[610] | 1 | // -*- c++ -*- |
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| 2 | #ifndef HUGO_MINLENGTHPATHS_H |
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| 3 | #define HUGO_MINLENGTHPATHS_H |
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| 4 | |
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[759] | 5 | ///\ingroup flowalgs |
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[610] | 6 | ///\file |
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| 7 | ///\brief An algorithm for finding k paths of minimal total length. |
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| 8 | |
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[611] | 9 | |
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[610] | 10 | #include <hugo/maps.h> |
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| 11 | #include <vector> |
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| 12 | #include <hugo/mincostflows.h> |
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| 13 | |
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| 14 | namespace hugo { |
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| 15 | |
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[759] | 16 | /// \addtogroup flowalgs |
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[610] | 17 | /// @{ |
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| 18 | |
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[860] | 19 | ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes |
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[610] | 20 | /// of minimal total length |
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| 21 | /// |
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[860] | 22 | /// The class \ref hugo::MinLengthPaths implements |
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[610] | 23 | /// an algorithm for finding k edge-disjoint paths |
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| 24 | /// from a given source node to a given target node in an |
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[860] | 25 | /// edge-weighted directed graph having minimal total weight (length). |
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[610] | 26 | /// |
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[860] | 27 | ///\warning Length values should be nonnegative. |
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| 28 | /// |
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| 29 | ///\param Graph The directed graph type the algorithm runs on. |
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| 30 | ///\param LengthMap The type of the length map (values should be nonnegative). |
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[610] | 31 | /// |
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| 32 | ///\author Attila Bernath |
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| 33 | template <typename Graph, typename LengthMap> |
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| 34 | class MinLengthPaths{ |
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| 35 | |
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| 36 | |
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| 37 | typedef typename LengthMap::ValueType Length; |
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| 38 | |
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| 39 | typedef typename Graph::Node Node; |
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| 40 | typedef typename Graph::NodeIt NodeIt; |
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| 41 | typedef typename Graph::Edge Edge; |
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| 42 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 43 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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| 44 | |
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| 45 | typedef ConstMap<Edge,int> ConstMap; |
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| 46 | |
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| 47 | //Input |
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| 48 | const Graph& G; |
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| 49 | |
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| 50 | //Auxiliary variables |
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| 51 | //This is the capacity map for the mincostflow problem |
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| 52 | ConstMap const1map; |
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| 53 | //This MinCostFlows instance will actually solve the problem |
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| 54 | MinCostFlows<Graph, LengthMap, ConstMap> mincost_flow; |
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| 55 | |
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| 56 | //Container to store found paths |
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| 57 | std::vector< std::vector<Edge> > paths; |
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| 58 | |
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| 59 | public : |
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| 60 | |
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| 61 | |
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[860] | 62 | /// The constructor of the class. |
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| 63 | |
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| 64 | ///\param _G The directed graph the algorithm runs on. |
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| 65 | ///\param _length The length (weight or cost) of the edges. |
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[610] | 66 | MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G), |
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| 67 | const1map(1), mincost_flow(_G, _length, const1map){} |
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| 68 | |
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| 69 | ///Runs the algorithm. |
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| 70 | |
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| 71 | ///Runs the algorithm. |
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| 72 | ///Returns k if there are at least k edge-disjoint paths from s to t. |
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[851] | 73 | ///Otherwise it returns the number of found edge-disjoint paths from s to t. |
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[860] | 74 | /// |
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| 75 | ///\param s The source node. |
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| 76 | ///\param t The target node. |
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| 77 | ///\param k How many paths are we looking for? |
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| 78 | /// |
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[610] | 79 | int run(Node s, Node t, int k) { |
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| 80 | |
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| 81 | int i = mincost_flow.run(s,t,k); |
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[860] | 82 | |
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[610] | 83 | |
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| 84 | //Let's find the paths |
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| 85 | //We put the paths into stl vectors (as an inner representation). |
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| 86 | //In the meantime we lose the information stored in 'reversed'. |
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| 87 | //We suppose the lengths to be positive now. |
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| 88 | |
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| 89 | //We don't want to change the flow of mincost_flow, so we make a copy |
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| 90 | //The name here suggests that the flow has only 0/1 values. |
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| 91 | EdgeIntMap reversed(G); |
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| 92 | |
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[788] | 93 | for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) |
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[610] | 94 | reversed[e] = mincost_flow.getFlow()[e]; |
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| 95 | |
