Block swap algorithm for array rotation
The block swap algorithm is a popular method for rotating an array in-place. It works by dividing the array into two blocks, and then swapping the elements of these blocks in a specific way to achieve the desired rotation.
Let's say we have an array of length n and we want to rotate it by k positions. We first divide the array into two blocks, A and B, where A contains the first k elements of the array and B contains the remaining n-k elements.
To perform the rotation, we swap the elements of A and B in the following way:
- Swap the first element of A with the first element of B.
- Swap the second element of A with the second-to-last element of B.
- Swap the third element of A with the third-to-last element of B.
- Continue this pattern, swapping the i-th element of A with the (n-k+i)-th element of B, until we have swapped all k elements of A with their corresponding elements in B.
After performing these swaps, the array will be rotated by k positions. The time complexity of this algorithm is O(n), as we only need to perform n swaps.
It is worth noting that this algorithm only works if k is less than n. If k is greater than or equal to n, we can simply take the remainder of k when divided by n and perform the rotation using that value instead.
Code Solution
// C program for
// Block swap algorithm for array rotation
#include <stdio.h>
// This is display the given array elements
void printData(int arr[], int n)
{
// Executing the loop through by the size of array
for (int i = 0; i < n; ++i)
{
printf(" %d", arr[i]);
}
printf("\n");
}
// This is swapping given block elements
void swapSubArray(int arr[], int s, int e, int n)
{
// Executing the loop through by the n
for (int i = 0; i < n; i++)
{
// Swap array element
arr[s + i] = arr[s + i] + arr[e + i];
arr[e + i] = arr[s + i] - arr[e + i];
arr[s + i] = arr[s + i] - arr[e + i];
}
}
void blockSwapAlgo(int arr[], int n, int k)
{
if (k == 0 || k >= n)
{
// When k = 0 then result are not change
// And k >= n is greater than or equal to size n
return;
}
// Display given array
printf("\n Before rotation ");
printf("\n Array : ");
printData(arr, n);
printf(" Given rotation k is : %d", k);
int i = k;
int j = n - k;
while (i != j)
{
if (i < j)
{
// When i is less than j
swapSubArray(arr, k - i, k + j - i, i);
// Reduce i in j
j = j - i;
}
else
{
// When j is less than i
swapSubArray(arr, k - i, k, j);
i = i - j;
}
}
swapSubArray(arr, k - i, k, i);
// Display resultant array
printf("\n After rotation ");
printf("\n Array : ");
printData(arr, n);
}
int main(int argc, char const *argv[])
{
// Array of integer elements
int arr[] = {
8 , 7 , 6 , 5 , 4 , 3 , 2 , 1 , 0
};
// Get the number of elements
int n = sizeof(arr) / sizeof(arr[0]);
// Test case
blockSwapAlgo(arr, n, 5);
blockSwapAlgo(arr, n, 3);
return 0;
}
input
Before rotation
Array : 8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array : 3 2 1 0 8 7 6 5 4
Before rotation
Array : 3 2 1 0 8 7 6 5 4
Given rotation k is : 3
After rotation
Array : 0 8 7 6 5 4 3 2 1
/*
Java Program for
Block swap algorithm for array rotation
*/
public class Rotation
{
// This is display the given array elements
public void printData(int[] arr, int n)
{
// Executing the loop through by the size of array
for (int i = 0; i < n; ++i)
{
System.out.print(" " + arr[i]);
