Task: Catalan numbers



C#: namespace CatalanNumbers
{
    
    
    
    public class CatalanNumberGenerator
    {
        private static double Factorial(double n)
        {
            if (n == 0)
                return 1;

            return n * Factorial(n - 1);
        }

        public double FirstOption(double n)
        {
            const double topMultiplier = 2;
            return Factorial(topMultiplier * n) / (Factorial(n + 1) * Factorial(n));
        }

        public double SecondOption(double n)
        {
            if (n == 0)
            {
                return 1;
            }
            double sum = 0;
            double i = 0;
            for (; i <= (n - 1); i++)
            {
                sum += SecondOption(i) * SecondOption((n - 1) - i);
            }
            return sum;
        }

        public double ThirdOption(double n)
        {
            if (n == 0)
            {
                return 1;
            }
            return ((2 * (2 * n - 1)) / (n + 1)) * ThirdOption(n - 1);
        }
    }
}



using System;
using System.Configuration;










namespace CatalanNumbers
{
    class Program
    {
        static void Main(string[] args)
        {
            CatalanNumberGenerator generator = new CatalanNumberGenerator();
            int i = 0;
            DateTime initial;
            DateTime final;
            TimeSpan ts;

            try
            {
                initial = DateTime.Now;
                for (; i <= Convert.ToInt32(ConfigurationManager.AppSettings["MaxCatalanNumber"]); i++)
                {
                    Console.WriteLine("CatalanNumber({0}):{1}", i, generator.FirstOption(i));
                }
                final = DateTime.Now;
                ts = final - initial;
                Console.WriteLine("It took {0}.{1} to execute\n", ts.Seconds, ts.Milliseconds);

                i = 0;
                initial = DateTime.Now;
                for (; i <= Convert.ToInt32(ConfigurationManager.AppSettings["MaxCatalanNumber"]); i++)
                {
                    Console.WriteLine("CatalanNumber({0}):{1}", i, generator.SecondOption(i));
                }
                final = DateTime.Now;
                ts = final - initial;
                Console.WriteLine("It took {0}.{1} to execute\n", ts.Seconds, ts.Milliseconds);   

                i = 0;
                initial = DateTime.Now;
                for (; i <= Convert.ToInt32(ConfigurationManager.AppSettings["MaxCatalanNumber"]); i++)
                {
                    Console.WriteLine("CatalanNumber({0}):{1}", i, generator.ThirdOption(i));
                }
                final = DateTime.Now;
                ts = final - initial;
                Console.WriteLine("It took {0}.{1} to execute", ts.Seconds, ts.Milliseconds, ts.TotalMilliseconds);
                Console.ReadLine();
            }
            catch (Exception ex)
            {
                Console.WriteLine("Stopped at index {0}:", i);
                Console.WriteLine(ex.Message);
                Console.ReadLine();
            }
        }
    }
}





Python: from math import factorial
import functools


def memoize(func):
    cache = {}

    def memoized(key):
        
        if key not in cache:
            cache[key] = func(key)
        return cache[key]
    return functools.update_wrapper(memoized, func)


@memoize
def fact(n):
    return factorial(n)


def cat_direct(n):
    return fact(2 * n) // fact(n + 1) // fact(n)


@memoize
def catR1(n):
    return 1 if n == 0 else (
        sum(catR1(i) * catR1(n - 1 - i) for i in range(n))
    )


@memoize
def catR2(n):
    return 1 if n == 0 else (
        ((4 * n - 2) * catR2(n - 1)) // (n + 1)
    )


if __name__ == '__main__':
    def pr(results):
        fmt = '%-10s %-10s %-10s'
        print((fmt % tuple(c.__name__ for c in defs)).upper())
        print(fmt % (('=' * 10,) * 3))
        for r in zip(*results):
            print(fmt % r)

    defs = (cat_direct, catR1, catR2)
    results = [tuple(c(i) for i in range(15)) for c in defs]
    pr(results)