My first instinct was to just expand the array and pick uniformly, which works but is terrible on memory for large weights.
Start by clarifying the problem and constraints, then propose a solution using prefix sums and binary search to achieve O(n) preprocessing and O(log n) sampling. Discuss the trade-offs between this approach and a linear scan, and mention how to handle edge cases like zero weights.
Pro tip: Emphasize the importance of randomness quality and reproducibility by discussing seeding and testing with statistical tests. Also, relate the problem to real-world ML scenarios like weighted sampling in recommendation systems.
Ask about input size, weight distribution, and whether weights can be zero. Confirm the need for uniform random number generation and any performance requirements.
Propose using prefix sums to represent cumulative weights, then generate a random number between 0 and total sum, and binary search to find the corresponding index. Explain why this is efficient.
Compare the prefix sum + binary search approach (O(n) preprocessing, O(log n) per sample) with a linear scan approach (O(n) per sample). Discuss when each is appropriate.
Address zero weights, floating-point precision, and random number generator seeding. Discuss how to test the implementation for correctness.
Connect the problem to ML use cases like weighted sampling in data loaders, reinforcement learning, or recommendation systems, showing broader understanding.
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