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12. Maximum Depth of Binary Tree

easyAsked at TripAdvisor

Find the maximum depth of a binary tree.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given the root of a binary tree, return its maximum depth. A binary tree's maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

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

Use queue, count levels 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. Recursive DFS

Depth = 1 + max(left, right). Clean recurrence.

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

Tradeoff:

TripAdvisor-specific tips

TripAdvisor uses tree-depth questions to gauge how you bound traversal cost when paginating deeply nested reply threads.

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