The 60-second answer
Use DFS that returns subtree height while updating the best path through each node. Target O(n) time and O(h) recursion space.
Build the answer in this order
1
Clarify constraints
Use DFS that returns subtree height while updating the best path through each node.
2
Choose the approach
Target O(n) time and O(h) recursion space.
3
Prove complexity
Call out edge cases such as single-node tree, skewed tree, and whether diameter is counted in nodes or edges.
4
Test edge cases
Explain the invariant before coding, then dry-run a small case and state time/space complexity.
A useful interview mental model
This is the shape of a strong answer—not a script to memorize.
01Clarify
02Approach
03Implement
04Test
05Complexity
Senior-level signal
- Clarify the metric definition before coding; edge-vs-node diameter causes off-by-one mistakes.
- For very deep trees, discuss iterative traversal to avoid recursion limits.
What the interviewer is really testing
Problem decomposition, correctness, data-structure choice, complexity reasoning, and clean implementation under pressure.
Likely follow-up questions
Can you improve the time or space complexity?
Which edge case is most likely to break this solution?
How would you test this under interview time pressure?
Common weak-answer patterns
- Starting to code before constraints are clear.
- Giving complexity without explaining why it is correct.
- Skipping adversarial and boundary cases.