Lychrel Number Implementation

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 Lychrel 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

Following are the steps to solve this problem :

1. Create functions to check for palindromes and reverse numbers.
2. Define a function that iterates a certain amount of times while looking for Lychrel numbers.
3. Initialize a long integer variable with the number to be checked in the main function.
4. Call the isLychrel function and store the result.
5. Print the input number and the isLychrel function’s result.
6. Run the program while changing the input numbers. 

Below is the implementation of the above approach :

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

Complexity Analysis :

• Time Complexity  : O(log N) ; it is because time complexity of the reverse and isPalindrome functions is O(log N), where N is the number of digits in the input number 
• Auxiliary Space : O(1) ; this is constant since it does not depend on the input size