# 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 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Refer this Post for Count Set Bit
Naive Approach, we can produce all subset using Power Set then calculate Bit-wise AND sum of all subset.

A Better approach, we are trying to calculate which array element is responsible in producing the sum into 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 contain a 0 will not give any contribution. All nonempty subset 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. 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 ` `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); ` `    ``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

 ` `

Output:

```9
```

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