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5. Maximum Depth of Binary Tree

easyAsked at Autodesk

Compute the maximum depth (number of nodes along the 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. 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 <= node count <= 10^4
  • -100 <= node value <= 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

Walk level-by-level with a queue, incrementing depth per level.

Time
O(n)
Space
O(n)
let q=[root], d=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; d++;
}
return d;

Tradeoff:

2. DFS recursion

Each node's depth is 1 plus the max depth of its two children. Recursion mirrors the tree shape.

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

Tradeoff:

Autodesk-specific tips

Autodesk uses tree depth checks when traversing BVH and scene-graph hierarchies, so they expect comfort with both iterative and recursive forms.

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