My first instinct was itertools.product and call it a day, but they wanted an actual implementation.
Clarify the problem constraints and edge cases, then present both recursive and iterative solutions. Explain the recursive backtracking approach and the iterative BFS using a queue, analyzing time and space complexity. Discuss trade-offs and potential optimizations.
Pro tip: Mention that the iterative BFS approach naturally handles large outputs without recursion depth limits, and that you can optimize by precomputing the Cartesian product size to allocate memory efficiently.
Ask about input size, key order, duplicate keys, empty values, and whether the query keys are guaranteed to exist. Confirm output format.
Describe a backtracking function that builds combinations by iterating over values for the current key and recursing to the next key. Base case: when all keys processed, add the current combination to results.
Use a queue (BFS) to build combinations level by level: start with an empty combination, for each key, dequeue each partial combination and enqueue extended combinations with each value. After processing all keys, the queue contains the final combinations.
Time complexity is O(N * M) where N is the number of combinations and M is the number of keys (or total output size). Space complexity is O(N * M) for storing results. Recursive uses call stack; iterative uses queue. Discuss which is better for large inputs.
Mention precomputing total combinations to reserve space, handling missing keys gracefully, and potential parallelization or lazy evaluation if not all combinations are needed.
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