Pretty standard problem if you've seen it before.
Clarify the problem constraints (e.g., array size, element types, handling zeros) and then propose a solution using prefix and suffix products. Explain that you can compute prefix products in one pass and suffix products in another, then multiply them to get the result without division. Analyze time and space complexity, aiming for O(n) time and O(1) extra space (excluding output array).
Pro tip: Mention that this approach handles zeros gracefully, unlike division-based solutions, and discuss potential optimizations like using the output array to store prefix products and then computing suffix products on the fly to achieve O(1) extra space.
Ask about input size, element ranges, and whether zeros are allowed. Discuss how zeros affect the result (e.g., if more than one zero, all products are zero; if exactly one zero, only that position gets the product of others).
Explain that you'll use prefix and suffix products. Compute an array where each element is the product of all elements to its left, then multiply by the product of all elements to its right.
Describe two passes: first, compute prefix products and store in the output array; second, traverse from right to left, maintaining a running suffix product and multiplying it with the corresponding prefix product.
State that time complexity is O(n) and space complexity is O(1) extra space (output array not counted). Mention that this avoids division and handles zeros correctly.
Walk through a simple example (e.g., [1,2,3,4]) and an edge case with zeros (e.g., [1,0,3,4]) to verify correctness.
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