Published: 05 Feb 2025 | Reading Time: 4 min read
Automorphic numbers are very interesting from both mathematics and programming point of view. To explain simply, a number is considered automorphic if the square of the number has an ending that is the same as the digits of the number itself. This unique property makes automorphic numbers in Java intriguing and a good choice for various programming exercises.
Writing code for automorphic numbers in Java is a great exercise in logical thinking, which is essential for programming. They can be used to understand many things like modular arithmetic, patterns in number systems, and even cryptography.
Automorphic numbers help beginners learn concepts like modulo operations, pattern matching, and writing good algorithms. They are also useful when you enter competitive programming to test coding skills. They are also used in number theory for mathematical analysis. In this article, we'll learn how to write a Java program to check automorphic numbers.
An automorphic number is a special number where the square of the number has the same digits as the number itself. In simpler terms, if you square the number and the last digits of the resulting number are the same as the original number, we can say that it's an automorphic number.
Given a number N, the task is to check whether the number is an Automorphic number or not. Let's take a look at how to write a Java program to check automorphic numbers:
First, take the given number and calculate its square. For example, if the number is 25, you will calculate 25 x 25 = 625.
Next, focus on the last digits of the squared result. There are a couple of ways to do this:
Now, compare the last digits of the square with the original number. If the digits match, the number is automorphic. For example, with the number 25, the square is 625, and the last two digits (25) match the original number, so 25 is automorphic.
Continuing from the last example, let's see how 25 is an automorphic number in Java. The program follows the same logic by squaring the number and comparing the last digits of the square to the original number. If they match, the number is automorphic.
public class Main {
public static void main(String[] args) {
int number = 25;
// Step 1: Compute the square of the number
int square = number * number;
// Step 2: Get the number of digits in the original number
int numDigits = String.valueOf(number).length();
// Step 3: Get the last digits of the square
int lastDigits = square % (int) Math.pow(10, numDigits);
// Step 4: Compare and check for a match
if (lastDigits == number) {
System.out.println(number + " is an Automorphic number.");
} else {
System.out.println(number + " is not an Automorphic number.");
}
}
}
25 is an Automorphic number.
=== Code Execution Successful ===
In this section, we will delve into different Java programs to check for automorphic numbers. We will explore various approaches, from basic iterations to more optimized solutions, showcasing how Java can be utilized to tackle this intriguing mathematical concept. With hands-on examples and code snippets, you'll gain practical experience in checking automorphic numbers and enhancing your programming skills.
Now, let's write a Java program to check automorphic number:
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
// Create a Scanner object to take user input
Scanner scanner = new Scanner(System.in);
// Ask the user to enter a number
System.out.print("Enter a number: ");
int number = scanner.nextInt();
// Step 1: Compute the square of the number
int square = number * number;
// Step 2: Convert both the number and its square to strings
String numStr = String.valueOf(number);
String squareStr = String.valueOf(square);
// Step 3: Check if the last digits of the square match the number
if (squareStr.endsWith(numStr)) {
System.out.println(number + " is an Automorphic number.");
} else {
System.out.println(number + " is not an Automorphic number.");
}
// Close the scanner
scanner.close();
}
}
Enter a number: 65
65 is not an Automorphic number.
=== Code Execution Successful ===
The automorphic number in Java can be implemented using different approaches. One variation involves using the modulus operator. Here's a program that checks if a number is automorphic using the modulus operator:
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
// Create a Scanner object to take user input
Scanner scanner = new Scanner(System.in);
// Ask the user to enter a number
System.out.print("Enter a number: ");
int number = scanner.nextInt();
// Step 1: Compute the square of the number
int square = number * number;
// Step 2: Find the number of digits in the original number
int digits = (int) Math.log10(number) + 1;
// Step 3: Get the last digits of the square using modulus
int lastDigits = square % (int) Math.pow(10, digits);
// Step 4: Check if the last digits match the original number
if (lastDigits == number) {
System.out.println(number + " is an Automorphic number.");
} else {
System.out.println(number + " is not an Automorphic number.");
}
// Close the scanner
scanner.close();
}
}
Enter a number: 85
85 is not an Automorphic number.
=== Code Execution Successful ===
In this program we check whether a number is automorphic using a for loop. It iterates through the digits of the number and compares them with the last digits of its square.
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
// Create a Scanner object for user input
Scanner scanner = new Scanner(System.in);
// Ask the user to enter a number
System.out.print("Enter a number: ");
int number = scanner.nextInt();
// Compute the square of the number
int square = number * number;
int temp = number;
boolean isAutomorphic = true;
// Check each digit using a for loop
for (; temp > 0; temp /= 10, square /= 10) {
if (temp % 10 != square % 10) {
isAutomorphic = false;
break;
}
}
// Print the result
if (isAutomorphic) {
System.out.println(number + " is an Automorphic number.");
} else {
System.out.println(number + " is not an Automorphic number.");
}
// Close the scanner
scanner.close();
}
}
Enter a number: 376
376 is an Automorphic number.
