Algorithm to rotate an array in linear time

Question

How to rotate an integer array by i times using swap function only in linear time.

Answer 1

Let us say we have a function called arr_reverse(arr,i,j) which reverses the elements of the array arr between index i and j using the swap function.

Example:

arr = {1,2,3,4,5} 
i = 0
j = 2

then the function will return:

{3,2,1,4,5} 
 ^^^^^

Implementing this function is straight forward and is O(N).

Now let's use this function in rotating the array.

arr     = {1,2,3,4,5} // input array
k       = 2 // amount of right rotation
result  = {4,5,1,2,3} // expected result 
l       = 5 // length of array.

Step 1: Call arr_reverse(arr,l-k,l-1) which is arr_reverse(arr,3,4)
we get {1,2,3,5,4} 
              ^^^

Step 2: Call arr_reverse(arr,0,l-k-1) which is arr_reverse(arr,0,2)
we get {3,2,1,5,4}
        ^^^^^     

Step 3: Call arr_reverse(arr,0,l-1) which is arr_reverse(arr,0,4)
we get {4,5,1,2,3} 
        ^^^^^^^^^

The entire process makes use of arr_reverse 3 times, making it O(N)