[2409] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 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) 2003-2007 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 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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| 19 | #ifndef LEMON_MIN_MEAN_CYCLE_H |
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| 20 | #define LEMON_MIN_MEAN_CYCLE_H |
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| 21 | |
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| 22 | /// \ingroup min_cost_flow |
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| 23 | /// |
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| 24 | /// \file |
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| 25 | /// \brief Karp algorithm for finding a minimum mean cycle. |
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| 26 | |
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| 27 | #include <lemon/graph_utils.h> |
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| 28 | #include <lemon/topology.h> |
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| 29 | #include <lemon/path.h> |
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| 30 | |
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| 31 | namespace lemon { |
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| 32 | |
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| 33 | /// \addtogroup min_cost_flow |
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| 34 | /// @{ |
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| 35 | |
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| 36 | /// \brief Implementation of Karp's algorithm for finding a |
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| 37 | /// minimum mean cycle. |
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| 38 | /// |
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| 39 | /// The \ref lemon::MinMeanCycle "MinMeanCycle" implements Karp's |
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| 40 | /// algorithm for finding a minimum mean cycle. |
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| 41 | /// |
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| 42 | /// \param Graph The directed graph type the algorithm runs on. |
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| 43 | /// \param LengthMap The type of the length (cost) map. |
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| 44 | /// |
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| 45 | /// \author Peter Kovacs |
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| 46 | |
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| 47 | #ifdef DOXYGEN |
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| 48 | template <typename Graph, typename LengthMap> |
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| 49 | #else |
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| 50 | template <typename Graph, |
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| 51 | typename LengthMap = typename Graph::template EdgeMap<int> > |
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| 52 | #endif |
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| 53 | |
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| 54 | class MinMeanCycle |
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| 55 | { |
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| 56 | typedef typename Graph::Node Node; |
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| 57 | typedef typename Graph::NodeIt NodeIt; |
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| 58 | typedef typename Graph::Edge Edge; |
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| 59 | typedef typename Graph::EdgeIt EdgeIt; |
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| 60 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 61 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 62 | |
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| 63 | typedef typename LengthMap::Value Length; |
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| 64 | |
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| 65 | typedef typename Graph::template NodeMap<int> IntNodeMap; |
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| 66 | typedef typename Graph::template NodeMap<Edge> PredNodeMap; |
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| 67 | typedef Path<Graph> Path; |
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| 68 | typedef std::vector<Node> NodeVector; |
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| 69 | typedef typename NodeVector::iterator NodeVectorIt; |
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| 70 | |
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| 71 | protected: |
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| 72 | |
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| 73 | /// \brief Data sturcture for path data. |
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| 74 | struct PathData { |
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| 75 | bool found; |
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| 76 | Length dist; |
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| 77 | Edge pred; |
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| 78 | PathData(bool _found = false, Length _dist = 0) : |
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| 79 | found(_found), dist(_dist), pred(INVALID) {} |
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| 80 | PathData(bool _found, Length _dist, Edge _pred) : |
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| 81 | found(_found), dist(_dist), pred(_pred) {} |
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| 82 | }; |
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| 83 | |
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| 84 | private: |
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| 85 | |
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| 86 | typedef typename Graph::template NodeMap<std::vector<PathData> > PathVectorNodeMap; |
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| 87 | |
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| 88 | protected: |
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| 89 | |
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| 90 | /// \brief Node map for storing path data. |
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| 91 | /// |
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| 92 | /// Node map for storing path data of all nodes in the current |
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| 93 | /// component. dmap[v][k] is the length of a shortest directed walk |
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| 94 | /// to node v from the starting node containing exactly k edges. |
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| 95 | PathVectorNodeMap dmap; |
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| 96 | |
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| 97 | /// \brief The directed graph the algorithm runs on. |
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| 98 | const Graph& graph; |
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| 99 | /// \brief The length of the edges. |
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| 100 | const LengthMap& length; |
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| 101 | |
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| 102 | /// \brief The total length of the found cycle. |
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| 103 | Length cycle_length; |
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| 104 | /// \brief The number of edges in the found cycle. |
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| 105 | int cycle_size; |
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| 106 | /// \brief The found cycle. |
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| 107 | Path *cycle_path; |
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| 108 | /// \brief The found cycle. |
