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Graph

Graph Valid Tree

**Problem Statement:** Given the required input arguments, write an efficient algorithm to solve the **Graph Valid Tree** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge. **Hint / Expected Approach:** n−1 edges + connected (no cycle) via Union-Find **Edge Cases to Consider:** - (1) Single node, no edges - (2) Extra edge - (3) Disconnected with n−1 edges

Examples

Example 1
Input: 5, [[0,1],[0,2],[0,3],[1,4]]
Output: true
Explanation: Valid tree
Example 2
Input: 5, [[0,1],[1,2],[2,3],[1,3],[1,4]]
Output: false
Explanation: Cycle present
Example 3
Input: 1, []
Output: true
Explanation: Single node

Constraints

  • ▪2 <= vertices <= 1000
  • ▪0 <= edges <= 5000
  • ▪Avoid infinite cycles during depth traversal

Watch Out For Edge Cases

  • ▪Single node, no edges
  • ▪Extra edge
  • ▪Disconnected with n−1 edges
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