# 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++

`// 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

`// 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

`# 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#

`// 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

`<?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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