COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/work/athos/lp/magic_square.cc @ 1241:dadc9987c537

Last change on this file since 1241:dadc9987c537 was 1241:dadc9987c537, checked in by athos, 15 years ago

Modified a bit.

File size: 2.4 KB
Line 
1// -*- c++ -*-
2#include <iostream>
3#include <fstream>
4
5#include <lemon/time_measure.h>
6#include <lp_solver_glpk.h>
7
8using std::cout;
9using std::endl;
10using 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
19int main(int, char **) {
20  const int n=4;
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    // sum of rows and columns
47    lp.addRow(expr1==row_sum);
48    lp.addRow(expr2==row_sum);
49    expr3+=x[std::make_pair(i, i)];
50    expr4+=x[std::make_pair(i, (n+1)-i)];
51  }
52  // sum of the diagonal entries
53  lp.addRow(expr3==row_sum);
54  lp.addRow(expr4==row_sum);
55  lp.solveSimplex();
56  cout << "elapsed time: " << ts << endl;
57  for (int i=1; i<=n; ++i) {
58    for (int j=1; j<=n; ++j) {
59      cout << "x("<<i<<","<<j<<")="<<lp.getPrimal(x[std::make_pair(i,j)])
60           << endl;
61    }
62  }
63  // we make new binary variables for each pair of
64  // entries of the square to achieve that
65  // the values of different entries are different
66  lp.setMIP();
67  for (Coords::const_iterator it=x.begin(); it!=x.end(); ++it) {
68    Coords::const_iterator jt=it; ++jt;
69    for(; jt!=x.end(); ++jt) {
70      Col col1=(*it).second;
71      Col col2=(*jt).second;
72      Col col=lp.addCol();
73      lp.setColLowerBound(col, 0.0);
74      lp.setColUpperBound(col, 1.0);
75      lp.addRow(double(-n*n+1.0)<=1.0*col2-1.0*col1-double(n*n)*col<=-1.0);
76      lp.setColInt(col);
77    }
78  }
79  cout << "elapsed time: " << ts << endl;
80  lp.solveSimplex();
81  // let's solve the integer problem
82  lp.solveBandB();
83  cout << "elapsed time: " << ts << endl;
84  for (int i=1; i<=n; ++i) {
85    for (int j=1; j<=n; ++j) {
86      cout << "x("<<i<<","<<j<<")="<<lp.getMIPPrimal(x[std::make_pair(i,j)])
87           << endl;
88    }
89  }
90}
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