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12. Maximum Depth of Binary Tree

easyAsked at Glassdoor

Return the maximum depth of a binary tree — Glassdoor uses this as a quick warm-up to grade your recursion height intuition.

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

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 down to the farthest leaf.

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. Recursive DFS

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:

2. BFS level count

Iterate level by level using a queue; count iterations.

Time
O(n)
Space
O(w)
function maxDepthBFS(root) {
  if (!root) return 0;
  let q = [root], depth = 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;
    depth++;
  }
  return depth;
}

Tradeoff:

Glassdoor-specific tips

Glassdoor likes when candidates offer both DFS and BFS and pick BFS for deep trees — their nested-comment trees on review pages can exceed JS recursion limits.

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Output

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