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Graph Valid Tree

Understand how to analyze graphs to determine if they form a valid tree by ensuring all nodes are connected and no cycles exist. This lesson helps you apply graph theory concepts and algorithms to solve coding interview problems involving tree validation.

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Statement

Given n as the number of nodes and an array of the edges of a graph, find out if the graph is a valid tree. The nodes of the graph are labeled from 00 to n−1n - 1, and edges[i]=[x,y]edges[i] = [x, y] represents an undirected edge connecting the nodes xx and yy of the graph.

A graph is a valid tree when all the nodes are connected and there is no cycle between them.

Constraints:

  • 1≤1 \leq n ≤1000\leq 1000
  • 0≤0 \leq edges.length ≤2000\leq 2000
  • edges[i].length =2= 2
  • 0≤0 \leq xx, yy << n
  • xx !=!= yy
  • There are no repeated edges.

Examples

Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

Graph Valid Tree

1.

Consider the following graph with four nodes:

What is the correct array of connected edges that would make the graph above?

A.

edges = [[0, 1], [0, 2], [0, 3]]

B.

edges = [[0, 1], [0, 2], [1, 2]]

C.

edges = [[0, 1], [0, 2], [2, 3]]

1 / 3

Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Sequence - Vertical
Drag and drop the cards to rearrange them in the correct sequence.
1
2
3
4
5

Try it yourself

Implement your solution in the following coding playground.

Java
usercode > Solution.java
import java.util.*;
public class Solution {
    public static boolean validTree(int n, int[][] edges) {
        // Replace this placeholder return statement with your code
        return false;
    }
}
Graph Valid Tree