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12. Maximum Depth of Binary Tree

easyAsked at Activision

Return the depth of a binary tree — Activision uses this to confirm DFS basics before asking about leaderboard tree depth for season-rank tiers.

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

  • Node count in range [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

Queue-based level-order, count levels.

Time
O(n)
Space
O(n)
let depth = 0, q = root ? [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; depth++;
}
return depth;

Tradeoff:

2. Recursive DFS

Depth = 1 + max(left depth, right depth). Base case empty tree returns 0.

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

Tradeoff:

Activision-specific tips

Activision likes when you state the recurrence in plain English before coding — same shape they reuse for season-rank tier trees and matchmaking-pool depth checks.

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Output

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