Hailstone Numbers - GeeksforGeeks

29 Apr, 2021
We are provided with a number N. Our task is to generate all the Hailstone Numbers from N and find the number of steps taken by N to reduce to
Collatz Conjecture: A problem posed by L. Collatz in 1937, also called the 3x+1 mapping, 3n+1 problem. Let N be a integer. According to Collatz conjecture, if we keep iterating N as following N = N / 2 // For Even N and N = 3 * N + 1 // For Odd N Our number will eventually converge to 1 irrespective of the choice of N. Hailstone Numbers: The sequence of integers generated by Collatz conjecture are called Hailstone Numbers.
Examples: 
Input : N = 7
Output : 
Hailstone Numbers: 7, 22, 11, 34, 17,
                   52, 26, 13, 40, 20,
                   10, 5, 16, 8, 4, 2,
                    1
No. of steps Required: 17

Input : N = 9
Output : 
Hailstone Numbers: 9, 28, 14, 7, 22, 11,
                   34, 17, 52, 26, 13, 
                   40, 20, 10, 5, 16, 8,
                   4, 2, 1
No. of steps Required: 20

In the first example, N = 7. 
The numbers will be calculated as follows:
7
3 * 7 + 1 = 22     // Since 7 is odd.
22 / 2 = 11        // 22 is even.
3 * 11 + 1 = 34    // 11 is odd.
.... and so on upto 1.
The idea is simple, we recursively print numbers until we reach base case. 
C++
Java
Python
C#
PHP
Javascript
// C++ program to generate hailstone// numbers and calculate steps required// to reduce them to 1#include <bits/stdc++.h>using namespace std; // function to print hailstone numbers// and to calculate the number of steps// requiredint HailstoneNumbers(int N){    static int c;     cout << N << " ";     if (N == 1 && c == 0) {         // N is initially 1.        return c;    }    else if (N == 1 && c != 0) {         // N is reduced to 1.        c++;        return c;    }    else if (N % 2 == 0) {         // If N is Even.        c++;        HailstoneNumbers(N / 2);    }    else if (N % 2 != 0) {         // N is Odd.        c++;        HailstoneNumbers(3 * N + 1);    }} // Driver codeint main(){    int N = 7;    int x;     // Function to generate Hailstone    // Numbers    x = HailstoneNumbers(N);     // Output: Number of Steps    cout << endl;    cout << "Number of Steps: " << x;    return 0;}
// Java program to generate hailstone// numbers and calculate steps required// to reduce them to 1import java.util.*;class GFG {    static int c;     // function to print hailstone numbers    // and to calculate the number of steps    // required    static int HailstoneNumbers(int N)    {        System.out.print(N + " ");         if (N == 1 && c == 0) {             // N is initially 1.            return c;        }        else if (N == 1 && c != 0) {             // N is reduced to 1.            c++;            return c;        }        else if (N % 2 == 0) {             // If N is Even.            c++;            HailstoneNumbers(N / 2);        }        else if (N % 2 != 0) {             // N is Odd.            c++;            HailstoneNumbers(3 * N + 1);        }        return c;    }     // Driver code    public static void main(String[] args)    {        int N = 7;        int x;         // Function to generate Hailstone        // Numbers        x = HailstoneNumbers(N);         // Output: Number of Steps        System.out.println();        System.out.println("Number of Steps: " + x);    }}/* This code is contributed by Kriti Shukla */
# Python3 program to generate# hailstone numbers and# calculate steps required# to reduce them to 1 # function to print hailstone# numbers and to calculate# the number of steps required  def HailstoneNumbers(N, c):    print(N, end=" ")    if (N == 1 and c == 0):         # N is initially 1.        return c    elif (N == 1 and c != 0):         # N is reduced to 1.        c = c + 1    elif (N % 2 == 0):         # If N is Even.        c = c + 1        c = HailstoneNumbers(int(N / 2), c)    elif (N % 2 != 0):         # N is Odd.        c = c + 1        c = HailstoneNumbers(3 * N + 1, c)    return c  # Driver CodeN = 7 # Function to generate# Hailstone Numbersx = HailstoneNumbers(N, 0) # Output: Number of Stepsprint("\nNumber of Steps: ", x) # This code is contributed# by mits
// C# program to generate hailstone// numbers and calculate steps required// to reduce them to 1using System; class GFG {    static int c;     // function to print hailstone numbers    // and to calculate the number of steps    // required    static int HailstoneNumbers(int N)    {        Console.Write(N + " ");         if (N == 1 && c == 0) {             // N is initially 1.            return c;        }        else if (N == 1 && c != 0) {             // N is reduced to 1.            c++;            return c;        }        else if (N % 2 == 0) {             // If N is Even.            c++;            HailstoneNumbers(N / 2);        }        else if (N % 2 != 0) {             // N is Odd.            c++;            HailstoneNumbers(3 * N + 1);        }        return c;    }     // Driver code    public static void Main()    {        int N = 7;        int x;         // Function to generate Hailstone        // Numbers        x = HailstoneNumbers(N);         // Output: Number of Steps        Console.WriteLine();        Console.WriteLine("Number of Steps: " + x);    }}// This code is contributed by vt_m
<?php// PHP program to generate // hailstone numbers and// calculate steps required// to reduce them to 1 // function to print hailstone// numbers and to calculate the// number of steps requiredfunction HailstoneNumbers($N){    static $c;     echo $N." ";     if ($N == 1 && $c == 0)    {         // N is initially 1.        return $c;    }    else if ($N == 1 && $c != 0)    {         // N is reduced to 1.        $c++;        return $c;    }    else if ($N % 2 == 0)    {         // If N is Even.        $c++;        HailstoneNumbers((int)($N / 2));    }    else if ($N % 2 != 0)    {         // N is Odd.        $c++;        HailstoneNumbers(3 * $N + 1);    }    return $c;} // Driver Code$N = 7; // Function to generate// Hailstone Numbers$x = HailstoneNumbers($N); // Output: Number of Stepsecho "\nNumber of Steps: ". $x;     // This code is contributed// by mits?>
<script> // JavaScript program to generate hailstone// numbers and calculate steps required// to reduce them to 1  let c = 0;     // function to print hailstone numbers    // and to calculate the number of steps    // required    function HailstoneNumbers(N)    {        document.write(N + " ");          if (N == 1 && c == 0) {              // N is initially 1.            return c;        }        else if (N == 1 && c != 0) {              // N is reduced to 1.            c++;            return c;        }        else if (N % 2 == 0) {              // If N is Even.            c++;            HailstoneNumbers(N / 2);        }        else if (N % 2 != 0) {              // N is Odd.            c++;            HailstoneNumbers(3 * N + 1);        }        return c;    }       // Driver Code        let N = 7;        let x;          // Function to generate Hailstone        // Numbers        x = HailstoneNumbers(N);          // Output: Number of Steps        document.write("<br/>");        document.write("Number of Steps: " + x); // This code is contributed by susmitakundugoaldanga.</script>
7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 
Number of Steps: 17
This article is contributed by Vineet Joshi. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to contribute@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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