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13. Maximum Depth of Binary Tree

easyAsked at Datadog

Return the maximum depth of a binary tree. Datadog uses this as the simplest height question and then escalates to bounded-memory variants for trees stored on disk in chunked form.

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

Source citations

Public interview reports confirming this problem appears in Datadog loops.

  • Glassdoor (2026-Q1)— Datadog phone screen tree warmup.
  • LeetCode Discuss (2025-10)— Listed in Datadog tagged problems.

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. BFS level count

Iterate level by level with a queue; count levels.

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

Tradeoff: O(w) space (width). Good when the tree is deeper than it is wide.

2. Recursive DFS (optimal for balanced trees)

depth = 1 + max(depth(left), depth(right)). Base case: null returns 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: Three lines. O(h) recursion stack — h can be n in a degenerate (linked-list-shaped) tree.

Datadog-specific tips

Datadog interviewers will follow up with: 'Now compute the depth of a tree stored on disk where each node is a separate read.' Show that BFS minimizes random reads (level-by-level batching), while DFS pipelines well for sequential reads. The tradeoff depends on storage layout.

Common mistakes

  • Returning maxDepth(root.left) + maxDepth(root.right) — that's the sum of two subtree heights, not the max plus root.
  • Forgetting the +1 for the current node.
  • Treating null as 1 instead of 0 — returns depth as if every leaf was at depth 1 above where it actually is.

Follow-up questions

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

  • Balanced Binary Tree (LC 110) — depth + balance check in one pass.
  • Minimum Depth (LC 111) — careful: a single-child node is not a leaf.
  • Diameter of Binary Tree (LC 543) — depth as a building block.

Solve it now

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Output

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FAQ

DFS or BFS — which does Datadog prefer?

Either is accepted. The follow-up usually pushes toward BFS because their TSDB chunks are read level-by-level, so BFS aligns with the storage layout.

What's the difference between depth and height?

Depth = distance from root. Height = distance to deepest descendant. For the root, depth(root) == height(tree). For internal nodes they differ.

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