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| 109 | bool local_path; |
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| 110 | |
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| 111 | /// \brief Node map for identifying strongly connected components. |
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| 112 | IntNodeMap comp; |
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| 113 | /// \brief The number of strongly connected components. |
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| 114 | int comp_num; |
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| 115 | /// \brief %Counter for identifying the current component. |
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| 116 | int comp_cnt; |
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| 117 | /// \brief Nodes of the current component. |
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| 118 | NodeVector nodes; |
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| 119 | /// \brief The processed nodes in the last round. |
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| 120 | NodeVector process; |
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| 121 | |
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| 122 | public : |
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| 123 | |
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| 124 | /// \brief The constructor of the class. |
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| 125 | /// |
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| 126 | /// The constructor of the class. |
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| 127 | /// |
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| 128 | /// \param _graph The directed graph the algorithm runs on. |
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| 129 | /// \param _length The length (cost) of the edges. |
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| 130 | MinMeanCycle( const Graph& _graph, |
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| 131 | const LengthMap& _length ) : |
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| 132 | graph(_graph), length(_length), dmap(_graph), |
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| 133 | cycle_length(0), cycle_size(-1), comp(_graph), |
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| 134 | cycle_path(NULL), local_path(false) |
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| 135 | { } |
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| 136 | |
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| 137 | /// \brief The destructor of the class. |
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| 138 | ~MinMeanCycle() { |
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| 139 | if (local_path) delete cycle_path; |
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| 140 | } |
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| 141 | |
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| 142 | protected: |
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| 143 | |
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| 144 | /// \brief Initializes the internal data structures. |
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| 145 | void init() { |
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| 146 | comp_num = stronglyConnectedComponents(graph, comp); |
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| 147 | if (!cycle_path) { |
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| 148 | local_path = true; |
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| 149 | cycle_path = new Path; |
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| 150 | } |
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| 151 | } |
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| 152 | |
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| 153 | /// \brief Initializes the internal data structures for the current |
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| 154 | /// component. |
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| 155 | void initCurrent() { |
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| 156 | nodes.clear(); |
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| 157 | // Finding the nodes of the current component |
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| 158 | for (NodeIt v(graph); v != INVALID; ++v) { |
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| 159 | if (comp[v] == comp_cnt) nodes.push_back(v); |
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| 160 | } |
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| 161 | |
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| 162 | // Creating vectors for all nodes |
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| 163 | int n = nodes.size(); |
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| 164 | for (NodeVectorIt vi = nodes.begin(); vi != nodes.end(); ++vi) { |
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| 165 | dmap[*vi].resize(n + 1); |
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| 166 | } |
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| 167 | } |
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| 168 | |
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| 169 | /// \brief Processes all rounds of computing required path data. |
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| 170 | void processRounds() { |
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| 171 | dmap[nodes[0]][0] = PathData(true, 0); |
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| 172 | process.clear(); |
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| 173 | for (OutEdgeIt oe(graph, nodes[0]); oe != INVALID; ++oe) { |
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| 174 | Node v = graph.target(oe); |
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| 175 | if (comp[v] != comp_cnt || v == nodes[0]) continue; |
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| 176 | dmap[v][1] = PathData(true, length[oe], oe); |
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| 177 | process.push_back(v); |
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| 178 | } |
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| 179 | int n = nodes.size(), k; |
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| 180 | for (k = 2; k <= n && process.size() < n; ++k) { |
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| 181 | processNextBuildRound(k); |
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| 182 | } |
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| 183 | for ( ; k <= n; ++k) { |
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| 184 | processNextFullRound(k); |
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| 185 | } |
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| 186 | } |
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| 187 | |
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| 188 | /// \brief Processes one round of computing required path data and |
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| 189 | /// rebuilds \ref process vector. |
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| 190 | void processNextBuildRound(int k) { |
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| 191 | NodeVector next; |
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| 192 | for (NodeVectorIt ui = process.begin(); ui != process.end(); ++ui) { |
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| 193 | for (OutEdgeIt oe(graph, *ui); oe != INVALID; ++oe) { |
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| 194 | Node v = graph.target(oe); |
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| 195 | if (comp[v] != comp_cnt) continue; |
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| 196 | if ( !dmap[v][k].found || (dmap[v][k].dist > dmap[*ui][k-1].dist + length[oe]) ) { |
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| 197 | if (!dmap[v][k].found) next.push_back(v); |
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| 198 | dmap[v][k] = PathData(true, dmap[*ui][k-1].dist + length[oe], oe); |
