[805] | 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) 2003-2008 |
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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 shortest_path |
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| 23 | /// |
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| 24 | /// \file |
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| 25 | /// \brief Howard's algorithm for finding a minimum mean cycle. |
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| 26 | |
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| 27 | #include <vector> |
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| 28 | #include <lemon/core.h> |
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| 29 | #include <lemon/path.h> |
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| 30 | #include <lemon/tolerance.h> |
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| 31 | #include <lemon/connectivity.h> |
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| 32 | |
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| 33 | namespace lemon { |
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| 34 | |
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| 35 | /// \addtogroup shortest_path |
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| 36 | /// @{ |
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| 37 | |
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| 38 | /// \brief Implementation of Howard's algorithm for finding a minimum |
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| 39 | /// mean cycle. |
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| 40 | /// |
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| 41 | /// \ref MinMeanCycle implements Howard's algorithm for finding a |
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| 42 | /// directed cycle of minimum mean length (cost) in a digraph. |
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| 43 | /// |
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| 44 | /// \tparam GR The type of the digraph the algorithm runs on. |
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| 45 | /// \tparam LEN The type of the length map. The default |
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| 46 | /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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| 47 | /// |
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| 48 | /// \warning \c LEN::Value must be convertible to \c double. |
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| 49 | #ifdef DOXYGEN |
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| 50 | template <typename GR, typename LEN> |
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| 51 | #else |
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| 52 | template < typename GR, |
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| 53 | typename LEN = typename GR::template ArcMap<int> > |
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| 54 | #endif |
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| 55 | class MinMeanCycle |
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| 56 | { |
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| 57 | public: |
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| 58 | |
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| 59 | /// The type of the digraph the algorithm runs on |
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| 60 | typedef GR Digraph; |
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| 61 | /// The type of the length map |
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| 62 | typedef LEN LengthMap; |
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| 63 | /// The type of the arc lengths |
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| 64 | typedef typename LengthMap::Value Value; |
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| 65 | /// The type of the paths |
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| 66 | typedef lemon::Path<Digraph> Path; |
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| 67 | |
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| 68 | private: |
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| 69 | |
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| 70 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 71 | |
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| 72 | // The digraph the algorithm runs on |
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| 73 | const Digraph &_gr; |
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| 74 | // The length of the arcs |
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| 75 | const LengthMap &_length; |
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| 76 | |
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[807] | 77 | // Data for the found cycles |
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| 78 | bool _curr_found, _best_found; |
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| 79 | Value _curr_length, _best_length; |
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| 80 | int _curr_size, _best_size; |
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| 81 | Node _curr_node, _best_node; |
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| 82 | |
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[805] | 83 | Path *_cycle_path; |
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[807] | 84 | bool _local_path; |
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[805] | 85 | |
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[807] | 86 | // Internal data used by the algorithm |
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| 87 | typename Digraph::template NodeMap<Arc> _policy; |
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| 88 | typename Digraph::template NodeMap<bool> _reached; |
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| 89 | typename Digraph::template NodeMap<int> _level; |
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| 90 | typename Digraph::template NodeMap<double> _dist; |
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[805] | 91 | |
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[807] | 92 | // Data for storing the strongly connected components |
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| 93 | int _comp_num; |
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[805] | 94 | typename Digraph::template NodeMap<int> _comp; |
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[807] | 95 | std::vector<std::vector<Node> > _comp_nodes; |
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| 96 | std::vector<Node>* _nodes; |
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| 97 | typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs; |
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| 98 | |
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| 99 | // Queue used for BFS search |
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| 100 | std::vector<Node> _queue; |
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| 101 | int _qfront, _qback; |
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| 102 | |
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[805] | 103 | Tolerance<double> _tol; |
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| 104 | |
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| 105 | public: |
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| 106 | |
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| 107 | /// \brief Constructor. |
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| 108 | /// |
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| 109 | /// The constructor of the class. |
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| 110 | /// |
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| 111 | /// \param digraph The digraph the algorithm runs on. |
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| 112 | /// \param length The lengths (costs) of the arcs. |
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| 113 | MinMeanCycle( const Digraph &digraph, |
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| 114 | const LengthMap &length ) : |
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[807] | 115 | _gr(digraph), _length(length), _cycle_path(NULL), _local_path(false), |
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| 116 | _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph), |
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| 117 | _comp(digraph), _in_arcs(digraph) |
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[805] | 118 | {} |
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| 119 | |
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| 120 | /// Destructor. |
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| 121 | ~MinMeanCycle() { |
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| 122 | if (_local_path) delete _cycle_path; |
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| 123 | } |
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| 124 | |
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| 125 | /// \brief Set the path structure for storing the found cycle. |
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| 126 | /// |
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| 127 | /// This function sets an external path structure for storing the |
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| 128 | /// found cycle. |
