Program 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

METHOD 1 (Using temp array)

```Input arr[] = [1, 2, 3, 4, 5, 6, 7], d = 2, n =7
1) Store d elements in a temp array
temp[] = [1, 2]
2) Shift rest of the arr[]
arr[] = [3, 4, 5, 6, 7, 6, 7]
3) Store back the d elements
arr[] = [3, 4, 5, 6, 7, 1, 2]```

Time complexity : O(n)
Auxiliary Space : O(d)

METHOD 2 (Rotate one by one)

```leftRotate(arr[], d, n)
start
For i = 0 to i < d
Left rotate all elements of arr[] by one
end```

To rotate by one, store arr[0] in a temporary variable temp, move arr[1] to arr[0], arr[2] to arr[1] …and finally temp to arr[n-1]

Let us take the same example arr[] = [1, 2, 3, 4, 5, 6, 7], d = 2
Rotate arr[] by one 2 times
We get [2, 3, 4, 5, 6, 7, 1] after first rotation and [ 3, 4, 5, 6, 7, 1, 2] after second rotation.

Below is the implementation of the above approach :

C++

 `// C++ program to rotate an array by ` `// d elements ` `#include ` `using` `namespace` `std; ` ` `  `/*Function to left Rotate arr[] of  ` `  ``size n by 1*/` `void` `leftRotatebyOne(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `temp = arr[0], i; ` `    ``for` `(i = 0; i < n - 1; i++) ` `        ``arr[i] = arr[i + 1]; ` ` `  `    ``arr[i] = temp; ` `} ` ` `  `/*Function to left rotate arr[] of size n by d*/` `void` `leftRotate(``int` `arr[], ``int` `d, ``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i < d; i++) ` `        ``leftRotatebyOne(arr, n); ` `} ` ` `  `/* utility function to print an array */` `void` `printArray(``int` `arr[], ``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``cout << arr[i] << ``" "``; ` `} ` ` `  `/* Driver program to test above functions */` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3, 4, 5, 6, 7 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` ` `  `    ``// Function calling ` `    ``leftRotate(arr, 2, n); ` `    ``printArray(arr, n); ` ` `  `    ``return` `0; ` `} `

C

 `// C program to rotate an array by ` `// d elements ` `#include ` ` `  `/* Function to left Rotate arr[] of size n by 1*/` `void` `leftRotatebyOne(``int` `arr[], ``int` `n); ` ` `  `/*Function to left rotate arr[] of size n by d*/` `void` `leftRotate(``int` `arr[], ``int` `d, ``int` `n) ` `{ ` `    ``int` `i; ` `    ``for` `(i = 0; i < d; i++) ` `        ``leftRotatebyOne(arr, n); ` `} ` ` `  `void` `leftRotatebyOne(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `temp = arr[0], i; ` `    ``for` `(i = 0; i < n - 1; i++) ` `        ``arr[i] = arr[i + 1]; ` `    ``arr[i] = temp; ` `} ` ` `  `/* utility function to print an array */` `void` `printArray(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `i; ` `    ``for` `(i = 0; i < n; i++) ` `        ``printf``(``"%d "``, arr[i]); ` `} ` ` `  `/* Driver program to test above functions */` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3, 4, 5, 6, 7 }; ` `    ``leftRotate(arr, 2, 7); ` `    ``printArray(arr, 7); ` `    ``return` `0; ` `} `

Java

 `// Java program to rotate an array by  ` `// d elements  ` ` `  `class` `RotateArray { ` `    ``/*Function to left rotate arr[] of size n by d*/` `    ``void` `leftRotate(``int` `arr[], ``int` `d, ``int` `n) ` `    ``{ ` `        ``for` `(``int` `i = ``0``; i < d; i++) ` `            ``leftRotatebyOne(arr, n); ` `    ``} ` ` `  `    ``void` `leftRotatebyOne(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``int` `i, temp; ` `        ``temp = arr[``0``]; ` `        ``for` `(i = ``0``; i < n - ``1``; i++) ` `            ``arr[i] = arr[i + ``1``]; ` `        ``arr[i] = temp; ` `    ``} ` ` `  `    ``/* utility function to print an array */` `    ``void` `printArray(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `            ``System.out.print(arr[i] + ``" "``); ` `    ``} ` ` `  `    ``// Driver program to test above functions ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``RotateArray rotate = ``new` `RotateArray(); ` `        ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7` `}; ` `        ``rotate.leftRotate(arr, ``2``, ``7``); ` `        ``rotate.printArray(arr, ``7``); ` `    ``} ` `} ` ` `  `// This code has been contributed by Mayank Jaiswal `

