Algorithms

Roger Wright wrote:

Over time, all casino games (except Craps) favor the house.

musefan wrote:

always less than 50%

Kirk Wood wrote:

I don't see a huge difference between a person who spends say $20 at a theater for two hours of enjoyment and one who spends $20 playing Keno for a couple hours of enjoyment.

Yuval Naveh wrote:

Open Source Audio DSP Algorithms or Filters? (.e.g Delay, Reverb, Chorus, etc.)

int f(int z)
{
   int result = 0;
   int x = 0;
   double m = 0; // m is 3*x*x
   double y;

   if (z < 3) return 0; // You could remove this line (the function will continue to work properly)

   while (m <= z)
   {
      y = sqrt(z - m);

      // Test if y is integer...
      if (y == floor(y)) result++;

      x++;
      m = 3*x*x;
   }

   return result;
}

public class Solutions
{
    Dictionary<int, bool> matches = new Dictionary<int, bool>();
    int maxZ = 0;

    public bool? EvenSolutions(int z)
    {
        if (z > maxZ)
        {
            int maxY = (int)Math.Sqrt(z - 3);
            int maxX = (int)(Math.Sqrt(z - 1 / 3d));
            int n = 4;

            for (int x = 1; x < maxX; x++)
            {
                for (int y = 1; y < maxY && (n = 3 * x * x + y * y) <= z; y++)
                {
                    if (n > maxZ)
                    {
                        if (!matches.ContainsKey(n))
                            matches.Add(n, false);
                        else
                            matches[n] = !matches[n];
                    }
                }
            }

            maxZ = z;
        }

        return (matches.ContainsKey(z)) ? (bool?)matches[z] : null;
    }
}

#include <utility>
#include <array>
#include <algorithm>

template <unsigned int z>
size_t NumSolutions()
{
	typedef std::pair<unsigned int, unsigned int> Solution;
	std::array<Solution, z * z + 2 * z> All;

	std::generate(All.begin(), All.end(), 
		[]()->Solution{
		static unsigned int x = 0, y = 0;
		return y == z ? Solution(++x, y = 0) : Solution(x , ++y);});

	return std::count_if(All.begin(), All.end(), 
		[](const Solution& sol){return z == 3 * sol.first * sol.first + sol.second * sol.second;});
}

#include <utility>
#include <vector>
#include <algorithm>

typedef std::pair<unsigned int, unsigned int> Solution;

template <unsigned int z>
bool IsSolution(const Solution& sol)
{
	return z == 3 * sol.first * sol.first + sol.second * sol.second;
}

template <unsigned int z>
Solution Next()
{
	static unsigned int x = 0, y = 0;
	return y == z ? Solution(++x, y = 0) : Solution(x , ++y);
}

template <unsigned int z>
size_t NumSolutions()
{
	std::vector<Solution> All(z *z + 2 * z);
	std::generate(All.begin(), All.end(), Next<z>);
	return std::count_if(All.begin(), All.end(), IsSolution<z>);
}

#include <iostream>
int main()
{
	using std::cout;
	using std::endl;

	cout << "NumSolutions<4>(): " << NumSolutions<4>() << endl;
	cout << "NumSolutions<7>(): " << NumSolutions<7>() << endl;
	cout << "NumSolutions<28>(): " << NumSolutions<28>() << endl;
	return 0;
}