Maximum Depth of Binary Tree

Given the root of a binary tree, return its maximum depth: the number of nodes along the longest path from the root down to the farthest leaf. This is the first problem to use the judge's typed TreeNode support: root is a real tree built from the JSON test fixture, not a flat array — your function must walk .left/.right pointers like a genuine LeetCode submission.

Input / output

• Input: root: TreeNode (JSON test fixture is a LeetCode-style level-order array using null for missing children, e.g. [3, 9, 20, null, null, 15, 7])
• Output: int — the maximum depth

Examples

1. root = [3, 9, 20, null, null, 15, 7] returns 3.
2. root = [] returns 0 (an empty tree has depth 0).
3. root = [1] returns 1.

Constraints

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

Follow-up Can you solve it both recursively (depth-first) and iteratively with an explicit stack or a level-by-level breadth-first traversal, and explain when you'd prefer one over the other?

Note Java, Go, and Rust starters are shown for reference only on this problem right now — the remote judge for those languages doesn't yet support the TreeNode structure. Use Python or JavaScript to run and submit.