/*Find the minimum value which satisfies the linear inequality:

     a*x + b*y >= 1 {a,b,x,y Integers} {a,b > 0} {a,b entered on command line}

   Nigel_Galloway@operamail.com

   February 2008

 */

 using System;

 using System.Runtime.InteropServices;

 unsafe class GLPK{

   double *lp;

   public int a;

   public int b;

   const string glpkLibrary = "libglpk.so";

   readonly int GLP_FR = 1;

   readonly int GLP_IV = 2;

   readonly int GLP_DB = 4;

   struct ConstraintMatrix{

     public fixed int ia[3];

     public fixed int ja[3];

     public fixed double ar[3];

   }

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern double* glp_create_prob();

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern void glp_add_rows(double* lp, int rows);

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern void glp_add_cols(double* lp, int cols);

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern void glp_set_col_bnds(double* lp, int col, int bound_type, double lower_bound, double upper_bound);

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern void glp_set_col_kind(double* lp, int col, int kind);

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern void glp_load_matrix(double* lp, int elements, int* ia, int* ja, double* ar);

   public GLPK(int a, int b){

     this.a = a;

     this.b = b;

     lp = glp_create_prob();

     //Col 1 is x, Col 2 is y

     glp_add_rows(lp, 1);

     glp_add_cols(lp, 2);

     glp_set_col_bnds(lp, 1, GLP_FR, 0.0, 0.0);

     glp_set_col_bnds(lp, 2, GLP_FR, 0.0, 0.0);

     glp_set_col_kind(lp, 1, GLP_IV);

     glp_set_col_kind(lp, 2, GLP_IV);

     //Row 1 is a*x + b*y

     ConstraintMatrix CM = new ConstraintMatrix();

     CM.ia[1]=1; CM.ja[1]=1; CM.ar[1]=a;

     CM.ia[2]=1; CM.ja[2]=2; CM.ar[2]=b;

     glp_load_matrix(lp, 2, CM.ia, CM.ja, CM.ar);

     Console.WriteLine("Hello Nigel");

   }

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern void glp_set_row_bnds(double* lp, int row, int bound_type, double lower_bound, double upper_bound);

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern void glp_simplex(double* lp, void* options);

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern void glp_intopt(double* lp, void* options);

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern double glp_mip_col_val(double* lp, int col);

   public int betterGuess(int upper_bound){

     //Find a new guess less than the old guess: 1 <= (a*x + b*y) <= (old guess - 1)

     glp_set_row_bnds(lp, 1, GLP_DB, 1.0, ((double)upper_bound)-0.5);

     glp_simplex(lp, null);

     glp_intopt(lp, null);

     int x = (int)glp_mip_col_val(lp, 1);

     int y = (int)glp_mip_col_val(lp, 2);

     int nextGuess = a*x + b*y;

     Console.WriteLine("x = {0}, y = {1}, a*x + b*y = {2}",x,y,nextGuess);

     return nextGuess;

   }

   [DllImport(glpkLibrary, SetLastError=true)]

   static extern void glp_delete_prob(double* lp);

   ~GLPK(){

     glp_delete_prob(lp);

     Console.WriteLine("Goodbye Nigel");

   }

 }

 class test{

   static bool isMinimum(int a, int b, int guess){

     Console.WriteLine("Trying {0}",guess);

     if (a%guess > 0) return false;

     if (b%guess > 0) return false;

     Console.WriteLine("Solution is {0}",guess);

     return true;

   }

   public static void Main(string[] args){

     Console.WriteLine("a = {0}, b = {1}",args[0], args[1]);

     GLPK lp = new GLPK(Int32.Parse(args[0]),Int32.Parse(args[1]));

     int guess = (lp.a > lp.b) ? lp.b : lp.a;

     while (!isMinimum(lp.a,lp.b,guess)) guess = lp.betterGuess(guess);

   }

 }