/*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);

  }

}