Open In App

We use cookies to ensure you have the best browsing experience on our website. By using our site, you acknowledge that you have read and understood our Cookie Policy & Privacy Policy

Sum of bitwise AND of all possible subsets of given set

Given an array, we need to calculate the Sum of Bit-wise AND of all possible subsets of the given array.

Examples:  



Input : 1 2 3
Output : 9
For [1, 2, 3], all possible subsets are {1}, 
{2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}
Bitwise AND of these subsets are, 1 + 2 + 
3 + 0 + 1 + 2 + 0 = 9.
So, the answer would be 9.

Input : 1 2 3 4
Output : 13

Refer to this Post for Count Set Bit 

Naive Approach, we can produce all subsets using Power Set then calculate Bit-wise AND sum of all subsets.



In a Better approach, we are trying to calculate which array element is responsible for producing the sum into a subset. 

Let’s start with the least significant bit. To remove the contribution from other bits, we calculate number AND bit for all numbers in the set. Any subset of this that contains a 0 will not give any contribution. All nonempty subsets that only consist of 1’s will give 1 in contribution. In total there will be 2^n – 1 such subset each giving 1 in contribution. The same goes for the other bit. We get [0, 2, 2], 3 subset each giving 2. Total 3*1 + 3*2 = 9 

Array = {1, 2, 3}
Binary representation
positions       2 1 0    
        1       0 0 1
        2       0 1 0
        3       0 1 1
              [ 0 2 2 ]
Count set bit for each position
[ 0 3 3 ] subset produced by each 
position 2^n -1 i.e. n is total sum 
for each position [ 0, 3*2^1, 3*2^0 ] 
Now calculate the sum by multiplying 
the position value i.e 2^0, 2^1 ... . 
 0 + 6 + 3 = 9

Implementation:




// C++ program to calculate sum of Bit-wise
// and sum of all subsets of an array
#include <bits/stdc++.h>
using namespace std;
 
#define BITS 32
 
int andSum(int arr[], int n)
{
    int ans = 0;
 
    // assuming representation of each element is
    // in 32 bit
    for (int i = 0; i < BITS; i++) {
        int countSetBits = 0;
 
        // iterating array element
        for (int j = 0; j < n; j++) {
 
            // Counting the set bit of array in
            // ith position
            if (arr[j] & (1 << i))
                countSetBits++;
        }
 
        // counting subset which produce sum when
        // particular bit position is set.
        int subset = (1 << countSetBits) - 1;
 
        // multiplying every position subset with 2^i
        // to count the sum.
        subset = (subset * (1 << i));
 
        ans += subset;
    }
 
    return ans;
}
 
// Drivers code
int main()
{
    int arr[] = { 1, 2, 3};
    int size = sizeof(arr) / sizeof(arr[0]);
    cout << andSum(arr, size);
 
    return 0;
}
 





                        























                                    



                                    




                                    




                                    


                                



















// Java program to calculate sum of Bit-wise 


// and sum of all subsets of an array



class GFG {




     



    static final int BITS = 32;




     



    static int andSum(int arr[], int n)




    {




        int ans = 0;




     



        // assuming representation of each




        // element is in 32 bit




        for (int i = 0; i < BITS; i++) {




            int countSetBits = 0;




     



            // iterating array element




            for (int j = 0; j < n; j++) {




     



                // Counting the set bit of




                // array in ith position




                if ((arr[j] & (1 << i)) != 0)




                    countSetBits++;




            }




     



            // counting subset which produce




            // sum when particular bit 




            // position is set.




            int subset = (1 << countSetBits) - 1;




     



            // multiplying every position 




            // subset with 2^i to count the




            // sum.




            subset = (subset * (1 << i));




     



            ans += subset;




        }




     



        return ans;




    }




     



    // Drivers code




    public static void main(String args[])




    {




        int arr[] = { 1, 2, 3};




        int size = 3;




        System.out.println (andSum(arr, size));




     



    }



}


 


// This code is contributed by Arnab Kundu.


















                        






                        























                                    



                                    




                                    




                                    


                                



















# Python3 program to calculate sum of


# Bit-wise and sum of all subsets of


# an array


 



BITS = 32;



 



def andSum(arr, n):




    ans = 0




     



    # assuming representation 




    # of each element is




    # in 32 bit




    for i in range(0, BITS):




        countSetBits = 0



 



        # iterating array element




        for j in range(0, n) :




             



            # Counting the set bit 




            # of array in ith




            # position




            if (arr[j] & (1 << i)) :




                countSetBits = (countSetBits




                                       + 1)



 



        # counting subset which 




        # produce sum when 




        # particular bit position




        # is set.




        subset = ((1 << countSetBits) 




                                 - 1)



 



        # multiplying every position 




        # subset with 2^i to count 




        # the sum.




        subset = (subset * (1 << i))



 



        ans = ans + subset



 



    return ans



 


# Driver code



arr = [1, 2, 3]




size = len(arr)




print (andSum(arr, size))




     


# This code is contributed by 


# Manish Shaw (manishshaw1)


















                        






                        























                                    



                                    




                                    




                                    


                                



















// C# program to calculate sum of Bit-wise 


// and sum of all subsets of an array



using System;



 



class GFG {




     



static int BITS = 32;



 



    static int andSum(int[] arr, int n)




    {




        int ans = 0;




     



