Compute rolling standard deviation in O(n)

Q: Compute rolling standard deviation in O(n)

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Question

Given an array of numbers and a window size k, compute the rolling standard deviation for every contiguous window. Design an O(n) algorithm that updates statistics incrementally rather than recomputing each window from scratch. Use the variance identity by maintaining running sum and sum of squares (or adapt a one-pass method like Welford’s algorithm for a sliding window), discuss numerical stability, analyze time and space complexity, and handle edge cases (k ≤ 0, k > n, k = 1, NaNs). Implement and provide tests.

Compute rolling standard deviation in O(n)

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