Skip to main content

12. Maximum Depth of Binary Tree

easyAsked at Etsy

Compute the longest root-to-leaf path length — Etsy uses it as a recursion-vs-BFS choice question.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

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 node.

Constraints

  • Node count in [0, 10^4]
  • -100 <= Node.val <= 100

Examples

Example 1

Input
root = [3,9,20,null,null,15,7]
Output
3

Example 2

Input
root = [1,null,2]
Output
2

Approaches

1. BFS level count

BFS level by level, increment a counter per level.

Time
O(n)
Space
O(n)
let q = root ? [root] : [], d = 0;
while (q.length) {
  d++;
  q = q.flatMap(n => [n.left, n.right].filter(Boolean));
}
return d;

Tradeoff:

2. Recursive max

Depth = 1 + max(depth(left), depth(right)).

Time
O(n)
Space
O(h)
function maxDepth(root) {
  if (!root) return 0;
  return 1 + Math.max(maxDepth(root.left), maxDepth(root.right));
}

Tradeoff:

Etsy-specific tips

Etsy will probe whether you choose iterative when the tree is wide and recursive when it's deep — articulate that tradeoff to win the bonus signal.

Solve it now

Free. No sign-up. Python and JavaScript run instantly in your browser.

Output

Press Run or Cmd+Enter to execute

Practice these live with InterviewChamp.AI

Drill Maximum Depth of Binary Tree and other Etsy interview questions under real-loop conditions with instant feedback on your reasoning, complexity claims, and code.

Practice these live with InterviewChamp.AI →