Write a function rotate(arr[], d, n) that rotates arr[] of size n by d elements.
Example :
Input : arr[] = [1, 2, 3, 4, 5, 6, 7] d = 2 Output : arr[] = [3, 4, 5, 6, 7, 1, 2]
Rotation of the above array by 2 will make array
The first 3 methods to rotate an array by d elements has been discussed in this post.
Method 4 (The Reversal Algorithm) :
Algorithm :
rotate(arr[], d, n) reverse(arr[], 1, d) ; reverse(arr[], d + 1, n); reverse(arr[], 1, n);
Let AB are the two parts of the input array where A = arr[0..d-1] and B = arr[d..n-1]. The idea of the algorithm is :
- Reverse A to get ArB, where Ar is reverse of A.
- Reverse B to get ArBr, where Br is reverse of B.
- Reverse all to get (ArBr) r = BA.
Example :
Let the array be arr[] = [1, 2, 3, 4, 5, 6, 7], d =2 and n = 7
A = [1, 2] and B = [3, 4, 5, 6, 7]
- Reverse A, we get ArB = [2, 1, 3, 4, 5, 6, 7]
- Reverse B, we get ArBr = [2, 1, 7, 6, 5, 4, 3]
- Reverse all, we get (ArBr)r = [3, 4, 5, 6, 7, 1, 2]
Below is the implementation of the above approach :
<?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 ?> |
Output :
3 4 5 6 7 1 2
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 refer complete article on Reversal algorithm for array rotation for more details!