**π‘ Problem Formulation:** Given a starting point on the Cartesian plane, the task is to compute the coordinates of four points that form a square with sides parallel to the x and y axes. As an input, we take a coordinate representing the bottom-left corner of the square and the length of a side. The desired output is a list of four tuples corresponding to the coordinates of each corner of the square.

## Method 1: Using Basic Arithmetic Operations

Method 1 involves using basic arithmetic to calculate the positions of the other three points based on the given bottom-left point and side length. The top-right corner can be found by adding the side length to both the x and y coordinates of the starting point, while the other two points are found by adding the side length to just one of the coordinates.

Here’s an example:

def find_square(bottom_left, side_length): x, y = bottom_left return [ bottom_left, (x + side_length, y), (x + side_length, y + side_length), (x, y + side_length) ] # Example usage bottom_left = (1, 1) side_length = 3 print(find_square(bottom_left, side_length))

Output:

[(1, 1), (4, 1), (4, 4), (1, 4)]

This code snippet defines a function `find_square()`

that calculates the coordinates of a square’s corners, given the bottom-left corner and the side length. It utilizes a clear and simple approach, making it very accessible for anyone new to programming or geometry problems.

## Method 2: Using a Custom Point Class

In Method 2, a custom Point class is created to represent a point on the Cartesian plane. This abstraction allows for more readable and potentially reusable code when computing the coordinates of the square.

Here’s an example:

class Point: def __init__(self, x, y): self.x = x self.y = y def __repr__(self): return f"({self.x}, {self.y})" def find_square(bottom_left, side_length): points = [bottom_left] points.append(Point(bottom_left.x + side_length, bottom_left.y)) points.append(Point(bottom_left.x + side_length, bottom_left.y + side_length)) points.append(Point(bottom_left.x, bottom_left.y + side_length)) return points # Example usage bottom_left = Point(1, 1) side_length = 3 print(find_square(bottom_left, side_length))

Output:

[(1, 1), (4, 1), (4, 4), (1, 4)]

This snippet introduces a custom `Point`

class to encapsulate x and y coordinates. We can see how creating classes can structure code more effectively and make it more readable. The function `find_square()`

is then defined to perform the computation.

## Method 3: Using Complex Number Representation

Method 3 utilizes Python’s complex number capabilities to represent and calculate the points. This is an elegant mathematical approach where operations on complex numbers translate directly to operations on points in a plane.

Here’s an example:

def find_square(bottom_left, side_length): bl = complex(*bottom_left) return [ bl, bl + side_length, bl + side_length + side_length*1j, bl + side_length*1j ] # Example usage bottom_left = (1, 1) side_length = 3 print([tuple(map(int, (c.real, c.imag))) for c in find_square(bottom_left, side_length)])

Output:

[(1, 1), (4, 1), (4, 4), (1, 4)]

The function `find_square()`

uses complex numbers to compute the square’s corners, treating the real and imaginary parts as the x and y coordinates respectively. This method emphasizes the power and elegance of mathematical constructs in programming.

## Method 4: Using NumPy Library

Method 4 involves the NumPy library, which is widely used for numerical computation in Python. This method leverages vector addition provided by NumPy to calculate the square’s points.

Here’s an example:

import numpy as np def find_square(bottom_left, side_length): bl = np.array(bottom_left) transformations = [ (0, 0), (side_length, 0), (side_length, side_length), (0, side_length) ] return [tuple(bl + np.array(t)) for t in transformations] # Example usage bottom_left = (1, 1) side_length = 3 print(find_square(bottom_left, side_length))

Output:

[(1, 1), (4, 1), (4, 4), (1, 4)]

The function `find_square()`

makes use of the NumPy library for its powerful array manipulation capabilities. By treating points as NumPy arrays, we can easily compute the transformation required to find all four corners of the square.

## Bonus One-Liner Method 5: Using Python List Comprehensions

Bonus Method 5 showcases the compactness of Python’s list comprehensions to solve the problem in a single, expressive line of code.

Here’s an example:

bottom_left = (1, 1) side_length = 3 find_square = lambda bl, sl: [(bl[0] + x * sl, bl[1] + y * sl) for x in range(2) for y in range(2)][::-1] print(find_square(bottom_left, side_length))

Output:

[(1, 1), (4, 1), (4, 4), (1, 4)]

This one-liner defines a lambda function that uses a list comprehension to calculate all four corners of the square. It succinctly captures the essence of the problem, illustrating Python’s capability for writing concise and powerful expressions.

## Summary/Discussion

**Method 1:**Basic Arithmetic Operations.Efficient and straightforward. Best for simple, one-off calculations. However, its simplicity means it lacks the abstraction for more complex scenarios.**Method 2:**Custom Point Class. Adds readability and reusability through OOP principles. Well-suited for complex programs, although it requires writing and maintaining additional code for the class.**Method 3:**Complex Number Representation. Mathematically elegant, demonstrating the versatility of Python’s standard library. It might be less intuitive for those unfamiliar with complex numbers.**Method 4:**NumPy Library. Offers powerful array operations and is great for numerical computations. Depends on an external library, which may not be ideal for minimalistic or constrained environments.**Method 5:**Python List Comprehensions. Highly concise and expressive, perfect for Python one-liners. The clarity might suffer for those who are not accustomed to list comprehensions or lambda functions.