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12. Maximum Depth of Binary Tree

easyAsked at Roblox

Return the maximum depth of a binary tree.

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

  • 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. BFS level count

Iterate level by level with a queue.

Time
O(n)
Space
O(n)
if (!root) return 0;
let depth = 0, q = [root];
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:

2. Recursive depth

Return 1 plus the max depth of either subtree.

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

Tradeoff:

Roblox-specific tips

Roblox engineers ask this to confirm you can reason about tree depth before diving into the Instance-tree depth limits that affect ReplicatedStorage.

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Output

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