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12. Maximum Depth of Binary Tree

easyAsked at Electronic Arts

Return the number of nodes on the longest root-to-leaf path.

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

  • 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

BFS layer by layer, incrementing depth.

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

Tradeoff:

2. Recursive max

Depth equals 1 + max(left depth, right depth).

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

Tradeoff:

Electronic Arts-specific tips

EA likes seeing the recursive one-liner first, then explicitly discussing recursion limits — deep skill trees in RPGs sometimes hit the limit.

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