Find all distinct subsets of a given set

Given a set of positive integers, find all its subsets. The set can contain duplicate elements, so any repeated subset should be considered only once in the output.

Examples:

Input:  S = {1, 2, 2}
Output:  {}, {1}, {2}, {1, 2}, {2, 2}, {1, 2, 2}

Explanation:
The total subsets of given set are -
{}, {1}, {2}, {2}, {1, 2}, {1, 2}, {2, 2}, {1, 2, 2}
Here {2} and {1, 2} are repeated twice so they are considered
only once in the output

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Prerequisite: Power Set

The idea is to use a bit-mask pattern to generate all the combinations as discussed in previous post. But previous post will print duplicate subsets if the elements are repeated in the given set. To handle duplicate elements, we construct a string out of given subset such that subsets having similar elements will result in same string. We maintain a list of such unique strings and finally we decode all such string to print its individual elements.

Below is its implementation –

C++

 // C++ program to find all subsets of given set. Any // repeated subset is considered only once in the output #include using namespace std;    // Utility function to split the string using a delim. Refer - // http://stackoverflow.com/questions/236129/split-a-string-in-c vector split(const string &s, char delim) {     vector elems;     stringstream ss(s);     string item;     while (getline(ss, item, delim))         elems.push_back(item);        return elems; }    // Function to find all subsets of given set. Any repeated // subset is considered only once in the output int printPowerSet(int arr[], int n) {     vector list;        /* Run counter i from 000..0 to 111..1*/     for (int i = 0; i < (int) pow(2, n); i++)     {         string subset = "";            // consider each element in the set         for (int j = 0; j < n; j++)         {             // Check if jth bit in the i is set. If the bit             // is set, we consider jth element from set             if ((i & (1 << j)) != 0)                 subset += to_string(arr[j]) + "|";         }            // if subset is encountered for the first time         // If we use set, we can directly insert         if (find(list.begin(), list.end(), subset) == list.end())             list.push_back(subset);     }        // consider every subset     for (string subset : list)     {         // split the subset and print its elements         vector arr = split(subset, '|');         for (string str: arr)             cout << str << " ";         cout << endl;     } }    // Driver code int main() {     int arr[] = { 10, 12, 12 };     int n = sizeof(arr)/sizeof(arr);        printPowerSet(arr, n);        return 0; }

Python3

 # Python3 program to find all subsets of  # given set. Any repeated subset is  # considered only once in the output def printPowerSet(arr, n):            # Function to find all subsets of given set.     # Any repeated subset is considered only      # once in the output     _list = []        # Run counter i from 000..0 to 111..1     for i in range(2**n):         subset = ""            # consider each element in the set         for j in range(n):                # Check if jth bit in the i is set.              # If the bit is set, we consider              # jth element from set             if (i & (1 << j)) != 0:                 subset += str(arr[j]) + "|"            # if subset is encountered for the first time         # If we use set, we can directly insert         if subset not in _list and len(subset) > 0:             _list.append(subset)        # consider every subset     for subset in _list:            # split the subset and print its elements         arr = subset.split('|')         for string in arr:             print(string, end = " ")         print()    # Driver Code if __name__ == '__main__':     arr = [10, 12, 12]     n = len(arr)     printPowerSet(arr, n)    # This code is contributed by vibhu4agarwal

Output:

10
12
10 12
12 12
10 12 12

This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.GeeksforGeeks.org or mail your article to contribute@GeeksforGeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Improved By : vibhu4agarwal