Recursion is an important part of understanding how algorithms work. It affects both how long they take to run and how much memory they use. Let’s break it down:

• Time Complexity: Some recursive algorithms can be fast, but others can get really slow. A good example is the Fibonacci sequence. In this case, the time it takes can go from being quick to super slow because the same problems get solved over and over again. This time goes from $O(n)$ (which is pretty good) to $O(2^n)$ (which is not good at all).

• Space Complexity: Every time you make a recursive call (that’s when a function calls itself), it takes up some memory space. If you keep calling it a lot, this can add up quickly. In many divide-and-conquer methods, this can use up $O(n)$ space.

When you understand recursion, you can better figure out how these complexities work!