Python3

 `# Python3 program to rotate an array by  ` `# d elements  ` `# Function to left rotate arr[] of size n by d*/ ` `def` `leftRotate(arr, d, n): ` `    ``for` `i ``in` `range``(d): ` `        ``leftRotatebyOne(arr, n) ` ` `  `# Function to left Rotate arr[] of size n by 1*/  ` `def` `leftRotatebyOne(arr, n): ` `    ``temp ``=` `arr[``0``] ` `    ``for` `i ``in` `range``(n``-``1``): ` `        ``arr[i] ``=` `arr[i ``+` `1``] ` `    ``arr[n``-``1``] ``=` `temp ` `         `  ` `  `# utility function to print an array */ ` `def` `printArray(arr, size): ` `    ``for` `i ``in` `range``(size): ` `        ``print` `(``"% d"``%` `arr[i], end ``=``" "``) ` ` `  `  `  `# Driver program to test above functions */ ` `arr ``=` `[``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``] ` `leftRotate(arr, ``2``, ``7``) ` `printArray(arr, ``7``) ` ` `  `# This code is contributed by Shreyanshi Arun `

C#

 `// C# program for array rotation ` `using` `System; ` ` `  `class` `GFG { ` `    ``/* Function to left rotate arr[] ` `    ``of size n by d*/` `    ``static` `void` `leftRotate(``int``[] arr, ``int` `d, ` `                           ``int` `n) ` `    ``{ ` `        ``for` `(``int` `i = 0; i < d; i++) ` `            ``leftRotatebyOne(arr, n); ` `    ``} ` ` `  `    ``static` `void` `leftRotatebyOne(``int``[] arr, ``int` `n) ` `    ``{ ` `        ``int` `i, temp = arr[0]; ` `        ``for` `(i = 0; i < n - 1; i++) ` `            ``arr[i] = arr[i + 1]; ` ` `  `        ``arr[i] = temp; ` `    ``} ` ` `  `    ``/* utility function to print an array */` `    ``static` `void` `printArray(``int``[] arr, ``int` `size) ` `    ``{ ` `        ``for` `(``int` `i = 0; i < size; i++) ` `            ``Console.Write(arr[i] + ``" "``); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int``[] arr = { 1, 2, 3, 4, 5, 6, 7 }; ` `        ``leftRotate(arr, 2, 7); ` `        ``printArray(arr, 7); ` `    ``} ` `} ` ` `  `// This code is contributed by Sam007 `

PHP

 ` `

Output :

```3 4 5 6 7 1 2
```

Time complexity : O(n * d)
Auxiliary Space : O(1)

METHOD 3 (A Juggling Algorithm)
This is an extension of method 2. Instead of moving one by one, divide the array in different sets
where number of sets is equal to GCD of n and d and move the elements within sets.
If GCD is 1 as is for the above example array (n = 7 and d =2), then elements will be moved within one set only, we just start with temp = arr[0] and keep moving arr[I+d] to arr[I] and finally store temp at the right place.

Here is an example for n =12 and d = 3. GCD is 3 and

```Let arr[] be {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

a) Elements are first moved in first set – (See below
diagram for this movement)

arr[] after this step --> {4 2 3 7 5 6 10 8 9 1 11 12}

b)    Then in second set.
arr[] after this step --> {4 5 3 7 8 6 10 11 9 1 2 12}

c)    Finally in third set.
arr[] after this step --> {4 5 6 7 8 9 10 11 12 1 2 3}
```

Below is the implementation of the above approach :

