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12. Maximum Depth of Binary Tree

easyAsked at Quora

Return the maximum depth (height) 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.

Constraints

  • 0 <= 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

Walk levels with a queue and count rounds.

Time
O(n)
Space
O(n)
let q = root ? [root] : [], d = 0;
while (q.length) {
  q = q.flatMap(n => [n.left, n.right].filter(Boolean));
  d++;
}
return d;

Tradeoff:

2. Recursive max

Depth = 1 + max(left depth, right depth).

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

Tradeoff:

Quora-specific tips

Quora cares about depth bounds because their comment-tree renderer caps thread nesting and needs an O(n) depth probe before deciding whether to truncate.

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Output

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