Juggler Sequence

21 Jun, 2022
Juggler Sequence is a series of integer number in which the first term starts with a positive integer number a and the remaining terms are generated from the immediate previous term using the below recurrence relation : Juggler Sequence starting with number 3: 5, 11, 36, 6, 2, 1Juggler Sequence starting with number 9: 9, 27, 140, 11, 36, 6, 2, 1Given a number n we have to print the Juggler Sequence for this number as the first term of the sequence. Examples:  
Input: 9
Output: 9, 27, 140, 11, 36, 6, 2, 1
We start with 9 and use above formula to get
next terms.

Input: 6
Output: 6, 2, 1
C++
C
Java
Python3
C#
PHP
Javascript
// C++ implementation of Juggler Sequence#include <bits/stdc++.h>using namespace std; // This function prints the juggler Sequencevoid printJuggler(long long n){    long long a = n;     // print the first term    cout << a << " ";     // calculate terms until    // last term is not 1    while (a != 1)    {        long long b = 0;         // Check if previous term        // is even or odd        if (a % 2 == 0)             // calculate next term            b = floor(sqrt(a));         else             // for odd previous term            // calculate next term            b = floor(sqrt(a) *                      sqrt(a) * sqrt(a));         cout << b << " ";        a = b;    }} // Driver Codeint main(){    printJuggler(37);    cout <<"\n";    printJuggler(9);    return 0;} // This code is contributed by shubhamsingh10
// C implementation of Juggler Sequence#include<stdio.h>#include<math.h> // This function prints the juggler Sequencevoid printJuggler(int n){    int a = n;     // print the first term    printf("%d ", a);     // calculate terms until last term is not 1    while (a != 1)    {        int b = 0;         // Check if previous term is even or odd        if (a%2 == 0)             // calculate next term            b  = floor(sqrt(a));         else             // for odd previous term calculate            // next term            b = floor(sqrt(a)*sqrt(a)*sqrt(a));         printf("%d ", b);        a = b;    }} //driver program to test above functionint main(){    printJuggler(3);    printf("\n");    printJuggler(9);    return 0;}
// Java implementation of Juggler Sequenceimport java.io.*;import java.math.*; class GFG {          // This function prints the juggler Sequence    static void printJuggler(int n)    {        int a = n;          // print the first term       System.out.print(a+" ");         // calculate terms until last term is not 1       while (a != 1)       {          int b = 0;              // Check if previous term is even or odd          if (a%2 == 0)                 // calculate next term                b  = (int)Math.floor(Math.sqrt(a));             else               // for odd previous term calculate            // next term                b =(int) Math.floor(Math.sqrt(a) *                               Math.sqrt(a) * Math.sqrt(a));             System.out.print( b+" ");          a = b;        }    } // Driver program to test above functionpublic static void main (String[] args) {    printJuggler(3);    System.out.println();    printJuggler(9);    }}  //This code is contributed by Nikita Tiwari.
import math #This function prints the juggler Sequencedef printJuggler(n) :    a = n         # print the first term    print (a,end=" ")         # calculate terms until last term is not 1    while (a != 1) :        b = 0                 # Check if previous term is even or odd        if (a%2 == 0) :                         # calculate next term            b  = (int)(math.floor(math.sqrt(a)))          else :            # for odd previous term calculate            # next term            b = (int) (math.floor(math.sqrt(a)*math.sqrt(a)*                                         math.sqrt(a)))          print (b,end=" ")        a = b printJuggler(3)print()printJuggler(9) # This code is contributed by Nikita Tiwari.
// C# implementation of Juggler Sequenceusing System; class GFG {         // This function prints the juggler Sequence    static void printJuggler(int n)    {        int a = n;     // print the first term    Console.Write(a+" ");     // calculate terms until last term is not 1    while (a != 1)    {        int b = 0;             // Check if previous term is even or odd        if (a%2 == 0)                 // calculate next term                b = (int)Math.Floor(Math.Sqrt(a));         else             // for odd previous term calculate            // next term                b =(int) Math.Floor(Math.Sqrt(a) *                     Math.Sqrt(a) * Math.Sqrt(a));         Console.Write( b+" ");        a = b;        }    } // Driver Codepublic static void Main () {    printJuggler(3);    Console.WriteLine();    printJuggler(9);    }} // This code is contributed by Nitin Mittal
<?php// PHP implementation of// Juggler Sequence // function prints the// juggler Sequencefunction printJuggler($n){    $a = $n;     // print the first term    echo($a . " ");     // calculate terms until    // last term is not 1    while ($a != 1)    {        $b = 0;         // Check if previous        // term is even or odd        if ($a % 2 == 0)             // calculate next term            $b = floor(sqrt($a));         else             // for odd previous term            // calculate next term            $b = floor(sqrt($a) * sqrt($a) *                                  sqrt($a));         echo($b . " ");        $a = $b;    }} // Driver CodeprintJuggler(3);echo("\n");printJuggler(9); // This code is contributed by Ajit.?>
<script> // Javascript implementation of Juggler Sequence     // This function prints the juggler Sequence    function printJuggler(n)    {        let a = n;            // print the first term       document.write(a+" ");           // calculate terms until last term is not 1       while (a != 1)       {          let b = 0;                // Check if previous term is even or odd          if (a%2 == 0)                   // calculate next term                b  = Math.floor(Math.sqrt(a));               else                 // for odd previous term calculate            // next term                b = Math.floor(Math.sqrt(a) *                               Math.sqrt(a) * Math.sqrt(a));               document.write( b+" ");          a = b;        }    } // Driver code to test above methods     printJuggler(3);    document.write("<br/>");    printJuggler(9);   // This code is contributed by avijitmondal1998.</script>
Output:  
3 5 11 36 6 2 1 
9 27 140 11 36 6 2 1
Time complexity: O(nlogn) since using a single while loop and finding square root takes logarithmic time.
Space complexity: O(1) for constant variables
Important Points: 
The terms in Juggler Sequence first increase to a peak value and then start decreasing.
The last term in Juggler Sequence is always 1.
Reference: https://en.wikipedia.org/wiki/Juggler_sequence This article is contributed by Harsh Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
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