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12. Maximum Depth of Binary Tree

easyAsked at GoDaddy

Return the maximum depth (longest root-to-leaf path) 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 along the longest path from the root 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 counter

BFS level by level; count levels.

Time
O(n)
Space
O(n)
// queue based BFS, increment depth per level

Tradeoff:

2. Recursive DFS

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:

GoDaddy-specific tips

GoDaddy frames tree depth as the longest delegation chain in DNS (root -> TLD -> registrar -> customer subzone) when reasoning about resolution latency.

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Output

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