I knew the prefix sum approach going in, build the cumulative array in the constructor, then on each pick generate a random number and binary search for the right bucket.
Start by clarifying the problem: weights are non-negative, at least one positive, and the function should return an index with probability proportional to its weight. Then present the prefix sum + binary search approach, explaining its O(n) preprocessing and O(log n) sampling, and discuss trade-offs with alternative methods like the alias method.
Pro tip: Mention that for ML systems, the alias method is often preferred for large-scale sampling due to O(1) sampling time, but it requires O(n) preprocessing and extra memory; choose based on whether the weights are static or dynamic.
Ask about weight properties (non-negative, zero handling), array size, frequency of sampling, and whether weights change over time. This determines the optimal algorithm.
Compute cumulative sums of weights, generate a random number between 0 and total sum, then binary search for the first index where cumulative sum exceeds the random value. This gives O(n) preprocessing and O(log n) per sample.
Explain that the alias method preprocesses weights into a table allowing O(1) sampling, but requires O(n) preprocessing and additional memory. It's ideal for static weights and many samples.
Compare time/space complexity, handling of zero weights, and dynamic updates. Mention that for dynamic weights, a Fenwick tree can support updates and sampling in O(log n).
Write clean code for the chosen approach, ensuring correct handling of edge cases (e.g., all weights zero). Optionally, describe how to test the distribution empirically.
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