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Google·Data Scientist·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
Apr 2026

Summary

Google Data Scientist interview with a coding question that was more of a math/CS fundamentals check than anything ML-related. One question, but it had layers.

Questions Asked (1)

Q1

Write a function that returns the nth Fibonacci number (0-indexed), handles n up to at least 10^6, and explain the time and space complexity. Also, what do you do if the numbers get too large for native integer types?

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The naive recursive solution is the obvious wrong answer and I knew that, so I jumped to the iterative approach pretty fast.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (n up to 10^6, 0-indexed) and then present an iterative O(n) time, O(1) space solution using two variables. Explain the complexity and discuss handling large numbers with arbitrary-precision arithmetic or modular arithmetic if needed.

Pro tip: Mention that for n=10^6, the Fibonacci number has about 208,988 digits, so native types overflow; use Python's built-in big integers or a library like GMP. Also, note that if only the last k digits are needed, you can use modular arithmetic to keep numbers small.

1. Clarify requirements and constraints

Confirm that n is 0-indexed, n can be up to 10^6, and discuss whether the result needs to be exact or modulo something. Ask about the expected return type and any memory constraints.

2. Choose an algorithm

Select an iterative approach with O(n) time and O(1) space, as it is simple and efficient for n up to 10^6. Mention alternatives like matrix exponentiation (O(log n)) but note that for n=10^6, O(n) is perfectly fine and avoids overhead.

3. Implement the solution

Write a function that initializes two variables (a=0, b=1) and iterates n times, updating a and b. Handle edge cases (n=0, n=1) and ensure the code is clean and efficient.

4. Analyze time and space complexity

Explain that the iterative solution runs in O(n) time and O(1) space, as it only uses a constant number of variables. Note that the time is linear in n, which is acceptable for n=10^6.

5. Address large number handling

Discuss that Fibonacci numbers grow exponentially, so for n=10^6, the result has ~208,988 digits. Native integer types overflow; use arbitrary-precision arithmetic (e.g., Python's int, Java's BigInteger, or GMP). If only modulo is needed, use modular arithmetic to keep numbers small.

Key Points to Mention

  • Iterative solution with O(n) time and O(1) space is optimal for n up to 10^6.
  • Fibonacci numbers grow exponentially; F(10^6) has about 208,988 digits, exceeding native integer limits.
  • Use arbitrary-precision arithmetic (e.g., Python's int, Java's BigInteger) to handle large numbers.
  • If only the last k digits are required, use modular arithmetic to avoid huge numbers.
  • Edge cases: n=0 returns 0, n=1 returns 1; ensure 0-indexing is correctly handled.
  • Alternative algorithms like matrix exponentiation (O(log n)) exist but may have higher constant factors; iterative is simpler and sufficient.

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