/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2008

 * 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.obj(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;

}