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12. Maximum Depth of Binary Tree

easyAsked at Slack

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. A binary tree's depth is the number of nodes along the longest path from the root down to the farthest leaf.

Constraints

  • Nodes count 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

Walk level by level, count levels.

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

Tradeoff:

2. Recursive DFS

Depth is 1 + max(depth of left, depth of right). Null returns 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:

Slack-specific tips

Slack will probe iterative versions for unbounded thread-reply trees — recursion stack is a risk on deep escalation threads.

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