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14. Maximum Depth of Binary Tree

easyAsked at Chime

Return the maximum depth of a binary tree, defined as the number of nodes along the longest root-to-leaf path.

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

  • The number of nodes 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. Level-order BFS

BFS level by level, incrementing depth each level.

Time
O(n)
Space
O(n)
if (!root) return 0;
let depth = 0;
let 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 DFS

Depth equals 1 plus the max depth of the two subtrees. Recursion is clean and matches the structural definition.

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

Tradeoff:

Chime-specific tips

Chime mirrors this recursion onto their merchant-category trees used in fraud heuristics, so explain the recursive substructure crisply before coding.

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Output

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