Python for Basic Data Analysis: 2.7 Recursive Functions

Recursive functions are functions that calls itself. It is always made up of 2 portions, the base case and the recursive case.

• The base case is the condition to stop the recursion.
• The recursive case is the part where the function calls on itself.

Let's use recursive functions to find the factorial of an integer. A factorial is the product of all integers from 1 to the number itself.

In the example below, we will be looking for the factorial of 4, or, 4!. 

Factorial of 4 is 4! = 1 * 2 * 3 * 4 = 24

Now let's analyse what is going on in the above recursive function.

1. First, when we pass the integer 4 into the function, it goes to the recursive case return(x * factorial(x-1)) which will give us return(4 * factorial(3)).
    
2. Next, the function will call factorial(3) which will give us return(3 * factorial(2)) and it goes on until we have x == 1 (the base case) and then the recursion will terminate. This means that if we do not have a base case to stop the recursion, the function will continue to call itself indefinitely.
    
3. At the end we will have return(4 * 3 * 2 * 1)

Visualize how the codes work by clicking on the Next button below.