# Construct original array starting with K from an array of XOR of all elements except elements at same index

Given an array A[] consisting of N integers and first element of the array B[] as K, the task is to construct the array B[] from A[] such that for any index i, A[i] is the Bitwise XOR of all the array elements of B[] except B[i].

Examples:

Input: A[] = {13, 14, 10, 6}, K = 2
Output: 2 1 5 9
Explanation:
For any index i, A[i] is the Bitwise XOR of all elements of B[] except B[i].

1. B[1] ^ B[2] ^ B[3] = 1 ^ 5 ^ 9 = 13 = A[0]
2. B[0] ^ B[2] ^ B[3] = 2 ^ 5 ^ 9 = 14 = A[1]
3. B[0] ^ B[1] ^ B[3] = 2 ^ 1 ^ 9 = 10 = A[2]
4. B[0] ^ B[1] ^ B[2] = 2 ^ 1 ^ 5 = 6 = A[3]

Input: A[] = {3, 5, 0, 2, 4}, K = 2
Output: 2 4 1 3 5

Approach: The idea is based on the observation that Bitwise XOR of the same value calculated even number of times is 0.

For any index i,
A[i] = B[0] ^ B[1] ^ … B[i-1] ^ B[i+1] ^ … B[n-1]
Therefore, XOR of all elements of B[], totalXor = B[0] ^ B[1] ^ … B[i – 1] ^ B[i] ^ B[i + 1] ^ … ^ B[N – 1].
Therefore, B[i] = totalXor ^ A[i]. (Since every element occurs twice except B[i])

Follow the below steps to solve the problem:

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach #include using namespace std;   // Function to construct an array // with each element equal to XOR // of all array elements except // the element at the same index void constructArray(int A[], int N,                     int K) {     // Original array     int B[N];       // Stores Bitwise XOR of array     int totalXOR = A[0] ^ K;       // Calculate XOR of all array elements     for (int i = 0; i < N; i++)         B[i] = totalXOR ^ A[i];       // Print the original array B[]     for (int i = 0; i < N; i++) {         cout << B[i] << " ";     } }   // Driver Code int main() {     int A[] = { 13, 14, 10, 6 }, K = 2;     int N = sizeof(A) / sizeof(A[0]);       // Function Call     constructArray(A, N, K);       return 0; }

## Java

 // Java program for the above approach class GFG{       // Function to construct an array // with each element equal to XOR // of all array elements except // the element at the same index static void constructArray(int A[], int N,                            int K) {           // Original array     int B[] = new int[N];         // Stores Bitwise XOR of array     int totalXOR = A[0] ^ K;         // Calculate XOR of all array elements     for(int i = 0; i < N; i++)         B[i] = totalXOR ^ A[i];         // Print the original array B[]     for(int i = 0; i < N; i++)     {         System.out.print(B[i] + " ");     } }   // Driver Code public static void main(String[] args) {     int A[] = { 13, 14, 10, 6 }, K = 2;     int N = A.length;           // Function Call     constructArray(A, N, K); } }   // This code is contributed by divyeshrabadiya07

## Python3

 # Python program for the above approach   # Function to construct an array # with each element equal to XOR # of all array elements except # the element at the same index def constructArray(A, N, K):         # Original array     B = [0] * N;       # Stores Bitwise XOR of array     totalXOR = A[0] ^ K;       # Calculate XOR of all array elements     for i in range(N):         B[i] = totalXOR ^ A[i];       # Print the original array B     for i in range(N):         print(B[i], end = " ");   # Driver Code if __name__ == '__main__':     A = [13, 14, 10, 6];     K = 2;     N = len(A);       # Function Call     constructArray(A, N, K);   # This code is contributed by Princi Singh

## C#

 // C# program for the above approach using System; using System.Collections; class GFG {           // Function to construct an array     // with each element equal to XOR     // of all array elements except     // the element at the same index     static void constructArray(int[] A, int N,                                int K)     {                    // Original array         int[] B = new int[N];                  // Stores Bitwise XOR of array         int totalXOR = A[0] ^ K;                  // Calculate XOR of all array elements         for(int i = 0; i < N; i++)             B[i] = totalXOR ^ A[i];                  // Print the original array B[]         for(int i = 0; i < N; i++)         {             Console.Write(B[i] + " ");         }     }     static void Main() {     int[] A = { 13, 14, 10, 6 };     int K = 2;     int N = A.Length;            // Function Call     constructArray(A, N, K);   } }   // This code is contributed by divyesh072019

## Javascript



Output:

2 1 5 9

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

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