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

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: 

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 ? 2 = 1. Now, X = 1
2. X ? 3 = 2. Now, X = 2
3. X ? 1 = 3. Now, X = 3
4. X ? 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 ? a = b, then x ? b = a). Suppose XOR of elements in the generated array with X till i^th index is X, and (i + 1)^th element of the generated array is B, then B can be calculated using the following steps :

X ? B = i + 1 
According to problem statement, using the property of XOR (if x? a = b then, x? b = a)... 
X ? i + 1 = B
Or
B = X ? 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 ? i.
• Update prev_xor as i.

Below is the implementation of the above approach.

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to print the required array
void GenerateArray(int N, int X)
{
    int prev_xor = X;

    // Iterative 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 program for the above approach
class GFG {

  // Function to print the required array
  static void GenerateArray(int N, int X)
  {
    int prev_xor = X;

    // Iterative 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.

# Python 3 program for the above approach

# Function to print the required array
def GenerateArray(N, X):
    prev_xor = X

    # Iterative 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# 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;

    // Iterative 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.

<script>

// JavaScript program for the above approach;

// Function to print the required array
function GenerateArray(N, X) 
{
    let prev_xor = X;
    
    // Iterative from 1 to N
    for(let i = 1; i <= N; i++) 
    {
        
        // Print the i-th element
        document.write((i ^ prev_xor));

        if (i != N) 
        {
            document.write(" ");
        }

        // Update prev_xor to i
        prev_xor = i;
    }
}

// Driver Code

// Given Input
let N = 4, X = 3;

// Function Call
document.write("The generated array is ");
GenerateArray(N, X);

// This code is contributed by Potta Lokesh

</script>

The generated array is 2 3 1 7

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