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, 1
Juggler Sequence starting with number 9:
9, 27, 140, 11, 36, 6, 2, 1
Given 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++ implementation of Juggler Sequence #include <bits/stdc++.h> using namespace std; // This function prints the juggler Sequence void printJuggler(int n) { int a = n; // print the first term cout << 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)); cout << b << " "; a = b; } } // Driver Code int main() { printJuggler(3); cout <<"\n"; printJuggler(9); return 0; } // This code is contributed by shubhamsingh10 |
C
// C implementation of Juggler Sequence #include<stdio.h> #include<math.h> // This function prints the juggler Sequence void 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 function int main() { printJuggler(3); printf("\n"); printJuggler(9); return 0; } |
Java
// Java implementation of Juggler Sequence import 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 function public static void main (String[] args) { printJuggler(3); System.out.println(); printJuggler(9); } } //This code is contributed by Nikita Tiwari. |
Python
import math #This function prints the juggler Sequence def printJuggler(n) : a = n # print the first term print 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 = (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, a = b printJuggler(3) printprintJuggler(9) # This code is contributed by Nikita Tiwari. |
C#
// C# implementation of Juggler Sequence using 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 Code public static void Main () { printJuggler(3); Console.WriteLine(); printJuggler(9); } } // This code is contributed by Nitin Mittal |
PHP
<?php // PHP implementation of // Juggler Sequence // function prints the // juggler Sequence function 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 Code printJuggler(3); echo("\n"); printJuggler(9); // This code is contributed by Ajit. ?> |
Output:
3 5 11 36 6 2 1 9 27 140 11 36 6 2 1
Important Points:
- The terms in Juggler Sequence first increases to a peak value and then starts decreasing.
- The last term in Juggler Sequence is always 1.
Reference:
https://en.wikipedia.org/wiki/Juggler_sequence
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