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Find all distinct subsets of a given set using BitMasking Approach

  • Difficulty Level : Hard
  • Last Updated : 23 Aug, 2021

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

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 <bits/stdc++.h>
using namespace std;
 
// Utility function to split the string using a delim. Refer -
vector<string> split(const string &s, char delim)
{
    vector<string> 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<string> 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<string>, 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<string> 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[0]);
 
    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<string>, 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 

Time Complexity of this approach is: (N*2N).

Refer to the below article to solve the problem using the backtracking approach.



https://www.geeksforgeeks.org/backtracking-to-find-all-subsets/

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.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

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