Swift Coding Test Course, Calculating the Area of a Polygon

1. Problem Definition

In this session, we will handle the problem of calculating the area of a given polygon. When the vertices of the polygon are provided, we will implement an algorithm to calculate the area using them. The algorithm used for area calculation is based on the Strassen Algorithm.

2. Problem Input

The function has the following shape:

func polygonArea(vertices: [(Double, Double)]) -> Double

Here, vertices is an array of tuples representing each vertex of the polygon. Each tuple contains the x and y coordinates.

3. Algorithm Explanation

To calculate the area of the polygon, we will use the polygon area formula. This formula is as follows:

Area = 0.5 * | Σ (x<sub>i</sub> * y<sub>i+1</sub> - y<sub>i</sub> * x<sub>i+1</sub>) |

Here, i represents the index from 0 to n-1, and the last vertex connects to the first vertex. To code this formula, we will follow these steps:

1. Calculate the number of vertices n.
2. Calculate the area contribution for each vertex.
3. Sum all contributions.
4. Convert the result to absolute value and multiply by 0.5.

4. Code Implementation

Now, let’s implement the above algorithm in Swift. Here is the complete code:

func polygonArea(vertices: [(Double, Double)]) -> Double {
    var area = 0.0
    let n = vertices.count

    for i in 0..<n {="" let="" j="(i" +="" 1)="" %="" n="" area="" *="" vertices[j].1="" -="" vertices[j].0="" vertices[i].1="" }="" return="" abs(area)="" 0.5="" }<="" code=""></n>

<h3>4.1 Code Explanation</h3> <p>The code above works as follows:</p> <ul> <li>First, the <code>area</code> variable is initialized to prepare for area calculation.</li> <li><code>n</code> stores the number of vertices of the polygon.</li> <li>For each vertex <code>i</code>, the next vertex <code>j</code> is calculated (where <code>j</code> is set to <code>(i + 1) % n</code> to connect the last vertex to the first vertex).</li> <li>The area contribution is calculated and accumulated in <code>area</code>.</li> <li>At the end of the loop, the absolute value of the area is divided by 2 to return the result.</li> </ul> <h2>5. Test Cases</h2> <p>Now we will validate this function with various test cases. Here are some examples:</p> <pre><code>let example1 = [(0.0, 0.0), (4.0, 0.0), (4.0, 3.0), (0.0, 4.0)] let area1 = polygonArea(vertices: example1) print(area1) // 12.0 let example2 = [(1.0, 1.0), (3.0, 1.0), (3.0, 3.0), (1.0, 3.0)] let area2 = polygonArea(vertices: example2) print(area2) // 4.0 let example3 = [(0.0, 0.0), (5.0, 0.0), (5.0, 5.0), (0.0, 5.0)] let area3 = polygonArea(vertices: example3) print(area3) // 25.0</code></pre> <h2>6. Conclusion</h2> <p>In this tutorial, we implemented an algorithm in Swift to calculate the area of a polygon. We verified that the algorithm works correctly through various test cases. These types of problems can deepen our understanding of data structures and algorithms, which will be useful in future coding tests.</p> <p>If more complex problems related to polygons or various types of area calculations are needed, we can consider additional optimizations and expansions based on this algorithm. In the next tutorial, we will cover these advanced techniques.</p>