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Lychrel Number Implementation

  • Difficulty Level : Medium
  • Last Updated : 12 May, 2021

Lychrel Number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers. The process is sometimes called the 196-algorithm, after the most famous number associated with the process. 
The first few numbers not known to produce palindromes when applying the 196-algorithm (i.e., a reverse-then-add sequence) are sometimes known as Lychrel numbers. 
Examples: 
 

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

The task is to find if a given number is Lycheral with a given limit on the number of iterations.
 

 

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>
Output: 
295 is lychrel ? true

 

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