DSA interview question

Maximum Depth of a Binary Tree

Medium · Data structures · Topics: tree, dfs, recursion

The problem

A UI framework lays out nested components as a tree, and deeply nested layouts render slowly. The profiler reports the maximum depth: the number of nodes on the longest path from the root down to a leaf. The recursive answer is one line. An empty tree has depth 0, and otherwise the depth is 1 plus the deeper of the two subtrees. A BFS that counts levels gives the same number without recursion.

Example: [3, 9, 20, null, null, 15, 7] → 3.

Function signature

int maxDepth(TreeNode* root);

Test cases

Input (level order)	Output	Explanation
`[3, 9, 20, null, null, 15, 7]`	`3`	3 → 20 → 15
`[1, null, 2]`	`2`
`[1, 2, null, 3, null, 4]`	`4`	A left chain
`[1]`	`1`
`[]`	`0`

(Confirm: depth counts nodes, not edges; an empty tree has depth 0.)

How interviewers phrase it

"Given the root of a binary tree, return its maximum depth" (LeetCode 104).

Clarifying questions to ask

Nodes or edges? (Nodes.)
Can the tree be empty? (Yes, so return 0.)
Could it be very deep? (Then prefer BFS or an explicit stack.)

Follow-ups to expect

"Recursive formula?"
"Iterative?"
"Minimum depth?"
"How does this relate to 'balanced tree' and 'diameter'?"
"Complexity?"

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