}
System.out.print("\n");
}
// This is swapping given block elements
public void swapSubArray(int[] arr, int s, int e, int n)
{
// Executing the loop through by the n
for (int i = 0; i < n; i++)
{
// Swap array element
arr[s + i] = arr[s + i] + arr[e + i];
arr[e + i] = arr[s + i] - arr[e + i];
arr[s + i] = arr[s + i] - arr[e + i];
}
}
public void blockSwapAlgo(int[] arr, int n, int k)
{
if (k == 0 || k >= n)
{
// When k = 0 then result are not change
// And k >= n is greater than or equal to size n
return;
}
// Display given array
System.out.println(" Before rotation ");
System.out.println(" Array : ");
printData(arr, n);
System.out.println(" Given rotation k is : " + k);
int i = k;
int j = n - k;
while (i != j)
{
if (i < j)
{
// When i is less than j
swapSubArray(arr, k - i, k + j - i, i);
// Reduce i in j
j = j - i;
}
else
{
// When j is less than i
swapSubArray(arr, k - i, k, j);
i = i - j;
}
}
swapSubArray(arr, k - i, k, i);
// Display resultant array
System.out.println(" After rotation ");
System.out.println(" Array : ");
printData(arr, n);
System.out.print("\n");
}
public static void main(String[] args)
{
Rotation task = new Rotation();
// Array of integer elements
int[] arr = {
8 , 7 , 6 , 5 , 4 , 3 , 2 , 1 , 0
};
// Get the number of elements
int n = arr.length;
// Test case
task.blockSwapAlgo(arr, n, 5);
task.blockSwapAlgo(arr, n, 3);
}
}
input
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array :
3 2 1 0 8 7 6 5 4
Before rotation
Array :
3 2 1 0 8 7 6 5 4
Given rotation k is : 3
After rotation
Array :
0 8 7 6 5 4 3 2 1
// Include header file
#include <iostream>
using namespace std;
/*
C++ Program for
Block swap algorithm for array rotation
*/
class Rotation
{
public:
// This is display the given array elements
void printData(int arr[], int n)
{
// Executing the loop through by the size of array
for (int i = 0; i < n; ++i)
{
cout << " " << arr[i];
}
cout << "\n";
}
// This is swapping given block elements
void swapSubArray(int arr[], int s, int e, int n)
{
// Executing the loop through by the n
for (int i = 0; i < n; i++)
{
// Swap array element
arr[s + i] = arr[s + i] + arr[e + i];
arr[e + i] = arr[s + i] - arr[e + i];
arr[s + i] = arr[s + i] - arr[e + i];
}
}
void blockSwapAlgo(int arr[], int n, int k)
{
if (k == 0 || k >= n)
{
// When k = 0 then result are not change
// And k >= n is greater than or equal to size n
return;
}
// Display given array
cout << " Before rotation " << endl;
cout << " Array : " << endl;
this->printData(arr, n);
cout << " Given rotation k is : " << k << endl;
int i = k;
int j = n - k;
while (i != j)
{
if (i < j)
{
// When i is less than j
this->swapSubArray(arr, k - i, k + j - i, i);
// Reduce i in j
j = j - i;
}
else
{
// When j is less than i
this->swapSubArray(arr, k - i, k, j);
i = i - j;
}
}
this->swapSubArray(arr, k - i, k, i);
// Display resultant array
cout << " After rotation " << endl;
cout << " Array : " << endl;
this->printData(arr, n);
cout << "\n";
}
};
int main()
{
Rotation *task = new Rotation();
// Array of integer elements
int arr[] = {
8 , 7 , 6 , 5 , 4 , 3 , 2 , 1 , 0
};
// Get the number of elements
int n = sizeof(arr) / sizeof(arr[0]);
// Test case
task->blockSwapAlgo(arr, n, 5);
task->blockSwapAlgo(arr, n, 3);
return 0;
}
input
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array :
3 2 1 0 8 7 6 5 4
