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12. Maximum Depth of Binary Tree

easyAsked at Spotify

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 number of nodes along the longest path from root to a 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

Level-order traversal counting levels

Time
O(n)
Space
O(w)
let depth=0; const q=[root].filter(Boolean);
while(q.length){let n=q.length;while(n--){const x=q.shift();if(x.left)q.push(x.left);if(x.right)q.push(x.right);} depth++;}
return depth;

Tradeoff:

2. Recursive DFS

Return 1 + max(left depth, right depth). Tail-rec friendly and trivial to extend to balance checks.

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

Tradeoff:

Spotify-specific tips

Spotify uses depth checks when traversing nested playlist-folder hierarchies; mention how depth would bound a recursive walk before they ask the follow-up.

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