261. Graph Valid Tree

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 check whether these edges make up a valid tree.

For example:

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

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

Hint:

1. Given n = 5 and edges = [[0, 1], [1, 2], [3, 4]], what should your return? Is this case a valid tree? 
2. According to the definition of tree on Wikipedia: “a tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any connected graph without simple cycles is a tree.”

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.

Similar: 

• 207. Course Schedule
• 323. Number of Connected Components in an Undirected Graph

public class Solution {
    public boolean validTree(int n, int[][] edges) {
        int[] pt = new int[n];
        for (int i=0; i<n; i++) { pt[i] = i; }
        
        for (int[] edge : edges) {
            int root1 = find(pt, edge[0]);
            int root2 = find(pt, edge[1]);
            
            if (root1 == root2) return false; // find circle
            
            pt[root1] = root2; // union
        }
        return edges.length == n-1; // tree w/ n notes have n-1 edges
    }
    private int find(int[] pt, int i) {
        while (pt[i] != i) {
            pt[i] = pt[pt[i]];
            i = pt[i];
        }
        return i;
    }
}