python coding test course, calculating the area of a polygon

Calculating the area of a polygon is an important problem that requires a fundamental understanding of programming and mathematical thinking.
This problem is commonly presented in actual coding tests, and the process relies on various logical foundations.
In this course, we will first define the problem, explain the corresponding algorithm, and finally write the code using the Python language.

Problem Definition

Let’s assume we form a polygon using multiple points given as input.
The given points are represented as a series of coordinates (x, y), and these points are connected to form the polygon.
At this point, we need to write an algorithm to calculate the area of the polygon.
An example of input is as follows:

The input above indicates that we can connect four points (0, 0), (4, 0), (4, 3), and (0, 3) to form a rectangle.
The formula for calculating the area is as follows:
Area = 1/2 × |Σ (x_i * y_{i+1} - x_{i+1} * y_i)|
Note that the last point (x_n, y_n) must be connected to the first point (x_0, y_0).

Approach to Problem Solving

The approach to calculating the area of a polygon can be broadly divided into two methods.
First, directly implementing a formula using the coordinates of the vertices of the polygon.
Second, utilizing a library to easily calculate the area.
In this course, we will implement the algorithm using the first method.

1. Data Input

We will input the number of vertices of the polygon and the coordinates of each vertex.
The data received from the user will be stored in a list for management.
We can use Python’s basic input functions to handle multiple points.

2. Implementing the Area Calculation Algorithm

Let’s implement the area calculation formula in Python.
One of the advantages of polygons is that their area can be easily calculated, and our algorithm will work based on the ‘Shoelace formula’.

Example Code

        def polygon_area(coords):
            n = len(coords)
            area = 0
            for i in range(n):
                x1, y1 = coords[i]
                x2, y2 = coords[(i + 1) % n]
                area += x1 * y2 - x2 * y1
            return abs(area) / 2

3. Complete Coding Process

Let’s wrap the entire algorithm into a single function.
The code below includes the part that receives input and the function for calculating the area.
This code requires the user to input integers and expects ideal data.

Final Code

        def polygon_area(coords):
            n = len(coords)
            area = 0
            for i in range(n):
                x1, y1 = coords[i]
                x2, y2 = coords[(i + 1) % n]
                area += x1 * y2 - x2 * y1
            return abs(area) / 2

        def main():
            n = int(input("Please enter the number of vertices of the polygon: "))
            coords = []
            for _ in range(n):
                x, y = map(int, input("Please enter the coordinates of the vertex (x y): ").split())
                coords.append((x, y))
            print("The area of the polygon is: ", polygon_area(coords))

        if __name__ == "__main__":
            main()

Conclusion and Additional Tips

Now we have implemented an algorithm to calculate the area of a polygon using Python.
In actual coding interviews, it is highly likely that you will encounter such basic problems.
Therefore, it is recommended to practice with various types of polygons and input data.
Additionally, if necessary, it is important to analyze and optimize the time complexity of the algorithm to improve efficiency.

References

Mathematical Foundations for Calculating the Area of a Polygon
Understanding Python’s Basic Functions and I/O Processing
Understanding and Utilizing the Shoelace Formula
Preparing for Coding Tests – Solving Various Algorithm Problems