Number of Connected Component in An Undirected Graph

Given n nodes labeled from 0 to n - 1 and a list of undirected edges (each edge is a pair of nodes), write a function to find the number of connected components in an undirected graph.

Example 1:

     0          3
     |          |
     1 --- 2    4

Given n = 5 and edges = [[0, 1], [1, 2], [3, 4]], return 2.

Example 2:

     0           4
     |           |
     1 --- 2 --- 3

Given n = 5 and edges = [[0, 1], [1, 2], [2, 3], [3, 4]], return 1.

Note:
You can assume that no duplicate edges will appear in edges. Since all edges are undirected, [0, 1] is the same as [1, 0] and thus will not appear together in edges.

public class Solution {
    public int countComponents(int n, int[][] edges) {
        int[] parent = new int[n];
        for (int i = 0; i < n; i++)
            parent[i] = i;
            
        int result = n;
        for (int[] edge : edges) {
            int start = updateParent(parent, edge[0]);
            int end = updateParent(parent, edge[1]);
            
            if (start != end) {
                parent[end] = start;
                result--;
            }
        }
        return result;
    }
    
    private int updateParent(int[] parent, int index) {
        while (parent[index] != index) {
            parent[index] = parent[parent[index]];
            index = parent[index];
        }
        return index;
    }
    
}