Solution: Graph Valid Tree

Let's solve the Graph Valid Tree problem using the Graphs pattern.

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 n1n - 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:

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

Solution

For the graph to be a valid tree, the number of edges must equal n1n - 1. If the total number of edges is less than n1n - 1, not all the graph nodes are connected, which defies the property of a tree. Similarly, more edges will mean that there is a cycle in the graph; Therefore, it is not a tree.

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