Tripped up on the negative number case for longer than I'd like to admit.
Use dynamic programming to track both the maximum and minimum product ending at each position, since a negative number can flip the sign and turn a minimum into a maximum. Iterate through the array, updating these values and the global maximum product.
Pro tip: Clearly explain why tracking the minimum product is necessary—this shows you understand the sign-flipping edge case that trips up many candidates. Also, discuss how you would handle zeros and negative numbers, and mention the time and space complexity.
Ask if the array can be empty, contain zeros, or have negative numbers. Confirm that the subarray must be contiguous and non-empty.
Maintain two variables: max_prod and min_prod, representing the maximum and minimum product of a subarray ending at the current index. Also keep a global max_product.
For each number, compute new max_prod and min_prod using the current number and the previous max_prod and min_prod. Update global max_product accordingly.
If the array is empty, return 0 or handle as appropriate. Zeros reset the product, so they are naturally handled by the updates.
State that the algorithm runs in O(n) time and O(1) space, which is optimal.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.