296. Diameter of Binary Tree

Given the root of a binary tree, return the length of the diameter of the tree.

The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.

The length of a path between two nodes is represented by the number of edges between them.

Find the longest path between any two nodes. The key insight is that the diameter at each node is the sum of the heights of its left and right subtrees.

Requirements

1. Basic Functionality

• Return the diameter (longest path in edges)
• Path may not pass through root
• Handle empty trees and single nodes

Example Usage

// Tree: [1,2,3,4,5]
//       1
//      / \
//     2   3
//    / \
//   4   5
// Diameter = 3 (path: 4→2→1→3 or 5→2→1→3)

Real-World Context

• Network latency: Finding the longest communication path in a network topology
• Organization charts: Longest reporting chain between any two employees
• File systems: Longest path between any two files in a directory tree