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Pinterest·Data Scientist·Technical Phone Screen·Senior

Senior
May 2026

Summary

Pinterest data science interview with a probability/sampling design problem that sounds approachable until you actually have to think about memory and numeric precision under real constraints. The question was meaty enough that I left unsure whether I'd handled the edge cases well.

Questions Asked (1)

Q1

Design a pick() function that samples an item with probability proportional to its weight, where weights can be arbitrarily large. Walk through the memory and precision trade-offs when weights go beyond 32-bit integer limits.

Algorithms & Data StructuresTechnical Trade-offsSystem Design
Author's notes

I went straight to prefix-sum plus binary search, which is fine, but then they pushed on what happens when weights are huge numbers and I kind of fumbled.

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AI HintsAI Generated

Suggested Approach

Start by explaining the classic weighted random sampling algorithm using prefix sums and binary search, then discuss how to handle arbitrarily large weights by using floating-point numbers or arbitrary-precision integers, and analyze the trade-offs in memory and precision. Emphasize the importance of numerical stability and efficient sampling for large-scale systems like Pinterest.

Pro tip: Mention that in practice, weights are often normalized to probabilities or stored as logarithms to avoid overflow, and that using a balanced binary search tree (e.g., Fenwick tree) can support dynamic updates efficiently. This shows awareness of real-world constraints beyond the basic algorithm.

1. Clarify requirements and assumptions

Ask about the expected size of the dataset, whether weights can change dynamically, and the required sampling throughput. This sets the stage for discussing trade-offs.

2. Describe the basic algorithm

Explain the prefix sum + binary search approach: compute cumulative weights, generate a random number between 0 and total weight, and binary search for the corresponding item. This gives O(n) preprocessing and O(log n) sampling.

3. Address large weights and precision

Discuss how weights beyond 32-bit integers can be handled using 64-bit integers, floating-point numbers, or arbitrary-precision types. Highlight precision loss with floats and potential overflow with integers.

4. Analyze memory and precision trade-offs

Compare storing cumulative sums as 64-bit integers vs. floating-point: integers are exact but may overflow; floats save memory but lose precision. Mention alternatives like storing weights as logarithms or normalizing to probabilities.

5. Discuss optimizations and alternatives

Mention data structures like Fenwick trees for dynamic updates, or the alias method for O(1) sampling with O(n) preprocessing. Relate to Pinterest's scale and need for efficiency.

Key Points to Mention

  • Prefix sum and binary search algorithm for weighted sampling
  • Handling arbitrarily large weights with 64-bit integers, floats, or arbitrary-precision types
  • Precision loss and overflow risks when using floating-point or fixed-size integers
  • Memory trade-offs: storing cumulative sums vs. original weights
  • Alternative algorithms: alias method, Fenwick tree for dynamic updates
  • Normalization of weights to probabilities to avoid overflow

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