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13. Maximum Depth of Binary Tree

easyAsked at Udemy

Find the maximum depth of a binary tree — Udemy uses this to probe recursive DFS fundamentals before asking about course-category tree traversals.

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

Problem

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

Constraints

  • 0 <= number of nodes <= 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. Brute force BFS

Level-order traversal counting each level.

Time
O(n)
Space
O(n)
function maxDepth(root) {
  if (!root) return 0;
  let depth = 0;
  const queue = [root];
  while (queue.length) {
    depth++;
    const size = queue.length;
    for (let i = 0; i < size; i++) {
      const node = queue.shift();
      if (node.left) queue.push(node.left);
      if (node.right) queue.push(node.right);
    }
  }
  return depth;
}

Tradeoff:

2. Recursive DFS

Return 1 + max of left and right subtree depths; base case returns 0 for null. Single-line elegance preferred by Udemy interviewers.

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

Tradeoff:

Udemy-specific tips

Udemy asks about e-learning recommendation systems, content search, and marketplace algorithms — balanced mix of arrays, hash maps, and dynamic programming problems.

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Output

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