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19. Maximum Depth of Binary Tree

easyAsked at Adyen

Return 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. A binary tree's max depth is the number of nodes along the longest path from the root down to the farthest leaf.

Constraints

  • The number of nodes is in the 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. Recursive DFS

Depth = 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:

2. Iterative BFS by level

Walk the tree one level at a time and count levels.

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

Tradeoff:

Adyen-specific tips

Adyen prefers iterative BFS in their merchant routing trees because deep recursion is risky inside their JVM-hosted payment workers.

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