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12. Maximum Depth of Binary Tree

easyAsked at Lyft

Compute 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 — the number of nodes along the longest path from the root down to the farthest leaf.

Constraints

  • Number of nodes in range [0, 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

Iterative breadth-first count of levels.

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

Tradeoff:

2. DFS recursion

Return 1 + max of left and right subtree depths.

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

Tradeoff:

Lyft-specific tips

Lyft will follow up by asking the depth of a geohash quad-tree; mention the O(h) call stack cost so they know you think about deep-tree stack overflow risk.

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Output

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