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

• Last Updated : 11 Jun, 2021

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

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 ^ B ^ … B[i-1] ^ B[i+1] ^ … B[n-1]
Therefore, XOR of all elements of B[], totalXor = B ^ B ^ … 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 ^ 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);` `    ``// 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 ^ 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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