Python Math: nth Catalan Number

Python Math: Exercise-25 with Solution

Write a Python program for nth Catalan Number.

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. They are named after the Belgian mathematician Eugène Charles Catalan (1814–1894).

Using zero-based numbering, the nth Catalan number is given directly in terms of binomial coefficients by

Catalan number

The first Catalan numbers for n = 0, 1, 2, 3, … are
1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, ....

Pictorial Presentation

The C5 = 42 noncrossing partitions of a 5-element set (below, the other 10 of the 52 partitions)

Catalan number

Image Credits: Watchduck

Sample Solution:-

Python Code:

def catalan_number(num):
    if num <=1:
         return 1
    res_num = 0
    for i in range(num):
        res_num += catalan_number(i) * catalan_number(num-i-1)
    return res_num
for n in range(10):

Sample Output:



Flowchart: nth Catalan Number

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Python: Tips of the Day

Lambdas for Sorting:

>>> students = [{'name': 'John', 'score': 98}, {'name': 'Mike', 'score': 94}, {'name': 'Jennifer', 'score': 99}]
>>> sorted(students, key=lambda x: x['score'])
[{'name': 'Mike', 'score': 94}, {'name': 'John', 'score': 98}, {'name': 'Jennifer', 'score': 99}]