The core idea clicked fast enough, build a prefix sum array and binary search on a random number in the total range.
Clarify the problem requirements, then propose using prefix sums of weights and binary search to achieve O(log n) pickIndex. Explain the init method that precomputes prefix sums in O(n) time, and detail how pickIndex generates a random number and uses binary search to find the index.
Pro tip: Mention edge cases like zero weights and discuss potential optimizations such as using a Fenwick tree for dynamic updates, showing depth beyond the basic solution.
Confirm that weights are non-negative, at least one weight is positive, and that pickIndex should run in O(log n) time. Discuss whether weights can be updated after initialization.
Propose storing prefix sums of weights in an array during init. Explain that this allows mapping a random number to an index via binary search.
Compute prefix sums in O(n) time, handling zero weights appropriately. Store the total sum for random number generation.
Generate a random integer between 1 and total sum (inclusive), then use binary search (e.g., bisect_left) on the prefix sums to find the smallest index where prefix sum >= random number. Return that index.
State that init is O(n) and pickIndex is O(log n) time, O(n) space. Discuss edge cases like all weights zero (invalid), single weight, and large weights causing overflow (use 64-bit integers).
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