# Bitwise XOR of all unordered pairs from a given array

Given an array arr[] of size N, the task is to find the bitwise XOR of all possible unordered pairs of the given array.

Examples:

Input: arr[] = {1, 5, 3, 7}
Output: 0
Explanation:
All possible unordered pairs are (1, 5), (1, 3), (1, 7), (5, 3), (5, 7), (3, 7)
Bitwise XOR of all possible pairs are = 1 ^ 5 ^ 1 ^3 ^ 1 ^ 7 ^ 5 ^ 3 ^ 5^ 7 ^ 3 ^ 7 = 0
Therefore, the required output is 0.

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

Naive approach: The idea is to traverse the array and generate all possible pairs of the given array. Finally, print the Bitwise XOR of each element present in these pairs of the given array. Follow the steps below to solve the problem:

• Initialize a variable, say totalXOR, to store Bitwise XOR of each element from these pairs.
• Traverse the given array and generate all possible pairs(arr[i], arr[j]) from the given array.
• For each pair (arr[i], arr[j]), update the value of totalXOR = (totalXOR ^ arr[i] ^ arr[j]).
• Finally, print the value of totalXOR.

Below is the implementation of the above approach:

## C++

 `// C++ program to implement` `// the above approach`   `#include ` `using` `namespace` `std;`   `// Function to get bitwise XOR` `// of all possible pairs of` `// the given array` `int` `TotalXorPair(``int` `arr[], ``int` `N)` `{` `    ``// Stores bitwise XOR` `    ``// of all possible pairs` `    ``int` `totalXOR = 0;`   `    ``// Generate all possible pairs` `    ``// and calculate bitwise XOR` `    ``// of all possible pairs` `    ``for` `(``int` `i = 0; i < N; i++) {` `        ``for` `(``int` `j = i + 1; j < N;` `             ``j++) {`   `            ``// Calculate bitwise XOR` `            ``// of each pair` `            ``totalXOR ^= arr[i]` `                        ``^ arr[j];` `        ``}` `    ``}` `    ``return` `totalXOR;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { 1, 2, 3, 4 };` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``cout << TotalXorPair(arr, N);` `}`

## Java

 `// Java program to implement ` `// the above approach ` `class` `GFG{` `  `  `// Function to get bitwise XOR ` `// of all possible pairs of ` `// the given array ` `public` `static` `int` `TotalXorPair(``int` `arr[], ` `                               ``int` `N) ` `{ ` `  ``// Stores bitwise XOR ` `  ``// of all possible pairs ` `  ``int` `totalXOR = ``0``; `   `  ``// Generate all possible pairs ` `  ``// and calculate bitwise XOR ` `  ``// of all possible pairs ` `  ``for` `(``int` `i = ``0``; i < N; i++) ` `  ``{ ` `    ``for` `(``int` `j = i + ``1``; j < N; j++) ` `    ``{ ` `      ``// Calculate bitwise XOR ` `      ``// of each pair ` `      ``totalXOR ^= arr[i] ^ arr[j]; ` `    ``} ` `  ``} ` `  `  `  ``return` `totalXOR; ` `} `   `// Driver code    ` `public` `static` `void` `main(String[] args) ` `{` `  ``int` `arr[] = {``1``, ``2``, ``3``, ``4``}; ` `  ``int` `N = arr.length;` `  ``System.out.print(TotalXorPair(arr, N));` `}` `}`   `// This code is contributed by divyeshrabadiya07`

## C#

 `// C# program to implement ` `// the above approach ` `using` `System;`   `class` `GFG{` `  `  `// Function to get bitwise XOR ` `// of all possible pairs of ` `// the given array ` `public` `static` `int` `TotalXorPair(``int` `[]arr, ` `                               ``int` `N) ` `{ ` `  `  `  ``// Stores bitwise XOR ` `  ``// of all possible pairs ` `  ``int` `totalXOR = 0; `   `  ``// Generate all possible pairs ` `  ``// and calculate bitwise XOR ` `  ``// of all possible pairs ` `  ``for``(``int` `i = 0; i < N; i++) ` `  ``{ ` `    ``for``(``int` `j = i + 1; j < N; j++) ` `    ``{ ` `      `  `      ``// Calculate bitwise XOR ` `      ``// of each pair ` `      ``totalXOR ^= arr[i] ^ arr[j]; ` `    ``} ` `  ``} ` `  ``return` `totalXOR; ` `} `   `// Driver code    ` `public` `static` `void` `Main(String[] args) ` `{` `  ``int` `[]arr = {1, 2, 3, 4}; ` `  ``int` `N = arr.Length;` `  `  `  ``Console.Write(TotalXorPair(arr, N));` `}` `}`   `// This code is contributed by Princi Singh`

Output

```4

```

Time Complexity: O(N2)
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach, follow the observations below:

Property of Bitwise XOR:
a ^ a ^ a …….( Even times ) = 0
a ^ a ^ a …….( Odd times ) = a

Each element of the given array occurs exactly (N – 1) times in all possible pairs.
Therefore, if N is even, then Bitwise XOR of all possible pairs are equal to bitwise XOR of all the array elements.
Otherwise, bitwise XOR of all possible pairs are equal to 0.

