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13. Maximum Depth of Binary Tree

easyAsked at Duolingo

Return the depth of the deepest leaf in 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.

Constraints

  • 0 <= number of 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 by level

Level-order traversal, count levels.

Time
O(n)
Space
O(n)
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. Recursive max

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

Duolingo-specific tips

Duolingo's skill-tree depth maps to course difficulty progression; show you can compute it without blowing the recursion stack on a 20-unit tree.

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