# Find all distinct subsets of a given set using BitMasking Approach

• Difficulty Level : Hard
• Last Updated : 28 Sep, 2022

Given an array of integers arr[], The task is to find all its subsets. The subset can not 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

Input:  S = {1, 2}
Output:  {}, {1}, {2}, {1, 2}
Explanation: The total subsets of given set are – {}, {1}, {2}, {1, 2}

Recommended Practice

Prerequisite: Power Set

Approach: Below is the idea to solve the problem:

The idea is to use a bit-mask pattern to generate all the combinations as discussed in post. To avoid printing duplicate subsets construct a string out of given subset such that subsets having similar elements will result in same string. Maintain a list of such unique strings and finally decode all such string to print its individual elements.

Illustration :

S = {1, 2, 2}

The binary digits from 0 to 7 are

0 –> 000    –> number formed with no setbits                              –> { }
1 –> 001    –> number formed with setbit at position 0                –> { 1 }
2 –> 010    –> number formed with setbit at position 1                –> { 2 }
3 –> 011    –> number formed with setbit at position 0  and 1     –> { 1 , 2 }
4 –> 100    –> number formed with setbit at position 2                –>  { 2 }
5 –> 101    –> number formed with setbit at position 0 and 2      –> { 1 , 2}
6 –> 110    –> number formed with setbit at position 1 and 2      –> { 2 , 2}
7 –> 111    –> number formed with setbit at position 0 , 1 and 2  –> {1 , 2 , 2}

After removing duplicates final result will be { }, { 1 }, { 2 }, { 1 , 2 }, { 2 , 2 }, { 1 , 2 , 2}

Note: This method will only work on sorted arrays.

Follow the below steps to Implement the idea:

• Initialize a variable pow_set_size as 2 raise to size of array and a vector of vector ans to store all subsets.
• Iterate over all bitmasks from 0 to pow_set_size  – 1.
• For every bitmask include the elements of array of indices where bits are set into a subset vector.
• If this subset doesn’t already exist then push the subset in the ans vector.
• Return ans.

Below is the implementation of the above approach:

## 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 Codeif __name__ == '__main__':    arr = [10, 12, 12]    n = len(arr)    printPowerSet(arr, n) # This code is contributed by vibhu4agarwal

## Javascript

 

Output

10
12
10 12
12 12
10 12 12 

Time Complexity: O(N*2N)
Auxiliary Space: O(N*N)

Analysis:

If is the total number of steps in the code, then the loop to generate all binary combinations runs till, and then the inner loop run till log(i).
Hence, , Raising to the power of two on both sides Using log on both sides and applying Sterling’s approximation, Hence the time complexity is ## Find all distinct subsets of a given set using BitMasking Approach using Backtracking

Refer to the article https://www.geeksforgeeks.org/backtracking-to-find-all-subsets/ to solve the problem using the backtracking approach.

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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