Recursion is a way of writing code where a function calls itself to solve smaller parts of a problem.

Think of it like Russian nesting dolls. Each doll has a smaller one inside it, and you keep opening them until you get to the smallest doll that can’t be opened anymore.

Let’s look at a simple example: calculating the factorial of a number, which we write as $n!$. The factorial of $n$ means you multiply $n$ by the factorial of one less than $n$. This looks like this:

$$n! = n \times (n-1)!$$

There’s also a starting point we call the base case, which is $0! = 1$. In this way of solving the problem, the function keeps calling itself with a smaller number until it reaches the base case.

Now, let’s talk about another way to solve problems called iteration. Instead of calling itself, it uses loops to repeat the process until it meets a condition. Here’s how you would calculate the factorial using a loop:

factorial = 1
for i in range(1, n + 1):
    factorial *= i

So, to sum it up:

• Recursion:

  • Calls itself
  • Can be neat and easy to read
  • Might use more memory because of the repeated calls

• Iteration:

  • Uses loops (like for and while)
  • Usually uses memory more efficiently
  • Can be harder to understand for tricky problems

Both recursion and iteration are important in programming. Learning how to use both will help you become a better coder!