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Databricks·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Databricks software engineer interview with a tricky tree problem that looks straightforward until you realize the naive approach blows up exponentially. The key insight they were testing was whether you'd recognize the memoization angle before writing anything.

Questions Asked (1)

Q1

Given a recursively defined 'Fibonacci tree' where F(0) and F(1) are leaves and F(n) has F(n-1) and F(n-2) as children, write a solution that operates in O(n) time relative to the tree's height n, not the total node count.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

I started thinking about traversal and immediately went down the wrong path mentally.

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AI HintsAI Generated

Suggested Approach

Recognize that the Fibonacci tree has exponential size, so any solution visiting all nodes is infeasible. Instead, exploit the recursive structure by computing the desired property (e.g., height, diameter, or a specific node value) using the Fibonacci recurrence, which can be done in O(n) time by iterating from the base cases up to n. Clearly define the problem and show how to avoid traversing the entire tree.

Pro tip: Emphasize that the key is to avoid materializing the tree; instead, use the recurrence to compute the answer directly. Mention that this approach is crucial for handling large n where the tree size is exponential.

1. Clarify the problem

Ask clarifying questions to ensure you understand what property of the Fibonacci tree needs to be computed (e.g., height, diameter, number of leaves, or value at a specific position). Confirm that the tree is defined recursively and that n is the height parameter.

2. Identify the recurrence

Derive a recurrence relation for the desired property based on the tree's recursive definition. For example, if computing height, note that height(F(n)) = 1 + max(height(F(n-1)), height(F(n-2))).

3. Design an O(n) algorithm

Use dynamic programming or iterative computation to compute the property from the base cases up to n, storing only the necessary previous values. This avoids traversing the exponential number of nodes.

4. Analyze time and space complexity

Explain that the algorithm runs in O(n) time because it performs a constant amount of work per step from 0 to n. Space can be O(1) if only a few previous values are needed, or O(n) if storing all values.

5. Discuss trade-offs and edge cases

Mention that while the tree itself is exponential, the recurrence allows efficient computation. Handle edge cases like n=0 or n=1, and discuss potential integer overflow for large n.

Key Points to Mention

  • The Fibonacci tree has exponential size (number of nodes grows like Fibonacci numbers), so any O(nodes) solution is impractical.
  • The recursive structure allows computing properties using the Fibonacci recurrence, leading to O(n) time relative to height n.
  • Dynamic programming or iterative computation can be used to avoid recursion depth issues and redundant computations.
  • Space complexity can often be reduced to O(1) by keeping only the last few values.
  • Clarify the specific property to compute; different properties may require different recurrences but still O(n) time.
  • Mention that this approach is scalable and can handle very large n, unlike naive traversal.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.