# Construct an array whose Prefix XOR array starting from X is an N-length increasing sequence

• Difficulty Level : Hard
• Last Updated : 21 Aug, 2021

Given two integers N and X, the task is to generate an array of size N, such that the prefix xor array of X with the generated array will be permutations of 1st N natural numbers.

Examples:

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Input: N = 4, X = 3
Output: [2, 3, 1, 7]
Explanation: Prefix XOR array for the array {2, 3, 1, 7} is as follows:

1. X âŠ• 2 = 1. Now, X = 1
2. X âŠ• 3 = 2. Now, X = 2
3. X âŠ• 1 = 3. Now, X = 3
4. X âŠ• 7 = 4. Now, X = 4

The array [1, 2, 3, 4] is a permutation of first 4 natural numbers.

Input: N = 7, X = 52
Output: [53, 3, 1, 7, 1, 3, 1]

Approach: This problem can be solved using the properties of XOR ( If x âŠ• a = b, then x âŠ• b = a). Suppose XOR of elements in the generated array with X till ith index is X, and (i + 1)th element of the generated array is B, then B can be calculated using the following steps :

X âŠ• B = i + 1
According to problem statement, using the property of XOR (if xâŠ• a = b then, xâŠ• b = a)…
X âŠ• i + 1 = B
Or
B = X âŠ• i + 1, which is the required value of B.

Follow the steps below to solve the problem:

• Initialize a variable, say prev_xor as X.
• Iterate a loop using a variable, say i, from 1 to N and print prev_xor âŠ• i.
• Update prev_xor as i.

Below is the implementation of the above approach.

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to print the required array``void` `GenerateArray(``int` `N, ``int` `X)``{``    ``int` `prev_xor = X;` `    ``// Iteratie from 1 to N``    ``for` `(``int` `i = 1; i <= N; i++) {` `        ``// Print the i-th element``        ``cout << (i ^ prev_xor);` `        ``if` `(i != N) {``            ``cout << ``" "``;``        ``}` `        ``// Update prev_xor to i``        ``prev_xor = i;``    ``}``}` `// Driver Code``int` `main()``{``    ``// Given Input``    ``int` `N = 4, X = 3;` `    ``// Function Call``    ``cout << ``"The generated array is "``;``    ``GenerateArray(N, X);``    ``return` `0;``}`

## Java

 `// Java program for the above approach``class` `GFG {` `  ``// Function to print the required array``  ``static` `void` `GenerateArray(``int` `N, ``int` `X)``  ``{``    ``int` `prev_xor = X;` `    ``// Iteratie from 1 to N``    ``for` `(``int` `i = ``1``; i <= N; i++) {` `      ``// Print the i-th element``      ``System.out.print(i ^ prev_xor);` `      ``if` `(i != N) {``        ``System.out.print(``" "``);``      ``}` `      ``// Update prev_xor to i``      ``prev_xor = i;``    ``}``  ``}` `  ``// Driver Code``  ``public` `static` `void` `main(String args[]) {` `    ``// Given Input``    ``int` `N = ``4``, X = ``3``;` `    ``// Function Call``    ``System.out.print(``"The generated array is "``);``    ``GenerateArray(N, X);``  ``}``}` `// This code is contributed by splevel62.`

## Python3

 `# Python 3 program for the above approach` `# Function to print the required array``def` `GenerateArray(N, X):``    ``prev_xor ``=` `X` `    ``# Iteratie from 1 to N``    ``for` `i ``in` `range``(``1``,N``+``1``,``1``):``        ``# Print the i-th element``        ``print``(i ^ prev_xor,end``=``"")` `        ``if` `(i !``=` `N):``            ``print``(``" "``,end``=``"")` `        ``# Update prev_xor to i``        ``prev_xor ``=` `i` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``# Given Input``    ``N ``=` `4``    ``X ``=` `3` `    ``# Function Call``    ``print``(``"The generated array is "``,end``=``"")``    ``GenerateArray(N, X)``    ` `    ``# This code is contributed by ipg2016107`

## C#

 `// C# program for above approach``using` `System;``class` `GFG``{` `// Function to print the required array``static` `void` `GenerateArray(``int` `N, ``int` `X)``{``    ``int` `prev_xor = X;` `    ``// Iteratie from 1 to N``    ``for` `(``int` `i = 1; i <= N; i++) {` `        ``// Print the i-th element``        ``Console.Write(i ^ prev_xor);` `        ``if` `(i != N) {``            ``Console.Write(``" "``);``        ``}` `        ``// Update prev_xor to i``        ``prev_xor = i;``    ``}``}`  `// Driver Code``static` `void` `Main()``{``  ` `    ``// Given Input``    ``int` `N = 4, X = 3;` `    ``// Function Call``    ``Console.Write(``"The generated array is "``);``    ``GenerateArray(N, X);``}``}` `// This code is contributed by sanjoy_62.`

## Javascript

 ``
Output:
`The generated array is 2 3 1 7`

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

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