My first instinct was to just brute-force enumerate subsets and collect products into a set, but the interviewer pushed me on why I didn't need the set at all.
Clarify that the input consists of distinct primes, so all subset products are unique. Use a recursive backtracking or iterative generation approach to build all non-empty subset products, then sort the results. Discuss time and space complexity, noting that the number of products is 2^n - 1, so the solution is exponential in the worst case.
Pro tip: Mention that since the primes are distinct, there is no need to deduplicate products; this simplifies the implementation and avoids unnecessary overhead. Also, consider using a BFS-style generation to produce products in ascending order without a final sort, which could be more efficient if the primes are sorted.
Confirm that the array contains distinct primes, the array size, and whether the output should include 1 (it should not, as subsets must be non-empty). Discuss handling of empty input.
Decide between recursive backtracking, iterative bitmask, or BFS generation. Explain that since all products are distinct, any method works, but BFS can yield sorted order if primes are sorted.
Write code to generate all subset products. For example, start with an empty list, and for each prime, add new products by multiplying the prime with existing products and the prime itself.
If not already sorted, sort the list of products in ascending order. Return the sorted list.
State that time complexity is O(2^n) for generation and O(2^n log 2^n) for sorting, which is optimal since output size is exponential. Space complexity is O(2^n) for storing results.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.