**π‘ Problem Formulation:** Computing the factorial of a number is a common mathematical problem in computer science that can be posed simply: given a non-negative integer, return the product of all positive integers less than or equal to that number. For example, the factorial of 5 (`5!`

) is `120`

(i.e., `5 * 4 * 3 * 2 * 1`

).

## Method 1: Iterative Approach Using a For Loop

This method uses a simple iterative approach. Starting at 1, the function iteratively multiplies the running total by each integer up to the input number. This is a self-contained loop structure that is fast and easy to understand, ideal for small to medium-sized integers.

Here’s an example:

def factorial(num): result = 1 for i in range(1, num + 1): result *= i return result print(factorial(5))

Output: `120`

This code defines a function `factorial(num)`

that takes an integer `num`

and iteratively calculates its factorial. It starts with `result`

set to 1 and multiplies `result`

by each number from 1 up to `num`

. The final result is the factorial of `num`

.

## Method 2: Iterative Approach Using a While Loop

In this approach, a while loop is used to create the factorial. Itβs quite similar to the for loop method but uses a while loop instead, decrementing the number each time until it reaches 1.

Here’s an example:

def factorial(num): result = 1 while num > 1: result *= num num -= 1 return result print(factorial(5))

Output: `120`

This function, `factorial(num)`

, also computes the factorial of the given number. It begins with `result`

as 1 and multiplies it by `num`

, then decrements `num`

by 1 until `num`

becomes less than 2. The loop exits, and the result is returned.

## Method 3: Using the math Library

Python’s `math`

library has a factorial function that’s optimized and ready to use. This method is very straightforward and involves just a single function call. It is highly recommended for applications requiring high performance.

Here’s an example:

import math print(math.factorial(5))

Output: `120`

This is the simplest method where Python’s `math.factorial()`

function is used to calculate the factorial of number 5. It abstracts away the logic of factorial calculation and provides a ready-to-use, efficient solution.

## Method 4: Using the reduce Function

This method leverages the functools library’s reduce function to successively apply a given operation (in this case, multiplication) across a sequence of values (1 through n).

Here’s an example:

from functools import reduce from operator import mul def factorial(num): return reduce(mul, range(1, num + 1), 1) print(factorial(5))

Output: `120`

This code snippet uses the `reduce()`

function from the `functools`

module to calculate the factorial. It multiplies all the numbers in the range from 1 to `num`

inclusive by using `mul`

from the `operator`

module as the function for reduction with a starting value of 1.

## Bonus One-Liner Method 5: Using a List Comprehension and the Built-in Function `prod()`

From Python 3.8 onwards, there’s a built-in function called `prod()`

that can compute the product of all elements in an iterable. This can be elegantly combined with a list comprehension for a concise one-liner factorial function.

Here’s an example:

from math import prod factorial = lambda num: prod(range(1, num + 1)) print(factorial(5))

Output: `120`

This one-liner uses a lambda function alongside `prod()`

from the `math`

module to calculate the factorial. It directly multiplies all the numbers created by the list comprehension from 1 up to the input number in a single line of code.

## Summary/Discussion

**Method 1:**Iterative Approach with For Loop. Strengths: Intuitive for beginners; grants visibility into each iterative step. Weaknesses: Verbosity compared to other methods; speed can be slower for very large numbers due to unoptimized looping.**Method 2:**Iterative Approach with While Loop. Strengths: Offers a clear breakdown of the decremental process; good for understanding control flow. Weaknesses: Similar to the for loop in terms of verbosity and speed drawbacks.**Method 3:**Using the math Library. Strengths: Extremely fast and reliable; highly optimized C backend. Weaknesses: Indirect; does not teach the algorithmic understanding of the process.**Method 4:**Using the reduce Function. Strengths: Elegant and functional approach; good for applications that prefer functional programming paradigms. Weaknesses: Requires understanding of the reduce function and higher-order functions.**Method 5:**List Comprehension with`prod()`

. Strengths: Clean and concise one-liner; modern Python syntax. Weaknesses: Less readability for those unfamiliar with list comprehensions; requires Python 3.8 or newer.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.