← Pinterest Interview Insights
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.
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.
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.
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.
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.
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.
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.
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