Java Coding Test Course, Exploring Geometry

Hello! Today, we will solve algorithm problems related to geometry in the Java coding test course. Geometric problems are often covered in algorithm exams and help in understanding basic shapes like plane geometry, triangles, circles, and polygons. These problems usually provide an opportunity to develop mathematical thinking skills based on the theoretical properties of shapes.

Problem Statement

Let’s solve the following geometric problem:

Problem: Given two points P1(1, 3) and P2(4, 6) on a plane, write a program to calculate the length of the line segment connecting these two points.

The length of the line segment is defined as the distance between the two points, and the distance between two points P1(x1, y1) and P2(x2, y2) can be calculated using the following formula:

distance = √((x2 - x1)² + (y2 - y1)²)

Problem Solving Process

1. Problem Analysis

Analyzing the problem, the coordinates of the two points P1 and P2 are fixed, and the goal is to find the distance between these two points. The mathematical concept that can be used here is the Pythagorean theorem. We can calculate the Euclidean distance using the coordinates of the given two points.

2. Mathematical Judgment

We are given two points P1(1, 3) and P2(4, 6). Based on this, we can calculate the differences in the x-coordinate and y-coordinate to apply the distance formula.

– Difference in x-coordinates: (x2 - x1) = (4 - 1) = 3
– Difference in y-coordinates: (y2 - y1) = (6 - 3) = 3

3. Distance Calculation

Substituting the calculated differences into the distance formula:

distance = √(3² + 3²) = √(9 + 9) = √18 = 3√2 ≈ 4.24

4. Writing Java Code

Now let’s implement this algorithm in Java code. The flow of the algorithm is as follows:

public class DistanceCalculator {
    public static void main(String[] args) {
        double x1 = 1, y1 = 3; // Coordinates of the first point P1
        double x2 = 4, y2 = 6; // Coordinates of the second point P2
        
        double distance = calculateDistance(x1, y1, x2, y2);
        System.out.println("Distance between points P1 and P2: " + distance);
    }

    // Method to calculate the distance between two points
    public static double calculateDistance(double x1, double y1, double x2, double y2) {
        return Math.sqrt(Math.pow((x2 - x1), 2) + Math.pow((y2 - y1), 2));
    }
}

5. Output Result

When the above code is run, the program calculates and outputs the distance between the two points P1 and P2. The result is approximately 4.24.

Conclusion

Through this lecture, we have understood how to calculate the distance between points in plane geometry. The problem-solving process proceeded as follows: problem analysis, mathematical judgment, distance calculation, writing Java code, and outputting the result. These geometric problems can be applied to various algorithm problems, and it is important to solidify the basic concepts.

We look forward to covering more geometric problems and algorithms in the future! Thank you.