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12. Maximum Depth of Binary Tree

easyAsked at Zoom

Find 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 maximum depth is the number of nodes along the longest path from the root down to the farthest leaf.

Constraints

  • 0 <= 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 level count

Walk level-by-level and count the levels.

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

Tradeoff:

2. DFS recursion

Depth equals 1 + max of left/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:

Zoom-specific tips

Zoom uses depth checks to validate breakout-room nesting limits before commit; mention you'd cap recursion depth or convert to iterative for production safety.

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Output

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