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8. Maximum Depth of Binary Tree

easyAsked at LINE

Return the maximum depth of a binary tree — LINE asks this to gauge whether you instinctively reach for recursion before BFS when the input is a 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

  • Number of nodes in the tree is 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

Run a queue-based BFS and increment depth for every full level processed.

Time
O(n)
Space
O(n)
let q=[root], d=0;
while(q.length && q[0]){
  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 DFS

Depth of a node equals one plus the max depth of its children. Recurse and return the larger subtree depth plus one.

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

Tradeoff:

LINE-specific tips

At LINE, link tree depth to chat-thread reply nesting — they like candidates who picture the data structure inside a real product surface.

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