Enumerate Distinct Subsets with Repeated Input Values

### Problem Return all distinct subsets of the integer entries in `nums`, which may contain repeated values. Each subset may use a value no more times than it occurs in the input. Include the empty subset, but do not return the same value-multiset more than once. The collection may appear in any order. ```cpp vector<vector<int>> subsetsWithDup(vector<int>& nums); ``` Member presentation order does not create a different subset. ### Examples ```text Input: nums = [-1,-1,2] One valid output: [[],[-1],[-1,-1],[2],[-1,2],[-1,-1,2]] ``` ```text Input: nums = [3,3] One valid output: [[3,3],[],[3]] ``` ### Constraints & Assumptions - `1 <= nums.length <= 10`. - Every entry lies between -10 and 10, inclusive. - Repeated input values are allowed and their available multiplicities matter. ### Clarifying Questions to Ask - May a subset contain two equal values? Yes, if the input contains at least two copies. - Do choosing different occurrences of the same values create different subsets? No. ```hint Keep multiplicity separate from duplication Two copies of one value may belong in a valid subset, while two returned subsets with the same member multiplicities are duplicates. ``` ### What a Strong Answer Covers - Complete enumeration with the correct multiplicities and no repeated subsets. - Inclusion of both empty and full value-multisets. - A duplicate-avoidance argument and output-sensitive complexity. ### Follow-up Questions - How does an all-equal input change the number of distinct subsets? - How should a judge compare collections whose subset or member orders differ?