src/work/athos/lp_old/magic_square.cc
author deba
Sat, 09 Apr 2005 19:27:48 +0000
changeset 1330 52ef02524468
parent 1243 41caee260bd4
permissions -rw-r--r--
Heap concept moved to namespace concept.
     1 // -*- c++ -*-
     2 #include <iostream>
     3 #include <fstream>
     4 
     5 #include <lemon/time_measure.h>
     6 #include <lp_solver_glpk.h>
     7 
     8 using std::cout;
     9 using std::endl;
    10 using namespace lemon;
    11 
    12 /*
    13   On an 1537Mhz PC, the run times with 
    14   glpk are the following.
    15   for n=3,4, some secondes
    16   for n=5, 25 hours
    17  */
    18 
    19 int main(int, char **) {
    20   const int n=3;
    21   const double row_sum=(1.0+n*n)*n/2;
    22   Timer ts;
    23   ts.reset();
    24   typedef LpGlpk LPSolver;
    25   typedef LPSolver::Col Col;
    26   LPSolver lp;
    27   typedef std::map<std::pair<int, int>, Col> Coords;
    28   Coords x;
    29   // we create a new variable for each entry 
    30   // of the magic square
    31   for (int i=1; i<=n; ++i) {
    32     for (int j=1; j<=n; ++j) { 
    33       Col col=lp.addCol();
    34       x[std::make_pair(i,j)]=col;
    35       lp.setColLowerBound(col, 1.0);
    36       lp.setColUpperBound(col, double(n*n));
    37     }
    38   }
    39   LPSolver::Expression expr3, expr4;
    40   for (int i=1; i<=n; ++i) {
    41     LPSolver::Expression expr1, expr2;
    42     for (int j=1; j<=n; ++j) {
    43       expr1+=x[std::make_pair(i, j)];
    44       expr2+=x[std::make_pair(j, i)];
    45     }
    46 
    47     // sum of rows and columns
    48     lp.addRow(expr1==row_sum);
    49     lp.addRow(expr2==row_sum);
    50       cout <<"Expr1: "<<expr1<<endl;
    51       cout <<"Expr2: "<<expr2<<endl;
    52 
    53     expr3+=x[std::make_pair(i, i)];
    54     expr4+=x[std::make_pair(i, (n+1)-i)];
    55   }
    56   cout <<"Expr3: "<<expr3<<endl;
    57   cout <<"Expr4: "<<expr4<<endl;
    58   // sum of the diagonal entries
    59   lp.addRow(expr3==row_sum);
    60   lp.addRow(expr4==row_sum);
    61   lp.solveSimplex();
    62   cout << "elapsed time: " << ts << endl;
    63   for (int i=1; i<=n; ++i) {
    64     for (int j=1; j<=n; ++j) { 
    65       cout << "x("<<i<<","<<j<<")="<<lp.getPrimal(x[std::make_pair(i,j)]) 
    66 	   << endl;
    67     }
    68   }
    69 
    70 
    71 
    72 //   // we make new binary variables for each pair of 
    73 //   // entries of the square to achieve that 
    74 //   // the values of different entries are different
    75 //   lp.setMIP();
    76 //   for (Coords::const_iterator it=x.begin(); it!=x.end(); ++it) {
    77 //     Coords::const_iterator jt=it; ++jt;
    78 //     for(; jt!=x.end(); ++jt) {
    79 //       Col col1=(*it).second;
    80 //       Col col2=(*jt).second;
    81 //       Col col=lp.addCol();
    82 //       lp.setColLowerBound(col, 0.0);
    83 //       lp.setColUpperBound(col, 1.0);
    84 //       lp.addRow(double(-n*n+1.0)<=1.0*col2-1.0*col1-double(n*n)*col<=-1.0);
    85 //       lp.setColInt(col);
    86 //     }
    87 //   }
    88 //   cout << "elapsed time: " << ts << endl;
    89 //   lp.solveSimplex();
    90 //   // let's solve the integer problem
    91 //   lp.solveBandB();
    92 //   cout << "elapsed time: " << ts << endl;
    93 //   for (int i=1; i<=n; ++i) {
    94 //     for (int j=1; j<=n; ++j) { 
    95 //       cout << "x("<<i<<","<<j<<")="<<lp.getMIPPrimal(x[std::make_pair(i,j)]) 
    96 // 	   << endl;
    97 //     }
    98 //   }
    99 }