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12. Maximum Depth of Binary Tree

easyAsked at Instacart

Compute the max depth of a binary tree — Instacart uses this to gate basic recursion against later store-hierarchy depth questions.

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 node.

Constraints

  • The number of nodes in the tree 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

Push root into a queue, increment depth per level processed.

Time
O(n)
Space
O(w)
if (!root) return 0;
let q = [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. DFS recursion

Max depth = 1 + max of subtree depths.

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

Tradeoff:

Instacart-specific tips

Instacart will ask why you'd choose DFS vs BFS — frame it around how the aisle-tree depth bounds shopper UI breadcrumbs.

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Output

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