Modify given array to a non-decreasing array by rotation
Given an array arr[] of size N (consisting of duplicates), the task is to check if the given array can be converted to a non-decreasing array by rotating it. If it’s not possible to do so, then print “No“. Otherwise, print “Yes“.
Examples:
Input: arr[] = {3, 4, 5, 1, 2}
Output: Yes
Explanation: After 2 right rotations, the array arr[] modifies to {1, 2, 3, 4, 5}Input: arr[] = {1, 2, 4, 3}
Output: No
Approach: The idea is based on the fact that a maximum of N distinct arrays can be obtained by rotating the given array and check for each individual rotated array, whether it is non-decreasing or not. Follow the steps below to solve the problem:
- Initialize a vector, say v, and copy all the elements of the original array into it.
- Sort the vector v.
- Traverse the original array and perform the following steps:
- Rotate by 1 in each iteration.
- If the array becomes equal to vector v, print “Yes“. Otherwise, print “No“.
Below is the implementation of the above approach:
C++
// C++ program for the above approach #include <bits/stdc++.h> using namespace std; // Function to check if a // non-decreasing array can be obtained // by rotating the original array void rotateArray(vector< int >& arr, int N) { // Stores copy of original array vector< int > v = arr; // Sort the given vector sort(v.begin(), v.end()); // Traverse the array for ( int i = 1; i <= N; ++i) { // Rotate the array by 1 rotate(arr.begin(), arr.begin() + 1, arr.end()); // If array is sorted if (arr == v) { cout << "YES" << endl; return ; } } // If it is not possible to // sort the array cout << "NO" << endl; } // Driver Code int main() { // Given array vector< int > arr = { 3, 4, 5, 1, 2 }; // Size of the array int N = arr.size(); // Function call to check if it is possible // to make array non-decreasing by rotating rotateArray(arr, N); } |
Java
// Java program for the above approach import java.util.*; class GFG{ // Function to check if a // non-decreasing array can be obtained // by rotating the original array static void rotateArray( int [] arr, int N) { // Stores copy of original array int [] v = arr; // Sort the given vector Arrays.sort(v); // Traverse the array for ( int i = 1 ; i <= N; ++i) { // Rotate the array by 1 int x = arr[N - 1 ]; i = N - 1 ; while (i > 0 ){ arr[i] = arr[i - 1 ]; arr[ 0 ] = x; i -= 1 ; } // If array is sorted if (arr == v) { System.out.print( "YES" ); return ; } } // If it is not possible to // sort the array System.out.print( "NO" ); } // Driver Code public static void main(String[] args) { // Given array int [] arr = { 3 , 4 , 5 , 1 , 2 }; // Size of the array int N = arr.length; // Function call to check if it is possible // to make array non-decreasing by rotating rotateArray(arr, N); } } // This code is contributed by splevel62. |
Python3
# Python 3 program for the above approach # Function to check if a # non-decreasing array can be obtained # by rotating the original array def rotateArray(arr, N): # Stores copy of original array v = arr # Sort the given vector v.sort(reverse = False ) # Traverse the array for i in range ( 1 , N + 1 , 1 ): # Rotate the array by 1 x = arr[N - 1 ] i = N - 1 while (i > 0 ): arr[i] = arr[i - 1 ] arr[ 0 ] = x i - = 1 # If array is sorted if (arr = = v): print ( "YES" ) return # If it is not possible to # sort the array print ( "NO" ) # Driver Code if __name__ = = '__main__' : # Given array arr = [ 3 , 4 , 5 , 1 , 2 ] # Size of the array N = len (arr) # Function call to check if it is possible # to make array non-decreasing by rotating rotateArray(arr, N) # This code is contributed by ipg2016107. |
C#
// C# program to implement // the above approach using System; class GFG { // Function to check if a // non-decreasing array can be obtained // by rotating the original array static void rotateArray( int [] arr, int N) { // Stores copy of original array int [] v = arr; // Sort the given vector Array.Sort(v); // Traverse the array for ( int i = 1; i <= N; ++i) { // Rotate the array by 1 int x = arr[N - 1]; i = N - 1; while (i > 0){ arr[i] = arr[i - 1]; arr[0] = x; i -= 1; } // If array is sorted if (arr == v) { Console.Write( "YES" ); return ; } } // If it is not possible to // sort the array Console.Write( "NO" ); } // Driver code public static void Main() { // Given array int [] arr = { 3, 4, 5, 1, 2 }; // Size of the array int N = arr.Length; // Function call to check if it is possible // to make array non-decreasing by rotating rotateArray(arr, N); } } // This code is contributed by susmitakundugoaldanga. |
Javascript
<script> // JavaScript program to implement // the above approach // Function to check if a // non-decreasing array can be obtained // by rotating the original array function rotateArray(arr, N) { // Stores copy of original array let v = arr; // Sort the given vector v.sort((a, b) => a - b); // Traverse the array for (let i = 1; i <= N; ++i) { // Rotate the array by 1 let x = arr[N - 1]; i = N - 1; while (i--) { arr[i] = arr[i - 1]; arr[0] = x; } // If array is sorted let isEqual = arr.every((e, i) => { return arr[i] == v[i] }) if (isEqual) { document.write( "YES" ); return ; } } // If it is not possible to // sort the array document.write( "NO" ); } // Driver code // Given array let arr = [3, 4, 5, 1, 2]; // Size of the array let N = arr.length; // Function call to check if it is possible // to make array non-decreasing by rotating rotateArray(arr, N); // This code is contributed by _saurabh_jaiswal </script> |
YES
Time Complexity: O(N2)
Auxiliary Space: O(N)
Approach#2: Using Sorting and Indexing
The approach used in this code is to iterate through all possible rotations of the input array and check whether the array can be modified to a non-decreasing array by rotation. To check this, the code first sorts the input array to get the non-decreasing order. Then, it iterates through all possible rotations of the input array by right-rotating the array one element at a time. For each rotation, the code checks whether the rotated array is equal to the sorted array. If it is, then the input array can be modified to a non-decreasing array by rotation, and the code returns ‘Yes’. Otherwise, it continues rotating the array until all possible rotations have been checked. If none of the rotations result in a non-decreasing array, then the code returns ‘No’.
