How to measure the length of a call stack? - recursion

Question

Recently had a test question asking "how deep" the call stack for fact1 where n = 5. Here is the code:
int fact1(int n)
{
if (n == 1)
{
return 1
}
else {
return n * fact(n-1)
}
}
The answer on the test was 5, but I believe it is 4. I don't believe the first call is to be counted in the number of calls.

Answer 1

Actually, every function call ends in the call stack.
Your example looks like C; in C, there is always a main function; even the main function ends on the call stack.
I don't think there is a way to examine the call stack in C; especially since the compiler is allowed to optimise away whatever it wants. For instance, it could optimise tail-recursion, and then the call stack would be smaller than you'd expect.
In Python the call stack is easy to examine; just crash the function whenever you want, by throwing an exception (for instance with assert(False)). Then the program will produce an error message containing the full "stack trace", including the list of every function on the stack.
Here is an example of a stack trace in python:
def fact1(n):
assert(n != 1)
return n * fact1(n-1)
def main():
f = fact1(3)
print(f)
main()
Output:
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "<stdin>", line 2, in main
File "<stdin>", line 3, in fact1
File "<stdin>", line 3, in fact1
File "<stdin>", line 2, in fact1
AssertionError
And another example just for fun:
def print_even(n):
if (n <= 1):
print('yes' if n == 0 else 'no')
assert(False)
else:
print_odd(n-1)
def print_odd(n):
if (n <= 1):
print('yes' if n == 1 else 'no')
assert(False)
else:
print_even(n-1)
def main():
n = 5
print('Is {} even?'.format(n))
print_even(n)
main()
Output:
Is 5 even?
no
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "<stdin>", line 4, in main
File "<stdin>", line 6, in print_even
File "<stdin>", line 6, in print_odd
File "<stdin>", line 6, in print_even
File "<stdin>", line 6, in print_odd
File "<stdin>", line 4, in print_even
AssertionError