C++ Program to Check Automorphic Number

Posted in C++ Tutorial

Updated on Nov 17, 2024

By Mari Selvan

👁️ 97 - Views

⏳ 4 mins

💬 1 Comment

Photo Credit to CodeToFun

🙋 Introduction

In the realm of C++ programming, exploring unique number properties is both fascinating and educational. An automorphic number is one such interesting concept.

An automorphic number (or circular number) is a number whose square ends with the number itself. In simpler terms, an n-digit number is called an automorphic number if the last n digits of its square are equal to the number itself.

In this tutorial, we'll explore a C++ program that checks whether a given number is an automorphic number or not.

The program will take a number as input, square it, and then compare the last digits to determine if it meets the criteria of an automorphic number.

📄 Example

Let's dive into the C++ code that accomplishes this task.

isAutomorphic.cpp

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#include <iostream>
#include <cmath>

// Function to check if a number is automorphic
bool isAutomorphic(int num) {
  // Calculate the square of the number
  long long square = static_cast < long long > (num) * num;

  // Count the number of digits in the original number
  int originalDigits = 0;
  int temp = num;
  while (temp != 0) {
    temp /= 10;
    originalDigits++;
  }

  // Extract the last digits from the square
  long long lastDigits = square % static_cast < long long > (std::pow(10, originalDigits));

  // Check if the last digits match the original number
  return lastDigits == num;
}

// Driver program
int main() {
  // Replace this value with your desired number
  int number = 76;

  // Check if the number is automorphic
  if (isAutomorphic(number)) {
    std::cout << number << " is an automorphic number." << std::endl;
  } else {
    std::cout << number << " is not an automorphic number." << std::endl;
  }
  return 0;
}

💻 Testing the Program

To test the program with different numbers, simply replace the value of number in the main function.

Output

76 is an automorphic number.

Compile and run the program to check if the given number is an automorphic number.

🧠 How the Program Works

The program defines a function isAutomorphic that takes a number as input and returns whether it is an automorphic number or not.
Inside the function, it calculates the square of the input number.
It counts the number of digits in the original number to extract the corresponding number of last digits from the square.
It compares the extracted last digits with the original number to determine if it's an automorphic number.

📏 Between the Given Range

Let's take a look at the C++ code that checks for automorphic numbers in the specified range.

isAutomorphic.cpp

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#include <iostream>
#include <cmath>

// Function to check if a number is automorphic
bool isAutomorphic(int num) {
  int square = num * num;
  int temp = num;

  // Calculate the number of digits in the original number
  int digits = 0;
  while (temp > 0) {
    temp /= 10;
    ++digits;
  }

  // Extract the last 'digits' digits from the square
  int lastDigits = square % static_cast < int > (pow(10, digits));

  return lastDigits == num;
}

// Driver program
int main() {
  std::cout << "Automorphic numbers in the range 1 to 50:\n";

  // Check numbers from 1 to 50
  for (int i = 1; i <= 50; ++i) {
    if (isAutomorphic(i)) {
      std::cout << i << " ";
    }
  }

  std::cout << std::endl;

  return 0;
}

💻 Testing the Program

Output

Automorphic numbers in the range 1 to 50:
1 5 6 25

The program is set to check for automorphic numbers in the range from 1 to 50. Simply compile and run the program to see the automorphic numbers in this specified range.

🧠 How the Program Works

The program defines a function isAutomorphic that takes a number as input and checks if it is an automorphic number.
Inside the function, it calculates the square of the number and extracts the last digits from the square.
The main function iterates through numbers from 1 to 50 and prints the automorphic numbers.

🧐 Understanding the Concept of Automorphic Numbers

Before delving into the code, let's take a moment to understand automorphic numbers.

An n-digit number is called an automorphic number if the last n digits of its square are equal to the number itself.

For example, 25 is an automorphic number because its square is 625, and the last two digits (25) match the original number.

🎢 Optimizing the Program

While the provided program effectively checks for automorphic numbers, you can explore and implement further optimizations or variations based on your specific needs or preferences.

Feel free to incorporate and modify this code as needed for your specific use case. Happy coding!