=== Code Execution Successful ===
In this program, we'll use a while loop to check for automorphic numbers:
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
// Create a Scanner object for user input
Scanner scanner = new Scanner(System.in);
// Ask the user to enter a number
System.out.print("Enter a number: ");
int number = scanner.nextInt();
// Compute the square of the number
int square = number * number;
// Initialize a temporary variable to store the number
int temp = number;
// Check if the number is Automorphic
boolean isAutomorphic = true;
// While loop to check the last digits
while (temp > 0) {
if (temp % 10 != square % 10) {
isAutomorphic = false;
break;
}
temp /= 10;
square /= 10;
}
// Print the result
if (isAutomorphic) {
System.out.println(number + " is an Automorphic number.");
} else {
System.out.println(number + " is not an Automorphic number.");
}
// Close the scanner
scanner.close();
}
}
Enter a number: 625
625 is an Automorphic number.
=== Code Execution Successful ===
Here's a program to check for automorphic numbers in the range of 0-10,000:
public class Main {
public static void main(String[] args) {
System.out.println("Automorphic numbers between 0 and 10000:");
// Loop through numbers from 0 to 10000
for (int number = 0; number <= 10000; number++) {
if (isAutomorphic(number)) {
System.out.print(number + " ");
}
}
}
// Function to check if a number is Automorphic
static boolean isAutomorphic(int number) {
int square = number * number;
int temp = number;
// Check if last digits of square match the number
while (temp > 0) {
if (temp % 10 != square % 10) {
return false;
}
temp /= 10;
square /= 10;
}
return true;
}
}
Automorphic numbers between 0 and 10000:
0 1 5 6 25 76 376 625 9376
=== Code Execution Successful ===
Understanding the complexity of automorphic number programs is crucial because it helps us evaluate the efficiency of the code. Now, let's look at the time and space complexity of these.
The time complexity of automorphic number programs that use digit-by-digit comparison like the modulus operator method is O(log₁₀N). Here, N is the input number. This is because the program processes each digit of N, and the number of digits in N is proportional to log₁₀N. The loop runs once for each digit of N, which makes it logarithmic in nature.
The space complexity of the discussed programs is O(1). The program uses a fixed amount of memory to store variables like N, sq, and intermediate values, regardless of the size of the input. No additional memory is allocated based on the input size, which makes the space usage constant.
Error: Sometimes the square of the number might be calculated wrong by the user. Then, the program gives the wrong result.
Tip: Make sure you're correctly squaring the number and checking it by printing the value to see if it's correct. Also, remember that the number should be positive before squaring it.
Error: The program may fail to correctly match the number's digits and its square, which means it won't give the right answer.
Tip: Add print statements to check which digits are being compared. The code should show you're comparing the number's last digit with the square's last digit. Both should be updated correctly in each step.
Error: Squaring a large number can sometimes cause an overflow, where the result is too big for the program to handle which can give errors.
Tip: Use a larger data type, like long, if the number is too big for an int. Print the squared value to ensure it doesn't exceed the maximum allowed value.
Error: Sometimes, loops may go one step too far or not far enough, which can cause the program to compare the wrong digits.
Tip: Check the loop conditions and make sure they are set up correctly. Print out the digits you're comparing so everything is being checked properly.
Error: Negative numbers might cause problems when squaring and comparing digits.
Tip: Always use the absolute value of the number (positive version) before squaring it. This will prevent issues with negative inputs.
Error: Some small numbers like 0 or 1 might not be handled correctly, leading to unexpected results.
Tip: Test your program with edge cases such as 0 and 1 to make sure it works in all situations.
Learning to write an automorphic number program is super important. It helps you understand how algorithms work, how to compare digits, and how to solve problems step by step. This problem builds your coding skills, sharpens your logical thinking, and prepares you for tough challenges. It's not just about checking if a number is automorphic but learning how to break down problems into smaller parts, which is all about coding. Plus, mastering such problems prepares you for coding competitions and even job interviews.
An automorphic number is a number whose square ends with the same digits as the number itself. Simple example? 25, because 25² = 625, and 25 is at the end!
Learning this helps you understand how to deal with numbers, use loops, and practice comparisons in coding. It's a solid skill for interviews and programming contests.
No negative numbers won't work when negative. You need to take the absolute value first. For example, -25 becomes 25, and we check its square then.
You won't use it much in daily life, but learning such problems improves your problem-solving skills. It helps in coding interviews and competitions where thinking sharp matters most.
Check if you're squaring the number correctly or if you're comparing the digits in the right way. Debug step by step and add print statements for help.
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