C++

 `// C++ program to rotate an array by ` `// d elements ` `#include ` `using` `namespace` `std; ` ` `  `/*Fuction to get gcd of a and b*/` `int` `gcd(``int` `a, ``int` `b) ` `{ ` `    ``if` `(b == 0) ` `        ``return` `a; ` ` `  `    ``else` `        ``return` `gcd(b, a % b); ` `} ` ` `  `/*Function to left rotate arr[] of siz n by d*/` `void` `leftRotate(``int` `arr[], ``int` `d, ``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i < gcd(d, n); i++) { ` `        ``/* move i-th values of blocks */` `        ``int` `temp = arr[i]; ` `        ``int` `j = i; ` ` `  `        ``while` `(1) { ` `            ``int` `k = j + d; ` `            ``if` `(k >= n) ` `                ``k = k - n; ` ` `  `            ``if` `(k == i) ` `                ``break``; ` ` `  `            ``arr[j] = arr[k]; ` `            ``j = k; ` `        ``} ` `        ``arr[j] = temp; ` `    ``} ` `} ` ` `  `// Function to print an array ` `void` `printArray(``int` `arr[], ``int` `size) ` `{ ` `    ``for` `(``int` `i = 0; i < size; i++) ` `        ``cout << arr[i] << ``" "``; ` `} ` ` `  `/* Driver program to test above functions */` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3, 4, 5, 6, 7 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` ` `  `    ``// Function calling ` `    ``leftRotate(arr, 2, n); ` `    ``printArray(arr, n); ` ` `  `    ``return` `0; ` `} `

C

 `// C program to rotate an array by  ` `// d elements  ` `#include ` ` `  `/* function to print an array */` `void` `printArray(``int` `arr[], ``int` `size); ` ` `  `/*Fuction to get gcd of a and b*/` `int` `gcd(``int` `a, ``int` `b); ` ` `  `/*Function to left rotate arr[] of siz n by d*/` `void` `leftRotate(``int` `arr[], ``int` `d, ``int` `n) ` `{ ` `    ``int` `i, j, k, temp; ` `    ``for` `(i = 0; i < gcd(d, n); i++) { ` `        ``/* move i-th values of blocks */` `        ``temp = arr[i]; ` `        ``j = i; ` `        ``while` `(1) { ` `            ``k = j + d; ` `            ``if` `(k >= n) ` `                ``k = k - n; ` `            ``if` `(k == i) ` `                ``break``; ` `            ``arr[j] = arr[k]; ` `            ``j = k; ` `        ``} ` `        ``arr[j] = temp; ` `    ``} ` `} ` ` `  `/*UTILITY FUNCTIONS*/` `/* function to print an array */` `void` `printArray(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `i; ` `    ``for` `(i = 0; i < n; i++) ` `        ``printf``(``"%d "``, arr[i]); ` `} ` ` `  `/*Fuction to get gcd of a and b*/` `int` `gcd(``int` `a, ``int` `b) ` `{ ` `    ``if` `(b == 0) ` `        ``return` `a; ` `    ``else` `        ``return` `gcd(b, a % b); ` `} ` ` `  `/* Driver program to test above functions */` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3, 4, 5, 6, 7 }; ` `    ``leftRotate(arr, 2, 7); ` `    ``printArray(arr, 7); ` `    ``getchar``(); ` `    ``return` `0; ` `} `

Java

 `// Java program to rotate an array by  ` `// d elements  ` `class` `RotateArray { ` `    ``/*Function to left rotate arr[] of siz n by d*/` `    ``void` `leftRotate(``int` `arr[], ``int` `d, ``int` `n) ` `    ``{ ` `        ``int` `i, j, k, temp; ` `        ``for` `(i = ``0``; i < gcd(d, n); i++) { ` `            ``/* move i-th values of blocks */` `            ``temp = arr[i]; ` `            ``j = i; ` `            ``while` `(``true``) { ` `                ``k = j + d; ` `                ``if` `(k >= n) ` `                    ``k = k - n; ` `                ``if` `(k == i) ` `                    ``break``; ` `                ``arr[j] = arr[k]; ` `                ``j = k; ` `            ``} ` `            ``arr[j] = temp; ` `        ``} ` `    ``} ` ` `  `    ``/*UTILITY FUNCTIONS*/` ` `  `    ``/* function to print an array */` `    ``void` `printArray(``int` `arr[], ``int` `size) ` `    ``{ ` `        ``int` `i; ` `        ``for` `(i = ``0``; i < size; i++) ` `            ``System.out.print(arr[i] + ``" "``); ` `    ``} ` ` `  `    ``/*Fuction to get gcd of a and b*/` `    ``int` `gcd(``int` `a, ``int` `b) ` `    ``{ ` `        ``if` `(b == ``0``) ` `            ``return` `a; ` `        ``else` `            ``return` `gcd(b, a % b); ` `    ``} ` ` `  `    ``// Driver program to test above functions ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``RotateArray rotate = ``new` `RotateArray(); ` `        ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7` `}; ` `        ``rotate.leftRotate(arr, ``2``, ``7``); ` `        ``rotate.printArray(arr, ``7``); ` `    ``} ` `} ` ` `  `// This code has been contributed by Mayank Jaiswal `

