C# Program for Block swap algorithm for array rotation

Write a function rotate(ar[], d, n) that rotates arr[] of size n by d elements. 

Rotation of the above array by 2 will make array

Algorithm : 

Initialize A = arr[0..d-1] and B = arr[d..n-1]
1) Do following until size of A is equal to size of B

  a)  If A is shorter, divide B into Bl and Br such that Br is of same 
       length as A. Swap A and Br to change ABlBr into BrBlA. Now A
       is at its final place, so recur on pieces of B.  

   b)  If A is longer, divide A into Al and Ar such that Al is of same 
       length as B Swap Al and B to change AlArB into BArAl. Now B
       is at its final place, so recur on pieces of A.

2)  Finally when A and B are of equal size, block swap them.

Recursive Implementation:

C#

using System;

class GFG{

// Wrapper over the recursive function
// leftRotateRec()
// It left rotates []arr by d.
public static void leftRotate(int []arr,
                              int d, int n)
{
    leftRotateRec(arr, 0, d, n);
}

public static void leftRotateRec(int []arr, int i,
                                 int d, int n)
{

    // Return If number of elements
    // to be rotated is zero or equal
    // to array size
    if(d == 0 || d == n)
        return;

    // If number of elements to be rotated
    // is exactly half of array size
    if(n - d == d)
    {
        swap(arr, i, n - d + i, d);
        return;
    }

    // If A is shorter
    if(d < n - d)
    {
        swap(arr, i, n - d + i, d);
        leftRotateRec(arr, i, d, n - d);
    }

    // If B is shorter
    else
    {
        swap(arr, i, d, n - d);

        // This is tricky
        leftRotateRec(arr, n - d + i,
                       2 * d - n, d);
    }
}

// UTILITY FUNCTIONS
// Function to print an array
public static void printArray(int []arr,
                              int size)
{
    int i;
    for(i = 0; i < size; i++)
        Console.Write(arr[i] + " ");

    Console.WriteLine();
}

// This function swaps d elements
// starting at index fi with d elements
// starting at index si
public static void swap(int []arr, int fi,
                        int si, int d)
{
    int i, temp;
    for(i = 0; i < d; i++)
    {
        temp = arr[fi + i];
        arr[fi + i] = arr[si + i];
        arr[si + i] = temp;
    }
}

// Driver Code
public static void Main(String[] args)
{
    int []arr = { 1, 2, 3, 4, 5, 6, 7 };

    leftRotate(arr, 2, 7);
    printArray(arr, 7);
}
}

// This code is contributed by amal kumar choubey

Output:

3 5 4 6 7 1 2

Time Complexity: O(N), where N represents the size of the given array.
Auxiliary Space: O(N), due to recursive stack space.

Iterative Implementation:
Here is iterative implementation of the same algorithm. Same utility function swap() is used here.

C#

// C# code for above implementation
static void leftRotate(int []arr, int d, int n)
{
    int i, j;
    if(d == 0 || d == n)
        return;
    i = d;
    j = n - d;
    while (i != j)
    {
        if(i < j) /*A is shorter*/
        {
            swap(arr, d-i, d+j-i, i);
            j -= i;
        }
        else /*B is shorter*/
        {
            swap(arr, d-i, d, j);
            i -= j;
        }

    }

    /*Finally, block swap A and B*/
    swap(arr, d-i, d, i);
}

// This code is contributed by Rajput-Ji

Time Complexity: O(N), where N represents the size of the given array.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

Please see following posts for other methods of array rotation: 
https://www.geeksforgeeks.org/array-rotation/
https://www.geeksforgeeks.org/program-for-array-rotation-continued-reversal-algorithm/

References:
http://www.cs.bell-labs.com/cm/cs/pearls/s02b.pdf
Please write comments if you find any bug in the above programs/algorithms or want to share any additional information about the block swap algorithm.

Please refer complete article on Block swap algorithm for array rotation for more details!