LeetCode - Redundant Connection

Question Definition

In this problem, a tree is an undirected graph that is connected and has no cycles.

The given input is a graph that started as a tree with N nodes (with distinct values 1, 2, …, N), with one additional edge added. The added edge has two different vertices chosen from 1 to N, and was not an edge that already existed.

The resulting graph is given as a 2D-array of edges. Each element of edges is a pair [u, v] with u < v, that represents an undirected edge connecting nodes u and v.

Return an edge that can be removed so that the resulting graph is a tree of N nodes. If there are multiple answers, return the answer that occurs last in the given 2D-array. The answer edge [u, v] should be in the same format, with u < v. Example 1:

Input: [[1,2], [1,3], [2,3]]
Output: [2,3]
Explanation: The given undirected graph will be like this:
  1
 / \
2 - 3

Example 2:

Input: [[1,2], [2,3], [3,4], [1,4], [1,5]]
Output: [1,4]
Explanation: The given undirected graph will be like this:
5 - 1 - 2
    |   |
    4 - 3

Note:

• The size of the input 2D-array will be between 3 and 1000.
• Every integer represented in the 2D-array will be between 1 and N, where N is the size of the input array.

Java Solution

public int[] findRedundantConnection(int[][] edges) {
    int[] root = new int[2001];
    for(int i = 0; i < root.length; i++)
        root[i] = -1;
    for (int[] edge : edges) {
        int x = find(root, edge[0]), y = find(root, edge[1]);
        if (x == y) return edge;
        root[x] = y;
    }
    return new int[0];
}

private int find(int[] root, int i) {
    while (root[i] != -1) {
        i = root[i];
    }
    return i;
}