Python3

 `# Python3 program to rotate an array by  ` `# d elements  ` `# Function to left rotate arr[] of size n by d ` `def` `leftRotate(arr, d, n): ` `    ``for` `i ``in` `range``(gcd(d, n)): ` `         `  `        ``# move i-th values of blocks  ` `        ``temp ``=` `arr[i] ` `        ``j ``=` `i ` `        ``while` `1``: ` `            ``k ``=` `j ``+` `d ` `            ``if` `k >``=` `n: ` `                ``k ``=` `k ``-` `n ` `            ``if` `k ``=``=` `i: ` `                ``break` `            ``arr[j] ``=` `arr[k] ` `            ``j ``=` `k ` `        ``arr[j] ``=` `temp ` ` `  `# UTILITY FUNCTIONS ` `# function to print an array  ` `def` `printArray(arr, size): ` `    ``for` `i ``in` `range``(size): ` `        ``print` `(``"% d"` `%` `arr[i], end ``=``" "``) ` `  `  `# Fuction to get gcd of a and b ` `def` `gcd(a, b): ` `    ``if` `b ``=``=` `0``: ` `        ``return` `a; ` `    ``else``: ` `        ``return` `gcd(b, a ``%` `b) ` `  `  `# Driver program to test above functions  ` `arr ``=` `[``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``] ` `leftRotate(arr, ``2``, ``7``) ` `printArray(arr, ``7``) ` ` `  `# This code is contributed by Shreyanshi Arun `

C#

 `// C# program for array rotation ` `using` `System; ` ` `  `class` `GFG { ` `    ``/* Function to left rotate arr[]  ` `    ``of size n by d*/` `    ``static` `void` `leftRotate(``int``[] arr, ``int` `d, ` `                           ``int` `n) ` `    ``{ ` `        ``int` `i, j, k, temp; ` `        ``for` `(i = 0; i < gcd(d, n); i++) { ` `            ``/* move i-th values of blocks */` `            ``temp = arr[i]; ` `            ``j = i; ` `            ``while` `(``true``) { ` `                ``k = j + d; ` `                ``if` `(k >= n) ` `                    ``k = k - n; ` `                ``if` `(k == i) ` `                    ``break``; ` `                ``arr[j] = arr[k]; ` `                ``j = k; ` `            ``} ` `            ``arr[j] = temp; ` `        ``} ` `    ``} ` ` `  `    ``/*UTILITY FUNCTIONS*/` `    ``/* Function to print an array */` `    ``static` `void` `printArray(``int``[] arr, ``int` `size) ` `    ``{ ` `        ``for` `(``int` `i = 0; i < size; i++) ` `            ``Console.Write(arr[i] + ``" "``); ` `    ``} ` ` `  `    ``/* Fuction to get gcd of a and b*/` `    ``static` `int` `gcd(``int` `a, ``int` `b) ` `    ``{ ` `        ``if` `(b == 0) ` `            ``return` `a; ` `        ``else` `            ``return` `gcd(b, a % b); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int``[] arr = { 1, 2, 3, 4, 5, 6, 7 }; ` `        ``leftRotate(arr, 2, 7); ` `        ``printArray(arr, 7); ` `    ``} ` `} ` ` `  `// This code is contributed by Sam007 `

Output :

```3 4 5 6 7 1 2
```

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

Please see following posts for other methods of array rotation:
Block swap algorithm for array rotation
Reversal algorithm for array rotation