Start by clarifying requirements and edge cases, then present an O(n) algorithm using rolling sums and sums of squares with Welford's method for numerical stability. Discuss trade-offs between naive and incremental approaches, and outline a comprehensive test suite covering edge cases and numerical accuracy.
Pro tip: Explicitly mention that DRW values production-ready code, so emphasize handling NaN values by propagating them and ensuring the algorithm remains O(n) even with missing data. Also, discuss how you would validate numerical stability with tests comparing against a high-precision reference.
Ask clarifying questions about input types, expected output format, and how to handle edge cases like k <= 0, k > n, k = 1, and NaN values. Confirm whether the standard deviation should be population or sample.
Propose using rolling sums and sums of squares, but highlight the numerical instability of the naive formula. Instead, recommend Welford's online algorithm or a compensated summation approach to update mean and variance incrementally.
Define behavior for invalid k (return empty array or raise error), k=1 (std dev = 0), and NaN values (propagate NaN in windows containing NaN). Ensure the algorithm remains O(n) by tracking NaN counts.
Write clean code with clear variable names and comments. Develop tests for normal cases, edge cases, and numerical stability (e.g., large numbers, small variance). Compare against a brute-force implementation for correctness.
Mention trade-offs: Welford's method is more stable but slightly more complex; rolling sums are simpler but risk catastrophic cancellation. Discuss when to use each and potential optimizations.
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