Catalan number calculation using Python?

Question

I am writing a Python code to generate Catalan numbers using the mathematical formula given here:

C(0) = 1 and C(n) = (2(2n − 1) / (n + 1)) * C(n − 1) per this website here. (https://rosettacode.org/wiki/Catalan_numbers)

However, when I am writing it in python as a function, it gives me false results.

eg: For 20 answer should be 6564120420.0 while my code gives me 344373768.

Here:

def catalan(cat_input):

    if cat_input==0:
    return 1 

    else:
    return  (((4*cat_input) - 2) / (cat_input + 1)) * (catalan(cat_input-1))

Can someone help me figure this out please ?

Whay do you mean by "false results" give an example (as far as i have tested it the program gives correct results at least up to 9) -- well except the results being floats instead of ints which can be fixed by using `//` instead of `/` — Drecker, Aug 30 '19 at 06:53

score 0 · Accepted Answer · answered Aug 30 '19 at 07:06

The problem is when dividing /. As-is the result (of the division itself, before multiplying) may not be whole number, and since / in python2 is by default int-division the decimal part gets "cropped" and you get the wrong results.

There are couple ways to fix that (pick your favorite):

Change the order in the equation, instead of (((4*cat_input) - 2) / (cat_input + 1)) * (catalan(cat_input-1)) use (((4*cat_input) - 2) * (catalan(cat_input-1)) / (cat_input + 1)), that way you are guaranteed to get whole number after division
change the type of the first part of the equation to float to force float division: (float((4*cat_input) - 2) / (cat_input + 1)) * (catalan(cat_input-1))
Use python3 instead of python2 as python3 uses decimal division by default
Use from __future__ import division to "activate" python3-like division

Edit: In general (at least in python) it is advised not to use recursion if possible, as it is not efficient and you may run to problems like recursion limit

Catalan number calculation using Python?

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