The division shortcut is the first thing your brain goes to and then you realize you can't use it.
Clarify the problem constraints (e.g., array size, integer overflow, zero handling) and then present an O(n) time, O(n) space solution using prefix and suffix products. Explain that for each index i, the result is the product of all elements before i times the product of all elements after i, computed in two passes without division.
Pro tip: Mention that you can optimize space to O(1) by using the output array to store prefix products and then computing suffix products on the fly, but only if the interviewer allows modifying the output array. This shows awareness of trade-offs and Amazon's leadership principle of 'Invent and Simplify'.
Ask about array size, possible zero values, integer overflow, and whether the output can be stored in the same array. Confirm that division is not allowed and that the solution should be efficient.
Describe how to compute prefix products (product of all elements before i) and suffix products (product of all elements after i) in two separate passes, then multiply them for each index.
Use a small array like [1,2,3,4] to demonstrate the algorithm step by step, showing the prefix and suffix arrays and the final result.
State that the time complexity is O(n) and space complexity is O(n) for the prefix and suffix arrays. Mention that space can be reduced to O(1) extra space (besides the output) by using the output array to store prefix products and computing suffix products on the fly.
Discuss how the algorithm handles zeros (e.g., if there is one zero, only that index gets the product of all non-zero elements; if multiple zeros, all outputs are zero) and confirm the solution meets the constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.