1 | #ifdef HAVE_CONFIG_H |
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2 | #include <config.h> |
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3 | #endif |
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4 | |
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5 | #include<lemon/graph_reader.h> |
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6 | #include<lemon/list_graph.h> |
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7 | |
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8 | |
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9 | #ifdef HAVE_GLPK |
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10 | #include <lemon/lp_glpk.h> |
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11 | #elif HAVE_CPLEX |
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12 | #include <lemon/lp_cplex.h> |
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13 | #endif |
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14 | |
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15 | using namespace lemon; |
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16 | |
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17 | #ifdef HAVE_GLPK |
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18 | typedef LpGlpk LpDefault; |
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19 | #elif HAVE_CPLEX |
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20 | typedef LpCplex LpDefault; |
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21 | #endif |
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22 | |
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23 | |
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24 | template<class G,class C> |
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25 | double maxFlow(const G &g,const C &cap,typename G::Node s,typename G::Node t) |
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26 | { |
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27 | LpDefault lp; |
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28 | |
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29 | typedef G Graph; |
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30 | typedef typename G::Node Node; |
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31 | typedef typename G::NodeIt NodeIt; |
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32 | typedef typename G::Edge Edge; |
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33 | typedef typename G::EdgeIt EdgeIt; |
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34 | typedef typename G::OutEdgeIt OutEdgeIt; |
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35 | typedef typename G::InEdgeIt InEdgeIt; |
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36 | |
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37 | //Define a map on the edges for the variables of the LP problem |
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38 | typename G::template EdgeMap<LpDefault::Col> x(g); |
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39 | lp.addColSet(x); |
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40 | |
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41 | //Nonnegativity and capacity constraints |
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42 | for(EdgeIt e(g);e!=INVALID;++e) { |
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43 | lp.colUpperBound(x[e],cap[e]); |
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44 | lp.colLowerBound(x[e],0); |
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45 | } |
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46 | |
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47 | |
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48 | //Flow conservation constraints for the nodes (except for 's' and 't') |
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49 | for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) { |
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50 | LpDefault::Expr ex; |
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51 | for(InEdgeIt e(g,n);e!=INVALID;++e) ex+=x[e]; |
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52 | for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e]; |
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53 | lp.addRow(ex==0); |
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54 | } |
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55 | |
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56 | //Objective function: the flow value entering 't' |
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57 | { |
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58 | LpDefault::Expr ex; |
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59 | for(InEdgeIt e(g,t);e!=INVALID;++e) ex+=x[e]; |
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60 | for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e]; |
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61 | lp.setObj(ex); |
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62 | } |
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63 | |
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64 | //Maximization |
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65 | lp.max(); |
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66 | |
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67 | #ifdef HAVE_GLPK |
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68 | lp.presolver(true); |
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69 | lp.messageLevel(3); |
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70 | #endif |
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71 | |
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72 | //Solve with the underlying solver |
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73 | lp.solve(); |
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74 | |
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75 | return lp.primalValue(); |
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76 | } |
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77 | |
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78 | int main() |
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79 | { |
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80 | ListGraph g; |
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81 | ListGraph::Node s; |
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82 | ListGraph::Node t; |
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83 | |
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84 | ListGraph::EdgeMap<double> cap(g); |
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85 | |
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86 | GraphReader<ListGraph> reader(std::cin,g); |
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87 | reader.readNode("source",s).readNode("target",t) |
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88 | .readEdgeMap("capacity",cap).run(); |
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89 | |
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90 | // std::ifstream file("../test/preflow_"); |
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91 | // readDimacs(file, g, cap, s, t); |
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92 | |
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93 | std::cout << "Max flow value = " << maxFlow(g,cap,s,t) << std::endl; |
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94 | |
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95 | } |
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