Function Overloading Simulation in Python

Python doesn't natively support function overloading like languages such as C++ or Java, where multiple functions can have the same name but different parameter lists. This challenge asks you to simulate function overloading in Python using techniques like default arguments, variable-length argument lists (*args and **kwargs), and conditional logic within a single function. This is a common pattern when you want to provide a flexible interface for a function that can handle different input types or numbers of arguments.

Problem Description

You need to create a function called calculate_area that can calculate the area of different shapes based on the input provided. The function should be able to handle the following scenarios:

1. Circle: Takes one argument, the radius (a number).
2. Rectangle: Takes two arguments, the length and width (numbers).
3. Triangle: Takes three arguments, base and height (numbers), and an optional third argument for the triangle type ('right', 'equilateral', 'isosceles'). If the triangle type is not provided, assume it's a right triangle.
4. Square: Takes one argument, the side length (a number).

The function should return the calculated area for the corresponding shape. If an invalid number of arguments or an unsupported shape is provided, the function should return None.

Examples

Example 1:

Input: calculate_area(5)
Output: 78.53981633974483
Explanation:  The function recognizes a single argument as the radius of a circle. Area = pi * r^2.

Example 2:

Input: calculate_area(4, 6)
Output: 24
Explanation: The function recognizes two arguments as length and width of a rectangle. Area = length * width.

Example 3:

Input: calculate_area(3, 4, 'right')
Output: 6.0
Explanation: The function recognizes three arguments as base, height, and triangle type ('right'). Area = 0.5 * base * height.

Example 4:

Input: calculate_area(7)
Output: 49
Explanation: The function recognizes a single argument as the side length of a square. Area = side * side.

Example 5:

Input: calculate_area(1, 2, 3)
Output: None
Explanation: Invalid number of arguments.

Constraints

• All numerical inputs (radius, length, width, base, height, side) must be non-negative numbers.
• The function must handle potential TypeError exceptions if non-numerical inputs are provided.
• The triangle type argument (if provided) must be a string and can only be 'right', 'equilateral', or 'isosceles'. The area calculation should only differ for right triangles. Equilateral and isosceles triangles should use the same area calculation as right triangles.
• The function should be reasonably efficient; avoid unnecessary computations.

Notes

• Consider using *args and **kwargs to handle a variable number of arguments.
• Use conditional statements (if, elif, else) to determine the shape based on the number and types of arguments.
• Remember to handle invalid input gracefully and return None in such cases.
• Import the math module for the value of pi.
• Focus on simulating function overloading within a single function definition. You are not creating multiple functions with the same name.