Algorithm
1. Sort the input array and store it in a variable sorted_arr.
2. For i = 0 to len(arr)-1, do the following:
a. If arr is equal to sorted_arr, return ‘Yes’.
b. Right-rotate the array by one element by slicing and concatenating, and store the result in arr.
3. If none of the rotations result in a non-decreasing array, return ‘No’.
C++
#include <iostream> #include <vector> #include <algorithm> using namespace std; // Function to check if the array is non-decreasing string checkNonDecreasingArray(vector< int >& arr) { vector< int > sortedArr = arr; sort(sortedArr.begin(), sortedArr.end()); // Sort a copy of the array for ( size_t i = 0; i < arr.size(); i++) { if (arr == sortedArr) { return "Yes" ; } // Right rotate the array int firstElement = arr[0]; for ( size_t j = 0; j < arr.size() - 1; j++) { arr[j] = arr[j + 1]; } arr[arr.size() - 1] = firstElement; } return "No" ; } // Driver Code int main() { vector< int > arr = {3, 4, 5, 1, 2}; string result = checkNonDecreasingArray(arr); cout << result << endl; // Output: Yes return 0; } |
Java
import java.util.ArrayList; import java.util.Collections; import java.util.List; public class NonDecreasingArrayCheck { // Function to check if the array is non-decreasing public static String checkNonDecreasingArray(List<Integer> arr) { List<Integer> sortedArr = new ArrayList<>(arr); Collections.sort(sortedArr); // Sort a copy of the array for ( int i = 0 ; i < arr.size(); i++) { if (arr.equals(sortedArr)) { return "Yes" ; } // Right rotate the array int firstElement = arr.get( 0 ); for ( int j = 0 ; j < arr.size() - 1 ; j++) { arr.set(j, arr.get(j + 1 )); } arr.set(arr.size() - 1 , firstElement); } return "No" ; } // Driver Code public static void main(String[] args) { List<Integer> arr = new ArrayList<>(); arr.add( 3 ); arr.add( 4 ); arr.add( 5 ); arr.add( 1 ); arr.add( 2 ); String result = checkNonDecreasingArray(arr); System.out.println(result); // Output: Yes } } |
Python3
def check_non_decreasing_array(arr): sorted_arr = sorted (arr) for i in range ( len (arr)): if arr = = sorted_arr: return 'Yes' arr = arr[ 1 :] + [arr[ 0 ]] # right rotate the array return 'No' # Example usage arr = [ 3 , 4 , 5 , 1 , 2 ] print (check_non_decreasing_array(arr)) # Output: Yes |
C#
using System; using System.Collections.Generic; class MainClass { // Function to check if the array is non-decreasing static string CheckNonDecreasingArray(List< int > arr) { List< int > sortedArr = new List< int >(arr); sortedArr.Sort(); // Sort a copy of the array for ( int i = 0; i < arr.Count; i++) { if (IsEqual(arr, sortedArr)) { return "Yes" ; } // Right rotate the array int firstElement = arr[0]; arr.RemoveAt(0); arr.Add(firstElement); } return "No" ; } // Function to check if two lists are equal static bool IsEqual(List< int > list1, List< int > list2) { if (list1.Count != list2.Count) { return false ; } for ( int i = 0; i < list1.Count; i++) { if (list1[i] != list2[i]) { return false ; } } return true ; } // Driver Code public static void Main( string [] args) { List< int > arr = new List< int > { 3, 4, 5, 1, 2 }; string result = CheckNonDecreasingArray(arr); Console.WriteLine(result); // Output: Yes } } |
Javascript
// Function to check if the array is non-decreasing function checkNonDecreasingArray(arr) { const sortedArr = [...arr].sort((a, b) => a - b); // Sort a copy of the array for (let i = 0; i < arr.length; i++) { if (JSON.stringify(arr) === JSON.stringify(sortedArr)) { return "Yes" ; } // Right rotate the array const firstElement = arr.shift(); arr.push(firstElement); } return "No" ; } // Driver Code const arr = [3, 4, 5, 1, 2]; const result = checkNonDecreasingArray(arr); console.log(result); // Output: Yes |
Yes
Time Complexity: O(n^2) because it uses a nested loop to iterate through all possible rotations of the input array. The outer loop iterates n times, and the inner loop iterates up to n times. The sorting operation also takes O(n log n) time. Therefore, the overall time complexity is O(n^2 + n log n) = O(n^2).
Space Complexity: O(n) because it uses additional space to store the sorted array and the rotated arrays. The sorted array takes O(n) space, and each rotated array takes O(n) space. Therefore, the overall space complexity is O(n + n) = O(n).