Generar todas las permutaciones cíclicas de un número

Dado un número N, nuestra tarea es generar todas las permutaciones cíclicas posibles del número. 
Una permutación cíclica desplaza todos los elementos de un conjunto por un desplazamiento fijo. Para un conjunto con elementos  ,  , …,  , una permutación cíclica de un lugar a la izquierda produciría  , …,  ,  , y una permutación cíclica de un lugar a la derecha produciría  ,  ,  , ….
Ejemplos: 
 

Input :  123
Output : 123
         312
         231

Input :  5674
Output : 5674
         4567
         7456
         6745

La idea es generar la siguiente permutación de un número usando la siguiente fórmula. 
 

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

Mientras repetimos los pasos anteriores, si volvemos al número original, nos detenemos y regresamos. 
 

// 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 Program to generate all
// cyclic permutations of number
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 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 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
?>

<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>

Producción: 
 

 5674
 4567
 7456
 6745

Complejidad de Tiempo: O(N), donde N es el número de dígitos
Espacio Auxiliar: O(1)  

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