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| 129 | /// |
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| 130 | /// If you don't call this function before calling \ref run() or |
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[806] | 131 | /// \ref findMinMean(), it will allocate a local \ref Path "path" |
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[805] | 132 | /// structure. The destuctor deallocates this automatically |
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| 133 | /// allocated object, of course. |
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| 134 | /// |
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| 135 | /// \note The algorithm calls only the \ref lemon::Path::addBack() |
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| 136 | /// "addBack()" function of the given path structure. |
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| 137 | /// |
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| 138 | /// \return <tt>(*this)</tt> |
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| 139 | /// |
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| 140 | /// \sa cycle() |
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| 141 | MinMeanCycle& cyclePath(Path &path) { |
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| 142 | if (_local_path) { |
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| 143 | delete _cycle_path; |
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| 144 | _local_path = false; |
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| 145 | } |
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| 146 | _cycle_path = &path; |
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| 147 | return *this; |
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| 148 | } |
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| 149 | |
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| 150 | /// \name Execution control |
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| 151 | /// The simplest way to execute the algorithm is to call the \ref run() |
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| 152 | /// function.\n |
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[806] | 153 | /// If you only need the minimum mean length, you may call |
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| 154 | /// \ref findMinMean(). |
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[805] | 155 | |
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| 156 | /// @{ |
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| 157 | |
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| 158 | /// \brief Run the algorithm. |
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| 159 | /// |
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| 160 | /// This function runs the algorithm. |
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[806] | 161 | /// It can be called more than once (e.g. if the underlying digraph |
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| 162 | /// and/or the arc lengths have been modified). |
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[805] | 163 | /// |
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| 164 | /// \return \c true if a directed cycle exists in the digraph. |
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| 165 | /// |
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[806] | 166 | /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
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[805] | 167 | /// \code |
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[806] | 168 | /// return mmc.findMinMean() && mmc.findCycle(); |
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[805] | 169 | /// \endcode |
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| 170 | bool run() { |
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| 171 | return findMinMean() && findCycle(); |
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| 172 | } |
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| 173 | |
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[806] | 174 | /// \brief Find the minimum cycle mean. |
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[805] | 175 | /// |
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[806] | 176 | /// This function finds the minimum mean length of the directed |
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| 177 | /// cycles in the digraph. |
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[805] | 178 | /// |
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[806] | 179 | /// \return \c true if a directed cycle exists in the digraph. |
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| 180 | bool findMinMean() { |
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[807] | 181 | // Initialize and find strongly connected components |
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| 182 | init(); |
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| 183 | findComponents(); |
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| 184 | |
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[806] | 185 | // Find the minimum cycle mean in the components |
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[805] | 186 | for (int comp = 0; comp < _comp_num; ++comp) { |
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[807] | 187 | // Find the minimum mean cycle in the current component |
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| 188 | if (!buildPolicyGraph(comp)) continue; |
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[805] | 189 | while (true) { |
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[807] | 190 | findPolicyCycle(); |
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[805] | 191 | if (!computeNodeDistances()) break; |
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| 192 | } |
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[807] | 193 | // Update the best cycle (global minimum mean cycle) |
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| 194 | if ( !_best_found || (_curr_found && |
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| 195 | _curr_length * _best_size < _best_length * _curr_size) ) { |
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| 196 | _best_found = true; |
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| 197 | _best_length = _curr_length; |
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| 198 | _best_size = _curr_size; |
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| 199 | _best_node = _curr_node; |
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| 200 | } |
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[805] | 201 | } |
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[807] | 202 | return _best_found; |
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[805] | 203 | } |
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| 204 | |
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| 205 | /// \brief Find a minimum mean directed cycle. |
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| 206 | /// |
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| 207 | /// This function finds a directed cycle of minimum mean length |
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| 208 | /// in the digraph using the data computed by findMinMean(). |
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| 209 | /// |
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| 210 | /// \return \c true if a directed cycle exists in the digraph. |
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| 211 | /// |
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[806] | 212 | /// \pre \ref findMinMean() must be called before using this function. |
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[805] | 213 | bool findCycle() { |
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[807] | 214 | if (!_best_found) return false; |
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| 215 | _cycle_path->addBack(_policy[_best_node]); |
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| 216 | for ( Node v = _best_node; |
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| 217 | (v = _gr.target(_policy[v])) != _best_node; ) { |
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[805] | 218 | _cycle_path->addBack(_policy[v]); |
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| 219 | } |
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| 220 | return true; |
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| 221 | } |
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| 222 | |
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| 223 | /// @} |
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| 224 | |
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| 225 | /// \name Query Functions |
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[806] | 226 | /// The results of the algorithm can be obtained using these |
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[805] | 227 | /// functions.\n |
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| 228 | /// The algorithm should be executed before using them. |
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| 229 | |
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| 230 | /// @{ |
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| 231 | |
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| 232 | /// \brief Return the total length of the found cycle. |
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| 233 | /// |
