Start by clarifying the problem constraints (e.g., array size, k validity) and then propose an efficient sliding window approach to compute the averages in O(n) time. Explain the algorithm step-by-step, handle edge cases, and analyze time and space complexity.
Pro tip: Mention that using a sliding window avoids redundant computations, and discuss potential floating-point precision issues when returning averages. Also, consider if the output should be rounded or if exact precision is required.
Ask about input constraints (e.g., array length, k value, possible negative numbers) and output format (e.g., floating-point precision, rounding). Confirm that k is always valid (1 ≤ k ≤ n).
Acknowledge that a brute force approach would compute each subarray sum independently, leading to O(n*k) time. Then propose the sliding window technique to achieve O(n) time by reusing the sum of the previous window.
Describe initializing the sum of the first k elements, then iterating from index k to n-1: subtract the element leaving the window, add the new element, and compute the average. Handle the first window separately.
State that time complexity is O(n) and space complexity is O(n-k+1) for the output array (or O(1) extra space). Mention edge cases: k=1, k=n, and empty array (if allowed).
Walk through a small example (e.g., [1,2,3,4], k=2) to verify the algorithm and demonstrate correctness. Discuss potential floating-point precision and whether to return double or float.
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