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11. Maximum Depth of Binary Tree

easyAsked at Yelp

Compute the maximum depth of a binary tree — Yelp uses this to gauge whether candidates can recurse cleanly over a category-tree before walking deeper geo-indexing problems.

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

Problem

Given the root of a binary tree, return its maximum depth, which is the number of nodes along the longest path from the root down to the farthest leaf node.

Constraints

  • The number of nodes is 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

Walk the tree level by level and count the levels visited.

Time
O(n)
Space
O(n)
let q = root ? [root] : [], d = 0;
while (q.length) {
  const next = [];
  for (const n of q) { if (n.left) next.push(n.left); if (n.right) next.push(n.right); }
  q = next; d++;
}
return d;

Tradeoff:

2. DFS recursion

Depth of a node is 1 + max(depth(left), depth(right)). Recurse from the root.

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

Tradeoff:

Yelp-specific tips

Yelp interviewers will pivot this into geo indexing — be ready to discuss how depth-bounded recursion maps to bounded quad-tree traversal for nearby-business lookups.

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