Before rotation
Array :
3 2 1 0 8 7 6 5 4
Given rotation k is : 3
After rotation
Array :
0 8 7 6 5 4 3 2 1
// Include namespace system
using System;
/*
Csharp Program for
Block swap algorithm for array rotation
*/
public class Rotation
{
// This is display the given array elements
public void printData(int[] arr, int n)
{
// Executing the loop through by the size of array
for (int i = 0; i < n; ++i)
{
Console.Write(" " + arr[i]);
}
Console.Write("\n");
}
// This is swapping given block elements
public void swapSubArray(int[] arr, int s, int e, int n)
{
// Executing the loop through by the n
for (int i = 0; i < n; i++)
{
// Swap array element
arr[s + i] = arr[s + i] + arr[e + i];
arr[e + i] = arr[s + i] - arr[e + i];
arr[s + i] = arr[s + i] - arr[e + i];
}
}
public void blockSwapAlgo(int[] arr, int n, int k)
{
if (k == 0 || k >= n)
{
// When k = 0 then result are not change
// And k >= n is greater than or equal to size n
return;
}
// Display given array
Console.WriteLine(" Before rotation ");
Console.WriteLine(" Array : ");
this.printData(arr, n);
Console.WriteLine(" Given rotation k is : " + k);
int i = k;
int j = n - k;
while (i != j)
{
if (i < j)
{
// When i is less than j
this.swapSubArray(arr, k - i, k + j - i, i);
// Reduce i in j
j = j - i;
}
else
{
// When j is less than i
this.swapSubArray(arr, k - i, k, j);
i = i - j;
}
}
this.swapSubArray(arr, k - i, k, i);
// Display resultant array
Console.WriteLine(" After rotation ");
Console.WriteLine(" Array : ");
this.printData(arr, n);
Console.Write("\n");
}
public static void Main(String[] args)
{
Rotation task = new Rotation();
// Array of integer elements
int[] arr = {
8 , 7 , 6 , 5 , 4 , 3 , 2 , 1 , 0
};
// Get the number of elements
int n = arr.Length;
// Test case
task.blockSwapAlgo(arr, n, 5);
task.blockSwapAlgo(arr, n, 3);
}
}
input
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array :
3 2 1 0 8 7 6 5 4
Before rotation
Array :
3 2 1 0 8 7 6 5 4
Given rotation k is : 3
After rotation
Array :
0 8 7 6 5 4 3 2 1
<?php
/*
Php Program for
Block swap algorithm for array rotation
*/
class Rotation
{
// This is display the given array elements
public function printData($arr, $n)
{
// Executing the loop through by the size of array
for ($i = 0; $i < $n; ++$i)
{
echo " ".strval($arr[$i]);
}
echo "\n";
}
// This is swapping given block elements
public function swapSubArray($arr, $s, $e, $n)
{
// Executing the loop through by the n
for ($i = 0; $i < $n; $i++)
{
// Swap array element
$arr[$s + $i] = $arr[$s + $i] + $arr[$e + $i];
$arr[$e + $i] = $arr[$s + $i] - $arr[$e + $i];
$arr[$s + $i] = $arr[$s + $i] - $arr[$e + $i];
}
}
public function blockSwapAlgo($arr, $n, $k)
{
if ($k == 0 || $k >= $n)
{
// When k = 0 then result are not change
// And k >= n is greater than or equal to size n
return;
}
// Display given array
echo " Before rotation ".
"\n";
echo " Array : ".
"\n";
$this->printData($arr, $n);
echo " Given rotation k is : ".strval($k).
"\n";
$i = $k;
$j = $n - $k;
while ($i != $j)
{
if ($i < $j)
{
// When i is less than j
$this->swapSubArray($arr, $k - $i, $k + $j - $i, $i);
// Reduce i in j
$j = $j - $i;
}
else
{
// When j is less than i
$this->swapSubArray($arr, $k - $i, $k, $j);
$i = $i - $j;
}
}
$this->swapSubArray($arr, $k - $i, $k, $i);
// Display resultant array
echo " After rotation ".
"\n";
echo " Array : ".
