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13. Maximum Depth of Binary Tree

easyAsked at Wix

Find the maximum depth of a binary tree; Wix uses tree depth as a complexity proxy for template render-cost estimates.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given the root of a binary tree, return its maximum depth, defined as 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

Use a queue and count levels.

Time
O(n)
Space
O(w)
let d=0,q=root?[root]:[]; 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. Recursive

Depth is 1 + max(left, right).

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

Tradeoff:

Wix-specific tips

Wix wants you to note when BFS is preferable for deeply-skewed trees — relevant for sites where users nest containers more than 30 deep.

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Output

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