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Compute rolling standard deviation in O(n)
Problem Description
Given an array of numerical values and an integer window size k, the task is to compute the rolling standard deviation for every contiguous sub-array (window) of size k.
Requirements
- Algorithm Efficiency: Design an algorithm that achieves O(n) time complexity, where
nis the length of the input array. This implies updating statistics incrementally for each window rather than recomputing from scratch. - Statistical Method: The solution should leverage the variance identity by maintaining running sums and sums of squares. Alternatively, a one-pass method suitable for sliding windows, such as an adaptation of Welford's algorithm, can be used.
- Numerical Stability: Discuss the numerical stability of the chosen approach, especially concerning potential issues with floating-point arithmetic.
- Complexity Analysis: Analyze the time and space complexity of the proposed algorithm.
- Edge Case Handling: The implementation must correctly handle various edge cases:
k <= 0(invalid window size)k > n(window size larger than array length)k = 1(single-element window)NaNvalues within the input array.
- Implementation & Testing: Provide a working implementation along with appropriate test cases to demonstrate correctness and robustness.
AI interview prep
Core dilemma
Achieving O(N) computational efficiency for a sliding window statistical calculation while ensuring numerical stability and correctness across diverse data distributions and edge cases.
Mid-level signals3
Senior signals3
Red flags3
2 tradeoffs and 3 stress tests locked
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Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Compute rolling standard deviation in O(n)
Problem Description
Given an array of numerical values and an integer window size k, the task is to compute the rolling standard deviation for every contiguous sub-array (window) of size k.
Requirements
- Algorithm Efficiency: Design an algorithm that achieves O(n) time complexity, where
nis the length of the input array. This implies updating statistics incrementally for each window rather than recomputing from scratch. - Statistical Method: The solution should leverage the variance identity by maintaining running sums and sums of squares. Alternatively, a one-pass method suitable for sliding windows, such as an adaptation of Welford's algorithm, can be used.
- Numerical Stability: Discuss the numerical stability of the chosen approach, especially concerning potential issues with floating-point arithmetic.
- Complexity Analysis: Analyze the time and space complexity of the proposed algorithm.
- Edge Case Handling: The implementation must correctly handle various edge cases:
k <= 0(invalid window size)k > n(window size larger than array length)k = 1(single-element window)NaNvalues within the input array.
- Implementation & Testing: Provide a working implementation along with appropriate test cases to demonstrate correctness and robustness.