#9- Case Study | Mastering Recursion in Python: A Beginner’s Guide

A recursive function is a function that calls itself, with a base case that determines when the recursion should stop.

Here’s how recursive functions work in Python:

1. The function defines a base case, which is a condition that determines when the recursion should stop.
2. The function takes a step forward by performing some calculation or operation on the input data.
3. The function calls itself with a modified version of the input data.
4. The function repeats steps 2 and 3 until it reaches the base case.
5. When the base case is reached, the function returns a result.

Here is an example of a simple recursive function that calculates the factorial of a number:

def factorial(n):
  # Base case: if n is 1, return 1
  if n == 1:
    return 1
  
  # Take a step forward by calculating n * (n-1)!
  result = n * factorial(n-1)
  
  # Return the result
  return result

In this example, the base case is when n is equal to 1. When the function is called with an n value of 1, it returns 1 and the recursion stops. For all other values of n, the function takes a step forward by calculating n * (n-1)!, and then calling itself with an n value of n-1. This process continues until the base case is reached, at which point the function returns the result of the calculation.

To use this function, you can call it with a number as an argument, like this:

fact = factorial(5)
print(fact)  # Output: 120

Here is a case study that will help you understand recursive functions in Python:

Suppose you have a list of integers, and you want to find the sum of all the numbers in the list. You can write a recursive function to do this as follows:

1. Define the base case. In this case, the base case is when the list is empty. If the list is empty, we can return 0, because there are no numbers to add.
2. Define how to take a step forward. In this case, we can take a step forward by taking the first element of the list, and then calling the function recursively with the rest of the list (the list without the first element).
3. Define how to handle the result of the recursive call. In this case, we can handle the result by adding it to the first element that we took, and then returning the result as the answer.

Here is the implementation of the recursive function in Python:

def sum_list(lst):
  # Base case: if the list is empty, return 0
  if not lst:
    return 0
  
  # Take the first element of the list
  first = lst[0]
  
  # Call the function recursively with the rest of the list
  rest = lst[1:]
  sum = sum_list(rest)
  
  # Add the first element to the sum, and return the result
  return sum + first

To use this function, you can call it with a list as an argument, like this:

numbers = [1, 2, 3, 4]
total = sum_list(numbers)
print(total)  # Output: 10