Task: Catalan numbers


C++: #if !defined __ALGORITHMS_H__
#define __ALGORITHMS_H__

namespace rosetta
  {
  namespace catalanNumbers
    {
    namespace detail
      {

      class Factorial
        {
        public:
          unsigned long long operator()(unsigned n)const;
        };

      class BinomialCoefficient
        {
        public:
          unsigned long long operator()(unsigned n, unsigned k)const;
        };

      } 

    class CatalanNumbersDirectFactorial
      {
      public:
        CatalanNumbersDirectFactorial();
        unsigned long long operator()(unsigned n)const;
      private:
        detail::Factorial factorial;
      };

    class CatalanNumbersDirectBinomialCoefficient
      {
      public:
        CatalanNumbersDirectBinomialCoefficient();
        unsigned long long operator()(unsigned n)const;
      private:
        detail::BinomialCoefficient binomialCoefficient;
      };

    class CatalanNumbersRecursiveSum
      {
      public:
        CatalanNumbersRecursiveSum();
        unsigned long long operator()(unsigned n)const;
      };

    class CatalanNumbersRecursiveFraction
      {
      public:
        CatalanNumbersRecursiveFraction();
        unsigned long long operator()(unsigned n)const;
      };

    }   
  }     

#endif 


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();
            }
        }
    }
}