Counting recursive calls of a function

python allows you to attach a variable (catalan.counter in the snippet below) to the function object, so you don’t have to pass the counter along all the time and don’t need a global variable:

def catalan(n):

    catalan.counter += 1

    if n <= 1:
        return 1
    res = 0
    for i in range(n):
        res += catalan(i) * catalan(n-i-1)
    return res

catalan.counter = 0

print(catalan(5))
print(catalan.counter)

and seeing that the function is called several times with the same arguments: for more efficiency you could use the lru_cache; but this of course defeats the purpose of counting how many times the function was called; you’d only get the number the function was called with a unique n.

from functools import lru_cache

@lru_cache(maxsize=128)
def catalan(n):

    ...

this may be a bit off-topic… but in case you need separate instances of the function with separate counters, a closure might be just what you need:

def make_catalan():

    counter = 0

    def catalan(n):

        nonlocal counter
        counter += 1
        catalan.counter = counter

        if n <= 1:
            return 1
        res = 0
        for i in range(n):
            res += catalan(i) * catalan(n-i-1)
        return res

    return catalan

catalan_1 = make_catalan()
print(catalan_1(2))
print(catalan_1.counter)

catalan_2 = make_catalan()
print(catalan_2(3))
print(catalan_2.counter)