alpar@9: /*Find the minimum value which satisfies the linear inequality:
alpar@9:     a*x + b*y >= 1 {a,b,x,y Integers} {a,b > 0} {a,b entered on command line}
alpar@9: 
alpar@9:   Nigel_Galloway@operamail.com
alpar@9:   February 2008
alpar@9: */
alpar@9: using System;
alpar@9: using System.Runtime.InteropServices;
alpar@9: 
alpar@9: unsafe class GLPK{
alpar@9:   double *lp;
alpar@9:   public int a;
alpar@9:   public int b;
alpar@9: 
alpar@9:   const string glpkLibrary = "libglpk.so";
alpar@9:   readonly int GLP_FR = 1;
alpar@9:   readonly int GLP_IV = 2;
alpar@9:   readonly int GLP_DB = 4;
alpar@9:   struct ConstraintMatrix{
alpar@9:     public fixed int ia[3];
alpar@9:     public fixed int ja[3];
alpar@9:     public fixed double ar[3];
alpar@9:   }
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern double* glp_create_prob();
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern void glp_add_rows(double* lp, int rows);
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern void glp_add_cols(double* lp, int cols);
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern void glp_set_col_bnds(double* lp, int col, int bound_type, double lower_bound, double upper_bound);
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern void glp_set_col_kind(double* lp, int col, int kind);
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern void glp_load_matrix(double* lp, int elements, int* ia, int* ja, double* ar);
alpar@9:   public GLPK(int a, int b){
alpar@9:     this.a = a;
alpar@9:     this.b = b;
alpar@9:     lp = glp_create_prob();
alpar@9:     //Col 1 is x, Col 2 is y
alpar@9:     glp_add_rows(lp, 1);
alpar@9:     glp_add_cols(lp, 2);
alpar@9:     glp_set_col_bnds(lp, 1, GLP_FR, 0.0, 0.0);
alpar@9:     glp_set_col_bnds(lp, 2, GLP_FR, 0.0, 0.0);
alpar@9:     glp_set_col_kind(lp, 1, GLP_IV);
alpar@9:     glp_set_col_kind(lp, 2, GLP_IV);
alpar@9:     //Row 1 is a*x + b*y
alpar@9:     ConstraintMatrix CM = new ConstraintMatrix();
alpar@9:     CM.ia[1]=1; CM.ja[1]=1; CM.ar[1]=a;
alpar@9:     CM.ia[2]=1; CM.ja[2]=2; CM.ar[2]=b;
alpar@9:     glp_load_matrix(lp, 2, CM.ia, CM.ja, CM.ar);
alpar@9:     Console.WriteLine("Hello Nigel");
alpar@9:   }
alpar@9: 
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern void glp_set_row_bnds(double* lp, int row, int bound_type, double lower_bound, double upper_bound);
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern void glp_simplex(double* lp, void* options);
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern void glp_intopt(double* lp, void* options);
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern double glp_mip_col_val(double* lp, int col);
alpar@9:   public int betterGuess(int upper_bound){
alpar@9:     //Find a new guess less than the old guess: 1 <= (a*x + b*y) <= (old guess - 1)
alpar@9:     glp_set_row_bnds(lp, 1, GLP_DB, 1.0, ((double)upper_bound)-0.5);
alpar@9:     glp_simplex(lp, null);
alpar@9:     glp_intopt(lp, null);
alpar@9:     int x = (int)glp_mip_col_val(lp, 1);
alpar@9:     int y = (int)glp_mip_col_val(lp, 2);
alpar@9:     int nextGuess = a*x + b*y;
alpar@9:     Console.WriteLine("x = {0}, y = {1}, a*x + b*y = {2}",x,y,nextGuess);
alpar@9:     return nextGuess;
alpar@9:   }
alpar@9: 
alpar@9:   [DllImport(glpkLibrary, SetLastError=true)]
alpar@9:   static extern void glp_delete_prob(double* lp);
alpar@9:   ~GLPK(){
alpar@9:     glp_delete_prob(lp);
alpar@9:     Console.WriteLine("Goodbye Nigel");
alpar@9:   }
alpar@9: 
alpar@9: }
alpar@9: 
alpar@9: class test{
alpar@9:   static bool isMinimum(int a, int b, int guess){
alpar@9:     Console.WriteLine("Trying {0}",guess);
alpar@9:     if (a%guess > 0) return false;
alpar@9:     if (b%guess > 0) return false;
alpar@9:     Console.WriteLine("Solution is {0}",guess);
alpar@9:     return true;
alpar@9:   }
alpar@9: 
alpar@9:   public static void Main(string[] args){
alpar@9:     Console.WriteLine("a = {0}, b = {1}",args[0], args[1]);
alpar@9:     GLPK lp = new GLPK(Int32.Parse(args[0]),Int32.Parse(args[1]));
alpar@9:     int guess = (lp.a > lp.b) ? lp.b : lp.a;
alpar@9:     while (!isMinimum(lp.a,lp.b,guess)) guess = lp.betterGuess(guess);
alpar@9:   }
alpar@9: }