"\n";
$this->printData($arr, $n);
echo "\n";
}
}
function main()
{
$task = new Rotation();
// Array of integer elements
$arr = array(8, 7, 6, 5, 4, 3, 2, 1, 0);
// Get the number of elements
$n = count($arr);
// Test case
$task->blockSwapAlgo($arr, $n, 5);
$task->blockSwapAlgo($arr, $n, 3);
}
main();
input
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array :
8 7 6 5 4 3 2 1 0
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 3
After rotation
Array :
8 7 6 5 4 3 2 1 0
/*
Node JS Program for
Block swap algorithm for array rotation
*/
class Rotation
{
// This is display the given array elements
printData(arr, n)
{
// Executing the loop through by the size of array
for (var i = 0; i < n; ++i)
{
process.stdout.write(" " + arr[i]);
}
process.stdout.write("\n");
}
// This is swapping given block elements
swapSubArray(arr, s, e, n)
{
// Executing the loop through by the n
for (var i = 0; i < n; i++)
{
// Swap array element
arr[s + i] = arr[s + i] + arr[e + i];
arr[e + i] = arr[s + i] - arr[e + i];
arr[s + i] = arr[s + i] - arr[e + i];
}
}
blockSwapAlgo(arr, n, k)
{
if (k == 0 || k >= n)
{
// When k = 0 then result are not change
// And k >= n is greater than or equal to size n
return;
}
// Display given array
console.log(" Before rotation ");
console.log(" Array : ");
this.printData(arr, n);
console.log(" Given rotation k is : " + k);
var i = k;
var j = n - k;
while (i != j)
{
if (i < j)
{
// When i is less than j
this.swapSubArray(arr, k - i, k + j - i, i);
// Reduce i in j
j = j - i;
}
else
{
// When j is less than i
this.swapSubArray(arr, k - i, k, j);
i = i - j;
}
}
this.swapSubArray(arr, k - i, k, i);
// Display resultant array
console.log(" After rotation ");
console.log(" Array : ");
this.printData(arr, n);
process.stdout.write("\n");
}
}
function main()
{
var task = new Rotation();
// Array of integer elements
var arr = [8, 7, 6, 5, 4, 3, 2, 1, 0];
// Get the number of elements
var n = arr.length;
// Test case
task.blockSwapAlgo(arr, n, 5);
task.blockSwapAlgo(arr, n, 3);
}
main();
input
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array :
3 2 1 0 8 7 6 5 4
Before rotation
Array :
3 2 1 0 8 7 6 5 4
Given rotation k is : 3
After rotation
Array :
0 8 7 6 5 4 3 2 1
# Python 3 Program for
# Block swap algorithm for array rotation
class Rotation :
# This is display the given list elements
def printData(self, arr, n) :
i = 0
# Executing the loop through by the size of list
while (i < n) :
print(" ", arr[i], end = "")
i += 1
print(end = "\n")
# This is swapping given block elements
def swapSubArray(self, arr, s, e, n) :
i = 0
# Executing the loop through by the n
while (i < n) :
# Swap list element
arr[s + i] = arr[s + i] + arr[e + i]
arr[e + i] = arr[s + i] - arr[e + i]
arr[s + i] = arr[s + i] - arr[e + i]
i += 1
def blockSwapAlgo(self, arr, n, k) :
if (k == 0 or k >= n) :
# When k = 0 then result are not change
# And k >= n is greater than or equal to size n
return
# Display given list
print(" Before rotation ")
print(" Array : ")
self.printData(arr, n)
print(" Given rotation k is : ", k)
i = k
j = n - k
while (i != j) :
if (i < j) :
# When i is less than j
self.swapSubArray(arr, k - i, k + j - i, i)
# Reduce i in j
j = j - i
else :
# When j is less than i
self.swapSubArray(arr, k - i, k, j)
i = i - j
self.swapSubArray(arr, k - i, k, i)
# Display resultant list
print(" After rotation ")
print(" Array : ")
self.printData(arr, n)
print(end = "\n")
def main() :
task = Rotation()
arr = [8, 7, 6, 5, 4, 3, 2, 1, 0]
n = len(arr)
# Test case
task.blockSwapAlgo(arr, n, 5)
task.blockSwapAlgo(arr, n, 3)
if __name__ == "__main__": main()
input
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array :
