Java Coding Test Course, Euclidean Algorithm

This blog post will explore the Euclidean algorithm, which frequently appears in Java coding tests. The Euclidean algorithm is an efficient method for finding the greatest common divisor (GCD) of two numbers and requires basic mathematical knowledge. In this article, we will present a problem using the Euclidean algorithm and explain the solution process in detail.

Problem Description

Introduction to the Euclidean Algorithm

The Euclidean algorithm is a method devised by the ancient Greek mathematician Euclid, which is used to find the greatest common divisor of two given numbers. When two numbers A and B are given, the property GCD(A, B) = GCD(B, A % B) is used. This process is repeated until A becomes 0, at which point B’s value becomes the GCD.

The Euclidean Algorithm

1. If A is not 0: GCD(A, B) = GCD(B % A, A)
2. If A is 0: GCD(A, B) = B

Now, let’s apply the above algorithm to solve the problem through coding.

Problem Solving

Step 1: Designing the Function

First, we design a function to find the greatest common divisor of two numbers. We will use a recursive function.

public static int gcd(int a, int b) {
    if (b == 0) {
        return a;
    }
    return gcd(b, a % b);
}

The code above takes two integers A and B as arguments and calculates the greatest common divisor recursively. If B is 0, A is the GCD. In other cases, it calls GCD(B, A % B) to continue calculating the GCD.

Step 2: Writing the Main Function

Now, we will write the main function to handle input and call the previously created GCD function.

import java.util.Scanner;

public class GCDExample {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter two integers (A B): ");
        int a = scanner.nextInt();
        int b = scanner.nextInt();

        int result = gcd(a, b);
        System.out.println("The greatest common divisor of " + a + " and " + b + " is: " + result);
    }

    public static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }
}

The above code takes two numbers from the user to calculate and print the greatest common divisor. It uses the Scanner class to get input and calls the gcd method to obtain the calculation result.

Step 3: Testing the Code

Now, let’s run the program to calculate the greatest common divisor of the two numbers. For example, if we input 48 and 18, the following result is obtained.

Enter two integers (A B): 48 18
The greatest common divisor of 48 and 18 is: 6

Optimization and Additional Considerations

The Euclidean algorithm is a very efficient algorithm, with a time complexity of O(log(min(A, B))). However, in the given problem, we could also consider more diverse applications or performance optimizations.

Using an Array for Greatest Common Divisor

For example, if we have an array of several numbers, we can think of a way to calculate the greatest common divisor for multiple numbers. This can be implemented in the following form.

public static int gcdArray(int[] numbers) {
    int result = numbers[0];
    for (int i = 1; i < numbers.length; i++) {
        result = gcd(result, numbers[i]);
    }
    return result;
}

The above method takes an integer array as an argument and calculates the greatest common divisor of all the numbers in the array.

Conclusion

In this article, we solved the problem of finding the greatest common divisor using the Euclidean algorithm. This algorithm frequently appears in coding tests and serves as a good tool for assessing candidates’ problem-solving skills. We have shown that by appropriately handling input, we can create programs that function reliably for numbers of various sizes.

Organizing and practicing such algorithmic problems systematically will greatly aid you in preparing for coding tests. It is essential to practice various problems to refine your skills and be able to adapt flexibly when faced with difficult problems.

References

• Euclidean Algorithm – Wikipedia