My first instinct was just to build a giant array repeating each index by its weight and sample from it.
Use prefix sums to convert weights into cumulative ranges, then binary search to find the index for a random target. This gives O(n) preprocessing and O(log n) per pick, meeting the scale requirements. Discuss trade-offs like memory and alternative approaches (e.g., segment tree) to show depth.
Pro tip: Mention that using a random double and binary search on prefix sums is standard, but also note that you can optimize by using a random integer in [0, totalWeight) and searching for the first prefix sum greater than that value. This avoids floating-point precision issues and is slightly faster.
Confirm that weights are positive, the array is static, and pickIndex will be called many times. Discuss expected time complexity for initialization and pickIndex.
Explain that you'll compute prefix sums of weights, then for each pick, generate a random number between 0 and total weight, and binary search for the first prefix sum greater than that number.
State that preprocessing is O(n) time and space, and each pick is O(log n). Compare with alternatives like linear scan (O(n) per pick) or segment tree (O(log n) but more complex).
Discuss handling zero weights, large total weight (use 64-bit integers), and potential optimizations like early termination or using a random integer to avoid floating-point issues.
Write clean code for the data structure, and suggest testing with small examples and verifying distribution with a large number of calls.
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