Skip to content
Related Articles

Related Articles

Improve Article
Sum of bitwise AND of all possible subsets of given set
  • Difficulty Level : Hard
  • Last Updated : 21 Apr, 2021

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

 

CPP




// 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



// 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



# 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#



// 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
// 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.
?>
Javascript



<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
 
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.
In case you wish to attend live classes with industry experts, please refer DSA Live Classes



My Personal Notes
arrow_drop_up
Previous
Sum of bitwise OR of all possible subsets of given set
Next

Remove characters from the first string which are present in the second string
Recommended Articles
Page :
Sum of bitwise OR of all possible subsets of given set
27, Apr 18
Maximum sum of Bitwise XOR of all elements of two equal length subsets
21, Aug 20
Count distinct possible Bitwise XOR values of subsets of an array
08, Mar 21
Partition array into two subsets with minimum Bitwise XOR between their maximum and minimum
20, Jan 21
Total pairs in an array such that the bitwise AND, bitwise OR and bitwise XOR of LSB is 1
07, May 19
Calculate Bitwise OR of two integers from their given Bitwise AND and Bitwise XOR values
02, Dec 20
Maximum number of subsets an array can be split into such that product of their minimums with size of subsets is at least K
21, Apr 21
Split array into minimum number of subsets such that elements of all pairs are present in different subsets at least once
04, Jan 21
Partition an array of non-negative integers into two subsets such that average of both the subsets is equal
11, Jul 19
Divide array in two Subsets such that sum of square of sum of both subsets is maximum
07, Feb 20
Maximize count of pairs whose Bitwise AND exceeds Bitwise XOR by replacing such pairs with their Bitwise AND
22, Feb 21
Leftover element after performing alternate Bitwise OR and Bitwise XOR operations on adjacent pairs
01, Apr 18
Split an array into subarrays with maximum Bitwise XOR of their respective Bitwise OR values
14, Jun 21
Maximize sum of squares of array elements possible by replacing pairs with their Bitwise AND and Bitwise OR
12, Oct 20
Count ways to generate pairs having Bitwise XOR and Bitwise AND equal to X and Y respectively
16, Sep 20
Find the triplet from given Bitwise XOR and Bitwise AND values of all its pairs
10, Dec 20
Count pairs from an array whose Bitwise OR is greater than Bitwise AND
08, Feb 21
Count pairs with bitwise XOR exceeding bitwise AND from a given array
04, Oct 20
Count pairs whose Bitwise AND exceeds Bitwise XOR from a given array
18, Mar 21
Minimum possible Bitwise OR of all Bitwise AND of pairs generated from two given arrays
17, Sep 20
Count pairs with odd Bitwise XOR that can be removed and replaced by their Bitwise OR
25, Mar 21
Count pairs with equal Bitwise AND and Bitwise OR value
29, Oct 20
Find all possible pairs with given Bitwise OR and Bitwise XOR values
31, May 21
Non-negative pairs with sum of Bitwise OR and Bitwise AND equal to N
09, Nov 20
Article Contributed By :
https://media.geeksforgeeks.org/auth/avatar.png
ram8603
@ram8603
Vote for difficulty
Current difficulty :
Hard





Improved By :
Article Tags :
Practice Tags :
Report Issue

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

Lightbox