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| 234 | /// This function returns the total length of the found cycle. |
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| 235 | /// |
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[807] | 236 | /// \pre \ref run() or \ref findMinMean() must be called before |
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[805] | 237 | /// using this function. |
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| 238 | Value cycleLength() const { |
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[807] | 239 | return _best_length; |
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[805] | 240 | } |
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| 241 | |
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| 242 | /// \brief Return the number of arcs on the found cycle. |
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| 243 | /// |
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| 244 | /// This function returns the number of arcs on the found cycle. |
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| 245 | /// |
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[807] | 246 | /// \pre \ref run() or \ref findMinMean() must be called before |
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[805] | 247 | /// using this function. |
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| 248 | int cycleArcNum() const { |
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[807] | 249 | return _best_size; |
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[805] | 250 | } |
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| 251 | |
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| 252 | /// \brief Return the mean length of the found cycle. |
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| 253 | /// |
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| 254 | /// This function returns the mean length of the found cycle. |
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| 255 | /// |
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[807] | 256 | /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the |
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[805] | 257 | /// following code. |
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| 258 | /// \code |
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[807] | 259 | /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum(); |
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[805] | 260 | /// \endcode |
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| 261 | /// |
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| 262 | /// \pre \ref run() or \ref findMinMean() must be called before |
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| 263 | /// using this function. |
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| 264 | double cycleMean() const { |
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[807] | 265 | return static_cast<double>(_best_length) / _best_size; |
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[805] | 266 | } |
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| 267 | |
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| 268 | /// \brief Return the found cycle. |
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| 269 | /// |
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| 270 | /// This function returns a const reference to the path structure |
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| 271 | /// storing the found cycle. |
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| 272 | /// |
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| 273 | /// \pre \ref run() or \ref findCycle() must be called before using |
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| 274 | /// this function. |
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| 275 | /// |
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| 276 | /// \sa cyclePath() |
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| 277 | const Path& cycle() const { |
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| 278 | return *_cycle_path; |
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| 279 | } |
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| 280 | |
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| 281 | ///@} |
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| 282 | |
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| 283 | private: |
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| 284 | |
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[807] | 285 | // Initialize |
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| 286 | void init() { |
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| 287 | _tol.epsilon(1e-6); |
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| 288 | if (!_cycle_path) { |
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| 289 | _local_path = true; |
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| 290 | _cycle_path = new Path; |
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[805] | 291 | } |
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[807] | 292 | _queue.resize(countNodes(_gr)); |
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| 293 | _best_found = false; |
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| 294 | _best_length = 0; |
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| 295 | _best_size = 1; |
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| 296 | _cycle_path->clear(); |
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| 297 | } |
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| 298 | |
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| 299 | // Find strongly connected components and initialize _comp_nodes |
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| 300 | // and _in_arcs |
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| 301 | void findComponents() { |
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| 302 | _comp_num = stronglyConnectedComponents(_gr, _comp); |
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| 303 | _comp_nodes.resize(_comp_num); |
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| 304 | if (_comp_num == 1) { |
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| 305 | _comp_nodes[0].clear(); |
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| 306 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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| 307 | _comp_nodes[0].push_back(n); |
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| 308 | _in_arcs[n].clear(); |
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| 309 | for (InArcIt a(_gr, n); a != INVALID; ++a) { |
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| 310 | _in_arcs[n].push_back(a); |
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| 311 | } |
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| 312 | } |
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| 313 | } else { |
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| 314 | for (int i = 0; i < _comp_num; ++i) |
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| 315 | _comp_nodes[i].clear(); |
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| 316 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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| 317 | int k = _comp[n]; |
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| 318 | _comp_nodes[k].push_back(n); |
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| 319 | _in_arcs[n].clear(); |
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| 320 | for (InArcIt a(_gr, n); a != INVALID; ++a) { |
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| 321 | if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a); |
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| 322 | } |
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| 323 | } |
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[805] | 324 | } |
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[807] | 325 | } |
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| 326 | |
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| 327 | // Build the policy graph in the given strongly connected component |
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| 328 | // (the out-degree of every node is 1) |
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| 329 | bool buildPolicyGraph(int comp) { |
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| 330 | _nodes = &(_comp_nodes[comp]); |
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| 331 | if (_nodes->size() < 1 || |
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| 332 | (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) { |
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| 333 | return false; |
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[805] | 334 | } |
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[807] | 335 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 336 | _dist[(*_nodes)[i]] = std::numeric_limits<double>::max(); |
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| 337 | } |
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| 338 | Node u, v; |
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| 339 | Arc e; |
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| 340 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 341 | v = (*_nodes)[i]; |
