Rearrange array to make decimal equivalents of reversed binary representations of array elements sorted

Given an array arr[] consisting of N positive integers, the task is to rearrange the array such that the reversed binary representation of all the array elements is sorted.

If the decimal equivalent of reversed binary representations of two or more array elements is equal, then the original value is taken into consideration while rearranging the array.

Examples:

Input: arr[] = {43, 52, 61, 41}
Output: 52 41 61 43
Explanation:
Below are the reversed binary representation of the array elements:

1. 43 –> (101011)₂ –> reversed –> 53.
2. 52 –> (110100)₂ –> reversed –> 11.
3. 61 –> (111101)₂ –> reversed –> 47.
4. 41 –> (101001)₂ –> reversed –> 37.

Therefore, after rearranging the array element as {52, 41, 61, 43}, the reversed binary representation of rearranged array elements is in sorted order.

Input: arr[] = {5, 3, 6, 2, 4}
Output: 2 4 3 6 5

Approach: Follow the steps below to solve the problem:

• Initialize an array, say newArr[], insert all the array elements as the reversed binary representation of the number.
• Sort the array newArr[] in increasing order.
• Traverse the array newArr[] and copy all the elements to the array arr[].
• Now, update all the array elements as the reversed binary representation of the number.
• After completing the above steps, print the elements of the array arr[] as the output.

Below is the implementation of the above approach:

C++

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

// Function to reverse the bits of a number
int keyFunc(int n)
{

    // Stores the reversed number
    int rev = 0;

    while (n > 0)
    {

        // Divide rev by 2
        rev = rev << 1;

        // If the value of N is odd
        if (n & 1 == 1)
            rev = rev ^ 1;

        // Update the value of N
        n = n >> 1;
      }

    // Return the final value of rev
    return rev;
}

// Function for rearranging the array
// element according to the given rules
vector<vector<int>> getNew(vector<int> arr)
{

    // Stores the new array elements
    vector<vector<int>> ans;

    for (int i:arr)
        ans.push_back({keyFunc(i), i});

    return ans;
}

// Function for rearranging the array
vector<int> getArr(vector<vector<int> > arr){

    // Stores the new array
    vector<int> ans;

    for (auto i:arr)
        ans.push_back(i[1]);
    return ans;
}


// Function to sort the array by reversing
// binary representation
void sortArray(vector<int> arr)
{

  // Creating a new array
  vector<vector<int> > newArr = getNew(arr);

  // Sort the array with the key
  sort(newArr.begin(),newArr.end());

  // Get arr from newArr
  arr = getArr(newArr);

  // Print the sorted array
  int n = arr.size();
  cout<<"[";
  for(int i = 0; i < n - 1; i++)
    cout << arr[i] << ", ";
  cout << arr[n - 1] << "]";
}

// Driver Code
int main()
{

  vector<int> arr = {43, 52, 61, 41};
  sortArray(arr);

  return 0;
}

// This code is contributed by mohit kumar 29.

Java

// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;

class GFG{

// Function to reverse the bits of a number
static int keyFunc(int n)
{

    // Stores the reversed number
    int rev = 0;

    while (n > 0)
    {

        // Divide rev by 2
        rev = rev << 1;

        // If the value of N is odd
        if ((n & 1) == 1)
            rev = rev ^ 1;

        // Update the value of N
        n = n >> 1;
    }

    // Return the final value of rev
    return rev;
}

// Function for rearranging the array
// element according to the given rules
static int[][] getNew(int arr[])
{

    // Stores the new array elements
    int ans[][] = new int[arr.length][2];

    for(int i = 0; i < arr.length; i++)
        ans[i] = new int[]{ keyFunc(arr[i]), arr[i] };

    return ans;
}

// Function for rearranging the array
static int[] getArr(int[][] arr)
{

    // Stores the new array
    int ans[] = new int[arr.length];
    int idx = 0;
    for(int i[] : arr)
        ans[idx++] = i[1];

    return ans;
}

// Function to sort the array by reversing
// binary representation
static void sortArray(int arr[])
{

    // Creating a new array
    int[][] newArr = getNew(arr);

    // Sort the array with the key
    Arrays.sort(newArr, (a, b) -> {
        if (Integer.compare(a[0], b[0]) == 0)
            return Integer.compare(a[1], b[1]);

        return Integer.compare(a[0], b[0]);
    });

