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

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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: 
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:
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 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:

  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.

  3.  
    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 %=
      
        # Mth element after k left rotations 
        # is (K+M-1)%N th element of the 
        # original array 
        index = (K + M - 1) %
      
        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!


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Last Updated : 14 Oct, 2022
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