Sort decreasing permutation of N using triple swaps

Given an array A[] consisting of decreasing permutation of N numbers, the task is to sort the array using triple swaps. If it is not possible to sort the array then print -1.  

Triple swaps refer to cyclic right shift on chosen indices. Cyclic Right Shift: x --> y --> z --> x. 

Examples:  

Input: A[] = {4, 3, 2, 1} 
Output: 1 2 3 4 
Explanation: 
For the given array the first step is choosing indexes: x = 0, y = 2, z = 3 
Therefore, A[3] = A[2]; A[2] = A[0]; A[0] = A[3]. 
Before Swapping: 4 3 2 1 and After Swapping: 1 3 4 2.
For the given array the second step is choosing indexes: x = 1, y = 2, z = 3 Therefore, A[3] = A[2]; A[2] = A[1]; A[1] = A[3]. 
Before Swapping: 1 3 4 2 and After Swapping: 1 2 3 4.
Input: A[] = {5, 4, 3, 2, 1} 
Output: 1 2 3 4 5 
Explanation: 
For the given array the first step is choosing indexes: x = 0, y = 3, z = 4 therefore, 
A[4] = A[3]; A[3] = A[0]; A[0] = A[4], Before Swapping: 5 4 3 2 1 and After Swapping: 1 4 3 5 2 
For the given array the second step is choosing indexes: x = 1, y = 3, z = 4 therefore, 
A[4] = A[3]; A[3] = A[1]; A[1] = A[4], Before Swapping: 1 4 3 5 2 and After Swapping: 1 2 3 4 5  

Approach: 
To solve the problem mentioned above we have to choose three indexes in such a way so that we can bring at least one element at the correct position. By that, we mean that we have to bring 1 at index 0, 2 at index 1, and so on.  

1. x is chosen as the current index number i,
2. z is chosen as the index of x + 1 which is always N - i - 1 and
3. y is chosen accordingly.

Then we have to perform the swapping of elements by the cyclic right shift of elements using these indices.

Below is the implementation of the above approach:  

// C++ implementation to sort
// decreasing permutation of N
// using triple swaps

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

// Function to sort Array
void sortArray(int A[], int N)
{

    // The three indices that
    // has to be chosen
    int x, y, z;

    // Check if possible to sort array
    if (N % 4 == 0 || N % 4 == 1) {

        // Swapping to bring element
        // at required position
        // Bringing at least one
        // element at correct position
        for (int i = 0; i < N / 2; i++) {

            x = i;
            if (i % 2 == 0) {

                y = N - i - 2;
                z = N - i - 1;
            }

            // Tracing changes in Array
            A[z] = A[y];
            A[y] = A[x];
            A[x] = x + 1;
        }

        // Print the sorted array
        cout << "Sorted Array: ";

        for (int i = 0; i < N; i++)

            cout << A[i] << " ";
    }

    // If not possible to sort
    else

        cout << "-1";
}

// Driver code
int main()
{

    int A[] = { 5, 4, 3, 2, 1 };

    int N = sizeof(A) / sizeof(A[0]);

    sortArray(A, N);

    return 0;
}

// Java implementation to sort
// decreasing permutation of N
// using triple swaps

class GFG{

// Function to sort array
static void sortArray(int A[], int N)
{

    // The three indices that
    // has to be chosen
    int x = 0, y = 0, z = 0;

    // Check if possible to sort array
    if (N % 4 == 0 || N % 4 == 1)
    {

        // Swapping to bring element
        // at required position
        // Bringing at least one
        // element at correct position
        for(int i = 0; i < N / 2; i++)
        {
           x = i;
           
           if (i % 2 == 0)
           {
               y = N - i - 2;
               z = N - i - 1;
           }
           
           // Tracing changes in array
           A[z] = A[y];
           A[y] = A[x];
           A[x] = x + 1;
        }
        
        // Print the sorted array
        System.out.print("Sorted Array: ");

        for(int i = 0; i < N; i++)
           System.out.print(A[i] + " ");
    }

    // If not possible to sort
    else
    {
        System.out.print("-1");
    }
}

// Driver code
public static void main(String[] args)
{

    int A[] = { 5, 4, 3, 2, 1 };
    int N = A.length;

    sortArray(A, N);
}
}

// This code is contributed by sapnasingh4991

# Python3 implementation to sort 
# decreasing permutation of N 
# using triple swaps 

# Function to sort array 
def sortArray(A, N):
    
    # Check if possible to sort array 
    if (N % 4 == 0 or N % 4 == 1): 

        # Swapping to bring element 
        # at required position 
        # Bringing at least one 
        # element at correct position 
        for i in range(N // 2): 
            x = i
            if (i % 2 == 0): 
                y = N - i - 2
                z = N - i - 1

            # Tracing changes in Array 
            A[z] = A[y] 
            A[y] = A[x] 
            A[x] = x + 1

        # Print the sorted array 
        print("Sorted Array: ", end = "") 

        for i in range(N): 
            print(A[i], end = " ") 

    # If not possible to sort 
    else:
        print("-1")
        
# Driver code 
A = [ 5, 4, 3, 2, 1 ] 
N = len(A) 

sortArray(A, N)

# This code is contributed by yatinagg

// C# implementation to sort
// decreasing permutation of N
// using triple swaps
using System;
class GFG{

// Function to sort array
static void sortArray(int []A, int N)
{

    // The three indices that
    // has to be chosen
    int x = 0, y = 0, z = 0;

    // Check if possible to sort array
    if (N % 4 == 0 || N % 4 == 1)
    {

        // Swapping to bring element
        // at required position
        // Bringing at least one
        // element at correct position
        for(int i = 0; i < N / 2; i++)
        {
            x = i;
                
            if (i % 2 == 0)
            {
                y = N - i - 2;
                z = N - i - 1;
            }
                
            // Tracing changes in array
            A[z] = A[y];
            A[y] = A[x];
            A[x] = x + 1;
        }
        
        // Print the sorted array
        Console.Write("Sorted Array: ");

        for(int i = 0; i < N; i++)
        Console.Write(A[i] + " ");
    }

    // If not possible to sort
    else
    {
        Console.Write("-1");
    }
}

// Driver code
public static void Main(String[] args)
{
    int []A = { 5, 4, 3, 2, 1 };
    int N = A.Length;

    sortArray(A, N);
}
}

// This code is contributed by sapnasingh4991

<script>

// Javascript implementation to sort
// decreasing permutation of N
// using triple swaps

// Function to sort array
function sortArray(A, N)
{
  
    // The three indices that
    // has to be chosen
    let x = 0, y = 0, z = 0;
  
    // Check if possible to sort array
    if (N % 4 == 0 || N % 4 == 1)
    {
  
        // Swapping to bring element
        // at required position
        // Bringing at least one
        // element at correct position
        for(let i = 0; i < N / 2; i++)
        {
           x = i;
             
           if (i % 2 == 0)
           {
               y = N - i - 2;
               z = N - i - 1;
           }
             
           // Tracing changes in array
           A[z] = A[y];
           A[y] = A[x];
           A[x] = x + 1;
        }
          
        // Print the sorted array
        document.write("Sorted Array: ");
  
        for(let i = 0; i < N; i++)
           document.write(A[i] + " ");
    }
  
    // If not possible to sort
    else
    {
        document.write("-1");
    }
}


// Driver Code
    
    let A = [ 5, 4, 3, 2, 1 ];
    let N = A.length;
  
    sortArray(A, N);
    
</script>

Sorted Array: 1 2 3 4 5

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