Generate all cyclic permutations of a number

Last Updated : 07 Jan, 2024

Given a number N, our task is to generate all the possible cyclic permutations of the number.
A cyclic permutation shifts all the elements of a set by a fixed offset. For a set with elements a_0 , a_1 , ..., a_n , a cyclic permutation of one place to the left would yield a_1 , ..., a_n , a_0 , and a cyclic permutation of one place to the right would yield a_n , a_0 , a_1 , ....
Examples:

Input :  123
Output : 123
         312
         231

Input :  5674
Output : 5674
         4567
         7456
         6745

The idea is to generate next permutation of a number using below formula.

    rem = num % 10;
    div = num / 10;
    num = (pow(10, n - 1)) * rem + div;

While repeating above steps, if we come back to original number, we stop and return.

C++

// Program to generate all cyclic permutations
// of number
#include <bits/stdc++.h>
using namespace std;

// Function to count the total number of digits 
// in a number.
int countdigits(int N)
{
    int count = 0;
    while (N) {
        count++;
        N = N / 10;
    }
    return count;
}

// Function to generate all cyclic permutations
// of a number
void cyclic(int N)
{
    int num = N;
    int n = countdigits(N);

    while (1) {
        cout << num << endl;

        // Following three lines generates a
        // circular permutation of a number.
        int rem = num % 10;
        int div = num / 10;
        num = (pow(10, n - 1)) * rem + div;

        // If all the permutations are checked
        // and we obtain original number exit
        // from loop.
        if (num == N) 
            break;        
    }
}

// Driver Program
int main()
{
    int N = 5674;
    cyclic(N);
    return 0;
}

Java

// Java Program to generate all 
// cyclic permutations of number
public class GFG
{

    // Function to count the total number
    // of digits in a number.
    static int countdigits(int N)
    {
        int count = 0;
        while (N>0) {
            count++;
            N = N / 10;
        }
        return count;
    }

    // Function to generate all cyclic
    // permutations of a number
    static void cyclic(int N)
    {
        int num = N;
        int n = countdigits(N);

        while (true) {
            System.out.println(num); 

            // Following three lines generates a
            // circular permutation of a number.
            int rem = num % 10;
            int dev = num / 10;
            num = (int)((Math.pow(10, n - 1)) *
                                rem + dev);

            // If all the permutations are 
            // checked and we obtain original
            // number exit from loop.
            if (num == N) 
                break; 
        }
    }

    // Driver Program
    public static void main (String[] args) {
    int N = 5674;
    cyclic(N);
    }
}

/* This code is contributed by Mr. Somesh Awasthi */

Python3

# Python3 Program to 
# generate all cyclic
# permutations of number
import math

# Function to count the 
# total number of digits
# in a number.
def countdigits(N):
    count = 0;
    while (N):
        count = count + 1;
        N = int(math.floor(N / 10));
    return count;
    
# Function to generate 
# all cyclic permutations
# of a number
def cyclic(N):
    num = N;
    n = countdigits(N);
    while (1):
        print(int(num));
        
        # Following three lines 
        # generates a circular 
        # permutation of a number.
        rem = num % 10;
        div = math.floor(num / 10);
        num = ((math.pow(10, n - 1)) * 
                           rem + div);
        
        # If all the permutations 
        # are checked and we obtain 
        # original number exit from loop.
        if (num == N):
            break; 
            
# Driver Code
N = 5674;
cyclic(N);

# This code is contributed by mits

// C# Program to generate all 
// cyclic permutations of number
using System;

class GFG
{
    // Function to count the total number
    // of digits in a number.
    static int countdigits(int N)
    {
        int count = 0;
        while (N > 0) {
            count++;
            N = N / 10;
        }
        return count;
    }

    // Function to generate all cyclic
    // permutations of a number
    static void cyclic(int N)
    {
        int num = N;
        int n = countdigits(N);

        while (true) {
            Console.WriteLine(num); 

            // Following three lines generates a
            // circular permutation of a number.
            int rem = num % 10;
            int dev = num / 10;
            num = (int)((Math.Pow(10, n - 1)) *
                                    rem + dev);

            // If all the permutations are 
            // checked and we obtain original
            // number exit from loop.
            if (num == N) 
                break; 
        }
    }

    // Driver Program
    public static void Main () 
    {
      int N = 5674;
      cyclic(N);
    }
}

// This code is contributed by nitin mittal

PHP

<?php
// PHP Program to generate all 
// cyclic permutations of number

// Function to count the total 
// number of digits in a number.
function countdigits($N)
{
    $count = 0;
    while ($N) 
    {
        $count++;
        $N = floor($N / 10);
    }
    return $count;
}

// Function to generate all 
// cyclic permutations of a number
function cyclic($N)
{
    $num = $N;
    $n = countdigits($N);

    while (1)
    {
        echo ($num);
        echo "\n" ;
        
        // Following three lines generates a
        // circular permutation of a number.
        $rem = $num % 10;
        $div = floor($num / 10);
        $num = (pow(10, $n - 1)) * $rem + $div;

        // If all the permutations are checked
        // and we obtain original number exit
        // from loop.
        if ($num == $N) 
            break;     
    }
}

    // Driver Code
    $N = 5674;
    cyclic($N);

// This code is contributed by nitin mittal
?>

JavaScript

<script>

// javascript Program to generate all 
// cyclic permutations of number   
// Function to count the total number
// of digits in a number.

function countdigits(N)
{
    var count = 0;
    while (N>0) {
        count++;
        N = parseInt(N / 10);
    }
    return count;
}

// Function to generate all cyclic
// permutations of a number
function cyclic(N)
{
    var num = N;
    var n = countdigits(N);

    while (true) {
        document.write(num+"<br>"); 

        // Following three lines generates a
        // circular permutation of a number.
        var rem = num % 10;
        var dev = parseInt(num / 10);
        num = parseInt(((Math.pow(10, n - 1)) *
                            rem + dev));

        // If all the permutations are 
        // checked and we obtain original
        // number exit from loop.
        if (num == N) 
            break; 
    }
}

// Driver Program
var N = 5674;
cyclic(N);

// This code is contributed by Amit Katiyar
</script>

Output

Time Complexity: O(N), where N is the number of digits
Auxiliary Space: O(1)

Print all permutations of a number N greater than itself

Vineet Joshi

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Generate all cyclic permutations of a number

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