Hailstone Numbers

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 1.
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) + 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++

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// 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 
// required
int 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 function
int 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;
}

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Java

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// Java program to generate hailstone 
// numbers and calculate steps required 
// to reduce them to 1
import 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 function
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 */

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Python3

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# 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 Code
N = 7;
  
# Function to generate 
# Hailstone Numbers
x = HailstoneNumbers(N, 0);
  
# Output: Number of Steps
print("\nNumber of Steps: ", x);
  
# This code is contributed
# by mits

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C#

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// C# program to generate hailstone 
// numbers and calculate steps required 
// to reduce them to 1
using 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 function
    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

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PHP

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<?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 required
function 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 Steps
echo "\nNumber of Steps: ". $x;
      
// This code is contributed
// by mits
?>

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Output:

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 contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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