    // Get arr from newArr
    arr = getArr(newArr);

    // Print the sorted array
    int n = arr.length;
    System.out.print("[");
    for(int i = 0; i < n - 1; i++)
        System.out.print(arr[i] + ", ");

    System.out.print(arr[n - 1] + "]");
}

// Driver Code
public static void main(String[] args)
{
    int arr[] = { 43, 52, 61, 41 };
    sortArray(arr);
}
}

// This code is contributed by Kingash

Python3

# Python3 program for the above approach

# Function to reverse the bits of a number
def keyFunc(n):

    # Stores the reversed number
    rev = 0

    while (n > 0):

        # Divide rev by 2
        rev = rev << 1

        # If the value of N is odd
        if (n & 1 == 1):
            rev = rev ^ 1

        # Update the value of N
        n = n >> 1

    # Return the final value of rev
    return rev

# Function for rearranging the array
# element according to the given rules
def getNew(arr):

    # Stores the new array elements
    ans = []

    for i in arr:
        ans.append([keyFunc(i), i])
    return ans

# Function for rearranging the array
def getArr(arr):

    # Stores the new array
    ans = []

    for i in arr:
        ans.append(i[1])
    return ans

# Function to sort the array by reversing
# the binary representation
def sortArray(arr):

    # Creating a new array
    newArr = getNew(arr)

    # Sort the array with the key
    newArr.sort()

    # Get arr from newArr
    arr = getArr(newArr)

    # Print the sorted array
    print(arr)


# Driver Code

arr = [43, 52, 61, 41]
sortArray(arr)

C#

// C# program for the above approach
using System;
class GFG {

  // Function to reverse the bits of a number
  static int keyFunc(int n)
  {

    // Stores the reversed number
    int rev = 0;

    while (n > 0) {

      // Divide rev by 2
      rev = rev << 1;

      // If the value of N is odd
      if ((n & 1) == 1)
        rev = rev ^ 1;

      // Update the value of N
      n = n >> 1;
    }

    // Return the final value of rev
    return rev;
  }

  // Function for rearranging the array
  // element according to the given rules
  static int[][] getNew(int[] arr)
  {

    // Stores the new array elements
    int[][] ans = new int[arr.Length][];

    for (int i = 0; i < arr.Length; i++)
      ans[i] = new int[] { keyFunc(arr[i]), arr[i] };

    return ans;
  }

  // Function for rearranging the array
  static int[] getArr(int[][] arr)
  {

    // Stores the new array
    int[] ans = new int[arr.Length];
    int idx = 0;
    foreach(var i in arr) ans[idx++] = i[1];

    return ans;
  }

  // Function to sort the array by reversing
  // binary representation
  static void sortArray(int[] arr)
  {

    // Creating a new array
    int[][] newArr = getNew(arr);

    // Sort the array with the key
    Array.Sort(
      newArr, new Comparison<int[]>((a, b) => {
        return (a[0] == b[0]) ? (a[1] - b[1])
          : (a[0] - b[0]);
      }));

    // Get arr from newArr
    arr = getArr(newArr);

    // Print the sorted array
    int n = arr.Length;
    Console.Write("[");
    for (int i = 0; i < n - 1; i++)
      Console.Write(arr[i] + ", ");

    Console.Write(arr[n - 1] + "]");
  }

  // Driver Code
  public static void Main(string[] args)
  {
    int[] arr = { 43, 52, 61, 41 };
    sortArray(arr);
  }
}

// This code is contributed by phasing17

Javascript

<script>

// JavaScript program for the above approach

// Function to reverse the bits of a number
function keyFunc(n) {

    // Stores the reversed number
    let rev = 0;

    while (n > 0) {

        // Divide rev by 2
        rev = rev << 1;

        // If the value of N is odd
        if (n & 1 == 1)
            rev = rev ^ 1;

        // Update the value of N
        n = n >> 1;
    }

    // Return the final value of rev
    return rev;
}

// Function for rearranging the array
// element according to the given rules
function getNew(arr) {

    // Stores the new array elements
    let ans = [];

    for (let i of arr)
        ans.push([keyFunc(i), i]);

    return ans;
}

// Function for rearranging the array
function getArr(arr) {

    // Stores the new array
    let ans = [];

    for (let i of arr)
        ans.push(i[1]);
    return ans;
}


// Function to sort the array by reversing
// binary representation
function sortArray(arr) {

