1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/work/athos/lp_old/magic_square.cc	Wed Mar 23 09:49:41 2005 +0000
     1.3 @@ -0,0 +1,99 @@
     1.4 +// -*- c++ -*-
     1.5 +#include <iostream>
     1.6 +#include <fstream>
     1.7 +
     1.8 +#include <lemon/time_measure.h>
     1.9 +#include <lp_solver_glpk.h>
    1.10 +
    1.11 +using std::cout;
    1.12 +using std::endl;
    1.13 +using namespace lemon;
    1.14 +
    1.15 +/*
    1.16 +  On an 1537Mhz PC, the run times with 
    1.17 +  glpk are the following.
    1.18 +  for n=3,4, some secondes
    1.19 +  for n=5, 25 hours
    1.20 + */
    1.21 +
    1.22 +int main(int, char **) {
    1.23 +  const int n=3;
    1.24 +  const double row_sum=(1.0+n*n)*n/2;
    1.25 +  Timer ts;
    1.26 +  ts.reset();
    1.27 +  typedef LpGlpk LPSolver;
    1.28 +  typedef LPSolver::Col Col;
    1.29 +  LPSolver lp;
    1.30 +  typedef std::map<std::pair<int, int>, Col> Coords;
    1.31 +  Coords x;
    1.32 +  // we create a new variable for each entry 
    1.33 +  // of the magic square
    1.34 +  for (int i=1; i<=n; ++i) {
    1.35 +    for (int j=1; j<=n; ++j) { 
    1.36 +      Col col=lp.addCol();
    1.37 +      x[std::make_pair(i,j)]=col;
    1.38 +      lp.setColLowerBound(col, 1.0);
    1.39 +      lp.setColUpperBound(col, double(n*n));
    1.40 +    }
    1.41 +  }
    1.42 +  LPSolver::Expression expr3, expr4;
    1.43 +  for (int i=1; i<=n; ++i) {
    1.44 +    LPSolver::Expression expr1, expr2;
    1.45 +    for (int j=1; j<=n; ++j) {
    1.46 +      expr1+=x[std::make_pair(i, j)];
    1.47 +      expr2+=x[std::make_pair(j, i)];
    1.48 +    }
    1.49 +
    1.50 +    // sum of rows and columns
    1.51 +    lp.addRow(expr1==row_sum);
    1.52 +    lp.addRow(expr2==row_sum);
    1.53 +      cout <<"Expr1: "<<expr1<<endl;
    1.54 +      cout <<"Expr2: "<<expr2<<endl;
    1.55 +
    1.56 +    expr3+=x[std::make_pair(i, i)];
    1.57 +    expr4+=x[std::make_pair(i, (n+1)-i)];
    1.58 +  }
    1.59 +  cout <<"Expr3: "<<expr3<<endl;
    1.60 +  cout <<"Expr4: "<<expr4<<endl;
    1.61 +  // sum of the diagonal entries
    1.62 +  lp.addRow(expr3==row_sum);
    1.63 +  lp.addRow(expr4==row_sum);
    1.64 +  lp.solveSimplex();
    1.65 +  cout << "elapsed time: " << ts << endl;
    1.66 +  for (int i=1; i<=n; ++i) {
    1.67 +    for (int j=1; j<=n; ++j) { 
    1.68 +      cout << "x("<<i<<","<<j<<")="<<lp.getPrimal(x[std::make_pair(i,j)]) 
    1.69 +	   << endl;
    1.70 +    }
    1.71 +  }
    1.72 +
    1.73 +
    1.74 +
    1.75 +//   // we make new binary variables for each pair of 
    1.76 +//   // entries of the square to achieve that 
    1.77 +//   // the values of different entries are different
    1.78 +//   lp.setMIP();
    1.79 +//   for (Coords::const_iterator it=x.begin(); it!=x.end(); ++it) {
    1.80 +//     Coords::const_iterator jt=it; ++jt;
    1.81 +//     for(; jt!=x.end(); ++jt) {
    1.82 +//       Col col1=(*it).second;
    1.83 +//       Col col2=(*jt).second;
    1.84 +//       Col col=lp.addCol();
    1.85 +//       lp.setColLowerBound(col, 0.0);
    1.86 +//       lp.setColUpperBound(col, 1.0);
    1.87 +//       lp.addRow(double(-n*n+1.0)<=1.0*col2-1.0*col1-double(n*n)*col<=-1.0);
    1.88 +//       lp.setColInt(col);
    1.89 +//     }
    1.90 +//   }
    1.91 +//   cout << "elapsed time: " << ts << endl;
    1.92 +//   lp.solveSimplex();
    1.93 +//   // let's solve the integer problem
    1.94 +//   lp.solveBandB();
    1.95 +//   cout << "elapsed time: " << ts << endl;
    1.96 +//   for (int i=1; i<=n; ++i) {
    1.97 +//     for (int j=1; j<=n; ++j) { 
    1.98 +//       cout << "x("<<i<<","<<j<<")="<<lp.getMIPPrimal(x[std::make_pair(i,j)]) 
    1.99 +// 	   << endl;
   1.100 +//     }
   1.101 +//   }
   1.102 +}