Databricks·Software Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say

Jun 2026Remote

Summary

Databricks technical phone screen for a software engineer role. The problem was a tree traversal question but with a twist that made it way harder than it sounds on the surface.

Questions Asked (1)

Given a Fibonacci-structured binary tree where each node's subtree sizes follow the Fibonacci sequence, find the path between two specified nodes without building the actual tree in memory.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was to just construct the tree and do a standard LCA traversal.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

First clarify the Fibonacci tree structure and how subtree sizes are determined. Then design an algorithm that navigates from the root to each target node using only size calculations, and finally combine the paths to find the unique path between the nodes. Emphasize that no explicit tree is built, leveraging the recursive Fibonacci pattern.

Pro tip: Mention that the Fibonacci tree is essentially a recursive structure where each node's children have sizes F(n-1) and F(n-2), so you can compute the path by repeatedly subtracting Fibonacci numbers. This shows you understand the underlying math and can avoid unnecessary memory usage.

1. Clarify the problem and tree structure

Ask questions to confirm the definition: each node's subtree size follows Fibonacci numbers, and the tree is implicitly defined. Ensure you understand how nodes are indexed or labeled.

2. Design a path-finding algorithm without building the tree

Use the Fibonacci property to determine the path from the root to a given node by recursively deciding which child subtree contains the node based on its index and the Fibonacci sizes.

3. Find paths to both nodes and compute the LCA

Compute the root-to-node paths for both target nodes, then find their lowest common ancestor by comparing the paths. The final path is the concatenation of the two paths from the LCA.

4. Analyze time and space complexity

Discuss that the algorithm runs in O(log n) time due to the Fibonacci growth, and uses O(log n) space for the paths, without building the tree.

5. Consider edge cases and trade-offs

Address cases like when one node is an ancestor of the other, or when nodes are the same. Also discuss trade-offs: implicit navigation saves memory but may be slower than direct traversal if the tree were built.

Key Points to Mention

Fibonacci tree properties: subtree sizes follow F(n) = F(n-1) + F(n-2), with base cases.
Implicit tree navigation: using indices and sizes to decide left/right child without pointers.
Path finding via root-to-node paths and LCA computation.
Time complexity: O(log n) because Fibonacci numbers grow exponentially.
Space complexity: O(log n) for storing paths, no tree construction.
Trade-offs: memory efficiency vs. potential overhead of repeated calculations.

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