Blanked for a second because I kept thinking about maximum subarray sum (Kadane's) and tried to apply the same logic directly.
Start by clarifying the problem constraints (e.g., array size, presence of zeros, negative numbers) and then propose an O(n) dynamic programming solution that tracks both the maximum and minimum product ending at each position. Explain how negative numbers can flip the sign, so maintaining both extremes is crucial, and walk through a small example to demonstrate correctness.
Pro tip: Mention that you would handle edge cases like empty array, single element, and zeros explicitly, and discuss how the algorithm can be adapted to return the subarray itself if needed. This shows attention to detail and practical thinking beyond just the algorithm.
Ask about input size, possible values (negatives, zeros), and whether the subarray must be non-empty. Confirm the expected output (product value or the subarray).
Acknowledge that checking all subarrays is O(n^2) or O(n^3) and not scalable, motivating the need for an optimized approach.
Explain that at each index, you compute the maximum and minimum product ending there by considering the current element, the previous max times current, and the previous min times current. Update global max accordingly.
Use a small array with negatives and zeros (e.g., [2,3,-2,4] or [-2,0,-1]) to illustrate how the algorithm works step by step.
State time O(n) and space O(1) (or O(n) if storing subarray). Discuss handling of empty array, all negatives, zeros, and overflow considerations.
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