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

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  • Last Updated : 27 Jan, 2022

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}
st 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:

    Javascript




    <script>
      
    // Javascript program for the above approach 
      
        // Function to return Mth element of
        // array after k left rotations
        function 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
            var index = (K + M - 1) % N;
      
            var result = a[index];
      
            // Return the result
            return result;
        }
      
        // Driver code
          
      
            // Array initialization
            var a = [ 3, 4, 5, 23 ];
      
            // Size of the array
            var N = a.length;
      
            // Given K rotation and Mth element
            // to be found after K rotation
            var K = 2, M = 1;
      
            // Function call
            document.write(getFirstElement(a, N, K, M));
      
    // This code contributed by gauravrajput1 
      
    </script>

    
    

    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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