# 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 = A; A = A; A = A.
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 = A; A = A; A = A.
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 = A; A = A; A = A, 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 = A; A = A; A = A, Before Swapping: 1 4 3 5 2 and After Swapping: 1 2 3 4 5

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 `// C++ implementation to sort ` `// decreasing permutation of N ` `// using triple swaps ` ` `  `#include ` `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); ` ` `  `    ``sortArray(A, N); ` ` `  `    ``return` `0; ` `} `

## Java

 `// 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

 `# 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#

 `// 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 `

Output:

```Sorted Array: 1 2 3 4 5
```

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Improved By : yatinagg, sapnasingh4991