원시 피타고라스 삼조를 생성하는 C# 소스

 

 

원시 피타고라스 삼조(primitive pythagorea triplet)를 생성하는

명령줄 어플(Command Line Application) C# 소스

 

C# 소스:

// Filename: GeneratePrimitivePythagoreanTriplets.cs
//
// Compile: csc GeneratePrimitivePythagoreanTriplets.cs
//
// Execute: GeneratePrimitivePythagoreanTriplets 7

using System;
using System.Collections.Generic;

namespace GeneralCommandLineApp
{
   class Program
    {
    	   public static Int64 GetGCD(Int64 xa, Int64 xb)
    	  {
    	  	  Int64 a = Math.Abs(xa);
    	  	  Int64 b = Math.Abs(xb);
    	  	  Int64 c;
    	  	  if (b > a) {
    	  	  	  c = b;
    	  	  	  b = a;
    	  	  	  a = c;
    	  	  }
    	  	  Int64 r;
    	  	  r = b;
    	  	  while (r > 0)
    	  	  {
    	  	  	  r = a % b;
    	  	  	  a = b;
    	  	  	  b = r;
    	  	  }
    	  	  return a;
    	  }

    	  public static void GeneratePrimitivePythagoreanTriplets(List<PythagoreanTriplet> data, Int64 k)
    	  {
    	  	  for (Int64 m = 2; m <= k; m++)
    	  	  {
    	  	      for (Int64 n = 1; n < m; n++)
    	  	      {
    	  	      	     if (GetGCD(m, n) == 1 && ((m % 2 == 0 && n % 2 != 0) || (m % 2 != 0 && n % 2 == 0))) {
    	  	  	         data.Add(new PythagoreanTriplet(m, n));
    	  	  	     }
    	  	      }
    	  	  }
        }

    	  public static void PrintTripletsAsTableForm(List<PythagoreanTriplet> data)
    	  {
    	  	  Int64 k = data.Count;
    	  	  Int64 a, b, c, m, n;
    	  	  Console.WriteLine("Print out some primitive Pythagorean triplets (a, b, c)\neach of which satisfies a^2 + b^2 = c^2.");
    	  	  Console.WriteLine();
    	  	  Console.WriteLine("      +--------+--------+-----------+-----------+-----------+");
    	  	  Console.WriteLine("      |        |        | m^2 - n^2 |     2mn   | m^2 + n^2 |");
    	  	  Console.WriteLine("      |     m  |     n  |      a    |      b    |      c    |");
    	  	  Console.WriteLine("      +--------+--------+-----------+-----------+-----------+");
    	  	  for (int i = 0; i < k; i++) {
    	  	      a = data[i].GetA();
    	  	  b = data[i].GetB();
    	  	  c = data[i].GetC();
    	  	  m = (Int64) Math.Sqrt((a + c)/2);
    	  	  n = b/(2*m);
    	  	  Console.WriteLine("      | {0, 6} | {1, 6} | {2, 9} | {3, 9} | {4, 9} |", m, n, a, b, c);
               }
               Console.WriteLine("      +--------+--------+-----------+-----------+-----------+");
        }

        static void Main(string[] args)
        {
        	Int64 c;
        	if (args.Length == 1) {
                c = Convert.ToInt64(args[0]);
                if (c < 1) {
                     Console.WriteLine("Sorry, you should a positive integer as an upper boud.");
                     return;
                }
                else {
                    List<PythagoreanTriplet> data = new List<PythagoreanTriplet>();
                    GeneratePrimitivePythagoreanTriplets(data, c);
                    PrintTripletsAsTableForm(data);
                    return;
                }
            }
            else
                Console.WriteLine("Usage:  GeneratePrimitivePythagoreanTriplets [UpperBound]");
        }
    }


     class PythagoreanTriplet {
        Int64 a, b, c;
        public PythagoreanTriplet(Int64 m, Int64 n) {
           	this.a = m*m - n*n;
            	this.b = 2*m*n;;
           	this.c = m*m + n*n;
       }
        public Int64 GetA() {
        	return this.a;
        }
        public Int64 GetB() {
        	return this.b;
        }
        public Int64 GetC() {
        	return this.c;
        }

        public override string ToString() {
        	return "(" + this.a + ", " + this.b + ", " + this.c + ")";
        }

        public bool IsPrimitive(Int64 xa, Int64 xb, Int64 xc)
        {
            return GCD(xa, xb, xc) == 1;
        

        public Int64 GCD(Int64 xa, Int64 xb)
        {
            Int64 a = Math.Abs(xa);
            Int64 b = Math.Abs(xb);
            Int64 c;
            if (b > a) {
                c = b;
                b = a;
                a = c;
            }
            Int64 r;
            r = b;
            while (r > 0)
            {
                r = a % b;
                 a = b;
                b = r;
            }
            return a;
        }

        public Int64 GCD(Int64 xa, Int64 xb, Int64 xc)
        {
            Int64 t = GCD(xa, xb);
            Int64 y = GCD(t, xc);
            return y;
        }
    }
}

 

명령 GeneratePrimitivePythagoreanTriplets 7 에 의한 실행 결과:

Print out some primitive Pythagorean triplets (a, b, c)
each of which satisfies a^2 + b^2 = c^2.

      +--------+--------+-----------+-----------+-----------+
      |        |        | m^2 - n^2 |     2mn   | m^2 + n^2 |
      |     m  |     n  |      a    |      b    |      c    |
      +--------+--------+-----------+-----------+-----------+
      |      2 |      1 |         3 |         4 |         5 |
      |      3 |      2 |         5 |        12 |        13 |
      |      4 |      1 |        15 |         8 |        17 |
      |      4 |      3 |         7 |        24 |        25 |
      |      5 |      2 |        21 |        20 |        29 |
      |      5 |      4 |         9 |        40 |        41 |
      |      6 |      1 |        35 |        12 |        37 |
      |      6 |      5 |        11 |        60 |        61 |
      |      7 |      2 |        45 |        28 |        53 |
      |      7 |      4 |        33 |        56 |        65 |
      |      7 |      6 |        13 |        84 |        85 |
      +--------+--------+-----------+-----------+-----------+