# Sum of XOR of sum of all pairs in an array

Given an array, find the XOR of sum of all pairs in an array.

Examples:

```Input  : arr[] = {1, 2, 3}
Output : 0
(1 + 1) ^ (1 + 2) ^ (1 + 3) ^ (2 + 1) ^ (2 + 2) ^
(2 + 3) ^ (3 + 1) ^ (3 + 2) ^ (3 + 3) = 0

Input  : arr[] = {1, 2, 3, 4}
Output : 8```

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

A naive approach is to consider all the pairs one by one, calculate their XOR one after the other.

## C++

 `// CPP program to find XOR of pair ` `// sums. ` `#include ` ` `  `using` `namespace` `std; ` ` `  `int` `xorPairSum(``int` `ar[], ``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `        ``for` `(``int` `j = 0; j < n; j++)  ` `            ``sum = sum ^ (ar[i] + ar[j]); ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3 }; ` `    ``int` `n = ``sizeof``(arr)/``sizeof``(arr[0]); ` `    ``cout << xorPairSum(arr, n); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find XOR of pair sums. ` `import` `java.io.*; ` `  `  `class` `GFG { ` ` `  `// method to find XOR of pair sums ` `static` `int` `xorPairSum(``int` `ar[], ``int` `n) ` `{ ` `    ``int` `sum = ``0``; ` `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `        ``for` `(``int` `j = ``0``; j < n; j++)  ` `            ``sum = sum ^ (ar[i] + ar[j]); ` `    ``return` `sum; ` `} ` `  `  `    ``// Driver code ` `    ``public` `static` `void` `main (String[] args)  ` `    ``{ ` `        ``int` `arr[] = {``1``, ``2``, ``3``}; ` `        ``int` `n = arr.length; ` `        ``System.out.print( xorPairSum(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by chandan_jnu. `

## Python3

 `# Python program to find  ` `# XOR of pair sums. ` ` `  `def` `xor_pair_sum(ar, n): ` `    ``total ``=` `0` `    ``for` `i ``in` `range``(n): ` `        ``for` `j ``in` `range``(n): ` `            ``total ``=` `total ^ (ar[i] ``+` `ar[j]) ` ` `  `    ``return` `total ` ` `  ` `  `# Driver program to test the above function ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``data ``=` `[``1``, ``2``, ``3``] ` `    ``print``(xor_pair_sum(data, ``len``(data))) ` ` `  `# This code is contributed ` `# by Kanav Malhotra `

## C#

 `// C# program to find ` `// XOR of pair sums. ` `using` `System; ` ` `  `class` `GFG ` `{  ` `static` `int` `xorPairSum(``int` `[]ar,  ` `                    ``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `        ``for` `(``int` `j = 0; j < n; j++)  ` `            ``sum = sum ^ (ar[i] + ar[j]); ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `static` `public` `void` `Main(String []args) ` `{ ` `    ``int` `[]arr = { 1, 2, 3 }; ` `    ``int` `n = arr.Length; ` `    ``Console.WriteLine(xorPairSum(arr, n)); ` `} ` `} ` ` `  `// This code is contributed ` `// by Arnab Kundu `

## PHP

 ` `

Output:

```0
```

Time Complexity : O(N2)

An efficient solution is based on XOR properties. We simply calculate the XOR of every element and then just multiply it by two.

## C++

 `// CPP program to find XOR of pair ` `// sums. ` `#include ` ` `  `using` `namespace` `std; ` ` `  `int` `xorPairSum(``int` `ar[], ``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `       ``sum = sum ^ ar[i]; ` `    ``return` `2*sum; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3 }; ` `    ``int` `n = ``sizeof``(arr)/``sizeof``(arr[0]); ` `    ``cout << xorPairSum(arr, n); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find  ` `// XOR of pair sums. ` `class` `GFG ` `{  ` `     `  `static` `int` `xorPairSum(``int` `ar[], ` `                      ``int` `n) ` `{ ` `    ``int` `sum = ``0``; ` `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``sum = sum ^ ar[i]; ` `    ``return` `2` `* sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `arr[] = { ``1``, ``2``, ``3` `}; ` `    ``int` `n = arr.length; ` `    ``System.out.println( xorPairSum(arr, n)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by Arnab Kundu `

## Python3

 `# Python3 program to find  ` `# XOR of pair sums. ` ` `  `def` `xor_pair_sum(ar, n): ` `    ``total ``=` `0` `    ``for` `i ``in` `range``(n): ` `        ``total ``=` `total ^ ar[i] ` ` `  `    ``return` `2` `*` `total ` ` `  ` `  `# Driver program to test the above function ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``data ``=` `[``1``, ``2``, ``3``] ` `    ``print``(xor_pair_sum(data, ``len``(data))) ` ` `  `# This code is contributed ` `# by Kanav Malhotra `

## C#

 `// C# program to find  ` `// XOR of pair sums. ` `using` `System; ` ` `  `class` `GFG ` `{  ` `     `  `static` `int` `xorPairSum(``int` `[]ar,  ` `                    ``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `    ``sum = sum ^ ar[i]; ` `    ``return` `2 * sum; ` `} ` ` `  `// Driver code ` `static` `public` `void` `Main(String []args) ` `{ ` `    ``int` `[]arr = { 1, 2, 3 }; ` `    ``int` `n = arr.Length; ` `    ``Console.WriteLine( xorPairSum(arr, n)); ` `} ` `} ` ` `  `// This code is contributed ` `// by Arnab Kundu `

## PHP

 ` `

Output:

```0
```

Time Complexity : O(N)

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