## Design a Population-Weighted Random Country Picker Design a class initialized with country names and positive population weights. Each call to `pick()` must return country `i` with probability: ```text population[i] / sum(population) ``` The country list is immutable after construction, and `pick()` will be called many times. ### Constraints & Assumptions - `1 <= number of countries <= 200_000`. - Country names are unique. - Every population is a positive integer, and their sum fits in a signed 64-bit integer. - A standard uniform pseudorandom-number source is available. - Exact mathematical weights are required; floating-point boundary bias should be avoided when practical. ### Clarifying Questions to Ask - Are weights fixed after initialization? - Must results be reproducible under a supplied random seed? - What are the maximum individual and total weights? - Is query latency or initialization cost more important? ### Hints - Separate one-time preprocessing from the repeated selection operation. - Map equal-probability points in one total range onto country-specific intervals. - Pay attention to inclusive and exclusive interval boundaries. ### What a Strong Answer Covers - A precise mapping from a uniform draw to weighted outcomes. - Correct boundary handling without zero-width or overlapping intervals. - Initialization, query, and memory complexity. - Random-source injection and deterministic unit testing. - Tradeoffs for mutable weights or stricter constant-time sampling. ### Follow-up Questions - How would you support frequent population updates? - Can preprocessing produce `O(1)` expected selection time? - How would you test distributional correctness without flaky tests? - What goes wrong when a floating-point draw lands on a cumulative boundary?