Given non-negative integers K, M, and an array arr[ ] consisting of N elements, the task is to find the Mth element of the array after K right rotations.
Examples:
Input: arr[] = {3, 4, 5, 23}, K = 2, M = 1
Output: 5
Explanation:
The array after first right rotation a1[ ] = {23, 3, 4, 5}
The array after second right rotation a2[ ] = {5, 23, 3, 4}
1st element after 2 right rotations is 5.
Input: arr[] = {1, 2, 3, 4, 5}, K = 3, M = 2
Output: 4
Explanation:
The array after 3 right rotations has 4 at its second position.
Naive Approach:
The simplest approach to solve the problem is to Perform Right Rotation operation K times and then find the Mth element of the final array.
Algorithm:
- Define a function called leftrotate that takes a vector and an integer d as input. The function should reverse the elements of the vector from the beginning up to index d, then from index d to the end, and finally the entire vector.
- Define a function called rightrotate that takes a vector and an integer d as input. The function should call leftrotate with the vector and the difference between the size of the vector and d as arguments.
- Define a function called getFirstElement that takes an integer array a, its size N, and two integers K and M as input. The function should do the following:
a. Initialize a vector v with the elements of array a.
b. Right rotate the vector v K times by calling rightrotate in a loop with v and the integer value 1 as arguments, K times.
c. Return the Mth element of the rotated vector v.
4. In the main function, initialize an integer array a and its size N, and two integers K and M with appropriate values.
5. Call the function getFirstElement with array a, N, K, and M as arguments and print the returned value.
Below is the implementation of the approach:
C++
// C++ program to find the Mth element// of the array after K right rotations.#include <bits/stdc++.h>using namespace std;// In-place rotates s towards left by dvoid leftrotate(vector<int>& v, int d){ reverse(v.begin(), v.begin() + d); reverse(v.begin() + d, v.end()); reverse(v.begin(), v.end());}// In-place rotates s towards right by dvoid rightrotate(vector<int>& v, int d){ leftrotate(v, v.size() - d);}// Function to return Mth element of// array after k right rotationsint getFirstElement(int a[], int N, int K, int M){ vector<int> v; for (int i = 0; i < N; i++) v.push_back(a[i]); // Right rotate K times while (K--) { rightrotate(v, 1); } // return Mth element return v[M - 1];}// Driver codeint main(){ // Array initialization int a[] = { 1, 2, 3, 4, 5 }; int N = sizeof(a) / sizeof(a[0]); int K = 3, M = 2; // Function call cout << getFirstElement(a, N, K, M); return 0;} |
Java
// Java program to find the Mth element// of the array after K right rotations.import java.util.Arrays;public class GFG { // In-place rotates array towards left by d static void leftRotate(int[] arr, int d) { reverse(arr, 0, d - 1); reverse(arr, d, arr.length - 1); reverse(arr, 0, arr.length - 1); } // In-place rotates array towards right by d static void rightRotate(int[] arr, int d) { leftRotate(arr, arr.length - d); } // Function to reverse elements in array from start to end indices static void reverse(int[] arr, int start, int end) { while (start < end) { int temp = arr[start]; arr[start] = arr[end]; arr[end] = temp; start++; end--; } } // Function to return Mth element of array after K right rotations static int getFirstElement(int[] arr, int K, int M) { int[] rotatedArray = Arrays.copyOf(arr, arr.length); // Right rotate K times while (K > 0) { rightRotate(rotatedArray, 1); K--; } // Return Mth element return rotatedArray[M - 1]; } // Driver code public static void main(String[] args) { // Array initialization int[] arr = { 1, 2, 3, 4, 5 }; int K = 3, M = 2; // Function call System.out.println(getFirstElement(arr, K, M)); }} |
4
Time Complexity: O(N * K)
Auxiliary Space: O(N)
Efficient Approach:
To optimize the problem, the following observations need to be made:
- If the array is rotated N times it returns the initial array again.
