Databricks·Software Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Databricks SWE interview that went pretty deep into tree recursion, specifically around Fibonacci trees. Not your typical LeetCode grind, this one actually made me think about structural properties rather than just pattern matching.

Questions Asked (1)

Given the in-order traversal of a Fibonacci tree of unknown order n, reconstruct the original tree. Explain how the recursive size relationship between the left and right subtrees lets you locate the root, then describe your algorithm and analyze its complexity.

Algorithms & Data Structures

Author's notes

The key insight is that F(n) has F(n-1) nodes in the left subtree and F(n-2) in the right, so if you know the total size you can figure out the split point and recursively reconstruct.

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AI HintsAI Generated

Suggested Approach

First, clarify the definition of a Fibonacci tree and its recursive size property: a Fibonacci tree of order n has left subtree of order n-1 and right subtree of order n-2 (or vice versa), with sizes following Fibonacci numbers. Then, use the in-order sequence and the known subtree sizes to recursively locate the root and partition the sequence, reconstructing the tree. Finally, analyze the time and space complexity, noting the exponential growth of tree size with n.

Pro tip: Mention that the in-order traversal alone is insufficient without the Fibonacci property; explicitly state that the property provides the missing structural information. Also, note that the algorithm can be optimized to O(N) time by precomputing Fibonacci numbers and using indices, avoiding repeated size calculations.

1. Define Fibonacci Tree and Its Properties

Explain that a Fibonacci tree of order n is a binary tree where the left and right subtrees are Fibonacci trees of orders n-1 and n-2 (or vice versa), and its size is F_{n+2}-1 (or similar, depending on indexing). Clarify the recursive size relationship.

2. Locate the Root in the In-order Sequence

Given the total size N of the tree (derived from the length of the in-order sequence), find n such that the size matches a Fibonacci tree. Then, the root is at index size(left subtree) in the in-order sequence, where size(left) is the size of the left subtree (either F_{n+1}-1 or F_n-1).

3. Recursively Reconstruct Subtrees

Split the in-order sequence into left and right subsequences based on the root's position. Recursively apply the same process to each subsequence, using the appropriate Fibonacci orders for the subtrees.

4. Analyze Complexity

Discuss that the tree size grows exponentially with n (N = Θ(φ^n)), so the algorithm takes O(N) time if implemented efficiently (e.g., with precomputed Fibonacci numbers and linear-time partitioning). Space complexity is O(N) for the tree and O(n) for recursion stack.

Key Points to Mention

Definition of Fibonacci tree: recursive structure with left subtree of order n-1 and right of order n-2 (or vice versa).
Size relationship: size(T_n) = size(T_{n-1}) + size(T_{n-2}) + 1, leading to Fibonacci numbers.
In-order traversal gives sorted order of nodes (if keys are assigned in order), but the root's position is determined by the size of the left subtree.
Algorithm: compute total size N, find n such that size(T_n) = N, then recursively split the in-order sequence at the root index.
Complexity: O(N) time and O(N) space, where N is the number of nodes; N grows exponentially with n.
Edge cases: n=0 (empty tree), n=1 (single node), and ensuring the in-order sequence length matches a valid Fibonacci tree size.

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