**π‘ Problem Formulation:** When working with geometry in Python, one might face the challenge of determining whether a set of line segments can form a polygon with a specific number of sides. The input would be an integer representing the number of sides, and the desired output is a boolean indicating whether a polygon with that number of sides can exist.

## Method 1: Using Basic Mathematical Property

The first method involves leveraging the most basic property of polygons: a polygon must have at least three sides. Thus, by checking if the given number of sides, n, is greater than or equal to 3, we can determine the possibility of forming a polygon.

Here’s an example:

def can_form_polygon(n_sides): return n_sides >= 3 print(can_form_polygon(4)) # Example for 4 sides

Output:

True

This code snippet defines a function `can_form_polygon`

that returns True if the input `n_sides`

is greater than or equal to 3, indicating a polygon can be formed, or False otherwise. It is an effective and instant check for the polygon’s feasibility.

## Method 2: Checking for Non-Positive Sides

An alternative method is to verify that the number of sides is not only sufficient to form a polygon but also positive. This safeguards against invalid inputs such as negative numbers or zero.

Here’s an example:

def is_valid_polygon(n_sides): return n_sides > 2 and isinstance(n_sides, int) and n_sides > 0 print(is_valid_polygon(5)) # Example for 5 sides

Output:

True

This function `is_valid_polygon`

performs a more robust check. It assesses whether the `n_sides`

input is an integer greater than 2 and positive, ensuring the polygon’s side count is logical and feasible.

## Method 3: Using a Regular Expression for String Inputs

If the number of sides comes as a string input, a regular expression can ensure that only positive integers are considered valid. This is beneficial when inputs are read as strings from files or user input.

Here’s an example:

import re def can_form_polygon_regex(n_sides_str): return bool(re.match(r'^[1-9]\d*$', n_sides_str)) and int(n_sides_str) >= 3 print(can_form_polygon_regex('6')) # Example for '6' sides as a string

Output:

True

This function `can_form_polygon_regex`

uses a regular expression to check if the string `n_sides_str`

represents a positive integer, and then confirms if it is greater than or equal to 3, allowing for verification from string-based input.

## Method 4: Exception Handling for Non-Integer Inputs

For a robust application, we can add exception handling to our check. This manages instances where the input might not be an integer, such as floats or strings that don’t represent an integer, thus ensuring input validity.

Here’s an example:

def can_form_polygon_safe(n_sides): try: return int(n_sides) >= 3 except ValueError: return False print(can_form_polygon_safe('7')) # Example with '7' as a string

Output:

True

In the `can_form_polygon_safe`

function, a try-except block attempts to cast the input to an integer and perform the polygon check. If conversion fails, it catches the `ValueError`

and returns False, indicating that a polygon cannot be formed.

## Bonus One-Liner Method 5: Using a Lambda Function

For those who enjoy concise code, a one-liner lambda function can be a neat way to perform the check. Do note that lambda functions provide less readability for complex logic.

Here’s an example:

can_form_polygon_one_liner = lambda n: n >= 3 print(can_form_polygon_one_liner(8)) # Example for 8 sides

Output:

True

The `can_form_polygon_one_liner`

lambda function performs the same check as our first methodβsimply confirming the sides are more than three for a polygon to be possibleβin a compact form.

## Summary/Discussion

**Method 1:** Basic Mathematical Property. Quick and straightforward, but assumes integer input.

**Method 2:** Checking for Non-Positive Sides. Direct and considers input validity, but slightly verbose.

**Method 3:** Using Regular Expression for String Inputs. Allows for string input validation, but can be less efficient due to regex processing.

**Method 4:** Exception Handling for Non-Integer Inputs. Robust and handles a variety of inputs, but the catch-all exception handling may obscure other potential issues.

**Method 5:** Using a Lambda Function. Elegant and short, but best for simple checks and can impact readability for more complex logic.