My first instinct was to just slap a set on the output from the plain subsets solution and call it done.
Start by clarifying the problem and constraints, then propose a backtracking solution that sorts the array and skips duplicates at each recursion level to avoid generating duplicate subsets. Analyze the time and space complexity, and discuss potential optimizations or alternative approaches.
Pro tip: Demonstrate awareness of the trade-offs between sorting and using a hash set for deduplication, and mention how the solution scales with input size. Also, proactively discuss edge cases like empty array and all duplicates.
Ask about input size, range of integers, and whether the output order matters. Confirm that subsets are combinations, not permutations, and that duplicates in the input can lead to duplicate subsets if not handled.
Explain that you will sort the array to bring duplicates together, then use a recursive backtracking function that builds subsets incrementally. At each step, skip over duplicate elements to avoid generating the same subset multiple times.
Describe the recursion: start with an empty subset, iterate through the array from a given index, and for each element, include it and recurse. To skip duplicates, if the current element equals the previous and the previous was not included in the current path, skip it. Alternatively, use a set to track seen elements at each recursion level.
State that the time complexity is O(2^n) in the worst case (when all elements are unique), but with duplicates it's bounded by the number of unique subsets. Space complexity is O(n) for recursion depth plus O(2^n) for output. Discuss edge cases: empty array, all elements identical, and large n.
Mention that sorting is O(n log n) and enables efficient duplicate skipping. Alternatively, use a hash set to avoid sorting, but that may increase space. Also, consider iterative solution using bit manipulation for unique elements, but backtracking is more straightforward for duplicates.
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