/* -*- C++ -*-

  * demo/lp_demo.cc - Part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 /// \ingroup demos

 /// \file

 /// \brief A program demonstrating the LEMON LP solver interface

 ///

 /// This program is a simple application of the LEMON LP solver

 /// interface: we formulate a linear programming (LP) problem and then

 /// solve it using the underlying solver (GLPK or CPLEX for

 /// example). For the detailed documentation of the LEMON LP solver

 /// interface read \ref lemon::LpSolverBase "this".

 ///

 /// \include lp_demo.cc

 #include <lemon/lp.h>

 #include <iostream>

 using namespace lemon;

 int main()

 {     

  //The following example is taken from the documentation of the GLPK library.

  //See it in the GLPK reference manual and among the GLPK sample files (sample.c)

   //A default solver is taken

   Lp lp;

   typedef Lp::Row Row;

   typedef Lp::Col Col;

   std::cout<<"A program demonstrating the LEMON LP solver interface"<<std::endl; 

   std::cout<<"Solver used: "<<default_solver_name<<std::endl;

   //This will be a maximization

   lp.max();

   //We add coloumns (variables) to our problem

   Col x1 = lp.addCol();

   Col x2 = lp.addCol();

   Col x3 = lp.addCol();

   //Constraints

   lp.addRow(x1+x2+x3 <=100);  

   lp.addRow(10*x1+4*x2+5*x3<=600);  

   lp.addRow(2*x1+2*x2+6*x3<=300);  

   //Nonnegativity of the variables

   lp.colLowerBound(x1, 0);

   lp.colLowerBound(x2, 0);

   lp.colLowerBound(x3, 0);

   //Objective function

   lp.setObj(10*x1+6*x2+4*x3);

   //Call the routine of the underlying LP solver

   lp.solve();

   //Print results

   if (lp.primalStatus()==LpSolverBase::OPTIMAL){

     std::cout<<"Optimal solution found!"<<std::endl;

     printf("optimum value = %g; x1 = %g; x2 = %g; x3 = %g\n", 

 	   lp.primalValue(), 

 	   lp.primal(x1), lp.primal(x2), lp.primal(x3));

   }

   else{

     std::cout<<"Optimal solution not found!"<<std::endl;

   }

   //End of LEMON style code

   //Here comes the same problem written in C using GLPK API routines

 //   LPX *lp;

 //       int ia[1+1000], ja[1+1000];

 //       double ar[1+1000], Z, x1, x2, x3;

 // s1:   lp = lpx_create_prob();

 // s2:   lpx_set_prob_name(lp, "sample");

 // s3:   lpx_set_obj_dir(lp, LPX_MAX);

 // s4:   lpx_add_rows(lp, 3);

 // s5:   lpx_set_row_name(lp, 1, "p");

 // s6:   lpx_set_row_bnds(lp, 1, LPX_UP, 0.0, 100.0);

 // s7:   lpx_set_row_name(lp, 2, "q");

 // s8:   lpx_set_row_bnds(lp, 2, LPX_UP, 0.0, 600.0);

 // s9:   lpx_set_row_name(lp, 3, "r");

 // s10:  lpx_set_row_bnds(lp, 3, LPX_UP, 0.0, 300.0);

 // s11:  lpx_add_cols(lp, 3);

 // s12:  lpx_set_col_name(lp, 1, "x1");

 // s13:  lpx_set_col_bnds(lp, 1, LPX_LO, 0.0, 0.0);

 // s14:  lpx_set_obj_coef(lp, 1, 10.0);

 // s15:  lpx_set_col_name(lp, 2, "x2");

 // s16:  lpx_set_col_bnds(lp, 2, LPX_LO, 0.0, 0.0);

 // s17:  lpx_set_obj_coef(lp, 2, 6.0);

 // s18:  lpx_set_col_name(lp, 3, "x3");

 // s19:  lpx_set_col_bnds(lp, 3, LPX_LO, 0.0, 0.0);

 // s20:  lpx_set_obj_coef(lp, 3, 4.0);

 // s21:  ia[1] = 1, ja[1] = 1, ar[1] =  1.0; /* a[1,1] =  1 */

 // s22:  ia[2] = 1, ja[2] = 2, ar[2] =  1.0; /* a[1,2] =  1 */

 // s23:  ia[3] = 1, ja[3] = 3, ar[3] =  1.0; /* a[1,3] =  1 */

 // s24:  ia[4] = 2, ja[4] = 1, ar[4] = 10.0; /* a[2,1] = 10 */

 // s25:  ia[5] = 3, ja[5] = 1, ar[5] =  2.0; /* a[3,1] =  2 */

 // s26:  ia[6] = 2, ja[6] = 2, ar[6] =  4.0; /* a[2,2] =  4 */

 // s27:  ia[7] = 3, ja[7] = 2, ar[7] =  2.0; /* a[3,2] =  2 */

 // s28:  ia[8] = 2, ja[8] = 3, ar[8] =  5.0; /* a[2,3] =  5 */

 // s29:  ia[9] = 3, ja[9] = 3, ar[9] =  6.0; /* a[3,3] =  6 */

 // s30:  lpx_load_matrix(lp, 9, ia, ja, ar);

 // s31:  lpx_simplex(lp);

 // s32:  Z = lpx_get_obj_val(lp);

 // s33:  x1 = lpx_get_col_prim(lp, 1);

 // s34:  x2 = lpx_get_col_prim(lp, 2);

 // s35:  x3 = lpx_get_col_prim(lp, 3);

 // s36:  printf("\nZ = %g; x1 = %g; x2 = %g; x3 = %g\n", Z, x1, x2, x3);

 // s37:  lpx_delete_prob(lp);

 //       return 0;

   return 0;

 }