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| 199 | } |
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| 200 | } |
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| 201 | } |
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| 202 | process.swap(next); |
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| 203 | } |
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| 204 | |
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| 205 | /// \brief Processes one round of computing required path data |
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| 206 | /// using \ref nodes vector instead of \ref process vector. |
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| 207 | void processNextFullRound(int k) { |
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| 208 | for (NodeVectorIt ui = nodes.begin(); ui != nodes.end(); ++ui) { |
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| 209 | for (OutEdgeIt oe(graph, *ui); oe != INVALID; ++oe) { |
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| 210 | Node v = graph.target(oe); |
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| 211 | if (comp[v] != comp_cnt) continue; |
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| 212 | if ( !dmap[v][k].found || (dmap[v][k].dist > dmap[*ui][k-1].dist + length[oe]) ) { |
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| 213 | dmap[v][k] = PathData(true, dmap[*ui][k-1].dist + length[oe], oe); |
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| 214 | } |
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| 215 | } |
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| 216 | } |
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| 217 | } |
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| 218 | |
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| 219 | /// \brief Finds the minimum cycle mean value according to the path |
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| 220 | /// data stored in \ref dmap. |
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| 221 | /// |
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| 222 | /// Finds the minimum cycle mean value according to the path data |
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| 223 | /// stored in \ref dmap. |
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| 224 | /// |
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| 225 | /// \retval min_length The total length of the found cycle. |
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| 226 | /// \retval min_size The number of edges in the found cycle. |
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| 227 | /// \retval min_node A node for obtaining a critical cycle. |
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| 228 | /// |
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| 229 | /// \return \c true if a cycle exists in the graph. |
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| 230 | bool findMinCycleMean(Length &min_length, int &min_size, Node &min_node) { |
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| 231 | bool found_min = false; |
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| 232 | for (NodeVectorIt vi = nodes.begin(); vi != nodes.end(); ++vi) { |
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| 233 | Length len; |
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| 234 | int size; |
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| 235 | bool found_one = false; |
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| 236 | int n = nodes.size(); |
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| 237 | for (int k = 0; k < n; ++k) { |
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| 238 | Length _len = dmap[*vi][n].dist - dmap[*vi][k].dist; |
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| 239 | int _size = n - k; |
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| 240 | if ( dmap[*vi][n].found && dmap[*vi][k].found && (!found_one || len * _size < _len * size) ) { |
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| 241 | found_one = true; |
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| 242 | len = _len; |
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| 243 | size = _size; |
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| 244 | } |
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| 245 | } |
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| 246 | if (found_one && (!found_min || len * min_size < min_length * size)) { |
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| 247 | found_min = true; |
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| 248 | min_length = len; |
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| 249 | min_size = size; |
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| 250 | min_node = *vi; |
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| 251 | } |
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| 252 | } |
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| 253 | return found_min; |
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| 254 | } |
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| 255 | |
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| 256 | /// \brief Finds a critical (minimum mean) cycle according to the |
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| 257 | /// path data stored in \ref dmap. |
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| 258 | void findCycle(const Node &min_n) { |
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| 259 | IntNodeMap reached(graph, -1); |
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| 260 | int r = reached[min_n] = dmap[min_n].size() - 1; |
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| 261 | Node u = graph.source(dmap[min_n][r].pred); |
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| 262 | while (reached[u] < 0) { |
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| 263 | reached[u] = --r; |
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| 264 | u = graph.source(dmap[u][r].pred); |
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| 265 | } |
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| 266 | r = reached[u]; |
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| 267 | Edge ce = dmap[u][r].pred; |
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| 268 | cycle_path->addFront(ce); |
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| 269 | Node v; |
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| 270 | while ((v = graph.source(ce)) != u) { |
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| 271 | ce = dmap[v][--r].pred; |
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| 272 | cycle_path->addFront(ce); |
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| 273 | } |
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| 274 | } |
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| 275 | |
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| 276 | public: |
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| 277 | |
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| 278 | /// \brief Runs the algorithm. |
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| 279 | /// |
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| 280 | /// Runs the algorithm. |
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| 281 | /// |
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| 282 | /// \return \c true if a cycle exists in the graph. |
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| 283 | bool run() { |
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| 284 | init(); |
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| 285 | // Searching for the minimum mean cycle in all components |
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| 286 | bool found_cycle = false; |
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| 287 | Node cycle_node; |
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| 288 | for (comp_cnt = 0; comp_cnt < comp_num; ++comp_cnt) { |
