C++ Exercises: Find the Lychrel numbers and the number of Lychrel number within the range 1 to 1000

Last update on December 20 2024 12:24:21 (UTC/GMT +8 hours)

Write a C++ program to find the Lychrel numbers and the number of Lychrel numbers in the range 1 to 1000 (after 500 iterations).

Visual Presentation:

Sample Solution:

C++ Code :

#include <iostream> // Include the input/output stream library
using namespace std; // Use the standard namespace

// Function to reverse a number
long long int numReverse(long long int number)
{
    long long int rem = 0;
    while (number > 0)
    {
        rem = (rem * 10) + (number % 10); // Extract digits in reverse order
        number = number / 10; // Remove the last digit
    }
    return rem; // Return the reversed number
}

// Function to check if a number is a palindrome
bool is_Palindrome(long long int num)
{
    return (num == numReverse(num)); // Check if the number is equal to its reverse
}

// Function to check if a number is a Lychrel number
bool isLychrel(int num, const int iterCount = 500)
{
    long long int temp = num;
    long long int rev;
    for (int i = 0; i < iterCount; i++)
    {
        rev = numReverse(temp); // Get the reversed number
        if (is_Palindrome(rev + temp)) // Check if the sum of the number and its reverse is a palindrome
            return false; // If it's a palindrome, it's not a Lychrel number
        temp = temp + rev; // Update temp with the sum
    }
    return true; // If after iterations no palindrome is found, it's a Lychrel number
}

int main()
{
    int lyno, ctr = 0, i; // Initialize variables for number, counter, and iteration
    bool l; // Initialize a boolean variable to check Lychrel property
    cout << "\n\n Find the Lychrel numbers between 1 to 1000(after 500 iteration): \n"; // Display a message for user
    cout << " ----------------------------------------------------------------------\n";
    cout << " The Lychrel numbers are : ";

    for (i = 1; i <= 1000; i++) // Loop through numbers from 1 to 1000
    {
        lyno = i; // Assign the current number
        l = isLychrel(lyno); // Check if the number is a Lychrel number

        if (l == true) // If it's a Lychrel number
        {
            ctr++; // Increment the counter
            cout << lyno << " "; // Display the Lychrel number
        }
    }

    cout << endl;
    cout << " The number of Lychrel numbers are: " << ctr << endl; // Display the total count of Lychrel numbers
    return 0; // End of the program
}

Sample Output:

Find the Lychrel numbers between 1 to 1000(after 500 iteration):                                    
 ----------------------------------------------------------------------                              
 The Lychrel numbers are : 196 295 394 493 592 689 691 788 790 879 887 978 986                       
 The number of Lychrel numbers are: 13 

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