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13. Maximum Depth of Binary Tree

easyAsked at Expedia

Return the maximum depth from root to any 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. 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

  • The number of nodes is in [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. BFS level count

BFS counting levels.

Time
O(n)
Space
O(n)
let depth=0,q=root?[root]:[];
while(q.length){depth++;const next=[];
  for(const n of q){if(n.left)next.push(n.left);if(n.right)next.push(n.right);}q=next;}return depth;

Tradeoff:

2. DFS recursion

max(left depth, right depth) + 1. Expedia uses this to bound category-tree depth for product taxonomy lookups.

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

Tradeoff:

Expedia-specific tips

Expedia interviewers may push you to discuss iterative BFS for very deep trees to avoid stack overflow on multi-tier destination hierarchies.

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