# Check if the XOR of an array of integers is Even or Odd

Given an array arr containing integers of size N, the task is to check if the XOR of this array is even or odd

Examples:

Input: arr[] = { 2, 4, 7}
Output: Odd
Explanation:
XOR of array = 2 ^ 4 ^ 7 = 1, which is odd

Input: arr[] = { 3, 9, 12, 13, 15 }
Output: Even

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

Naive Solution: First find the XOR of the given array of integers, and then check if this XOR is even or odd.

Time Complexity: O(N)

Efficient Solution: A better Solution is based on bit manipulation fact, that:

• Bitwise XOR of any two even or any two odd numbers is always even.
• Bitwise XOR of an even and an odd number is always odd.

Therefore if the count of odd numbers in the array is odd, then the final XOR will be odd and if it is even, then final XOR will be even.

Below is the implementation of the above approach:

 `// C++ program to check if the XOR ` `// of an array is Even or Odd ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to check if the XOR of ` `// an array of integers is Even or Odd ` `string check(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `count = 0; ` ` `  `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// Count the number ` `        ``// of odd elements ` `        ``if` `(arr[i] & 1) ` `            ``count++; ` `    ``} ` ` `  `    ``// If count of odd elements ` `    ``// is odd, then XOR will be odd ` `    ``if` `(count & 1) ` `        ``return` `"Odd"``; ` ` `  `    ``// Else even ` `    ``else` `        ``return` `"Even"``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 3, 9, 12, 13, 15 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``// Function call ` `    ``cout << check(arr, n) << endl; ` ` `  `    ``return` `0; ` `} `

 `// Java rogram to check if the XOR ` `// of an array is Even or Odd ` `import` `java.util.*; ` ` `  `class` `GFG{ ` ` `  `// Function to check if the XOR of ` `// an array of integers is Even or Odd ` `static` `String check(``int` `[]arr, ``int` `n) ` `{ ` `    ``int` `count = ``0``; ` ` `  `    ``for` `(``int` `i = ``0``; i < n; i++) { ` ` `  `        ``// Count the number ` `        ``// of odd elements ` `        ``if` `((arr[i] & ``1``)!=``0``) ` `            ``count++; ` `    ``} ` ` `  `    ``// If count of odd elements ` `    ``// is odd, then XOR will be odd ` `    ``if` `((count & ``1``)!=``0``) ` `        ``return` `"Odd"``; ` ` `  `    ``// Else even ` `    ``else` `        ``return` `"Even"``; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `[]arr = { ``3``, ``9``, ``12``, ``13``, ``15` `}; ` `    ``int` `n = arr.length; ` ` `  `    ``// Function call ` `    ``System.out.println(check(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by Surendra_Gangwar `

 `# Python3 program to check if the XOR ` `# of an array is Even or Odd ` ` `  `# Function to check if the XOR of ` `# an array of integers is Even or Odd ` `def` `check(arr, n): ` `    ``count ``=` `0``; ` ` `  `    ``for` `i ``in` `range``(n): ` ` `  `        ``# Count the number ` `        ``# of odd elements ` `        ``if` `(arr[i] & ``1``): ` `            ``count ``=` `count ``+` `1``; ` `     `  `    ``# If count of odd elements ` `    ``# is odd, then XOR will be odd ` `    ``if` `(count & ``1``): ` `        ``return` `"Odd"``; ` ` `  `    ``# Else even ` `    ``else``: ` `        ``return` `"Even"``; ` ` `  `# Driver Code ` `if` `__name__``=``=``'__main__'``:  ` ` `  `    ``arr ``=` `[ ``3``, ``9``, ``12``, ``13``, ``15` `] ` `    ``n ``=` `len``(arr) ` ` `  `    ``# Function call ` `    ``print``(check(arr, n)) ` ` `  ` `  `# This code is contributed by Princi Singh `

 `// C# program to check if the XOR ` `// of an array is Even or Odd ` `using` `System; ` `using` `System.Collections.Generic; ` `using` `System.Linq; ` `  `  `class` `GFG  ` `{ ` ` `  `// Function to check if the XOR of ` `// an array of integers is Even or Odd ` `static` `String check(``int` `[]arr, ``int` `n) ` `{ ` `    ``int` `count = 0; ` ` `  `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// Count the number ` `        ``// of odd elements ` `        ``if` `(arr[i] == 1) ` `            ``count++; ` `    ``} ` ` `  `    ``// If count of odd elements ` `    ``// is odd, then XOR will be odd ` `    ``if` `(count == 1) ` `        ``return` `"Odd"``; ` ` `  `    ``// Else even ` `    ``else` `        ``return` `"Even"``; ` `} ` ` `  `// Driver Code ` `    ``public` `static` `void` `Main(String[] args)  ` `    ``{ ` `    ``int` `[]arr= { 3, 9, 12, 13, 15 }; ` `    ``int` `n = arr.Length;  ` ` `  `    ``// Function call ` `    ``Console.Write(check(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by shivanisinghss2110 `

Output:
```Even
```

Time Complexity: O(N)

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