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 :
- Create functions to check for palindromes and reverse numbers.
- Define a function that iterates a certain amount of times while looking for Lychrel numbers.
- Initialize a long integer variable with the number to be checked in the main function.
- Call the isLychrel function and store the result.
- Print the input number and the isLychrel function’s result.
- Run the program while changing the input numbers.
Below is the implementation of the above approach :
// 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 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 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# 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 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 ?> |
<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> |
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