Sort given Array using at most N cyclic shift on any subarray

Last Updated : 23 Jul, 2025

Given an array arr[] containing N integers, with duplicates. The task is to sort the array in increasing order using at most N cyclic shift on any sub-array.

Cyclic shift on any sub-array means cut out any subarray from the given array, use cyclic shift (rotate) in it by any offset, and put it back into the same place of the array.

Print the number of such shifting required to sort the array. There can be multiple possibilities.

Examples:

Input: arr[] = [1, 3, 2, 8, 5]
Output: 2
Explanation: Consider segment from index = 1 to index = 2. [1, 3, 2, 8, 5]. Now rotate this segment by 1 offset. The new array becomes, [1, 2, 3, 8, 5].
Then consider segment from index = 3 to index = 4, [1, 2, 3, 8, 5]. Rotate it by 1 offset, the new array becomes, [1, 2, 3, 5, 8].

Input: arr[] = [2, 4, 1, 3]
Output: 2
Explanation: From index = 0 to index = 2, [2, 4, 1, 3]. Rotate this segment by 2 offset on left, the new array becomes, [1, 2, 4, 3].
Taking second segment from index = 2 to index = 3 of offset 1, rotate it the new array becomes, [1, 2, 4, 3].

Approach: There can be two cases:

Case when the array is already sorted: Then we do not need to perform any shifting operation
Case when the array is not sorted: For that follow the steps mentioned below:
- Create a variable count = 0 to store the total number of counts.
- Iterate from i = 0 to i = N-2. And for each iteration do the following operations:
  - Create a variable minVal to store the minimum value found in this iteration and initiate it with the value of arr[i].
  - Start iterating from i+1 to N-1. If the current value is less than minVal, update minVal.
  - Mark that position right to perform cyclic shift from i to right by offset 1.
- If no such right value exists then simply move to the next iteration.
- Otherwise, rotate the array from i to right by 1 position and increment count by 1.
- Return the value of count as your answer.

Below is the C++ implementation for the above approach:

C++

// C++ code to implement the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to Sort given Array using
// at most N cyclic shift on any subarray
int ShiftingSort(vector<int>& arr, int n)
{
    vector<int> temp(arr.begin(), arr.end());
    sort(temp.begin(), temp.end());

    // Variable to store count of
    // shifting operations
    int count = 0;

    // If the vector arr is already sorted
    // the 0 operations shift required
    if (arr == temp) {
        return 0;
    }
    else {
        // Run a loop from 0 to n-2 index
        for (int index1 = 0; index1 < n - 1; index1++) {
            int minval = arr[index1];
            int left = index1;
            int right = -1;

            // Loop from i+1 to n-1
            // to find the minimum value
            for (int index2 = index1 + 1; index2 < n;
                 index2++) {
                if (minval > arr[index2]) {
                    minval = arr[index2];
                    right = index2;
                }
            }

            // Check if the shifting is required
            if (right != -1) {
                // Increment count operations
                count++;

                int index = right;
                int tempval = arr[right];

                // Loop for shifting the array arr
                // from index = left to index = right
                while (index > left) {
                    arr[index] = arr[index - 1];
                    index--;
                }
                arr[index] = tempval;
            }
        }
    }

    // Return the total operations
    return count;
}

// Driver code
int main()
{
    vector<int> arr{ 1, 3, 2, 8, 5 };
    int N = 5;

    cout << ShiftingSort(arr, N) << "\n";

    return 0;
}

Java

// Java code to implement the above approach
import java.util.*;

public class GFG
{
  
// Function to Sort given Array using
// at most N cyclic shift on any subarray
static int ShiftingSort(ArrayList<Integer> arr, int n)
{
    ArrayList<Integer> temp = new ArrayList<Integer>();
    for(int i = 0; i < arr.size(); i++) {
        temp.add(arr.get(i));
    }
    
    Collections.sort(temp);
    
    // Variable to store count of
    // shifting operations
    int count = 0;

    // If the vector arr is already sorted
    // the 0 operations shift required
    if (arr.equals(temp)) {
        return 0;
    }
    else {
        // Run a loop from 0 to n-2 index
        for (int index1 = 0; index1 < n - 1; index1++) {
            int minval = arr.get(index1);
            int left = index1;
            int right = -1;

            // Loop from i+1 to n-1
            // to find the minimum value
            for (int index2 = index1 + 1; index2 < n;
                 index2++) {
                if (minval > arr.get(index2)) {
                    minval = arr.get(index2);
                    right = index2;
                }
            }

            // Check if the shifting is required
            if (right != -1) {
                // Increment count operations
                count++;

                int index = right;
                int tempval = arr.get(right);

                // Loop for shifting the array arr
                // from index = left to index = right
                while (index > left) {
                    arr.set(index, arr.get(index - 1));
                    index--;
                }
                arr.set(index, tempval);
            }
        }
    }

    // Return the total operations
    return count;
}

// Driver code
public static void main(String args[])
{
    ArrayList<Integer> arr = new ArrayList<Integer>();
    
    arr.add(1);
    arr.add(3);
    arr.add(2);
    arr.add(8);
    arr.add(5);
    
    int N = 5;

    System.out.println(ShiftingSort(arr, N));
}
}

// This code is contributed by Samim Hossain Mondal.