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| 289 | |
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| 290 | initCurrent(); |
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| 291 | processRounds(); |
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| 292 | |
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| 293 | Length min_length; |
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| 294 | int min_size; |
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| 295 | Node min_node; |
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| 296 | bool found_min = findMinCycleMean(min_length, min_size, min_node); |
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| 297 | |
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| 298 | if ( found_min && (!found_cycle || min_length * cycle_size < cycle_length * min_size) ) { |
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| 299 | found_cycle = true; |
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| 300 | cycle_length = min_length; |
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| 301 | cycle_size = min_size; |
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| 302 | cycle_node = min_node; |
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| 303 | } |
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| 304 | } |
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| 305 | if (found_cycle) findCycle(cycle_node); |
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| 306 | return found_cycle; |
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| 307 | } |
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| 308 | |
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| 309 | /// \brief Returns the total length of the found critical cycle. |
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| 310 | /// |
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| 311 | /// Returns the total length of the found critical cycle. |
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| 312 | /// |
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| 313 | /// \pre \ref run() must be called before using this function. |
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| 314 | Length cycleLength() const { |
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| 315 | return cycle_length; |
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| 316 | } |
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| 317 | |
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| 318 | /// \brief Returns the number of edges in the found critical |
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| 319 | /// cycle. |
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| 320 | /// |
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| 321 | /// Returns the number of edges in the found critical cycle. |
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| 322 | /// |
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| 323 | /// \pre \ref run() must be called before using this function. |
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| 324 | int cycleEdgeNum() const { |
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| 325 | return cycle_size; |
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| 326 | } |
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| 327 | |
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| 328 | /// \brief Returns the mean length of the found critical cycle. |
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| 329 | /// |
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| 330 | /// Returns the mean length of the found critical cycle. |
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| 331 | /// |
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| 332 | /// \pre \ref run() must be called before using this function. |
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| 333 | /// |
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| 334 | /// \warning LengthMap::Value must be convertible to double. |
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| 335 | double minMean() const { |
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| 336 | return (double)cycle_length / (double)cycle_size; |
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| 337 | } |
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| 338 | |
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| 339 | /// \brief Returns a const reference to the \ref lemon::Path "Path" |
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| 340 | /// structure of the found flow. |
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| 341 | /// |
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| 342 | /// Returns a const reference to the \ref lemon::Path "Path" |
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| 343 | /// structure of the found flow. |
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| 344 | /// |
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| 345 | /// \pre \ref run() must be called before using this function. |
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| 346 | /// |
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| 347 | /// \sa \ref cyclePath() |
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| 348 | const Path &cycle() const { |
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| 349 | return *cycle_path; |
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| 350 | } |
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| 351 | |
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| 352 | /// \brief Sets the \ref lemon::Path "Path" structure storing the |
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| 353 | /// found cycle. |
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| 354 | /// |
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| 355 | /// Sets the \ref lemon::Path "Path" structure storing the found |
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| 356 | /// cycle. If you don't use this function before calling |
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| 357 | /// \ref run(), it will allocate one. The destuctor deallocates |
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| 358 | /// this automatically allocated map, of course. |
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| 359 | /// |
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| 360 | /// \note The algorithm calls only the \ref lemon::Path::addFront() |
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| 361 | /// "addFront()" method of the given \ref lemon::Path "Path" |
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| 362 | /// structure. |
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| 363 | /// |
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| 364 | /// \return \c (*this) |
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| 365 | MinMeanCycle &cyclePath(Path& path) { |
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| 366 | if (local_path) { |
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| 367 | delete cycle_path; |
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| 368 | local_path = false; |
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| 369 | } |
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| 370 | cycle_path = &path; |
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| 371 | return *this; |
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| 372 | } |
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| 373 | |
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| 374 | }; //class MinMeanCycle |
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| 375 | |
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| 376 | ///@} |
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| 377 | |
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| 378 | } //namespace lemon |
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| 379 | |
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| 380 | #endif //LEMON_MIN_MEAN_CYCLE_H |
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