Reversal algorithm for Array rotation

Given an array arr[] of size N, the task is to rotate the array by d position to the left.

Examples:

Input:  arr[] = {1, 2, 3, 4, 5, 6, 7}, d = 2
Output: 3, 4, 5, 6, 7, 1, 2
Explanation: If the array is rotated by 1 position to the left, 
it becomes {2, 3, 4, 5, 6, 7, 1}.
When it is rotated further by 1 position,
it becomes: {3, 4, 5, 6, 7, 1, 2}

Input: arr[] = {1, 6, 7, 8}, d = 3
Output: 8, 1, 6, 7

Approach: We have already discussed several methods in this post. The ways discussed there are:

• Using another temporary array.
• Rotating one by one.
• Using a juggling algorithm.

Another Approach (The Reversal Algorithm): Here we will be discussing another method which uses the concept of reversing a part of array. The intuition behind the idea is mentioned below:

Intuition:

If we observe closely, we can see that a group of array elements is changing its position. For example see the following array:
arr[] = {1, 2, 3, 4, 5, 6, 7} and d = 2. The rotated array is {3, 4, 5, 6, 7, 1, 2}

The group having the first two elements is moving to the end of the array. This is like reversing the array.

• But the issue is that if we only reverse the array, it becomes {7, 6, 5, 4, 3, 2, 1}. 
• After rotation the elements in the chunks having the first 5 elements {7, 6, 5, 4, 3} and the last 2 elements {2, 1} should be in the actual order as of the initial array [i.e., {3, 4, 5, 6, 7} and {1, 2}]but here it gets reversed. 
• So if those blocks are reversed again we get the desired rotated array.

So the sequence of operations is:

• Reverse the whole array 
• Then reverse the last ‘d’ elements and 
• Then reverse the first (N-d) elements.

As we are performing reverse operations it is also similar to the following sequence:

• Reverse the first ‘d’ elements
• Reverse last (N-d) elements
• Reverse the whole array.

Algorithm: The algorithm can be described with the help of the below pseudocode:

Pseudocode:

Algorithm reverse(arr, start, end):
    mid = (start + end)/2
    loop from i = start to mid:
        swap (arr[i], arr[end-(mid-i+1)])

Algorithm rotate(arr, d, N):
    reverse(arr, 1, d) ;
    reverse(arr, d + 1, N);
    reverse(arr, 1, N);

Illustration:

Follow the illustration below to for  better understanding of the algorithm and intuition:

For example take the array arr[] = {1, 2, 3, 4, 5, 6, 7} and d = 2.

Array

The rotated array will look like:

Rotated Array

1st Step: Consider the array as a combination of two blocks. One containing the first two elements and the other containing the remaining elements as shown above.

Considered 2 blocks

2nd Step: Now reverse the first d elements. It becomes as shown in the image

Reverse the first K elements

3rd Step: Now reverse the last (N-d) elements. It become as it is shown in the below image:

Reverse the last (N-K) elements

4th Step: Now the array is the exact reversed form of how it should be if left shifted d times. So reverse the whole array and you will get the required rotated array.

The total array is reversed

See that the array is now the same as the rotated array.

Below is the implementation of the above approach: 

C++

// C++ program for reversal algorithm
// of array rotation

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

// Function to reverse arr[]
// from index start to end
void reverseArray(int arr[], int start, int end)
{
    while (start < end) {
        int temp = arr[start];
        arr[start] = arr[end];
        arr[end] = temp;
        start++;
        end--;
    }
}

// Function to left rotate arr[] of size n by d
void leftRotate(int arr[], int d, int n)
{
    if (d == 0)
        return;

    // In case the rotating factor is
    // greater than array length
    d = d % n;

    reverseArray(arr, 0, d - 1);
    reverseArray(arr, d, n - 1);
    reverseArray(arr, 0, n - 1);
}

// Function to print an array
void printArray(int arr[], int size)
{
    for (int i = 0; i < size; i++)
        cout << arr[i] << " ";
}

// Driver code
int main()
{
    int arr[] = { 1, 2, 3, 4, 5, 6, 7 };
    int N = sizeof(arr) / sizeof(arr[0]);
    int d = 2;

    // Function call
    leftRotate(arr, d, N);
    printArray(arr, N);
    return 0;
}

C

// C/C++ program for reversal algorithm of array rotation
#include <stdio.h>

/*Utility function to print an array */
void printArray(int arr[], int size);

/* Utility function to reverse arr[] from start to end */
void reverseArray(int arr[], int start, int end);

/* Function to left rotate arr[] of size n by d */
void leftRotate(int arr[], int d, int n)
{

    if (d == 0)
        return;
    // in case the rotating factor is
    // greater than array length
    d = d % n;

    reverseArray(arr, 0, d - 1);
    reverseArray(arr, d, n - 1);
    reverseArray(arr, 0, n - 1);
}

/*UTILITY FUNCTIONS*/
/* function to print an array */
void printArray(int arr[], int size)
{
    int i;
    for (i = 0; i < size; i++)
        printf("%d ", arr[i]);
}

/*Function to reverse arr[] from index start to end*/
void reverseArray(int arr[], int start, int end)
{
    int temp;
    while (start < end) {
        temp = arr[start];
        arr[start] = arr[end];
        arr[end] = temp;
        start++;
        end--;
    }
}

/* Driver program to test above functions */
int main()
{
    int arr[] = { 1, 2, 3, 4, 5, 6, 7 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int d = 2;

    leftRotate(arr, d, n);
    printArray(arr, n);
    return 0;
}

Java

// Java program for reversal algorithm of array rotation
import java.io.*;

class LeftRotate {
    /* Function to left rotate arr[] of size n by d */
    static void leftRotate(int arr[], int d)
    {

        if (d == 0)
            return;

        int n = arr.length;
        // in case the rotating factor is
        // greater than array length
        d = d % n;
        reverseArray(arr, 0, d - 1);
        reverseArray(arr, d, n - 1);
        reverseArray(arr, 0, n - 1);
    }

