Se nos proporciona un número N. Nuestra tarea es generar todos los números de granizo a partir de N y encontrar el número de pasos tomados por N para reducir a
Conjetura de Collatz: un problema planteado por L. Collatz en 1937, también llamado mapeo 3x+1, problema 3n+1. Sea N un número entero. De acuerdo con la conjetura de Collatz, si seguimos iterando N de la siguiente manera
: N = N / 2 // Para N pares
y N = 3 * N + 1 // Para N impares
Nuestro número eventualmente convergerá a 1 independientemente de la elección de N. Piedra de
granizo Números: La secuencia de números enteros generados por la conjetura de Collatz se denominan números de granizo.
Ejemplos:
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.
La idea es simple, imprimimos números recursivamente hasta llegar al caso base.
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 code
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;
}
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 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 */
Python
# 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
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 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
// 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
?>
Javascript
<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
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Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA