Quickly find multiple left rotations of an array | Set 1

Given an array of size n and multiple values around which we need to left rotate the array. How to quickly find multiple left rotations?

Examples: 

Input: arr[] = {1, 3, 5, 7, 9}
           k1 = 1
           k2 = 3
           k3 = 4
           k4 = 6
Output: 3 5 7 9 1
              7 9 1 3 5
              9 1 3 5 7
              3 5 7 9 1

Input: arr[] = {1, 3, 5, 7, 9}
            k1 = 14 
Output: 9 1 3 5 7

Simple Approach: We have already discussed different approaches given in the below posts. 

1. Left Rotation of array (Simple and Juggling Algorithms).
2. Block swap algorithm for array rotation
3. Reversal algorithm for array rotation

The best of the above approaches take O(n) time and O(1) extra space. 

Simple Approach: We are using the reverse algorithm but this time for multiple k values - you can click on the above link to understand this approach.

Implementation:

5 7 9 1 3 
7 9 1 3 5 
9 1 3 5 7 

Time Complexity: O(n)
Auxiliary Space: O(n)

Efficient Approach: 

The above approaches work well when there is a single rotation required. The approaches also modify the original array. To handle multiple queries of array rotation, we use a temp array of size 2n and quickly handle rotations.

• Step 1: Copy the entire array two times in the temp[0..2n-1] array. 
• Step 2: Starting position of the array after k rotations in temp[] will be k % n. We do k 
• Step 3: Print temp[] array from k % n to k % n + n. 

Implementation:

5 7 9 1 3 
7 9 1 3 5 
9 1 3 5 7 

Time Complexity: O(n)
Note that the task to find starting address of rotation takes O(1) time. It is printing the elements that take O(n) time.

Auxiliary Space: O(n)

Space-optimized Approach: The above method takes extra space. Below given is a space-optimized solution. Thanks to frenzy77 for suggesting this approach.

Implementation:

5 7 9 1 3 
7 9 1 3 5 
9 1 3 5 7 

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