# 90 Subsets II

Given a collection of integers that might contain duplicates, **nums**, return all possible subsets.

**Note:**The solution set must not contain duplicate subsets.

For example,\
If **nums** =`[1,2,2]`, a solution is:

```
[
  [2],
  [1],
  [1,2,2],
  [2,2],
  [1,2],
  []
]
```

**The Idea:** Implement the power set recursive formula, with the added benefit of ignoring duplicates. Duplicates can be used if we first sort the vector, and then append to an `unordered_set`. Sorting the vector essentially renders the ordering the vector obsolete, and the `unordered_set`avoids direct duplication.

The powerset begins with the empty set, and the build across each set by appending a character to end of each set.

```
case 1: {}                         = P(0) (empty set);      2^0 = 1
case 2: {}, {a}                    = P('a');                2^1 = 2
case n: {}, {a}, {b}, {ab}         = P('ab');               2^2 = 4

' '
' ' a 
' ' a b ab 
' ' a b ab c ac bc abc 
' ' a b ab c ac bc abc d ad bd abd cd acd bcd abcd
```

**Complexity:** O(n^2) time and space

```cpp
struct VectorHash {
    size_t operator()(const std::vector<int>& v) const {
        std::hash<int> hasher;
        size_t seed = 0;
        for (int i : v) {
            seed ^= hasher(i) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
        }
        return seed;
    }
};

vector<vector<int>> subsetsWithDup(vector<int> &nums) {
    sort(nums.begin(), nums.end());
    unordered_set<vector<int>, VectorHash> unique_set;
    unique_set.reserve(1 << nums.size()); // pow(2, nums.size())
    unique_set.insert(vector<int>());

    for (int i = 1; i <= nums.size(); i++) {
        int cur_size = unique_set.size();

        unordered_set<vector<int>, VectorHash> unique_set_cp = unique_set;
        for (auto &v : unique_set_cp) {
            vector<int> next = v;
            next.push_back(nums.at(i - 1));
            unique_set.insert(next);
        }
    }

    vector<vector<int>> unique_subsets;
    unique_subsets.reserve(1 << nums.size());

    for (auto &v : unique_set)
        unique_subsets.push_back(v);

    return unique_subsets;
}
```

**Testing**

```cpp
int main()
{
    //vector<int> t1 = { 1,2,2 };
    //print2d(subsetsWithDup(t1));

    //vector<int> t2 = { 1,2,3 };
    //print2d(subsetsWithDup(t2));

    vector<int> t3 = { 4, 4, 4, 1, 4 };
    print2d(subsetsWithDup(t3));
}
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://maksimdan.gitbook.io/interview-practice-problems/leetcode_sessions/90-subsets-ii.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.