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10. Maximum Depth of Binary Tree

easyAsked at MercadoLibre

Compute the depth of the deepest leaf in 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.

Constraints

  • 0 <= node count <= 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

Process the tree level by level and count completed levels.

Time
O(n)
Space
O(n)
let depth = 0, q = root ? [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 DFS

Depth of a node is 1 + max(depth(left), depth(right)). Use recursion for a one-liner.

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

Tradeoff:

MercadoLibre-specific tips

MercadoLibre uses this warm-up to see if you reach for recursion fast — useful for traversing their category trees that span six levels deep across Latin American verticals.

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Output

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