Grokking Algorithms

EXERCISE
3.1
Suppose I show you a call stack like this.
What information can you give me, just based on this call stack? 
Now let’s see the call stack in action with a recursive function.
The call stack with recursion
Recursive functions use the call stack too! Let’s look at this in action 
with the 
factorial
function. 
factorial(5)
is written as 5!, and it’s 
defined like this: 5! = 5 * 4 * 3 * 2 * 1. Similarly, 
factorial(3)
is
3 * 2 * 1. Here’s a recursive function to calculate the factorial of a 
number:
def fact(x):
if x == 1:
return 1
else:
return x * fact(x-1)
Now you call 
fact(3)
. Let’s step through this call line by line and see 
how the stack changes. Remember, the topmost box in the stack tells 
you what call to 
fact
you’re currently on.

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Recursion

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The stack
Notice that each call to 
fact
has its own copy of 
x
. You can’t access a 
different function’s copy of 
x
.
The stack plays a big part in recursion. In the opening example, there 
were two approaches to find the key. Here’s the first way again.
This way, you make a pile of boxes to search through, so you always 
know what boxes you still need to search.

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Recursion
But in the recursive approach, there’s no pile.
If there’s no pile, how does your algorithm know what boxes you still 
have to look through? Here’s an example.

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The stack
At this point, the call stack looks like this.
The “pile of boxes” is saved on the stack! This is a stack of half-
completed function calls, each with its own half-complete list of boxes 
to look through. Using the stack is convenient because you don’t have to 
keep track of a pile of boxes yourself—the stack does it for you.
Using the stack is convenient, but there’s a cost: saving all that info can 
take up a lot of memory. Each of those function calls takes up some 
memory, and when your stack is too tall, that means your computer is 
saving information for many function calls. At that point, you have two 
options:
• You can rewrite your code to use a loop instead.
• You can use something called 
tail recursion
. That’s an advanced 
recursion topic that is out of the scope of this book. It’s also only 
supported by some languages, not all.