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| 96 | paths.clear(); |
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| 97 | //total_length=0; |
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| 98 | paths.resize(k); |
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| 99 | for (int j=0; j<i; ++j){ |
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| 100 | Node n=s; |
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| 101 | OutEdgeIt e; |
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| 102 | |
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| 103 | while (n!=t){ |
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| 104 | |
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| 105 | |
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| 106 | G.first(e,n); |
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| 107 | |
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| 108 | while (!reversed[e]){ |
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[776] | 109 | ++e; |
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[610] | 110 | } |
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| 111 | n = G.head(e); |
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| 112 | paths[j].push_back(e); |
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| 113 | //total_length += length[e]; |
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| 114 | reversed[e] = 1-reversed[e]; |
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| 115 | } |
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| 116 | |
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| 117 | } |
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| 118 | return i; |
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| 119 | } |
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| 120 | |
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| 121 | |
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[860] | 122 | ///Returns the total length of the paths |
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[851] | 123 | |
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[610] | 124 | ///This function gives back the total length of the found paths. |
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[851] | 125 | ///\pre \ref run() must |
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| 126 | ///be called before using this function. |
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[610] | 127 | Length totalLength(){ |
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| 128 | return mincost_flow.totalLength(); |
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| 129 | } |
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| 130 | |
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[860] | 131 | ///Returns the found flow. |
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[851] | 132 | |
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| 133 | ///This function returns a const reference to the EdgeMap \c flow. |
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| 134 | ///\pre \ref run() must |
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[610] | 135 | ///be called before using this function. |
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| 136 | const EdgeIntMap &getFlow() const { return mincost_flow.flow;} |
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| 137 | |
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[860] | 138 | /// Returns the optimal dual solution |
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[851] | 139 | |
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| 140 | ///This function returns a const reference to the NodeMap |
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| 141 | ///\c potential (the dual solution). |
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[610] | 142 | /// \pre \ref run() must be called before using this function. |
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| 143 | const EdgeIntMap &getPotential() const { return mincost_flow.potential;} |
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| 144 | |
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[851] | 145 | ///Checks whether the complementary slackness holds. |
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| 146 | |
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[860] | 147 | ///This function checks, whether the given solution is optimal. |
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| 148 | ///It should return true after calling \ref run() |
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[851] | 149 | ///Currently this function only checks optimality, |
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| 150 | ///doesn't bother with feasibility |
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[860] | 151 | ///It is meant for testing purposes. |
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[610] | 152 | /// |
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| 153 | bool checkComplementarySlackness(){ |
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| 154 | return mincost_flow.checkComplementarySlackness(); |
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| 155 | } |
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| 156 | |
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[851] | 157 | ///Read the found paths. |
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| 158 | |
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[610] | 159 | ///This function gives back the \c j-th path in argument p. |
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| 160 | ///Assumes that \c run() has been run and nothing changed since then. |
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[851] | 161 | /// \warning It is assumed that \c p is constructed to |
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| 162 | ///be a path of graph \c G. |
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| 163 | ///If \c j is not less than the result of previous \c run, |
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| 164 | ///then the result here will be an empty path (\c j can be 0 as well). |
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[860] | 165 | /// |
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| 166 | ///\param Path The type of the path structure to put the result to (must meet hugo path concept). |
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| 167 | ///\param p The path to put the result to |
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| 168 | ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively) |
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[851] | 169 | template<typename Path> |
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| 170 | void getPath(Path& p, size_t j){ |
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[860] | 171 | |
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[610] | 172 | p.clear(); |
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| 173 | if (j>paths.size()-1){ |
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| 174 | return; |
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| 175 | } |
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[853] | 176 | typename Path::Builder B(p); |
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[610] | 177 | for(typename std::vector<Edge>::iterator i=paths[j].begin(); |
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| 178 | i!=paths[j].end(); ++i ){ |
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| 179 | B.pushBack(*i); |
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| 180 | } |
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| 181 | |
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| 182 | B.commit(); |
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| 183 | } |
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| 184 | |
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| 185 | }; //class MinLengthPaths |
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| 186 | |
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| 187 | ///@} |
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| 188 | |
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| 189 | } //namespace hugo |
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| 190 | |
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| 191 | #endif //HUGO_MINLENGTHPATHS_H |
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