C# Coding Test Course, Calculating the Area of a Polygon

The problem of calculating the area of a polygon in a coding test requires a deep understanding of algorithms and geometry. In this article, we will present the problem of calculating the area of a polygon and discuss in detail the approaches, algorithms, and code explanations to solve it.

Problem Description

Problem: Write a program to calculate the area of a regular polygon given the coordinates of its vertices. Each vertex is provided in order, connected in a clockwise or counterclockwise manner. The coordinates are represented on a two-dimensional plane.

Input: The first line contains the number of vertices n (3 ≤ n ≤ 1000). The next n lines contain the x and y coordinates of each vertex.

Output: Print the area rounded to two decimal places on the last line.

Approach to Solve the Problem

One of the algorithms to calculate the area of a polygon is
using the Shoelace formula. This method allows for efficient calculation of the area when the coordinates of the polygon’s vertices are given. The formula is based on the vertices connected in a clockwise or counterclockwise order to determine the area of the polygon.

The area calculation formula is as follows:

        Area = 0.5 * | Σ (x_i * y_i+1 - y_i * x_i+1) |

Here, i is an integer from 0 to n-1, and (x_n, y_n) connects back to (x₀, y₀). Using this formula, the area of the polygon can be easily calculated.

C# Implementation Steps

Now, let’s implement the given algorithm in C#. The implementation steps are as follows:

1. Input Handling

First, we will read the number of polygon vertices and the coordinates of each vertex from the user.

2. Area Calculation

Using the Shoelace formula, we will calculate the area from the input coordinates.

3. Output the Result

We will output the calculated area rounded to two decimal places.

Code Implementation

        
        using System;

        class Program
        {
            static void Main(string[] args)
            {
                int n = int.Parse(Console.ReadLine());
                double[,] points = new double[n, 2];

                // Read coordinates
                for (int i = 0; i < n; i++)
                {
                    string[] input = Console.ReadLine().Split();
                    points[i, 0] = double.Parse(input[0]);
                    points[i, 1] = double.Parse(input[1]);
                }

                double area = CalculatePolygonArea(points, n);
                Console.WriteLine("{0:F2}", Math.Abs(area));
            }

            static double CalculatePolygonArea(double[,] points, int n)
            {
                double area = 0;

                for (int i = 0; i < n; i++)
                {
                    int next = (i + 1) % n;  // Index of the next point
                    area += points[i, 0] * points[next, 1];
                    area -= points[next, 0] * points[i, 1];
                }

                return area * 0.5;  // Area
            }
        }

Code Explanation

– Point Definition: A 2D array points is declared to store the input coordinates.
– Coordinate Input: The user inputs x and y values through a for loop.
– Area Calculation: The area is calculated using the Shoelace formula in the CalculatePolygonArea method. The coordinates of each vertex are used to compute the area, and 0.5 is multiplied to return the final area.
– Output: The area is printed to two decimal places. The Math.Abs() function ensures that the area is always positive, even if it is negative.

Example

Input Example:
4
0 0
4 0
4 3
0 3
Output Example:
12.00

In the above example, we calculate the area of a rectangle by starting at 0,0, moving to 4,0, continuing to 4,3, and finally returning to 0,3, forming a square. The area of this polygon is 4*3=12.

Conclusion

In this article, we learned how to calculate the area of a polygon using C#. The problem of calculating the area of polygons is frequently encountered in various coding tests and is a great opportunity to develop algorithmic thinking. It is important to always consider different approaches when solving algorithmic problems. In the next session, I hope to gain more experience through another algorithm problem.