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Count clockwise array rotations required to maximize count of array elements present at indices same as their value
  • Last Updated : 07 Dec, 2020

Given an array arr[] consisitng of a permutation of first N natural numbers, the task is to find the minimum number of clockwise circular rotations of the array required to maximise the number of elements satisfying the condition arr[i] = i ( 1-based indexing ) where 1 ≤ i ≤ N.

Examples:

Input: arr[] = {4, 5, 1, 2, 3}
Output: 3
Explanation: Rotating the array thrice, the array modifies to {1, 2, 3, 4, 5}. All the array elements satisfy the condition arr[i] = i.

Input: arr[] = {3, 4, 1, 5, 2}
Output: 2
Explanation: Rotating the array twice, the array modifies to {5, 2, 3, 4, 1}. Three array elements satisfy the condition arr[i] = i, which is the maximum possible for the given array.

Approach: Follow the steps below to solve the problem:



  • Initialize two integers maxi and ans, and two arrays new_arr[] and freq[].
  • Traverse the array arr[] an for each element, count the number of indices separating it from its correct position, i.e |(arr[i] – i + N) % N|.
  • Store the counts for each array element in a new array new_arr[].
  • Store the count of frequencies of each element in new_arr[] in the array freq[].
  • Print the element ith maximum frequency as the required answer.

Below is the implementation of the above approach:

C++

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// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to count the number of
// clockwise array rotations required
// to maximize count of array elements
// present at indices same as their value
void find_min_rot(int arr[], int n)
{
    // Stores count of indices seperating
    // elements from its correct position
    int new_arr[n + 1];
    int maxi = 1, ans = 0;
 
    // Stores frequencies of counts of
    // indices seperating
    int freq[n + 1];
    for (int i = 1; i <= n; i++) {
        freq[i] = 0;
    }
 
    // Count indices separating each
    // element from its correct position
    for (int i = 1; i <= n; i++) {
 
        new_arr[i] = (arr[i] - i + n) % n;
    }
 
    // Update frequencies of counts obtaiend
    for (int i = 1; i <= n; i++) {
 
        freq[new_arr[i]]++;
    }
 
    // Find the count with maximum frequency
    for (int i = 1; i <= n; i++) {
        if (freq[i] > maxi) {
            maxi = freq[i];
            ans = i;
        }
    }
 
    // Print the answer
    cout << ans << endl;
}
 
// Driver Code
int main()
{
 
    int N = 5;
    int arr[] = { -1, 3, 4, 1, 5, 2 };
 
    // Find minimum number of
    // array rotations required
    find_min_rot(arr, N);
 
    return 0;
}

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Java

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// Java program for the above approach
import java.util.*;
    
class GFG{
    
// Function to count the number of
// clockwise array rotations required
// to maximize count of array elements
// present at indices same as their value
static void find_min_rot(int arr[], int n)
{
     
    // Stores count of indices seperating
    // elements from its correct position
    int[] new_arr = new int[n + 1];
    int maxi = 1, ans = 0;
  
    // Stores frequencies of counts of
    // indices seperating
    int[] freq = new int[n + 1];
    for(int i = 1; i <= n; i++)
    {
        freq[i] = 0;
    }
  
    // Count indices separating each
    // element from its correct position
    for(int i = 1; i <= n; i++)
    {
        new_arr[i] = (arr[i] - i + n) % n;
    }
  
    // Update frequencies of counts obtaiend
    for(int i = 1; i <= n; i++)
    {
        freq[new_arr[i]]++;
    }
  
    // Find the count with maximum frequency
    for(int i = 1; i <= n; i++)
    {
        if (freq[i] > maxi)
        {
            maxi = freq[i];
            ans = i;
        }
    }
  
    // Print the answer
    System.out.print(ans);
}
    
// Driver Code
public static void main(String[] args)
{
    int N = 5;
    int[] arr = { -1, 3, 4, 1, 5, 2 };
  
    // Find minimum number of
    // array rotations required
    find_min_rot(arr, N);
}
}
 
// This code is contributed by sanjoy_62

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Python3

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# Python3 program for the above approach
  
# Function to count the number of
# clockwise array rotations required
# to maximize count of array elements
# present at indices same as their value
def find_min_rot(arr, n):
     
    # Stores count of indices seperating
    # elements from its correct position
    new_arr = [0] * (n + 1)
    maxi = 1
    ans = 0
  
    # Stores frequencies of counts of
    # indices seperating
    freq = [0] * (n + 1)
    for i in range(1, n + 1):
        freq[i] = 0
  
    # Count indices separating each
    # element from its correct position
    for i in range(1, n + 1):
         new_arr[i] = (arr[i] - i + n) % n
  
    # Update frequencies of counts obtaiend
    for i in range(1, n + 1):
        freq[new_arr[i]] += 1
  
    # Find the count with maximum frequency
    for i in range(1, n + 1):
        if (freq[i] > maxi):
            maxi = freq[i]
            ans = i
             
    # Print the answer
    print(ans)
  
# Driver Code
if __name__ == '__main__':
  
    N = 5
    arr = [ -1, 3, 4, 1, 5, 2 ]
  
    # Find minimum number of
    # array rotations required
    find_min_rot(arr, N)
     
# This code is contributed by jana_sayantan

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C#

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// C# program for the above approach
using System;
 
class GFG
{
    
// Function to count the number of
// clockwise array rotations required
// to maximize count of array elements
// present at indices same as their value
static void find_min_rot(int []arr, int n)
{
     
    // Stores count of indices seperating
    // elements from its correct position
    int[] new_arr = new int[n + 1];
    int maxi = 1, ans = 0;
  
    // Stores frequencies of counts of
    // indices seperating
    int[] freq = new int[n + 1];
    for(int i = 1; i <= n; i++)
    {
        freq[i] = 0;
    }
  
    // Count indices separating each
    // element from its correct position
    for(int i = 1; i <= n; i++)
    {
        new_arr[i] = (arr[i] - i + n) % n;
    }
  
    // Update frequencies of counts obtaiend
    for(int i = 1; i <= n; i++)
    {
        freq[new_arr[i]]++;
    }
  
    // Find the count with maximum frequency
    for(int i = 1; i <= n; i++)
    {
        if (freq[i] > maxi)
        {
            maxi = freq[i];
            ans = i;
        }
    }
  
    // Print the answer
    Console.Write(ans);
}
    
// Driver Code
public static void Main(String[] args)
{
    int N = 5;
    int[] arr = { -1, 3, 4, 1, 5, 2 };
  
    // Find minimum number of
    // array rotations required
    find_min_rot(arr, N);
}
}
 
// This code is contributed by 29AjayKumar

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Output: 

2

 

Time Complexity: O(N)
Auxiliary Space: O(N)

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