        // assuming representation of each




        // element is in 32 bit




        for (int i = 0; i < BITS; i++) {




            int countSetBits = 0;




     



            // iterating array element




            for (int j = 0; j < n; j++) {




     



                // Counting the set bit of




                // array in ith position




                if ((arr[j] & (1 << i)) != 0)




                    countSetBits++;




            }




     



            // counting subset which produce




            // sum when particular bit position




            // is set.




            int subset = (1 << countSetBits) - 1;




     



            // multiplying every position subset




            // with 2^i to count the sum.




            subset = (subset * (1 << i));




     



            ans += subset;




        }




     



        return ans;




    }




     



    // Drivers code




    static public void Main()




    {




        int []arr = { 1, 2, 3};




        int size = 3;




        Console.WriteLine (andSum(arr, size));




     



    }



}


 


// This code is contributed by Arnab Kundu.


















                        






                        























                                    



                                    




                                    




                                    


                                



















<?php


// PHP program to calculate sum of Bit-wise 


// and sum of all subsets of an array


 



$BITS = 32;



 



function andSum( $arr, $n)



{



    global $BITS;




    $ans = 0;



 



    // assuming representation 




    // of each element is




    // in 32 bit




    for($i = 0; $i < $BITS; $i++)




    {




        $countSetBits = 0;



 



        // iterating array element




        for ( $j = 0; $j < $n; $j++) {



 



            // Counting the set bit 




            // of array in ith position




            if ($arr[$j] & (1 << $i))




                $countSetBits++;




        }



 



        // counting subset which 




        // produce sum when 




        // particular bit position




        // is set.




        $subset = (1 << $countSetBits) - 1;



 



        // multiplying every position 




        // subset with 2^i to count 




        // the sum.




        $subset = ($subset * (1 << $i));



 



        $ans += $subset;




    }



 



    return $ans;



}


 



    // Driver code




    $arr = array(1, 2, 3);




    $size = count($arr);




    echo andSum($arr, $size);




     


// This code is contributed by anuj_67.


?>


















                        






                        























                                    



                                    




                                    




                                    


                                



















<script>


// javascript program to calculate sum of Bit-wise 


// and sum of all subsets of an array    



var BITS = 32;



 



    function andSum(arr , n) {




        var ans = 0;



 



        // assuming representation of each




        // element is in 32 bit




        for (i = 0; i < BITS; i++) {




            var countSetBits = 0;



 



            // iterating array element




            for (j = 0; j < n; j++) {



 



                // Counting the set bit of




                // array in ith position




                if ((arr[j] & (1 << i)) != 0)




                    countSetBits++;




            }



 



            // counting subset which produce




            // sum when particular bit




            // position is set.




            var subset = (1 << countSetBits) - 1;



 



            // multiplying every position




            // subset with 2^i to count the




            // sum.




            subset = (subset * (1 << i));



 



            ans += subset;




        }



 



        return ans;




    }



 



    // Drivers code




     



        var arr = [ 1, 2, 3 ];




        var size = 3;




        document.write(andSum(arr, size));



 


// This code contributed by gauravrajput1 


</script>


















                        






                        








Output

9


Complexity Analysis:


	

        Article Tags : 
        

            Bit Magic
DSA        


		
	

	


      

      

          
Recommended Articles

      

      

          
          
1. Sum of bitwise OR of all possible subsets of given set

          
2. Bitwise OR of Bitwise AND of all subsets of an Array for Q queries

          
3. Minimum possible Bitwise OR of all Bitwise AND of pairs generated from two given arrays

          
4. Find all possible pairs with given Bitwise OR and Bitwise XOR values

          
5. Calculate Bitwise OR of two integers from their given Bitwise AND and Bitwise XOR values

          
6. Maximize sum of squares of array elements possible by replacing pairs with their Bitwise AND and Bitwise OR

          
7. Sum of Bitwise AND of sum of pairs and their Bitwise AND from a given array

          
8. Bitwise OR of bitwise AND of all possible non-empty subarrays after Q query updates

          
9. Sum of subsets of all the subsets of an array | O(3^N)

          
10. Sum of subsets of all the subsets of an array | O(2^N)

          
11. Sum of subsets of all the subsets of an array | O(N)

          
12. Total pairs in an array such that the bitwise AND, bitwise OR and bitwise XOR of LSB is 1

          
13. Maximize count of pairs whose Bitwise AND exceeds Bitwise XOR by replacing such pairs with their Bitwise AND

          
14. Divide array in two Subsets such that sum of square of sum of both subsets is maximum

          
15. Count distinct possible Bitwise XOR values of subsets of an array

          
16. Sum of values of all possible non-empty subsets of the given array

          
17. Sum of products of all possible K size subsets of the given array

          
18. Maximum sum of Bitwise XOR of all elements of two equal length subsets

          
19. Sum of length of two smallest subsets possible from a given array with sum at least K

          
20. Split array into minimum number of subsets such that elements of all pairs are present in different subsets at least once

          
21. Find the triplet from given Bitwise XOR and Bitwise AND values of all its pairs

          
22. Find sum of difference of maximum and minimum over all possible subsets of size K

          
23. Bitwise XOR of Bitwise AND of all pairs from two given arrays

          
24. Maximize sum of LSBs of Bitwise OR of all possible N/2 pairs from given Array

          
25. Sum of the sums of all possible subsets