Arrays;

public class Solution {

    private static final int IMPOSSIBLE_TO_CONNECT = -1;
    private int disconnectedComputers;
    private int[] parent;
    private int[] rank;

    public int makeConnected(int totalNumberOfComputers, int[][] connections) {
        if (connections.length < totalNumberOfComputers - 1) {
            return IMPOSSIBLE_TO_CONNECT;
        }

        disconnectedComputers = totalNumberOfComputers;
        rank = new int[totalNumberOfComputers];
        parent = new int[totalNumberOfComputers];
        Arrays.setAll(parent, intFromZero -> intFromZero++);

        for (final int[] connection : connections) {
            unionFind(connection[0], connection[1]);
        }

        return disconnectedComputers - 1;
    }

    private void unionFind(int first, int second) {
        int parentFirst = findParent(first);
        int parentSecond = findParent(second);

        if (parentFirst != parentSecond) {
            joinByRank(parentFirst, parentSecond);
            disconnectedComputers--;
        }
    }

    private int findParent(int index) {
        if (parent[index] != index) {
            parent[index] = findParent(parent[index]);
        }
        return parent[index];
    }

    private void joinByRank(int first, int second) {
        if (rank[first] < rank[second]) {
            parent[first] = second;
        } else if (rank[second] < rank[first]) {
            parent[second] = first;
        } else {
            parent[first] = second;
            rank[second]++;
        }
    }
}

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