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12. Maximum Depth of Binary Tree

easyAsked at Tesla

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 on the longest path from root to any leaf.

Constraints

  • 0 <= node count <= 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

Count levels until the queue is empty.

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

Tradeoff:

2. Recursion

Height = 1 + max(left, 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:

Tesla-specific tips

Tesla path planners traverse decision trees this way — the recursive max-depth pattern shows up directly when computing the worst-case lookahead horizon for a planner branch.

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