Follow the steps below to solve the problem:

• If N is odd then print 0.
• If N is even then print the value of bitwise XOR of all the elements of the given array.

Below is the implementation of the above approach

## C++

 `// C++ program to implement` `// the above approach`   `#include ` `using` `namespace` `std;`   `// Function to get bitwise XOR` `// of all possible pairs of` `// the given array` `int` `TotalXorPair(``int` `arr[], ``int` `N)` `{` `    ``// Stores bitwise XOR` `    ``// of all possible pairs` `    ``int` `totalXOR = 0;`   `    ``// Check if N is odd` `    ``if` `(N % 2 != 0) {` `        ``return` `0;` `    ``}`   `    ``// If N is even then calculate` `    ``// bitwise XOR of all elements` `    ``// of the given array.` `    ``for` `(``int` `i = 0; i < N; i++) {` `        ``totalXOR ^= arr[i];` `    ``}` `    ``return` `totalXOR;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { 1, 2, 3, 4 };` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``cout << TotalXorPair(arr, N);` `}`

## Java

 `// Java program to implement ` `// the above approach ` `class` `GFG{` `  `  `// Function to get bitwise XOR ` `// of all possible pairs of ` `// the given array ` `public` `static` `int` `TotalXorPair(``int` `arr[], ` `                               ``int` `N) ` `{ ` `  ``// Stores bitwise XOR ` `  ``// of all possible pairs ` `  ``int` `totalXOR = ``0``; `   `  ``// Check if N is odd` `  ``if``( N % ``2` `!= ``0` `)` `  ``{` `    ``return` `0``;` `  ``}`   `  ``// If N is even then calculate` `  ``// bitwise XOR of all elements` `  ``// of the array` `  ``for``(``int` `i = ``0``; i < N; i++) ` `  ``{ ` `    ``totalXOR ^= arr[i]; ` `  ``} `   `  ``return` `totalXOR; ` `} `   `// Driver code    ` `public` `static` `void` `main(String[] args) ` `{` `  ``int` `arr[] = {``1``, ``2``, ``3``, ``4``}; ` `  ``int` `N = arr.length;` `  ``System.out.print(TotalXorPair(arr, N));` `}` `}`   `// This code is contributed by math_lover`

## Python3

 `# Python3 program to implement` `# the above appraoch`   `# Function to get bitwise XOR` `# of all possible pairs of` `# the given array ` `def` `TotalXorPair(arr, N):`   `    ``# Stores bitwise XOR` `    ``# of all possible pairs` `    ``totalXOR ``=` `0`   `    ``# Check if N is odd` `    ``if` `(N ``%` `2` `!``=` `0``):` `        ``return` `0`   `    ``# If N is even then calculate` `    ``# bitwise XOR of all elements` `    ``# of the given array.` `    ``for` `i ``in` `range``(N):` `        ``totalXOR ^``=` `arr[i]`   `    ``return` `totalXOR`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:`   `    ``arr ``=` `[ ``1``, ``2``, ``3``, ``4` `]` `    ``N ``=` `len``(arr)` `    `  `    ``print``(TotalXorPair(arr, N))`   `# This code is contributed by Shivam Singh`

## C#

 `// C# program to implement ` `// the above approach ` `using` `System;`   `class` `GFG{` `  `  `// Function to get bitwise XOR ` `// of all possible pairs of ` `// the given array ` `static` `int` `TotalXorPair(``int` `[]arr, ` `                        ``int` `N) ` `{ ` `    `  `    ``// Stores bitwise XOR ` `    ``// of all possible pairs ` `    ``int` `totalXOR = 0; ` `    `  `    ``// Check if N is odd` `    ``if` `(N % 2 != 0)` `    ``{` `        ``return` `0;` `    ``}` `    `  `    ``// If N is even then calculate` `    ``// bitwise XOR of all elements` `    ``// of the array` `    ``for``(``int` `i = 0; i < N; i++) ` `    ``{ ` `        ``totalXOR ^= arr[i]; ` `    ``} ` `    ``return` `totalXOR; ` `} `   `// Driver code    ` `public` `static` `void` `Main(String[] args) ` `{` `    ``int` `[]arr = { 1, 2, 3, 4 }; ` `    ``int` `N = arr.Length;` `    `  `    ``Console.Write(TotalXorPair(arr, N));` `}` `}`   `// This code is contributed by doreamon_`

Output

```4

```

Time Complexity: O(N)
Auxiliary Space: O(1)

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