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13. Maximum Depth of Binary Tree

easyAsked at Coinbase

Return the depth of a binary tree. Coinbase uses this to verify recursion fundamentals before moving to harder tree problems.

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

Source citations

Public interview reports confirming this problem appears in Coinbase loops.

  • Glassdoor (2026-Q1)— Coinbase warm-up.

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 counter

Level-order traversal counting levels.

Time
O(n)
Space
O(w) for width w
function maxDepth(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: Works, but allocates per level. Useful when the prompt forbids recursion.

2. Recursive 1 + max(left, right)

Base case: null → 0. Otherwise 1 + max(maxDepth(left), maxDepth(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: Three lines. The cleanest recurrence in DSA.

Coinbase-specific tips

Coinbase grades the one-line recurrence. They'll often follow with 'return the deepest leaf's value' or 'list all leaves at max depth' — recognize these as the same recursion with extra bookkeeping.

Common mistakes

  • Returning 0 for null root and then forgetting to start counting at 1 for non-null.
  • Tracking depth via global variable — unnecessary indirection.
  • Confusing 'depth' (root = 1) with 'height' (root depth = 0).

Follow-up questions

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

  • Minimum depth (LC 111) — careful with single-child nodes.
  • Return the deepest leaf's value.
  • Diameter of the tree (LC 543).

Solve it now

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Output

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FAQ

Is depth zero-indexed or one-indexed here?

One-indexed: a single-node tree has depth 1, an empty tree has depth 0. Always clarify the convention before coding.

When would BFS beat DFS?

When recursion depth would overflow the native stack (skewed tree with 10^4 nodes). BFS uses a heap-allocated queue with bounded width.

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