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| 342 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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| 343 | e = _in_arcs[v][j]; |
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| 344 | u = _gr.source(e); |
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| 345 | if (_length[e] < _dist[u]) { |
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| 346 | _dist[u] = _length[e]; |
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| 347 | _policy[u] = e; |
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| 348 | } |
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[805] | 349 | } |
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| 350 | } |
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| 351 | return true; |
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| 352 | } |
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| 353 | |
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[807] | 354 | // Find the minimum mean cycle in the policy graph |
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| 355 | void findPolicyCycle() { |
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| 356 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 357 | _level[(*_nodes)[i]] = -1; |
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| 358 | } |
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[805] | 359 | Value clength; |
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| 360 | int csize; |
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| 361 | Node u, v; |
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[807] | 362 | _curr_found = false; |
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| 363 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 364 | u = (*_nodes)[i]; |
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| 365 | if (_level[u] >= 0) continue; |
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| 366 | for (; _level[u] < 0; u = _gr.target(_policy[u])) { |
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| 367 | _level[u] = i; |
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| 368 | } |
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| 369 | if (_level[u] == i) { |
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| 370 | // A cycle is found |
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| 371 | clength = _length[_policy[u]]; |
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| 372 | csize = 1; |
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| 373 | for (v = u; (v = _gr.target(_policy[v])) != u; ) { |
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| 374 | clength += _length[_policy[v]]; |
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| 375 | ++csize; |
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[805] | 376 | } |
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[807] | 377 | if ( !_curr_found || |
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| 378 | (clength * _curr_size < _curr_length * csize) ) { |
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| 379 | _curr_found = true; |
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| 380 | _curr_length = clength; |
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| 381 | _curr_size = csize; |
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| 382 | _curr_node = u; |
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[805] | 383 | } |
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| 384 | } |
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| 385 | } |
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| 386 | } |
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| 387 | |
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[807] | 388 | // Contract the policy graph and compute node distances |
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[805] | 389 | bool computeNodeDistances() { |
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[807] | 390 | // Find the component of the main cycle and compute node distances |
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| 391 | // using reverse BFS |
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| 392 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 393 | _reached[(*_nodes)[i]] = false; |
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| 394 | } |
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| 395 | double curr_mean = double(_curr_length) / _curr_size; |
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| 396 | _qfront = _qback = 0; |
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| 397 | _queue[0] = _curr_node; |
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| 398 | _reached[_curr_node] = true; |
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| 399 | _dist[_curr_node] = 0; |
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[805] | 400 | Node u, v; |
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[807] | 401 | Arc e; |
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| 402 | while (_qfront <= _qback) { |
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| 403 | v = _queue[_qfront++]; |
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| 404 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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| 405 | e = _in_arcs[v][j]; |
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[805] | 406 | u = _gr.source(e); |
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[807] | 407 | if (_policy[u] == e && !_reached[u]) { |
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| 408 | _reached[u] = true; |
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| 409 | _dist[u] = _dist[v] + _length[e] - curr_mean; |
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| 410 | _queue[++_qback] = u; |
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[805] | 411 | } |
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| 412 | } |
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| 413 | } |
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[807] | 414 | |
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| 415 | // Connect all other nodes to this component and compute node |
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| 416 | // distances using reverse BFS |
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| 417 | _qfront = 0; |
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| 418 | while (_qback < int(_nodes->size())-1) { |
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| 419 | v = _queue[_qfront++]; |
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| 420 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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| 421 | e = _in_arcs[v][j]; |
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| 422 | u = _gr.source(e); |
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| 423 | if (!_reached[u]) { |
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| 424 | _reached[u] = true; |
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| 425 | _policy[u] = e; |
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| 426 | _dist[u] = _dist[v] + _length[e] - curr_mean; |
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| 427 | _queue[++_qback] = u; |
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| 428 | } |
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| 429 | } |
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| 430 | } |
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| 431 | |
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| 432 | // Improve node distances |
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[805] | 433 | bool improved = false; |
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[807] | 434 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 435 | v = (*_nodes)[i]; |
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| 436 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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| 437 | e = _in_arcs[v][j]; |
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| 438 | u = _gr.source(e); |
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| 439 | double delta = _dist[v] + _length[e] - curr_mean; |
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| 440 | if (_tol.less(delta, _dist[u])) { |
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| 441 | _dist[u] = delta; |
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| 442 | _policy[u] = e; |
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| 443 | improved = true; |
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| 444 | } |
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[805] | 445 | } |
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| 446 | } |
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| 447 | return improved; |
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| 448 | } |
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| 449 | |
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| 450 | }; //class MinMeanCycle |
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| 451 | |
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| 452 | ///@} |
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| 453 | |
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| 454 | } //namespace lemon |
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| 455 | |
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| 456 | #endif //LEMON_MIN_MEAN_CYCLE_H |
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