Java Coding Test Course, Calculating the Area of a Polygon

Hello! In this lecture, we will address the problem of calculating the area of a polygon. This problem will be implemented using Java, and I will explain the process of solving the problem in detail, applying basic mathematical concepts and algorithms.

Problem Description

Write a program to calculate the area of a polygon based on the coordinates of given points. The points are given in the form of (x<sub>1</sub>, y<sub>1</sub>), (x<sub>2</sub>, y<sub>2</sub>), ..., (x<sub>n</sub>, y<sub>n</sub>), and it is assumed that these points are connected to form the polygon. The area to be computed must satisfy the following conditions:

  • The points are given in a clockwise or counterclockwise direction.
  • An accurate and efficient algorithm must be implemented.

Input

The first line contains the number of points n. The following n lines contain the coordinates x, y of each point as integers.

Output

Output the area of the polygon as a real number, rounded to two decimal places.

Example Input

4
0 0
4 0
4 3
0 4

Example Output

12.00

Solution Method

There are various algorithms to calculate the area of a polygon, but in this lecture, we will use Schroder’s formula (or the polygon area formula). According to this formula, the area of a polygon A is calculated as follows:

A = 0.5 * |Σ (xiyi+1 - yixi+1)|

Here, (x<sub>i</sub>, y<sub>i</sub>) are the coordinates of each point of the polygon, and (x<sub>n+1</sub>, y<sub>n+1</sub>) = (x<sub>1</sub>, y<sub>1</sub>) to return to the first point.

Step 1: Designing the Algorithm Structure

First, let’s design the basic structure of the program. The program consists of the following four steps:

  1. Receive input
  2. Calculate area
  3. Print result
  4. Clean up

Step 2: Receiving Input

In Java, we can receive user input through the Scanner class. We will store the coordinates of each point using an ArrayList. Here is a sample code:

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class PolygonArea {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();  // Number of points
        List<point> points = new ArrayList&lt;&gt;();
        
        for (int i = 0; i &lt; n; i++) {
            int x = scanner.nextInt();
            int y = scanner.nextInt();
            points.add(new Point(x, y));
        }
        scanner.close();
    }
    
    static class Point {
        int x, y;

        Point(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }
}
</point>

Step 3: Calculating Area

Now it is time to add a method to calculate the area. The area calculation can be done by applying the above formula for each point using a for loop:

public static double calculateArea(List<point> points) {
    double area = 0.0;
    int n = points.size();

    for (int i = 0; i &lt; n; i++) {
        Point p1 = points.get(i);
        Point p2 = points.get((i + 1) % n); // Next point, the last point connects to the first point
        area += p1.x * p2.y - p2.x * p1.y;
    }
    return Math.abs(area) / 2.0;
}
</point>

Step 4: Printing the Result

Finally, let’s add the code to print the calculated area in the desired format. Add the following code to the main method:

double area = calculateArea(points);
System.out.printf("%.2f\n", area);

Complete Code

Now, if we organize all the code into one, it looks like this:

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class PolygonArea {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();  // Number of points
        List<point> points = new ArrayList&lt;&gt;();

        for (int i = 0; i &lt; n; i++) {
            int x = scanner.nextInt();
            int y = scanner.nextInt();
            points.add(new Point(x, y));
        }
        scanner.close();
        
        double area = calculateArea(points);
        System.out.printf("%.2f\n", area);
    }

    static class Point {
        int x, y;

        Point(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }

    public static double calculateArea(List<point> points) {
        double area = 0.0;
        int n = points.size();

        for (int i = 0; i &lt; n; i++) {
            Point p1 = points.get(i);
            Point p2 = points.get((i + 1) % n); // Next point, the last point connects to the first point
            area += p1.x * p2.y - p2.x * p1.y;
        }
        return Math.abs(area) / 2.0;
    }
}
</point></point>

Conclusion

In this lecture, we solved the problem of calculating the area of a polygon. The algorithm we covered is based on Schroder’s formula, which is frequently used in actual programming competitions. Writing code at each step and implementing the algorithm ourselves must have been a very beneficial experience.

Now, you can also tackle the problem of calculating the area for various types of polygons based on this algorithm. Furthermore, I encourage you to challenge yourself to solve more advanced problems by integrating other ideas and algorithms. In the next lecture, try different algorithm problems!