Python Function Overloading Simulation

Python, unlike some other languages, does not support direct function overloading in the traditional sense where multiple functions with the same name but different parameter lists can coexist. However, the concept of handling different input types or numbers of arguments for a function is crucial for creating flexible and user-friendly APIs. This challenge asks you to simulate function overloading in Python using a common and effective pattern.

Problem Description

Your task is to create a single Python function that can behave differently based on the number and type of arguments it receives. This simulates the behavior of overloaded functions in languages that support it. You will need to implement a function that can perform a simple calculation (e.g., addition or string concatenation) based on whether it's given two numbers, three numbers, or two strings.

Key Requirements:

1. Single Function Name: All overloaded behaviors must be accessible via a single function name.
2. Argument Handling: The function must correctly identify and process different argument combinations.
3. Type Checking: Implement basic type checking to ensure correct behavior.
4. Return Values: The function should return the appropriate result based on the operation performed.

Expected Behavior:

• If given two integers, the function should return their sum.
• If given three integers, the function should return their sum.
• If given two strings, the function should return their concatenation.
• If an invalid combination of arguments is provided (e.g., one integer and one string, or more than three arguments), the function should raise a TypeError with a descriptive message.

Edge Cases to Consider:

• What happens if non-numeric or non-string types are provided when numbers or strings are expected?
• What happens if the correct number of arguments are provided but they are of the wrong type?

Examples

Example 1:

Input: calculate(5, 3)
Output: 8
Explanation: Two integers provided, so the function performs addition.

Example 2:

Input: calculate(10, 20, 30)
Output: 60
Explanation: Three integers provided, so the function performs addition.

Example 3:

Input: calculate("Hello, ", "World!")
Output: "Hello, World!"
Explanation: Two strings provided, so the function performs concatenation.

Example 4:

Input: calculate(5, "hello")
Output: TypeError: Invalid argument types or combination.
Explanation: A mix of integer and string is provided, which is not a supported overload.

Example 5:

Input: calculate(1, 2, 3, 4)
Output: TypeError: Invalid argument types or combination.
Explanation: More than three arguments are provided, which is not a supported overload.

Constraints

• The function should accept at least one and at most three arguments.
• The function should primarily handle int and str types for its primary operations.
• Performance is not a critical concern for this simulation, but the solution should be reasonably efficient.

Notes

Consider using Python's *args syntax to accept a variable number of positional arguments. Within the function, you can then inspect the number of arguments and their types to decide which operation to perform. Raising custom exceptions with clear messages is a good practice for indicating invalid usage. Think about how you can check the types of arguments effectively.