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 Mth element of the array after K left rotations.
Examples:
Input: arr[] = {3, 4, 5, 23}, K = 2, M = 1
Output: 5
Explanation:Â
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: 5Â
Explanation:Â
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 Mth element of the final array.
Time Complexity: O(N * K)
Auxiliary Space: O(N)
Efficient Approach: To optimize the problem, observe the following points:
- 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.
- The Mth element of the array after K left rotations is
{ (K + M – 1) % N }th
element in the original array.
Â
Below is the implementation of the above approach:
Python3
def getFirstElement(a, N, K, M):
K % = N
index = (K + M - 1 ) % N
result = a[index]
return result
if __name__ = = '__main__' :
a = [ 3 , 4 , 5 , 23 ]
N = len (a)
K = 2
M = 1
print (getFirstElement(a, N, K, M))
|
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!
Last Updated :
14 Oct, 2022
Like Article
Save Article
Share your thoughts in the comments
Please Login to comment...