3 2 1 0 8 7 6 5 4
Before rotation
Array :
3 2 1 0 8 7 6 5 4
Given rotation k is : 3
After rotation
Array :
0 8 7 6 5 4 3 2 1
# Ruby Program for
# Block swap algorithm for array rotation
class Rotation
# This is display the given array elements
def printData(arr, n)
i = 0
# Executing the loop through by the size of array
while (i < n)
print(" ", arr[i])
i += 1
end
print("\n")
end
# This is swapping given block elements
def swapSubArray(arr, s, e, n)
i = 0
# Executing the loop through by the n
while (i < n)
# Swap array element
arr[s + i] = arr[s + i] + arr[e + i]
arr[e + i] = arr[s + i] - arr[e + i]
arr[s + i] = arr[s + i] - arr[e + i]
i += 1
end
end
def blockSwapAlgo(arr, n, k)
if (k == 0 || k >= n)
# When k = 0 then result are not change
# And k >= n is greater than or equal to size n
return
end
# Display given array
print(" Before rotation ", "\n")
print(" Array : ", "\n")
self.printData(arr, n)
print(" Given rotation k is : ", k, "\n")
i = k
j = n - k
while (i != j)
if (i < j)
# When i is less than j
self.swapSubArray(arr, k - i, k + j - i, i)
# Reduce i in j
j = j - i
else
# When j is less than i
self.swapSubArray(arr, k - i, k, j)
i = i - j
end
end
self.swapSubArray(arr, k - i, k, i)
# Display resultant array
print(" After rotation ", "\n")
print(" Array : ", "\n")
self.printData(arr, n)
print("\n")
end
end
def main()
task = Rotation.new()
# Array of integer elements
arr = [8, 7, 6, 5, 4, 3, 2, 1, 0]
# Get the number of elements
n = arr.length
# Test case
task.blockSwapAlgo(arr, n, 5)
task.blockSwapAlgo(arr, n, 3)
end
main()
input
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array :
3 2 1 0 8 7 6 5 4
Before rotation
Array :
3 2 1 0 8 7 6 5 4
Given rotation k is : 3
After rotation
Array :
0 8 7 6 5 4 3 2 1
/*
Scala Program for
Block swap algorithm for array rotation
*/
class Rotation()
{
// This is display the given array elements
def printData(arr: Array[Int], n: Int): Unit = {
var i: Int = 0;
// Executing the loop through by the size of array
while (i < n)
{
print(" " + arr(i));
i += 1;
}
print("\n");
}
// This is swapping given block elements
def swapSubArray(arr: Array[Int], s: Int, e: Int, n: Int): Unit = {
var i: Int = 0;
// Executing the loop through by the n
while (i < n)
{
// Swap array element
arr(s + i) = arr(s + i) + arr(e + i);
arr(e + i) = arr(s + i) - arr(e + i);
arr(s + i) = arr(s + i) - arr(e + i);
i += 1;
}
}
def blockSwapAlgo(arr: Array[Int], n: Int, k: Int): Unit = {
if (k == 0 || k >= n)
{
// When k = 0 then result are not change
// And k >= n is greater than or equal to size n
return;
}
// Display given array
println(" Before rotation ");
println(" Array : ");
printData(arr, n);
println(" Given rotation k is : " + k);
var i: Int = k;
var j: Int = n - k;
while (i != j)
{
if (i < j)
{
// When i is less than j
swapSubArray(arr, k - i, k + j - i, i);
// Reduce i in j
j = j - i;
}
else
{
// When j is less than i
swapSubArray(arr, k - i, k, j);
i = i - j;
}
}
swapSubArray(arr, k - i, k, i);
// Display resultant array
println(" After rotation ");
println(" Array : ");
printData(arr, n);
print("\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Rotation = new Rotation();
// Array of integer elements
var arr: Array[Int] = Array(8, 7, 6, 5, 4, 3, 2, 1, 0);
// Get the number of elements
var n: Int = arr.length;
// Test case
task.blockSwapAlgo(arr, n, 5);
task.blockSwapAlgo(arr, n, 3);
}
}
input
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array :
3 2 1 0 8 7 6 5 4
Before rotation
Array :
3 2 1 0 8 7 6 5 4
Given rotation k is : 3
After rotation
Array :
0 8 7 6 5 4 3 2 1
/*
Swift 4 Program for
Block swap algorithm for array rotation
