Mastering Catalan Numbers with Python: Where Math Comes Alive.

Catalan numbers use case.


There are special numbers in combinatorial mathematics named after the French-Belgian mathematician Eugène Charles Catalan who studied the Towers of Hanoi puzzle.

The Catalan numbers are a sequence of natural numbers that usually describe recursively defined objects and calculated by formula:

Cn = ( ( 2n! ) / ( (n+1)! n! ) ) , where n is always non-negative.

Catalan numbers.
Catalan numbers meme.

Python Knowledge Base: Make coding great again.
- Updated: 2024-12-01 by Andrey BRATUS, Senior Data Analyst.




    An example for the first Catalan numbers for n = 0, 1, 2, 3, 4, 5 are 1, 1, 2, 5, 14, 42.

    Today’s practical use cases of the Catalan numbers lay in the fields of computer science, geometry, GIS and geodesy, cryptography, and medicine.


  1. A recursive function to find n-th Catalan number with Python code:



  2. 
    def catalan(n):
       
        if n <= 1:
            return 1
     
        res = 0
        for i in range(n):
            res += catalan(i) * catalan(n-i-1)
     
        return res
     
     
    # Check
    N=6
    for i in range(N):
        print (catalan(i),end=",")
    
  3. Finding n-th Catalan number code result:


  4. OUT: 1,1,2,5,14,42,





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