The naive approach of expanding weights into a giant array works but kills you on memory.
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) sampling. Discuss trade-offs between preprocessing time, sampling time, and memory, and mention alternative approaches like the alias method for O(1) sampling.
Pro tip: Emphasize the importance of randomness quality and reproducibility in ML systems; mention setting a random seed for testing and using a cryptographically secure RNG if needed for production.
Ask about input size, frequency of sampling, need for reproducibility, and whether weights can change dynamically.
Describe a simple approach: compute total sum, generate a random number between 0 and total, then iterate through the array subtracting weights until the cumulative sum exceeds the random number.
Improve to O(log n) sampling by precomputing prefix sums and using binary search to find the index where the random number falls.
Compare with the alias method (O(1) sampling, O(n) preprocessing) and discuss when each is appropriate based on sampling frequency and memory constraints.
Cover handling of zero weights, floating-point precision, and ensuring uniform random number generation.
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