Diameter of Binary Tree

Kth Smallest Element in a BST

Symmetric Tree

Find the length in edges of the longest path between any two nodes in a binary tree.

Given the `root` of a binary tree, return the length of the diameter of the tree: the number of edges on the longest path between any two nodes. This path may or may not pass through `root`.

**Input / output**
- Input: `root: TreeNode` (JSON test fixture is a LeetCode-style level-order array, `null` marks a missing child)
- Output: `int` — the number of edges on the longest path

## Example
```json
Input: {"root":[1,2,3,4,5]}
Output: 3
```
(The longest path is `4 -> 2 -> 1 -> 3` or `5 -> 2 -> 1 -> 3`, 3 edges.)

## Constraints
- 0 <= number of nodes <= 10,000
- -100 <= node value <= 100

## Follow-up
Can you compute the diameter in a single O(n) pass instead of recomputing height at every node?

The key pattern is: Bottom-up DFS height computation that updates a running best at every node. Identify the state and invariant before coding.

Recognize the Pattern

Advance one state transition at a time. Mark or update state before exploring dependent work.

Build the Algorithm

Test empty or minimal input, skewed shapes, duplicates where allowed, and impossible outcomes.

Check Edge Cases

Time: O(n). Space: O(h) for the recursion stack.

All 5 languages below run and submit against the remote judge for this problem — Java/Go/Rust use the same real TreeNode structural-type support the judge added for the rest of the linked-list/tree track.