Skip to main content

12. Maximum Depth of Binary Tree

easyAsked at Square

Return the maximum depth of a binary tree. Square uses this as a warm-up to see whether you can write a clean post-order recursion before tackling harder tree problems like balance and path-sum.

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

Source citations

Public interview reports confirming this problem appears in Square loops.

  • Glassdoor (2025)— Square POS phone screen.
  • LeetCode Discuss (2026)— Cash App backend warm-up.

Problem

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

Constraints

  • The number of nodes in the tree is in the range [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. Recursive DFS

depth(node) = 1 + max(depth(left), depth(right)); null = 0.

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

Tradeoff: Clean and idiomatic. Stack depth = tree height — risky for adversarial inputs.

2. Iterative BFS with level count

Process the tree one level at a time, incrementing a counter.

Time
O(n)
Space
O(w)
function maxDepth(root) {
  if (!root) return 0;
  let q = [root];
  let depth = 0;
  while (q.length) {
    const next = [];
    for (const node of q) {
      if (node.left) next.push(node.left);
      if (node.right) next.push(node.right);
    }
    q = next;
    depth++;
  }
  return depth;
}

Tradeoff: Iterative — safer for deep trees. Swapping queues avoids the shift() O(n) trap.

Square-specific tips

Square interviewers grade this on whether your recursion has a clear base case and a single recursive step. Mention which version you'd ship in production (iterative for unbounded trees) and why — they care about defensive coding for transaction-graph traversals.

Common mistakes

  • Counting edges instead of nodes — the problem asks for node-count along the longest path.
  • Initializing depth = 1 even for null root (should be 0).
  • Using array.shift() inside the BFS loop — O(n^2) total.

Follow-up questions

An interviewer at Square may pivot to one of these next:

  • Minimum depth of a binary tree (LC 111) — careful, must reach a leaf.
  • Diameter of binary tree (LC 543).
  • Balanced binary tree (LC 110).

Solve it now

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

Output

Press Run or Cmd+Enter to execute

FAQ

Is depth measured in nodes or edges?

Nodes per this problem's definition. Some textbooks use edges; always clarify with the interviewer.

Why is recursion's space O(h), not O(n)?

The call stack only holds the current path from root to the deepest active node at any moment — that's the tree's height.

Practice these live with InterviewChamp.AI

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

Practice these live with InterviewChamp.AI →