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How to efficiently calculate the nth Catalan number, in Python?

Wissam answered on June 21, 2022 Popularity 10/10 Helpfulness 3/10

answer How to efficiently calculate the nth Catalan number, in Python?

How to efficiently calculate the nth Catalan number, in Python?

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"""
This implementation demonstrates how
to efficiently calculate the nth
Catalan number. For instance, 
the nth catalan number gives the 
number of unique binary search trees 
which has exactly n nodes of unique values
between 1 and n.

Let us denote it by Cn:
C0 = 1 and Cn+1 = 2(2n+1)Cn/(n+2)

More info at:
https://en.wikipedia.org/wiki/Catalan_number

Time complexity: O(n)
Space complexity: O(1)
"""


def C_n(n):
    C = 1
    for i in range(0, n):
        C = C * 2*(2*i+1)/(i+2)
    return int(C)


print("C1 =", C_n(1))  # C1 = 1
print("C3 =", C_n(3))  # C3 = 5

Popularity 10/10 Helpfulness 3/10 Language python

Source: Grepper

Tags: catalan python

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Contributed on Jun 21 2022

Wissam

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How to efficiently calculate the nth Catalan number, in Python?

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