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/*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); }}
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