El número de Lychrel es un número natural que no puede formar un palíndromo a través del proceso iterativo de invertir repetidamente sus dígitos y sumar los números resultantes. El proceso a veces se denomina algoritmo 196 , por el número más famoso asociado con el proceso.
Los primeros números que no se sabe que producen palíndromos cuando se aplica el algoritmo 196 (es decir, una secuencia inversa y luego suma) a veces se conocen como números de Lychrel.
Ejemplos:
Input : 56 Output : 56 is lychrel : false Explanation : 56 becomes palindromic after one iteration : 56 + 65 = 121 Input : 196 Output : 196 is lychrel : true Explanation : 196 becomes palindromic after 19 iterations : 196 + 691 = 887 887 + 788 = 1675 1675 + 5761 = 7436 7436 + 6347 = 13783 13783 + 38731 = 52514 .... 16403234045 + 54043230461 70446464506 + 60546464407
La tarea es encontrar si un número dado es Lycheral con un límite dado en el número de iteraciones.
1. Iterate given number of times
1. Add number to it's reverse
2. If
the newly formed number is palindrome
then
return false // Number is not lychrel.
2. return true // Number is lychrel
C++
// C++ Program to check whether the given number
// is Lychrel Number or not with given limit
// on number of iterations.
#include<iostream>
using namespace std;
long reverse(long);
bool isPalindrome(long);
// Max Iterations
static int MAX_ITERATIONS = 20;
// Function to check whether number is
// Lychrel Number
string isLychrel(long number)
{
for (int i = 0; i < MAX_ITERATIONS; i++)
{
number = number + reverse(number);
if (isPalindrome(number))
return "false";
}
return "true";
}
// Function to check whether the number is
// Palindrome
bool isPalindrome(long number)
{
return number == reverse(number);
}
// Function to reverse the number
long reverse(long number)
{
long reverse = 0;
while (number > 0)
{
long remainder = number % 10;
reverse = (reverse * 10) + remainder;
number = number / 10;
}
return reverse;
}
// Driver program
int main()
{
long number = 295;
cout<<number << " is lychrel? "
<< isLychrel(number);
}
// This code is contributed by Smitha
Java
// Java Program to check whether the given number
// is Lychrel Number or not with given limit
// on number of iterations.
import java.io.*;
public class LychrelNumberTest
{
// Max Iterations
private static int MAX_ITERATIONS = 20;
// Function to check whether number is Lychrel Number
private static boolean isLychrel(long number)
{
for (int i = 0; i < MAX_ITERATIONS; i++)
{
number = number + reverse(number);
if (isPalindrome(number))
return false;
}
return true;
}
// Function to check whether the number is Palindrome
private static boolean isPalindrome(final long number)
{
return number == reverse(number);
}
// Function to reverse the number
private static long reverse(long number)
{
long reverse = 0;
while (number > 0)
{
long remainder = number % 10;
reverse = (reverse * 10) + remainder;
number = number / 10;
}
return reverse;
}
// driver program
public static void main(String[] args)
{
long number = 295;
System.out.println(number + " is lychrel? "
+ isLychrel(number));
}
}
Python3
# Python3 Program to check whether the given number # is Lychrel Number or not with given limit # on number of iterations. # Max Iterations MAX_ITERATIONS = 20; # Function to check whether number is # Lychrel Number def isLychrel(number): for i in range(MAX_ITERATIONS): number = number + reverse(number); if (isPalindrome(number)): return "false"; return "true"; # Function to check whether the number # is Palindrome def isPalindrome(number): return number == reverse(number); # Function to reverse the number def reverse(number): reverse = 0; while (number > 0): remainder = number % 10; reverse = (reverse * 10) + remainder; number = int(number / 10); return reverse; # Driver Code number = 295; print(number," is lychrel? ",isLychrel(number)); # This code is contributed by mits
C#
// C# Program to check whether the given number
// is Lychrel Number or not with given limit
// on number of iterations.
using System;
class GFG
{
// Max Iterations
private static int MAX_ITERATIONS = 20;
// Function to check whether number is Lychrel Number
private static bool isLychrel(long number)
{
for (int i = 0; i < MAX_ITERATIONS; i++)
{
number = number + reverse(number);
if (isPalindrome(number))
return false;
}
return true;
}
// Function to check whether the number is Palindrome
private static bool isPalindrome( long number)
{
return number == reverse(number);
}
// Function to reverse the number
private static long reverse(long number)
{
long reverse = 0;
while (number > 0)
{
long remainder = number % 10;
reverse = (reverse * 10) + remainder;
number = number / 10;
}
return reverse;
}
// Driver program
public static void Main()
{
long number = 295;
Console.Write(number + " is lychrel? "
+ isLychrel(number));
}
}
// This code is contributed by vt_m.
PHP
<?php
// PHP Program to check whether the given number
// is Lychrel Number or not with given limit
// on number of iterations.
// Max Iterations
$MAX_ITERATIONS = 20;
// Function to check whether number is
// Lychrel Number
function isLychrel($number)
{
global $MAX_ITERATIONS;
for ($i = 0; $i < $MAX_ITERATIONS; $i++)
{
$number = $number + reverse($number);
if (isPalindrome($number))
return "false";
}
return "true";
}
// Function to check whether the number
// is Palindrome
function isPalindrome($number)
{
return $number == reverse($number);
}
// Function to reverse the number
function reverse($number)
{
$reverse = 0;
while ($number > 0)
{
$remainder = $number % 10;
$reverse = ($reverse * 10) + $remainder;
$number = (int)($number / 10);
}
return $reverse;
}
// Driver Code
$number = 295;
echo $number . " is lychrel? " .
isLychrel($number);
// This code is contributed by mits
?>
Javascript
<script>
// Javascript Program to check
// whether the given number is Lychrel
// Number or not with given limit
// on number of iterations.
// Max Iterations
var MAX_ITERATIONS = 20;
// Function to check whether
// number is Lychrel Number
function isLychrel(number)
{
for (var i = 0; i < MAX_ITERATIONS; i++)
{
number = number + reverse(number);
if (isPalindrome(number))
return false;
}
return true;
}
// Function to check whether the
// number is Palindrome
function isPalindrome(number)
{
return number == reverse(number);
}
// Function to reverse the number
function reverse(number)
{
var reverse = 0;
while (number > 0)
{
var remainder = number % 10;
reverse = (reverse * 10) + remainder;
number = parseInt(number / 10);
}
return reverse;
}
// driver program
var number = 295;
document.write(number + " is lychrel ? "
+ isLychrel(number));
// This code contributed by shikhasingrajput
</script>
Producción:
295 is lychrel ? true
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Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA