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12. Maximum Depth of Binary Tree

easyAsked at Unity

Compute the maximum depth of a binary tree. Unity uses this to bound LOD-tree depth checks during streaming.

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 a 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=[]
Output
0

Approaches

1. BFS level count

Walk levels with a queue; count rounds.

Time
O(n)
Space
O(w)
let q = root ? [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:

2. Recursive max

Depth = 1 + max(depth(left), depth(right)). Base case is 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:

Unity-specific tips

Unity grades for the streamer's perspective: clamp recursion when LOD trees exceed depth budgets to avoid frame spikes.

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Output

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