Python3

# Python Program to implement
# the above approach

# Function to Sort given Array using
# at most N cyclic shift on any subarray
def ShiftingSort(arr, n):
    temp = arr.copy()
    temp.sort()

    # Variable to store count of
    # shifting operations
    count = 0

    # If the vector arr is already sorted
    # the 0 operations shift required
    if (arr == temp):
        return 0
    else:

        # Run a loop from 0 to n-2 index
        for index1 in range(n - 1):
            minval = arr[index1]
            left = index1
            right = -1

            # Loop from i+1 to n-1
            # to find the minimum value
            for index2 in range(index1 + 1, n):
                if (minval > arr[index2]):
                    minval = arr[index2]
                    right = index2

            # Check if the shifting is required
            if (right != -1):

                # Increment count operations
                count += 1
                index = right
                tempval = arr[right]

                # Loop for shifting the array arr
                # from index = left to index = right
                while (index > left):
                    arr[index] = arr[index - 1]
                    index -= 1
                arr[index] = tempval

    # Return the total operations
    return count

# Driver code
arr = [1, 3, 2, 8, 5]
N = 5
print(ShiftingSort(arr, N))

# This code is contributed by gfgking

// C# code to implement the above approach
using System;
using System.Collections;
using System.Collections.Generic;

class GFG
{
  
// Function to Sort given Array using
// at most N cyclic shift on any subarray
static int ShiftingSort(ArrayList arr, int n)
{
    ArrayList temp = new ArrayList();
    for(int i = 0; i < arr.Count; i++) {
        temp.Add(arr[i]);
    }
    
    temp.Sort();
    
    // Variable to store count of
    // shifting operations
    int count = 0;

    // If the vector arr is already sorted
    // the 0 operations shift required
    if (arr.Equals(temp)) {
        return 0;
    }
    else 
    {
      
        // Run a loop from 0 to n-2 index
        for (int index1 = 0; index1 < n - 1; index1++) {
            int minval = (int)arr[index1];
            int left = index1;
            int right = -1;

            // Loop from i+1 to n-1
            // to find the minimum value
            for (int index2 = index1 + 1; index2 < n;
                 index2++) {
                if (minval > (int)arr[index2]) {
                    minval = (int)arr[index2];
                    right = index2;
                }
            }

            // Check if the shifting is required
            if (right != -1) 
            {
              
                // Increment count operations
                count++;

                int index = right;
                int tempval = (int)arr[right];

                // Loop for shifting the array arr
                // from index = left to index = right
                while (index > left) {
                    arr[index] = arr[index - 1];
                    index--;
                }
                arr[index] = tempval;
            }
        }
    }

    // Return the total operations
    return count;
}

// Driver code
public static void Main()
{
    ArrayList arr = new ArrayList();
    
    arr.Add(1);
    arr.Add(3);
    arr.Add(2);
    arr.Add(8);
    arr.Add(5);
    
    int N = 5;

    Console.Write(ShiftingSort(arr, N));
}
}

// This code is contributed by Samim Hossain Mondal.

JavaScript

<script>

        // JavaScript Program to implement
        // the above approach 

        // Function to Sort given Array using
        // at most N cyclic shift on any subarray
        function ShiftingSort(arr, n) {
            let temp = [...arr];
            temp.sort(function (a, b) { return a - b })

            // Variable to store count of
            // shifting operations
            let count = 0;

            // If the vector arr is already sorted
            // the 0 operations shift required
            if (arr == temp) {
                return 0;
            }
            else {
            
                // Run a loop from 0 to n-2 index
                for (let index1 = 0; index1 < n - 1; index1++) {
                    let minval = arr[index1];
                    let left = index1;
                    let right = -1;

                    // Loop from i+1 to n-1
                    // to find the minimum value
                    for (let index2 = index1 + 1; index2 < n;
                        index2++) {
                        if (minval > arr[index2]) {
                            minval = arr[index2];
                            right = index2;
                        }
                    }

                    // Check if the shifting is required
                    if (right != -1)
                    {
                    
                        // Increment count operations
                        count++;

                        let index = right;
                        let tempval = arr[right];

                        // Loop for shifting the array arr
                        // from index = left to index = right
                        while (index > left) {
                            arr[index] = arr[index - 1];
                            index--;
                        }
                        arr[index] = tempval;
                    }
                }
            }

            // Return the total operations
            return count;
        }

        // Driver code
        let arr = [1, 3, 2, 8, 5];
        let N = 5;
        document.write(ShiftingSort(arr, N) + '<br>');

    // This code is contributed by Potta Lokesh
    </script>

Output

Time Complexity: O(N²)
Space Complexity: O(1)

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