*/
class Rotation
{
// This is display the given array elements
func printData(_ arr: [Int], _ n: Int)
{
var i: Int = 0;
// Executing the loop through by the size of array
while (i < n)
{
print(" ", arr[i], terminator: "");
i += 1;
}
print(terminator: "\n");
}
// This is swapping given block elements
func swapSubArray(_ arr: inout[Int], _ s: Int, _ e: Int, _ n: Int)
{
var i: Int = 0;
// Executing the loop through by the n
while (i < n)
{
// Swap array element
arr[s + i] = arr[s + i] + arr[e + i];
arr[e + i] = arr[s + i] - arr[e + i];
arr[s + i] = arr[s + i] - arr[e + i];
i += 1;
}
}
func blockSwapAlgo(_ arr: inout[Int], _ n: Int, _ k: Int)
{
if (k == 0 || k >= n)
{
// When k = 0 then result are not change
// And k >= n is greater than or equal to size n
return;
}
// Display given array
print(" Before rotation ");
print(" Array : ");
self.printData(arr, n);
print(" Given rotation k is : ", k);
var i: Int = k;
var j: Int = n - k;
while (i != j)
{
if (i < j)
{
// When i is less than j
self.swapSubArray(&arr, k - i, k + j - i, i);
// Reduce i in j
j = j - i;
}
else
{
// When j is less than i
self.swapSubArray(&arr, k - i, k, j);
i = i - j;
}
}
self.swapSubArray(&arr, k - i, k, i);
// Display resultant array
print(" After rotation ");
print(" Array : ");
self.printData(arr, n);
print(terminator: "\n");
}
}
func main()
{
let task: Rotation = Rotation();
// Array of integer elements
var arr: [Int] = [8, 7, 6, 5, 4, 3, 2, 1, 0];
// Get the number of elements
let n: Int = arr.count;
// Test case
task.blockSwapAlgo(&arr, n, 5);
task.blockSwapAlgo(&arr, n, 3);
}
main();
input
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array :
3 2 1 0 8 7 6 5 4
Before rotation
Array :
3 2 1 0 8 7 6 5 4
Given rotation k is : 3
After rotation
Array :
0 8 7 6 5 4 3 2 1
/*
Kotlin Program for
Block swap algorithm for array rotation
*/
class Rotation
{
// This is display the given array elements
fun printData(arr: Array < Int > , n: Int): Unit
{
var i: Int = 0;
while (i < n)
{
print(" " + arr[i].toString());
i += 1;
}
print("\n");
}
// This is swapping given block elements
fun swapSubArray(arr: Array < Int > , s: Int, e: Int, n: Int): Unit
{
var i: Int = 0;
while (i < n)
{
// Swap array element
arr[s + i] = arr[s + i] + arr[e + i];
arr[e + i] = arr[s + i] - arr[e + i];
arr[s + i] = arr[s + i] - arr[e + i];
i += 1;
}
}
fun blockSwapAlgo(arr: Array < Int > , n: Int, k: Int): Unit
{
if (k == 0 || k >= n)
{
// When k = 0 then result are not change
// And k >= n is greater than or equal to size n
return;
}
// Display given array
println(" Before rotation ");
println(" Array : ");
this.printData(arr, n);
println(" Given rotation k is : " + k.toString());
var i: Int = k;
var j: Int = n - k;
while (i != j)
{
if (i < j)
{
// When i is less than j
this.swapSubArray(arr, k - i, k + j - i, i);
// Reduce i in j
j = j - i;
}
else
{
// When j is less than i
this.swapSubArray(arr, k - i, k, j);
i = i - j;
}
}
this.swapSubArray(arr, k - i, k, i);
// Display resultant array
println(" After rotation ");
println(" Array : ");
this.printData(arr, n);
print("\n");
}
}
fun main(args: Array < String > ): Unit
{
val task: Rotation = Rotation();
// Array of integer elements
val arr: Array < Int > = arrayOf(8, 7, 6, 5, 4, 3, 2, 1, 0);
// Get the number of elements
val n: Int = arr.count();
// Test case
task.blockSwapAlgo(arr, n, 5);
task.blockSwapAlgo(arr, n, 3);
}
input
Before rotation
Array :
8 7 6 5 4 3 2 1 0
Given rotation k is : 5
After rotation
Array :
3 2 1 0 8 7 6 5 4
Before rotation
Array :
3 2 1 0 8 7 6 5 4
Given rotation k is : 3
After rotation
Array :
0 8 7 6 5 4 3 2 1
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