[906] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[1956] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2006 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[906] | 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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[921] | 19 | #ifndef LEMON_SUURBALLE_H |
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| 20 | #define LEMON_SUURBALLE_H |
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[899] | 21 | |
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[2378] | 22 | ///\ingroup shortest_path |
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[899] | 23 | ///\file |
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| 24 | ///\brief An algorithm for finding k paths of minimal total length. |
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| 25 | |
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| 26 | |
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[921] | 27 | #include <lemon/maps.h> |
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[899] | 28 | #include <vector> |
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[2335] | 29 | #include <lemon/path.h> |
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[2276] | 30 | #include <lemon/ssp_min_cost_flow.h> |
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[899] | 31 | |
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[921] | 32 | namespace lemon { |
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[899] | 33 | |
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[2376] | 34 | /// \addtogroup shortest_path |
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[899] | 35 | /// @{ |
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| 36 | |
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[2276] | 37 | ///\brief Implementation of an algorithm for finding k edge-disjoint |
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| 38 | /// paths between 2 nodes of minimal total length |
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[899] | 39 | /// |
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[921] | 40 | /// The class \ref lemon::Suurballe implements |
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[899] | 41 | /// an algorithm for finding k edge-disjoint paths |
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| 42 | /// from a given source node to a given target node in an |
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| 43 | /// edge-weighted directed graph having minimal total weight (length). |
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| 44 | /// |
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[1527] | 45 | ///\warning Length values should be nonnegative! |
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[899] | 46 | /// |
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| 47 | ///\param Graph The directed graph type the algorithm runs on. |
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| 48 | ///\param LengthMap The type of the length map (values should be nonnegative). |
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| 49 | /// |
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[968] | 50 | ///\note It it questionable whether it is correct to call this method after |
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[1020] | 51 | ///%Suurballe for it is just a special case of Edmonds' and Karp's algorithm |
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[968] | 52 | ///for finding minimum cost flows. In fact, this implementation just |
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[2276] | 53 | ///wraps the SspMinCostFlow algorithms. The paper of both %Suurballe and |
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[899] | 54 | ///Edmonds-Karp published in 1972, therefore it is possibly right to |
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| 55 | ///state that they are |
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| 56 | ///independent results. Most frequently this special case is referred as |
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| 57 | ///%Suurballe method in the literature, especially in communication |
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| 58 | ///network context. |
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| 59 | ///\author Attila Bernath |
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| 60 | template <typename Graph, typename LengthMap> |
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| 61 | class Suurballe{ |
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| 62 | |
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| 63 | |
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[987] | 64 | typedef typename LengthMap::Value Length; |
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[899] | 65 | |
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| 66 | typedef typename Graph::Node Node; |
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| 67 | typedef typename Graph::NodeIt NodeIt; |
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| 68 | typedef typename Graph::Edge Edge; |
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| 69 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 70 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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| 71 | |
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| 72 | typedef ConstMap<Edge,int> ConstMap; |
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| 73 | |
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| 74 | const Graph& G; |
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| 75 | |
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[941] | 76 | Node s; |
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| 77 | Node t; |
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| 78 | |
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[899] | 79 | //Auxiliary variables |
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| 80 | //This is the capacity map for the mincostflow problem |
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| 81 | ConstMap const1map; |
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| 82 | //This MinCostFlow instance will actually solve the problem |
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[2276] | 83 | SspMinCostFlow<Graph, LengthMap, ConstMap> min_cost_flow; |
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[899] | 84 | |
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| 85 | //Container to store found paths |
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[2335] | 86 | std::vector<SimplePath<Graph> > paths; |
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[899] | 87 | |
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| 88 | public : |
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| 89 | |
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| 90 | |
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[2276] | 91 | /// \brief The constructor of the class. |
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| 92 | /// |
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| 93 | /// \param _G The directed graph the algorithm runs on. |
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| 94 | /// \param _length The length (weight or cost) of the edges. |
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| 95 | /// \param _s Source node. |
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| 96 | /// \param _t Target node. |
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[941] | 97 | Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) : |
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| 98 | G(_G), s(_s), t(_t), const1map(1), |
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| 99 | min_cost_flow(_G, _length, const1map, _s, _t) { } |
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[899] | 100 | |
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[2276] | 101 | /// \brief Runs the algorithm. |
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[899] | 102 | /// |
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[2276] | 103 | /// Runs the algorithm. |
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| 104 | /// Returns k if there are at least k edge-disjoint paths from s to t. |
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| 105 | /// Otherwise it returns the number of edge-disjoint paths found |
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| 106 | /// from s to t. |
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| 107 | /// |
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| 108 | /// \param k How many paths are we looking for? |
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[899] | 109 | /// |
