I knew prefix sums were involved but fumbled the boundary condition for like two minutes.
Start by clarifying the problem and edge cases, then propose a solution using prefix sums and binary search to achieve O(n) preprocessing and O(log n) per query. Discuss the trade-offs and potential optimizations, and be prepared to code the solution.
Pro tip: Mention that this is essentially inverse transform sampling and that using binary search on prefix sums is more efficient than linear scan for large arrays or repeated queries.
Ask about input constraints (e.g., array size, weight range, negative weights, zero weights) and whether the function will be called multiple times. Discuss handling of all-zero weights.
Explain that you will compute prefix sums of weights, generate a random number between 0 and total sum, and then find the index where the random number falls using binary search.
State that preprocessing takes O(n) time and O(n) space, and each query takes O(log n) time with binary search. Compare with linear scan O(n) per query.
Write clean code: compute prefix sums, generate random number, use binary search (e.g., bisect in Python) to find the index. Handle edge cases like zero total weight.
Walk through examples, test with small arrays, and mention potential optimizations like using a segment tree or alias method for O(1) query time if needed.
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