I went straight to recursion, which worked fine for the basic case.
Start by explaining the Cartesian product and its exponential growth, then discuss memory-efficient approaches like lazy generation or streaming. Emphasize trade-offs between time, memory, and randomness, and how to adapt based on constraints.
Pro tip: Mention that for NFT generation, you often need random sampling without replacement, so you can use combinatorial number system to map indices to combinations, avoiding full enumeration. This shows practical insight beyond textbook algorithms.
Ask about the expected number of categories and values, memory limits, and whether all combinations need to be generated or just a random subset. This determines the approach.
Describe how the total combinations = product of category sizes, which can be astronomically large. Mention that storing all in memory is infeasible for large sets.
Discuss lazy evaluation (generators), streaming, or iterative approaches that produce combinations on-the-fly without storing all. For random access, use combinatorial number system to map an index to a combination.
If only a subset is needed, explain how to randomly sample indices without replacement and convert to combinations, ensuring no duplicates. Mention reservoir sampling or hash-based approaches if needed.
Compare time vs. memory, and when to use distributed processing or external storage. Highlight that the choice depends on whether you need all combinations or just a sample.
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