Swift Coding Test Course, Exploring Geometry

Introduction

Hello! In this tutorial, we will learn how to solve geometric algorithm problems using Swift. Geometric problems are one of the frequently asked topics in coding tests, and the ability to solve problems related to points, lines, and surfaces in a coordinate system is crucial. In this article, we will present fundamental concepts of geometry, along with algorithmic problems that utilize these concepts, and we will explain the process of solving those problems in detail.

Basics of Geometry

Geometry is a branch of mathematics that studies shapes and the relationships between those shapes. The geometric objects mainly dealt with in algorithm problems include points, lines, triangles, and polygons. Various problems can be solved by utilizing the properties of these geometric figures. For example, calculating the distance between two points, whether lines intersect, and determining the perimeter and area of polygons are key aspects of geometric problems.

Problem Description

The problem at hand is to calculate the area of a polygon. You will need to write an algorithm that calculates the area of a polygon formed by connecting N given points.

Problem

Given N points, write an algorithm to calculate the area of the polygon formed by connecting these points. The points are provided in a two-dimensional plane, and their coordinates are expressed as integers.

Input

• The first line contains an integer N (3 ≤ N ≤ 10^6).
• In the next N lines, the X and Y coordinates of each point are given as integers.

Output

Print the area of the polygon rounded to the second decimal place.

Problem Solving Process

To design an algorithm for solving the problem, one must first understand how to calculate the area of a polygon. Generally, the most widely known method for calculating the area of a polygon is the ‘Shoelace Theorem’ (or ‘Surveyor’s Formula’). This method uses the following formula:

Shoelace Theorem

Given points (x₁, y₁), (x₂, y₂), …, (x_N, y_N), the area of the polygon can be calculated as follows:

$=\frac{({\displaystyle \sum }(x\_i·y\_\mathrm{i+1})–{\displaystyle \sum }(y\_i·x\_\mathrm{i+1}))}{2}$

To put this very simply, you take the absolute value of the sum obtained by applying the above formula to all the points of the polygon, and divide by 2 to get the area. Now, let’s implement this in Swift.

Swift Implementation

            
                import Foundation

                struct Point {
                    var x: Int
                    var y: Int
                }

                func polygonArea(points: [Point]) -> Double {
                    var area = 0
                    let n = points.count

                    for i in 0..<n {="" let="" j="(i" +="" 1)="" %="" n="" area="" *="" points[j].y)="" -="" double(points[j].x="" points[i].y)="" }="" return="" abs(area)="" 2.0="" func="" main()="" var="" points:="" [point]="[]" for="" _="" in="" 0..<n="" coordinates="readLine()!.split(separator:" "="" ")="" point="Point(x:" int(coordinates[0])!,="" y:="" int(coordinates[1])!)="" points.append(point)="" print(string(format:="" "%.2f",="" polygonarea(points:="" points)))="" <="" code="">
</n>