Python3 Program to Find the Mth element of the Array after K left rotations

Given non-negative integers K, M, and an array arr[] with N elements find the M^th element of the array after K left rotations.

Examples:

Input: arr[] = {3, 4, 5, 23}, K = 2, M = 1
Output: 5
Explanation: 
The array after first left rotation a₁[ ] = {4, 5, 23, 3}
The array after second left rotation a₂[ ] = {5, 23, 3, 4}
1st element after 2 left rotations is 5.

Input: arr[] = {1, 2, 3, 4, 5}, K = 3, M = 2
Output: 5 
Explanation: 
The array after 3 left rotation has 5 at its second position.

Naive Approach: The idea is to Perform Left rotation operation K times and then find the M^th element of the final array.

Time Complexity: O(N * K)
Auxiliary Space: O(N)

Efficient Approach: To optimize the problem, observe the following points:

1. If the array is rotated N times it returns the initial array again.
   

   For example, a[ ] = {1, 2, 3, 4, 5}, K=5 then the array after 5 left rotation a₅[ ] = {1, 2, 3, 4, 5}.

   Therefore, the elements in the array after Kth rotation is the same as the element at index K%N in the original array.

2. The Mth element of the array after K left rotations is
   

   { (K + M – 1) % N }th

   element in the original array.


Below is the implementation of the above approach:

Python3
# Python3 program for the above approach

# Function to return Mth element of
# array after k left rotations
def getFirstElement(a, N, K, M):

    # The array comes to original state
    # after N rotations
    K %= N

    # Mth element after k left rotations
    # is (K+M-1)%N th element of the
    # original array
    index = (K + M - 1) % N

    result = a[index]

    # Return the result
    return result

# Driver Code
if __name__ == '__main__':

    # Array initialization
    a = [ 3, 4, 5, 23 ]

    # Size of the array
    N = len(a)

    # Given K rotation and Mth element
    # to be found after K rotation
    K = 2
    M = 1

    # Function call
    print(getFirstElement(a, N, K, M))

# This code is contributed by mohit kumar 29
Output:

5

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

Please refer complete article on Find the Mth element of the Array after K left rotations for more details!