Google·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

A technical phone screen for an ML Engineer role at Google that was basically one long coding problem about probability-weighted sampling. The question had a lot of layers to it and I didn't expect them to push so hard on the testing angle.

Questions Asked (1)

Given a list of distinct integers and a corresponding list of probabilities that sum to 1, implement a Python generator that yields values indefinitely according to the given distribution. Your solution should validate inputs, handle floating-point edge cases, and use an efficient sampling approach. Then discuss the time and space trade-offs of your implementation and write unit tests including seeded deterministic checks and statistical distribution verification.

Algorithms & Data StructuresTechnical Trade-offsSystem Design

Author's notes

This one had way more surface area than I expected from a single question.

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AI HintsAI Generated

Suggested Approach

Start by clarifying requirements and edge cases, then outline a solution using cumulative distribution and binary search for O(log n) sampling. Implement the generator with input validation and floating-point tolerance, and discuss trade-offs between preprocessing and sampling efficiency. Finally, describe unit tests covering deterministic and statistical checks.

Pro tip: Mention that using a cumulative sum array with binary search (e.g., bisect) is efficient for large n, but for small n a linear scan may be faster due to cache locality. Also, highlight the importance of seeding for reproducibility in statistical tests.

1. Clarify Requirements and Edge Cases

Ask about input constraints (size, value range), whether probabilities are guaranteed to sum to 1, and how to handle floating-point errors. Discuss validation needs and expected performance.

2. Design the Sampling Algorithm

Propose using cumulative probabilities and binary search for O(log n) sampling. Alternatively, mention alias method for O(1) but with higher preprocessing. Explain how to handle floating-point precision by normalizing or using tolerance.

3. Implement the Generator

Write a Python generator that validates inputs (lengths match, probabilities non-negative, sum to 1 within tolerance), precomputes cumulative sums, and yields values indefinitely using random.random() and bisect.

4. Analyze Time and Space Trade-offs

Compare O(n) preprocessing and O(log n) per sample for cumulative+binary search vs O(n) preprocessing and O(1) per sample for alias method. Discuss memory usage and suitability for different n.

5. Write Unit Tests

Include tests for input validation (invalid probabilities, mismatched lengths), deterministic checks with a seeded RNG, and statistical tests (e.g., chi-square) to verify distribution over many samples.

Key Points to Mention

Input validation: check lengths match, probabilities are non-negative, and sum to 1 within a small epsilon (e.g., 1e-9).
Floating-point handling: normalize probabilities if sum is close to 1, and use a tolerance in validation.
Sampling efficiency: cumulative sum + binary search gives O(log n) per sample; alias method gives O(1) but requires O(n) preprocessing and memory.
Generator implementation: use yield in an infinite loop, precompute cumulative probabilities once, and use random.random() for uniform sampling.
Statistical testing: use chi-square goodness-of-fit test with a fixed seed to verify distribution, and check for edge cases like zero probabilities.
Trade-offs: binary search is simpler and memory-efficient for large n; alias method is faster for many samples but more complex.

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