# Print all distinct even and odd prefix Bitwise XORs of first N natural numbers

Given a positive integer N, the task is to print all the distinct even and odd values of prefix Bitwise XORs of first N natural numbers.

Examples:

Input: N = 6
Output:
Even: 0 4
Odd: 1 3 7
Explanation:
The prefix Bitwise XOR of the first 6 natural number si {1, 3, 0, 4, 1, 7}.
Even prefix Bitwise XORs are 0, 4.
Odd prefix Bitwise XORs are 1, 3, 7.

Input: N = 9
Output:
Even: 0 4 8
Odd: 1 3 7

Approach: The given problem can be solved based on the below observations:

• If the value of N modulo 4 is 0, then the value of Bitwise XOR of the first N natural numbers is N.
• If the value of N modulo 4 is 1, then the value of Bitwise XOR of the first N natural numbers is 1.
• If the value of N modulo 4 is 2, then the value of Bitwise XOR of the first N natural numbers is (N + 1).
• If the value of N modulo 4 is 3, then the value of Bitwise XOR of the first N natural numbers is 0.

Therefore, from the above principle, it can be said that Bitwise XOR as even numbers will always come as 0 or multiples of 4, and Bitwise XOR as odd numbers will always come as 1 or 1 less than multiples of 4.

Below is the implementation of the above approach.

## C++

 `// C++ program for the above approach`   `#include ` `using` `namespace` `std;`   `// Print all distinct even & odd` `// prefix Bitwise XORs from 1 to N` `void` `evenOddBitwiseXOR(``int` `N)` `{`   `    ``cout << ``"Even: "` `<< 0 << ``" "``;`   `    ``// Print the even number` `    ``for` `(``int` `i = 4; i <= N; i = i + 4) {` `        ``cout << i << ``" "``;` `    ``}`   `    ``cout << ``"\n"``;`   `    ``cout << ``"Odd: "` `<< 1 << ``" "``;`   `    ``// Print the odd number` `    ``for` `(``int` `i = 4; i <= N; i = i + 4) {` `        ``cout << i - 1 << ``" "``;` `    ``}`   `    ``if` `(N % 4 == 2)` `        ``cout << N + 1;` `    ``else` `if` `(N % 4 == 3)` `        ``cout << N;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `N = 6;` `    ``evenOddBitwiseXOR(N);`   `    ``return` `0;` `}`

## Java

 `// Java approach for the above approach` `class` `GFG{`   `// Print all distinct even & odd` `// prefix Bitwise XORs from 1 to N` `static` `void` `evenOddBitwiseXOR(``int` `N)` `{` `    ``System.out.print(``"Even: "` `+ ``0` `+ ``" "``);`   `    ``// Print the even number` `    ``for``(``int` `i = ``4``; i <= N; i = i + ``4``) ` `    ``{` `        ``System.out.print(i + ``" "``);` `    ``}`   `    ``System.out.print(``"\n"``);`   `    ``System.out.print(``"Odd: "` `+ ``1` `+ ``" "``);`   `    ``// Print the odd number` `    ``for``(``int` `i = ``4``; i <= N; i = i + ``4``)` `    ``{` `        ``System.out.print(i - ``1` `+ ``" "``);` `    ``}`   `    ``if` `(N % ``4` `== ``2``)` `        ``System.out.print(N + ``1``);` `    ``else` `if` `(N % ``4` `== ``3``)` `        ``System.out.print(N);` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `N = ``6``;` `    ``evenOddBitwiseXOR(N);` `}` `}`   `// This code is contributed by abhinavjain194`

## Python3

 `# Python3 program for the above approach`   `# Print all distinct even & odd` `# prefix Bitwise XORs from 1 to N` `def` `evenOddBitwiseXOR(N):` `    `  `    ``print``(``"Even: "``, ``0``, end ``=` `" "``)`   `    ``# Print the even number` `    ``for` `i ``in` `range``(``4``, N ``+` `1``, ``4``):` `        ``print``(i, end ``=` `" "``)` `        `  `    ``print``()`   `    ``print``(``"Odd: "``, ``1``, end ``=` `" "``)`   `    ``# Print the odd number` `    ``for` `i ``in` `range``(``4``, N ``+` `1``, ``4``):` `        ``print``(i ``-` `1``, end ``=` `" "``)` `    `  `    ``if` `(N ``%` `4` `=``=` `2``):` `        ``print``(N ``+` `1``)` `    ``elif` `(N ``%` `4` `=``=` `3``):` `        ``print``(N)`   `# Driver Code` `N ``=` `6`   `evenOddBitwiseXOR(N)`   `# This code is contributed by sanjoy_62`

## C#

 `// C# program for the above approach` `using` `System;`   `class` `GFG{` `    `  `// Print all distinct even & odd` `// prefix Bitwise XORs from 1 to N` `static` `void` `evenOddBitwiseXOR(``int` `N)` `{` `    ``Console.Write(``"Even: "` `+ 0 + ``" "``);` ` `  `    ``// Print the even number` `    ``for``(``int` `i = 4; i <= N; i = i + 4)` `    ``{` `        ``Console.Write(i + ``" "``);` `    ``}` ` `  `   ``Console.Write(``"\n"``);` ` `  `    ``Console.Write(``"Odd: "` `+ 1 + ``" "``);` ` `  `    ``// Print the odd number` `    ``for``(``int` `i = 4; i <= N; i = i + 4)` `    ``{` `        ``Console.Write(i - 1 + ``" "``);` `    ``}` ` `  `    ``if` `(N % 4 == 2)` `        ``Console.Write(N + 1);` `    ``else` `if` `(N % 4 == 3)` `        ``Console.Write(N);` `}`   `// Driver code` `public` `static` `void` `Main()` `{` `    ``int` `N = 6;` `    ``evenOddBitwiseXOR(N);` `}` `}`   `// This code is contributed by splevel62`

## Javascript

 ``

Output:

```Even: 0 4
Odd: 1 3 7```

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

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