    /*Function to reverse arr[] from index start to end*/
    static void reverseArray(int arr[], int start, int end)
    {
        int temp;
        while (start < end) {
            temp = arr[start];
            arr[start] = arr[end];
            arr[end] = temp;
            start++;
            end--;
        }
    }

    /*UTILITY FUNCTIONS*/
    /* function to print an array */
    static void printArray(int arr[])
    {
        for (int i = 0; i < arr.length; i++)
            System.out.print(arr[i] + " ");
    }

    /* Driver program to test above functions */
    public static void main(String[] args)
    {
        int arr[] = { 1, 2, 3, 4, 5, 6, 7 };
        int n = arr.length;
        int d = 2;

        leftRotate(arr, d); // Rotate array by d
        printArray(arr);
    }
}
/*This code is contributed by Devesh Agrawal*/

Python3

# Python program for reversal algorithm of array rotation

# Function to reverse arr[] from index start to end


def reverseArray(arr, start, end):
    while (start < end):
        temp = arr[start]
        arr[start] = arr[end]
        arr[end] = temp
        start += 1
        end = end-1

# Function to left rotate arr[] of size n by d


def leftRotate(arr, d):

    if d == 0:
        return
    n = len(arr)
    # in case the rotating factor is
    # greater than array length
    d = d % n
    reverseArray(arr, 0, d-1)
    reverseArray(arr, d, n-1)
    reverseArray(arr, 0, n-1)

# Function to print an array


def printArray(arr):
    for i in range(0, len(arr)):
        print (arr[i],end=' ')


# Driver function to test above functions
arr = [1, 2, 3, 4, 5, 6, 7]
n = len(arr)
d = 2

leftRotate(arr, d)  # Rotate array by 2
printArray(arr)

# This code is contributed by Devesh Agrawal

C#

// C# program for reversal algorithm
// of array rotation
using System;

class GFG {
    /* Function to left rotate arr[]
    of size n by d */
    static void leftRotate(int[] arr, int d)
    {

        if (d == 0)
            return;
        int n = arr.Length;
          // in case the rotating factor is
        // greater than array length
        d = d % n;
        reverseArray(arr, 0, d - 1);
        reverseArray(arr, d, n - 1);
        reverseArray(arr, 0, n - 1);
    }

    /* Function to reverse arr[] from
    index start to end*/
    static void reverseArray(int[] arr, int start,
                             int end)
    {
        int temp;
        while (start < end) {
            temp = arr[start];
            arr[start] = arr[end];
            arr[end] = temp;
            start++;
            end--;
        }
    }

    /*UTILITY FUNCTIONS*/
    /* function to print an array */
    static void printArray(int[] arr)
    {
        for (int i = 0; i < arr.Length; i++)
            Console.Write(arr[i] + " ");
    }

    // Driver code
    public static void Main()
    {
        int[] arr = { 1, 2, 3, 4, 5, 6, 7 };
        int n = arr.Length;
        int d = 2;

        leftRotate(arr, d); // Rotate array by 2
        printArray(arr);
    }
}

// This code is contributed by Sam007

PHP

<?php
// PHP program for reversal
// algorithm of array rotation

/* Function to left rotate
   arr of size n by d */
function leftRotate(&$arr, $d, $n)
{

    if ($d == 0)
        return;
      // in case the rotating factor is
      // greater than array length
      $d = ($d % $n);
    reverseArray($arr, 0, $d - 1);
    reverseArray($arr, $d, $n - 1);
    reverseArray($arr, 0, $n - 1);
}

/*Function to reverse $arr
  from index start to end*/
function reverseArray(&$arr,
                       $start, $end)
{
    while ($start < $end)
    {
        $temp = $arr[$start];
        $arr[$start] = $arr[$end];
        $arr[$end] = $temp;
        $start++;
        $end--;
    }
}

// Function to
// print an array
function printArray($arr, $size)
{
    for ($i = 0; $i < $size; $i++)
    print $arr[$i]." ";
}

// Driver code
$arr = array(1, 2, 3,
             4, 5, 6, 7);
$n = sizeof($arr);
$d = 2;

// Function calling
leftRotate($arr, $d, $n);
printArray($arr, $n);

// This code is contributed
// by ChitraNayal
?>

Javascript

<script>
      // JavaScript program for reversal algorithm
      // of array rotation

      /*Function to reverse arr[] from index start to end*/
      function reverseArray(arr, start, end) {
        while (start < end) {
          var temp = arr[start];
          arr[start] = arr[end];
          arr[end] = temp;
          start++;
          end--;
        }
      }

      /* Function to left rotate arr[] of size n by d */
      function leftRotate(arr, d, n) {
        if (d == 0) return;
        // in case the rotating factor is
        // greater than array length
        d = d % n;

        reverseArray(arr, 0, d - 1);
        reverseArray(arr, d, n - 1);
        reverseArray(arr, 0, n - 1);
      }

      // Function to print an array
      function printArray(arr, size)
      {
        for (var i = 0; i < size; i++) document.write(arr[i] + " ");
      }

      /* Driver program to test above functions */

      var arr = [1, 2, 3, 4, 5, 6, 7];
      var n = arr.length;
      var d = 2;

      // Function calling
      leftRotate(arr, d, n);
      printArray(arr, n);

      // This code is contributed by rdtank.
    </script>

Output

3 4 5 6 7 1 2 

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