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Google·Machine Learning Engineer·Technical Phone Screen·Senior

Senior
Jun 2026

Summary

Google MLE interview that centered on a weighted random sampling problem. The base version was straightforward but the follow-up is what actually tested whether you understood the tradeoffs, not just the happy path.

Questions Asked (2)

Q1

Given an array of positive integer weights, implement a function that randomly picks an index where the probability of picking index i equals w[i] divided by the total sum of weights.

Algorithms & Data Structures
Author's notes

Prefix sums plus binary search, pretty standard if you've seen it before.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and constraints, then propose a solution using prefix sums and binary search for O(n) preprocessing and O(log n) per query. Discuss the algorithm's correctness, complexity, and potential edge cases, and consider follow-up optimizations or alternative approaches.

Pro tip: Mention that this is a classic weighted random sampling problem and that Google often values clean, efficient code with clear reasoning. Also, be prepared to discuss how to handle dynamic updates to weights, as it shows deeper understanding.

1. Clarify requirements and constraints

Ask about input size, number of queries, whether weights can change, and if the function will be called multiple times. This helps determine the optimal approach.

2. Design the algorithm

Propose using prefix sums to create cumulative weights, then generate a random number between 0 and total sum, and binary search to find the index. Explain why this achieves the desired probabilities.

3. Analyze complexity and correctness

State that preprocessing takes O(n) time and O(n) space, and each pick takes O(log n) time. Prove that the probability of picking index i is w[i]/total sum.

4. Discuss edge cases and optimizations

Consider cases like zero weights, single element, large arrays, and potential floating-point issues. Mention alternatives like the alias method for O(1) picks if many queries are expected.

5. Implement and test

Write clean code, possibly in Python or C++, and walk through a small example to verify correctness. Discuss how to test the distribution statistically.

Key Points to Mention

  • Prefix sums (cumulative weights) for efficient range mapping
  • Binary search (bisect) to find the index in O(log n)
  • Probability calculation: P(i) = w[i] / sum(w)
  • Time and space complexity: O(n) preprocessing, O(log n) per pick, O(n) space
  • Edge cases: zero weights, empty array, single element, large sums
  • Alternative: Alias method for O(1) picks with O(n) preprocessing

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

Q2

How would you redesign your solution if the weights can change frequently, making the prefix-sum and binary-search approach impractical? Walk through the tradeoffs between approaches.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

This is where I stumbled a bit.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints: how frequently do weights change, and what are the query patterns? Then propose alternative data structures like Fenwick trees (Binary Indexed Trees) or segment trees that support point updates and prefix sum queries in O(log n). Finally, compare tradeoffs in terms of update/query complexity, implementation complexity, and memory usage.

Pro tip: Mention that in practice, if updates are extremely frequent and queries are rare, a simple array with O(1) update and O(n) query might be acceptable; always tie the choice to the actual workload.

1. Clarify requirements

Ask about the frequency of weight changes versus queries, and whether updates are point updates or range updates. This determines the appropriate data structure.

2. Propose alternative data structures

Suggest Fenwick trees (BIT) or segment trees, which support point updates and prefix sum queries in O(log n). Mention that segment trees can also handle range updates with lazy propagation.

3. Analyze tradeoffs

Compare time complexity: prefix-sum array gives O(1) query but O(n) update; BIT/segment tree gives O(log n) for both. Discuss memory: BIT uses O(n) space, segment tree uses O(4n). Also consider implementation complexity and constant factors.

4. Consider hybrid or advanced approaches

If updates are batched, consider rebuilding the prefix-sum array periodically. For very frequent updates, a balanced BST with subtree sums could work, but BIT/segment tree are usually simpler.

5. Recommend and justify

Based on the clarified requirements, recommend the most suitable approach, e.g., Fenwick tree for point updates and prefix queries, and explain why it balances performance and simplicity.

Key Points to Mention

  • Fenwick tree (Binary Indexed Tree) supports point updates and prefix sum queries in O(log n) time with O(n) space.
  • Segment tree supports point updates and range queries in O(log n) time, and can handle range updates with lazy propagation.
  • Tradeoff: prefix-sum array is O(1) query but O(n) update; BIT/segment tree are O(log n) for both, which is better when updates are frequent.
  • If updates are extremely frequent and queries are rare, a simple array with O(1) update and O(n) query might be acceptable.
  • Batching updates and rebuilding the prefix-sum array periodically can be a hybrid approach.
  • Consider memory and implementation complexity: BIT is simpler and uses less memory than segment tree.

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