Took me longer than it should have to realize this is just repeated reduction, not a one-pass thing.
Start by clarifying the problem constraints and edge cases, such as the minimum array length and behavior when the window size exceeds the array length. Then, describe a straightforward simulation approach that repeatedly applies the sliding window sum until one element remains, and analyze its time and space complexity. Finally, discuss potential optimizations or alternative methods, like using prefix sums or recognizing the pattern of coefficients.
Pro tip: Mention that the final result is a linear combination of the original array elements with binomial coefficients, which can be computed in O(n) time without explicit simulation. This shows deeper insight and can impress the interviewer.
Ask about edge cases: What if the array length is less than 3? What if it's exactly 3? Confirm that the window slides by one each time and that the process stops when the array length is 1.
Explain that you can repeatedly compute sliding window sums of size 3 until one element remains. This is simple but may be inefficient for large arrays.
Calculate time complexity: each pass reduces the array size by 2, so the total work is O(n^2) in the worst case. Space complexity is O(n) for the new arrays.
Derive that the final result is the sum of original elements multiplied by binomial coefficients. For window size 3, the coefficient for element i is C(k, i) where k is the number of reductions, or use dynamic programming to compute in O(n) time.
Walk through a small example, such as [1,2,3,4,5], to verify the approach and ensure correctness. Discuss potential off-by-one errors.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.