Programming Challenge #71 /w Comments

Program.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ConsoleApplication1
{
    class Program
    {       
            //Problem:
            // A^2 + B^2 = C^2
            // A + B + C = Q
            // For a given Q Find all int A,B,C that this is true

            //Some Reasoning:
            
            // C = SQRT(A^2 + B^2) 
            // SQRT(A^2 + 2AB + B^2) = A + B
            // therefore C <= A + B

            // and also C >= A, C >= B, so C < 
            
            // 1/3CONST <= C <= 1/2CONST

            // Pick a C, aka Ci,
            // Then solve using quadratic formula (not iterate)
            // Find B in terms of Ci, and Constant Q

            // A = Q - (C + B)
            // A^2 + B^2 = C^2
            //      (Q - (C + B))^2 + B^2 = C^2
            //      Q^2 -2Q(C + B) + (C+B)^2 + B^2 = C^2
            //      Q^2 - 2QC - 2QB + C^2 + 2CB + B^2 + B^2 = C^2
            //      Q^2 - 2QC - 2QB + 2CB + 2B^2 = 0
            //      Q^2 - 2QC + (-2Q + 2C)B + 2B^2 = 0
            //      We can use the quadratic formula with these constants
            //      a = 2
            //      b = 2C - 2Q
            //      c = Q^2 - 2QC

            //  2Q - 2C +- SQRT((4C^2 - 8CQ + 4Q^2) - 8Q^2 + 16QC))
            //  -------------------------------
            //                  4

            //  2Q - 2C +- SQRT(4C^2 + 8CQ - 4Q^2)
            //  -------------------------------
            //                  4

            //  2Q - 2C +- 2 * SQRT(C^2 + 2CQ - Q^2)
            //  -------------------------------
            //                  4

            //  Q - C +- SQRT(C^2 + 2CQ - Q^2)
            //  -------------------------------
            //                  2

            //  Q - C +- SQRT(C^2 + 2CQ - Q^2)
            //  -------------------------------  = B (and A turns out to be the other root)
            //                  2

        static void Triples(long inputSum)
        {
            long CONSTANT_SUM = inputSum;

            long low = CONSTANT_SUM / 3 - 1; 
            long high = CONSTANT_SUM / 2 - 1;

            DateTime StartTime = DateTime.Now;

            for (long ci = low; ci <= high; ci++)
            {
                long insideSqrt = ci * ci + 2 * CONSTANT_SUM * ci - CONSTANT_SUM * CONSTANT_SUM;
                if (insideSqrt >= 0)
                {
                    double sqrt = Math.Sqrt((double)insideSqrt);
                    if (sqrt % 1 == 0)
                    {
                        long b_value_1 = (CONSTANT_SUM - ci + (long) sqrt) / 2;
                        long b_value_2 = (CONSTANT_SUM - ci - (long) sqrt) / 2;
                        Console.WriteLine("Triple: {0}, {1}, {2}", ci, b_value_1, b_value_2);
                    }
                }
            }
            Console.WriteLine("Took {0}", DateTime.Now - StartTime);

            Console.ReadKey(true);
        }

        static void Main(string[] args)
        {
            Triples(504);
        }
    }
}