// -*- c++ -*-

#include <iostream>

#include <fstream>

#include <lemon/time_measure.h>

#include <lp_solver_glpk.h>

using std::cout;

using std::endl;

using namespace lemon;

/*

  On an 1537Mhz PC, the run times with 

  glpk are the following.

  for n=3,4, some secondes

  for n=5, 25 hours

 */

int main(int, char **) {

  const int n=3;

  const double row_sum=(1.0+n*n)*n/2;

  Timer ts;

  ts.reset();

  typedef LpGlpk LPSolver;

  typedef LPSolver::Col Col;

  LPSolver lp;

  typedef std::map<std::pair<int, int>, Col> Coords;

  Coords x;

  // we create a new variable for each entry 

  // of the magic square

  for (int i=1; i<=n; ++i) {

    for (int j=1; j<=n; ++j) { 

      Col col=lp.addCol();

      x[std::make_pair(i,j)]=col;

      lp.setColLowerBound(col, 1.0);

      lp.setColUpperBound(col, double(n*n));

    }

  }

  LPSolver::Expression expr3, expr4;

  for (int i=1; i<=n; ++i) {

    LPSolver::Expression expr1, expr2;

    for (int j=1; j<=n; ++j) {

      expr1+=x[std::make_pair(i, j)];

      expr2+=x[std::make_pair(j, i)];

    }

    // sum of rows and columns

    lp.addRow(expr1==row_sum);

    lp.addRow(expr2==row_sum);

      cout <<"Expr1: "<<expr1<<endl;

      cout <<"Expr2: "<<expr2<<endl;

    expr3+=x[std::make_pair(i, i)];

    expr4+=x[std::make_pair(i, (n+1)-i)];

  }

  cout <<"Expr3: "<<expr3<<endl;

  cout <<"Expr4: "<<expr4<<endl;

  // sum of the diagonal entries

  lp.addRow(expr3==row_sum);

  lp.addRow(expr4==row_sum);

  lp.solveSimplex();

  cout << "elapsed time: " << ts << endl;

  for (int i=1; i<=n; ++i) {

    for (int j=1; j<=n; ++j) { 

      cout << "x("<<i<<","<<j<<")="<<lp.getPrimal(x[std::make_pair(i,j)]) 

	   << endl;

    }

  }

//   // we make new binary variables for each pair of 

//   // entries of the square to achieve that 

//   // the values of different entries are different

//   lp.setMIP();

//   for (Coords::const_iterator it=x.begin(); it!=x.end(); ++it) {

//     Coords::const_iterator jt=it; ++jt;

//     for(; jt!=x.end(); ++jt) {

//       Col col1=(*it).second;

//       Col col2=(*jt).second;

//       Col col=lp.addCol();

//       lp.setColLowerBound(col, 0.0);

//       lp.setColUpperBound(col, 1.0);

//       lp.addRow(double(-n*n+1.0)<=1.0*col2-1.0*col1-double(n*n)*col<=-1.0);

//       lp.setColInt(col);

//     }

//   }

//   cout << "elapsed time: " << ts << endl;

//   lp.solveSimplex();

//   // let's solve the integer problem

//   lp.solveBandB();

//   cout << "elapsed time: " << ts << endl;

//   for (int i=1; i<=n; ++i) {

//     for (int j=1; j<=n; ++j) { 

//       cout << "x("<<i<<","<<j<<")="<<lp.getMIPPrimal(x[std::make_pair(i,j)]) 

// 	   << endl;

//     }

//   }

}