C++ Program to Find the Mth element of the Array after K left rotations Last Updated : 14 Oct, 2022 Comments Improve Suggest changes Like Article Like Report 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 = 1Output: 5Explanation: 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 = 2Output: 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 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. Below is the implementation of the above approach: C++ // C++ program for the above approach #include <bits/stdc++.h> using namespace std; // Function to return Mth element of // array after k left rotations int getFirstElement(int a[], int N, int K, int 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 int index = (K + M - 1) % N; int result = a[index]; // Return the result return result; } // Driver Code int main() { // Array initialization int a[] = { 3, 4, 5, 23 }; // Size of the array int N = sizeof(a) / sizeof(a[0]); // Given K rotation and Mth element // to be found after K rotation int K = 2, M = 1; // Function call cout << getFirstElement(a, N, K, M); return 0; } 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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