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[941] | 110 | int run(int k) { |
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| 111 | int i = min_cost_flow.run(k); |
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[899] | 112 | |
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| 113 | //Let's find the paths |
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| 114 | //We put the paths into stl vectors (as an inner representation). |
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| 115 | //In the meantime we lose the information stored in 'reversed'. |
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| 116 | //We suppose the lengths to be positive now. |
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| 117 | |
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[941] | 118 | //We don't want to change the flow of min_cost_flow, so we make a copy |
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[899] | 119 | //The name here suggests that the flow has only 0/1 values. |
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| 120 | EdgeIntMap reversed(G); |
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| 121 | |
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| 122 | for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) |
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[941] | 123 | reversed[e] = min_cost_flow.getFlow()[e]; |
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[899] | 124 | |
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| 125 | paths.clear(); |
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| 126 | paths.resize(k); |
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| 127 | for (int j=0; j<i; ++j){ |
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| 128 | Node n=s; |
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| 129 | |
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| 130 | while (n!=t){ |
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| 131 | |
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[946] | 132 | OutEdgeIt e(G, n); |
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[899] | 133 | |
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| 134 | while (!reversed[e]){ |
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| 135 | ++e; |
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| 136 | } |
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[986] | 137 | n = G.target(e); |
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[2335] | 138 | paths[j].addBack(e); |
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[899] | 139 | reversed[e] = 1-reversed[e]; |
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| 140 | } |
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| 141 | |
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| 142 | } |
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| 143 | return i; |
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| 144 | } |
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| 145 | |
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| 146 | |
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[2276] | 147 | /// \brief Returns the total length of the paths. |
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| 148 | /// |
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| 149 | /// This function gives back the total length of the found paths. |
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[899] | 150 | Length totalLength(){ |
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[941] | 151 | return min_cost_flow.totalLength(); |
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[899] | 152 | } |
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| 153 | |
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[2276] | 154 | /// \brief Returns the found flow. |
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| 155 | /// |
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| 156 | /// This function returns a const reference to the EdgeMap \c flow. |
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[941] | 157 | const EdgeIntMap &getFlow() const { return min_cost_flow.flow;} |
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[899] | 158 | |
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[2276] | 159 | /// \brief Returns the optimal dual solution |
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| 160 | /// |
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| 161 | /// This function returns a const reference to the NodeMap \c |
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| 162 | /// potential (the dual solution). |
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[941] | 163 | const EdgeIntMap &getPotential() const { return min_cost_flow.potential;} |
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[899] | 164 | |
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[2276] | 165 | /// \brief Checks whether the complementary slackness holds. |
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| 166 | /// |
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| 167 | /// This function checks, whether the given solution is optimal. |
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| 168 | /// Currently this function only checks optimality, doesn't bother |
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| 169 | /// with feasibility. It is meant for testing purposes. |
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[899] | 170 | bool checkComplementarySlackness(){ |
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[941] | 171 | return min_cost_flow.checkComplementarySlackness(); |
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[899] | 172 | } |
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| 173 | |
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[2335] | 174 | typedef SimplePath<Graph> Path; |
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| 175 | |
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[2276] | 176 | /// \brief Read the found paths. |
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[899] | 177 | /// |
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[2276] | 178 | /// This function gives back the \c j-th path in argument p. |
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| 179 | /// Assumes that \c run() has been run and nothing has changed |
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| 180 | /// since then. |
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| 181 | /// |
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| 182 | /// \warning It is assumed that \c p is constructed to be a path |
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| 183 | /// of graph \c G. If \c j is not less than the result of |
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| 184 | /// previous \c run, then the result here will be an empty path |
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| 185 | /// (\c j can be 0 as well). |
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| 186 | /// |
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| 187 | /// \param j Which path you want to get from the found paths (in a |
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| 188 | /// real application you would get the found paths iteratively). |
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[2335] | 189 | Path path(int j) const { |
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| 190 | return paths[j]; |
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| 191 | } |
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[899] | 192 | |
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[2335] | 193 | /// \brief Gives back the number of the paths. |
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| 194 | /// |
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| 195 | /// Gives back the number of the constructed paths. |
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| 196 | int pathNum() const { |
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| 197 | return paths.size(); |
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[899] | 198 | } |
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| 199 | |
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| 200 | }; //class Suurballe |
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| 201 | |
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| 202 | ///@} |
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| 203 | |
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[921] | 204 | } //namespace lemon |
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[899] | 205 | |
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[921] | 206 | #endif //LEMON_SUURBALLE_H |
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