For example, a[ ] = {1, 2, 3, 4, 5}, K=5
Modified array after 5 right 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.
- If K >= M, the Mth element of the array after K right rotations is
{ (N-K) + (M-1) } th element in the original array.
- If K < M, the Mth element of the array after K right rotations is:
(M – K – 1) 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 rotationsint getFirstElement(int a[], int N, int K, int M){ // The array comes to original state // after N rotations K %= N; int index; if (K >= M) // Mth element after k right // rotations is (N-K)+(M-1) th // element of the array index = (N - K) + (M - 1); // Otherwise else // (M - K - 1) th element // of the array index = (M - K - 1); int result = a[index]; // Return the result return result;}// Driver Codeint main(){ // Array initialization int a[] = { 1, 2, 3, 4, 5 }; int N = sizeof(a) / sizeof(a[0]); int K = 3, M = 2; // Function call cout << getFirstElement(a, N, K, M); return 0;}// This code is contributed by GSSN Himabindu |
Java
// Java program to implement// the above approachimport java.io.*;class GFG{ // Function to return Mth element of// array after k right rotationsstatic int getFirstElement(int a[], int N, int K, int M){ // The array comes to original state // after N rotations K %= N; int index; // If K is greater or equal to M if (K >= M) // Mth element after k right // rotations is (N-K)+(M-1) th // element of the array index = (N - K) + (M - 1); // Otherwise else // (M - K - 1) th element // of the array index = (M - K - 1); int result = a[index]; // Return the result return result;} // Driver Codepublic static void main(String[] args){ int a[] = { 1, 2, 3, 4, 5 }; int N = 5; int K = 3, M = 2; System.out.println(getFirstElement(a, N, K, M));}}// This code is contributed by Ritik Bansal |
Python3
# Python program for the above approach# Function to return Mth element of# array after k left rotationsdef getFirstElement(a, N, K, M): # The array comes to original state # after N rotations K %= N index = 0 if (K >= M): # Mth element after k right # rotations is (N-K)+(M-1) th # element of the array index = (N - K) + (M - 1) # Otherwise else: # (M - K - 1) th element # of the array index = (M - K - 1) result = a[index] # Return the result return result# Driver Code# Array initializationa = [ 1, 2, 3, 4, 5 ]N = len(a)K,M = 3,2# Function callprint(getFirstElement(a, N, K, M))# This code is contributed by shinjanpatra |
C#
using System;using System.Linq;class GFG { // Function to return Mth element of // array after k left rotations static int getFirstElement(int []a, int N, int K, int M) { // The array comes to original state // after N rotations K %= N; int index; if (K >= M) // Mth element after k right // rotations is (N-K)+(M-1) th // element of the array index = (N - K) + (M - 1); // Otherwise else // (M - K - 1) th element // of the array index = (M - K - 1); int result = a[index]; // Return the result return result; } /* Driver program to test above functions */ public static void Main() { int []arr = {1, 2, 3, 4, 5}; int N = arr.Length; int K = 3, M = 2; Console.Write(getFirstElement(arr, N, K, M)); }}// This code is contributed by Aarti_Rathi |
Javascript
<script>// JavaScript program for the above approach// Function to return Mth element of// array after k left rotationsfunction getFirstElement(a, N, K, M){ // The array comes to original state // after N rotations K %= N let index if (K >= M) // Mth element after k right // rotations is (N-K)+(M-1) th // element of the array index = (N - K) + (M - 1) // Otherwise else // (M - K - 1) th element // of the array index = (M - K - 1) let result = a[index] // Return the result return result}// Driver Code// Array initializationlet a = [ 1, 2, 3, 4, 5 ]let N = a.lengthlet K = 3, M = 2// Function calldocument.write(getFirstElement(a, N, K, M))// This code is contributed by shinjanpatra</script> |
4
Time complexity: O(1)
Auxiliary Space: O(1)
Please refer complete article on Mth element after K Right Rotations of an Array for more details!