    // Creating a new array
    let newArr = getNew(arr);

    // Sort the array with the key
    newArr.sort();

    // Get arr from newArr
    arr = getArr(newArr);

    // Print the sorted array
    let n = arr.length;
    document.write("[");
    for (let i = 0; i < n - 1; i++)
        document.write(arr[i] + ", ");
    document.write(arr[n - 1] + "]");
}

// Driver Code


let arr = [43, 52, 61, 41];
sortArray(arr);

// This code is contributed by _saurabh_jaiswal

</script>

Output:

[52, 41, 61, 43]

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

Space-Optimized Approach: Follow the steps below to solve the problem:

• Declare a function to accept an array element as parameter and returns the decimal equivalent of its reversed binary representation.
• Sort the array by using the function as the key while sorting.
• Print the array elements as the output.

Below is the implementation of the above approach:

C++

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

// Function to reverse the bits of number
int keyFunc(int n)
{

    // Stores the reversed number
    int rev = 0;

    while (n > 0) {

        // Divide rev by 2
        rev = rev << 1;

        // If the value of N is odd
        if (n & 1 == 1)
            rev = rev ^ 1;

        // Update the value of N
        n = n >> 1;
    }

    // Return the final value of rev
    return rev;
}

//defining the comparison function
bool compare(int a, int b)
{
    return keyFunc(a) < keyFunc(b);
}
// Function to sort the array by reversing
// binary representation
void sortArray(int arr[], int n)
{
    // Sort the array with the key
    sort(arr, arr + n, compare);

    // Print the sorted array
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
}

int main()
{
    // Driver Code
    int arr[] = { 43, 52, 61, 41 };
    int n = 4;
    sortArray(arr, n);

    return 0;
}

// this code is contributed by phasing17

Python3

# Python3 program for the above approach

# Function to reverse the bits of number
def keyFunc(n):

    # Stores the reversed number
    rev = 0

    while (n > 0):

        # Divide rev by 2
        rev = rev << 1

        # If the value of N is odd
        if (n & 1 == 1):
            rev = rev ^ 1

        # Update the value of N
        n = n >> 1

    # Return the final value of rev
    return rev

# Function to sort the array by reversing
# binary representation
def sortArray(arr):

    # Sort the array with the key
    arr = sorted(arr, key = keyFunc)

    # Print the sorted array
    print(arr)

# Driver Code

arr = [43, 52, 61, 41]
sortArray(arr)

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

public class GFG
{

  // Function to reverse the bits of number
  public static int keyFunc(int n)
  {

    // Stores the reversed number
    int rev = 0;

    while (n > 0) {

      // Divide rev by 2
      rev = rev << 1;

      // If the value of N is odd
      if ((n & 1) == 1)
        rev = rev ^ 1;

      // Update the value of N
      n = n >> 1;
    }

    // Return the final value of rev
    return rev;
  }
  // defining the comparison function
  public static int compare(int a, int b)
  {
    return keyFunc(a) - keyFunc(b);
  }
  // Function to sort the array by reversing
  // binary representation
  public static void sortArray(int[] arr, int n)
  {
    // Sort the array with the key
    Array.Sort(arr, compare);

    // Print the sorted array
    for (int i = 0; i < n; i++)
      Console.Write(arr[i] + " ");
  }
  public static void Main(string[] args)
  {

    // Driver Code
    int[] arr = { 43, 52, 61, 41 };
    int n = 4;
    sortArray(arr, n);
  }
}

// This code is contributed by phasing17

Javascript

// JavaScript program for the above approach

// Function to reverse the bits of number
function keyFunc(n)
{

    // Stores the reversed number
    var rev = 0;

    while (n > 0)
    {

        // Divide rev by 2
        rev = rev << 1;

        // If the value of N is odd
        if (n & 1 == 1)
            rev = rev ^ 1;

        // Update the value of N
        n = n >> 1;
    }

    // Return the final value of rev
    return rev;
}

// Function to sort the array by reversing
// binary representation
function sortArray(arr)
{

    // Sort the array with the key
    arr.sort((a, b) => keyFunc(a) > keyFunc(b));

    // Print the sorted array
    console.log(arr);
}

// Driver Code
var arr = [43, 52, 61, 41];
sortArray(arr);

//this code is contributed by phasing17

Output:

[52, 41, 61, 43]

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