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