Generate Array whose average and bitwise OR of bitwise XOR are equal

Given an integer N (N is odd). the task is to construct an array arr[] of size N where 1 ≤ arr[i] ≤ N such that the bitwise OR of the bitwise XOR of every consecutive pair should be equal to the average of the constructed arr[]. Formally:

(arr[0] ^ arr[1]) | (arr[2] ^ arr[3] ) | (arr[4] ^ arr[5]) . . . (arr[N-3] ^ arr[N-2] ) |  arr[N-1] = ( arr[0] + arr[1] + arr[2] . . . +a[N-1]) / N

where ^ is the bitwise Xor and | is the bitwise Or.

Note: If there are multiple possible arrays, print any of them.

Examples:

Input: N = 1
Output: arr[] = {1}
Explanation:- Since n=1 hence an=1 and the average of these numbers is also 1.

Input: n = 5
Output: arr[] = {1, 2, 4, 5, 3}
Explanation: (1^2) | (4^5) | 3 = 3 and (1+2+3+4+5)/5 = 3. Hence it forms a valid integer array.

Approach: Implement the idea below to solve the problem:

XOR of two same values gives you 0. OR operation with a number will give you the same number. So, if we assign all values to X, then all the XOR values will be 0 except for the last element which does not form any pair. So the Xor will be X. Also the average will become N*X/N = X.

Follow the below steps to implement the idea:

• Initialize the array of size N.
• Assign each element of the array as any value X (where X is in the range of [1, N]).

Below is the implementation of the above approach.

C++

// C++ code to implement the approach

#include <bits/stdc++.h>
using namespace std;

// Function to generates valid array
// according to the given conditions
void valid_array_formation(int N)
{
    int arr[N];
    for (int i = 0; i < N; i++) {
        // Placing every value of the array
        // to  be N
        arr[i] = N;
    }

    // Print the constructed arr
    for (int i = 0; i < N; i++) {
        cout << arr[i] << " ";
    }
    cout << endl;
}

// Driver code
int main()
{
    // Test case 1
    int N = 1;
    valid_array_formation(N);

    // Test case 2
    N = 5;
    valid_array_formation(N);

    return 0;
}

Java

// Java code to implement the approach
import java.io.*;

class GFG {

  // Function to generates valid array
  // according to the given conditions
  static void valid_array_formation(int N)
  {
    int[] arr = new int[N];
    for (int i = 0; i < N; i++) {
      // Placing every value of the array
      // to  be N
      arr[i] = N;
    }

    // Print the constructed arr
    for (int i = 0; i < N; i++) {
      System.out.print(arr[i] + " ");
    }
    System.out.println();
  }

  public static void main(String[] args)
  {
    // Test case 1
    int N = 1;
    valid_array_formation(N);

    // Test case 2
    N = 5;
    valid_array_formation(N);
  }
}

// This code is contributed by lokeshmvs21.

Python3

# Python code to implement the approach

# Function to generate a valid array
# according to the given conditions
def valid_array_formation(N):

    # Initialize an empty list
    arr = []

    # Append N to the list N times
    for i in range(N):
        arr.append(N)

    # Print the constructed list
    for i in range(N):
        print(arr[i], end=" ")
    print()


# Test case 1
N = 1
valid_array_formation(N)

# Test case 2
N = 5
valid_array_formation(N)

# This code is contributed by lokesh.

C#

// C# code to implement the approach
using System;

public class GFG {

// Function to generates valid array
// according to the given conditions
static void valid_array_formation(int N)
{
    int[] arr = new int[N];
    for (int i = 0; i < N; i++) {
    // Placing every value of the array
    // to be N
    arr[i] = N;
    }

    // Print the constructed arr
    for (int i = 0; i < N; i++) {
    Console.Write(arr[i] + " ");
    }
    Console.WriteLine();
}

public static void Main()
{
    // Test case 1
    int N = 1;
    valid_array_formation(N);

    // Test case 2
    N = 5;
    valid_array_formation(N);
}
}

// This code is contributed by Pushpesh Raj.

Javascript

// js code

// Function to generates valid array
// according to the given conditions
function validArrayFormation(N) {
  let arr = new Array(N);
  for (let i = 0; i < N; i++) {
    // Placing every value of the array
    // to be N
    arr[i] = N;
  }

  // Print the constructed arr
  console.log(arr.join(" "));
}

// Test case 1
let N = 1;
validArrayFormation(N);

// Test case 2
N = 5;
validArrayFormation(N);

// This code is contributed by ksam24000

Output

1 
5 5 5 5 5 

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