# 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[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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