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12. Maximum Depth of Binary Tree

easyAsked at Booking

Compute depth of a binary tree — Booking screens this to confirm baseline tree recursion before scaling to region/destination hierarchies.

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 root-to-leaf path).

Constraints

  • 0 <= number of 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 by level

Walk level-by-level and count levels.

Time
O(n)
Space
O(n)
if (!root) return 0;
let d = 0, q = [root];
while (q.length) { d++; const nx=[]; for(const n of q){ if(n.left) nx.push(n.left); if(n.right) nx.push(n.right);} q=nx;}
return d;

Tradeoff:

2. Recursive depth

Depth = 1 + max(depth(left), depth(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:

Booking-specific tips

Booking maps tree depth to region hierarchy depth — explain how this bounds search-fanout latency when expanding 'continent → country → city → property' branches.

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Output

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