[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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[811] | 19 | #ifndef LEMON_HOWARD_H |
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| 20 | #define LEMON_HOWARD_H |
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[805] | 21 | |
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[815] | 22 | /// \ingroup min_mean_cycle |
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[805] | 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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[810] | 28 | #include <limits> |
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[805] | 29 | #include <lemon/core.h> |
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| 30 | #include <lemon/path.h> |
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| 31 | #include <lemon/tolerance.h> |
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| 32 | #include <lemon/connectivity.h> |
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| 33 | |
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| 34 | namespace lemon { |
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| 35 | |
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[811] | 36 | /// \brief Default traits class of Howard class. |
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[808] | 37 | /// |
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[811] | 38 | /// Default traits class of Howard class. |
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[808] | 39 | /// \tparam GR The type of the digraph. |
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| 40 | /// \tparam LEN The type of the length map. |
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| 41 | /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
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| 42 | #ifdef DOXYGEN |
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| 43 | template <typename GR, typename LEN> |
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| 44 | #else |
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| 45 | template <typename GR, typename LEN, |
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| 46 | bool integer = std::numeric_limits<typename LEN::Value>::is_integer> |
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| 47 | #endif |
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[811] | 48 | struct HowardDefaultTraits |
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[808] | 49 | { |
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| 50 | /// The type of the digraph |
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| 51 | typedef GR Digraph; |
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| 52 | /// The type of the length map |
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| 53 | typedef LEN LengthMap; |
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| 54 | /// The type of the arc lengths |
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| 55 | typedef typename LengthMap::Value Value; |
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| 56 | |
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| 57 | /// \brief The large value type used for internal computations |
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| 58 | /// |
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| 59 | /// The large value type used for internal computations. |
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| 60 | /// It is \c long \c long if the \c Value type is integer, |
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| 61 | /// otherwise it is \c double. |
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| 62 | /// \c Value must be convertible to \c LargeValue. |
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| 63 | typedef double LargeValue; |
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| 64 | |
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| 65 | /// The tolerance type used for internal computations |
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| 66 | typedef lemon::Tolerance<LargeValue> Tolerance; |
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| 67 | |
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| 68 | /// \brief The path type of the found cycles |
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| 69 | /// |
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| 70 | /// The path type of the found cycles. |
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| 71 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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| 72 | /// and it must have an \c addBack() function. |
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| 73 | typedef lemon::Path<Digraph> Path; |
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| 74 | }; |
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| 75 | |
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| 76 | // Default traits class for integer value types |
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| 77 | template <typename GR, typename LEN> |
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[811] | 78 | struct HowardDefaultTraits<GR, LEN, true> |
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[808] | 79 | { |
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| 80 | typedef GR Digraph; |
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| 81 | typedef LEN LengthMap; |
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| 82 | typedef typename LengthMap::Value Value; |
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| 83 | #ifdef LEMON_HAVE_LONG_LONG |
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| 84 | typedef long long LargeValue; |
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| 85 | #else |
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| 86 | typedef long LargeValue; |
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| 87 | #endif |
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| 88 | typedef lemon::Tolerance<LargeValue> Tolerance; |
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| 89 | typedef lemon::Path<Digraph> Path; |
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| 90 | }; |
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| 91 | |
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| 92 | |
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[815] | 93 | /// \addtogroup min_mean_cycle |
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[805] | 94 | /// @{ |
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| 95 | |
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| 96 | /// \brief Implementation of Howard's algorithm for finding a minimum |
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| 97 | /// mean cycle. |
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| 98 | /// |
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[811] | 99 | /// This class implements Howard's policy iteration algorithm for finding |
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| 100 | /// a directed cycle of minimum mean length (cost) in a digraph. |
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[815] | 101 | /// This class provides the most efficient algorithm for the |
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| 102 | /// minimum mean cycle problem, though the best known theoretical |
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| 103 | /// bound on its running time is exponential. |
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[805] | 104 | /// |
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| 105 | /// \tparam GR The type of the digraph the algorithm runs on. |
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| 106 | /// \tparam LEN The type of the length map. The default |
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| 107 | /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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| 108 | #ifdef DOXYGEN |
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[808] | 109 | template <typename GR, typename LEN, typename TR> |
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[805] | 110 | #else |
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| 111 | template < typename GR, |
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[808] | 112 | typename LEN = typename GR::template ArcMap<int>, |
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[811] | 113 | typename TR = HowardDefaultTraits<GR, LEN> > |
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[805] | 114 | #endif |
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[811] | 115 | class Howard |
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[805] | 116 | { |
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| 117 | public: |
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| 118 | |
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[808] | 119 | /// The type of the digraph |
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| 120 | typedef typename TR::Digraph Digraph; |
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[805] | 121 | /// The type of the length map |
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[808] | 122 | typedef typename TR::LengthMap LengthMap; |
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[805] | 123 | /// The type of the arc lengths |
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[808] | 124 | typedef typename TR::Value Value; |
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| 125 | |
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| 126 | /// \brief The large value type |
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| 127 | /// |
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| 128 | /// The large value type used for internal computations. |
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[811] | 129 | /// Using the \ref HowardDefaultTraits "default traits class", |
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[808] | 130 | /// it is \c long \c long if the \c Value type is integer, |
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| 131 | /// otherwise it is \c double. |
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| 132 | typedef typename TR::LargeValue LargeValue; |
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| 133 | |
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| 134 | /// The tolerance type |
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| 135 | typedef typename TR::Tolerance Tolerance; |
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| 136 | |
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| 137 | /// \brief The path type of the found cycles |
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| 138 | /// |
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| 139 | /// The path type of the found cycles. |
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[811] | 140 | /// Using the \ref HowardDefaultTraits "default traits class", |
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[808] | 141 | /// it is \ref lemon::Path "Path<Digraph>". |
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| 142 | typedef typename TR::Path Path; |
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| 143 | |
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[811] | 144 | /// The \ref HowardDefaultTraits "traits class" of the algorithm |
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[808] | 145 | typedef TR Traits; |
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[805] | 146 | |
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| 147 | private: |
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| 148 | |
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| 149 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 150 | |
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| 151 | // The digraph the algorithm runs on |
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| 152 | const Digraph &_gr; |
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| 153 | // The length of the arcs |
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| 154 | const LengthMap &_length; |
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| 155 | |
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[807] | 156 | // Data for the found cycles |
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| 157 | bool _curr_found, _best_found; |
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[808] | 158 | LargeValue _curr_length, _best_length; |
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[807] | 159 | int _curr_size, _best_size; |
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| 160 | Node _curr_node, _best_node; |
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| 161 | |
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[805] | 162 | Path *_cycle_path; |
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[807] | 163 | bool _local_path; |
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[805] | 164 | |
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[807] | 165 | // Internal data used by the algorithm |
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| 166 | typename Digraph::template NodeMap<Arc> _policy; |
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| 167 | typename Digraph::template NodeMap<bool> _reached; |
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| 168 | typename Digraph::template NodeMap<int> _level; |
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[808] | 169 | typename Digraph::template NodeMap<LargeValue> _dist; |
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[805] | 170 | |
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[807] | 171 | // Data for storing the strongly connected components |
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| 172 | int _comp_num; |
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[805] | 173 | typename Digraph::template NodeMap<int> _comp; |
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[807] | 174 | std::vector<std::vector<Node> > _comp_nodes; |
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| 175 | std::vector<Node>* _nodes; |
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| 176 | typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs; |
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| 177 | |
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| 178 | // Queue used for BFS search |
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| 179 | std::vector<Node> _queue; |
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| 180 | int _qfront, _qback; |
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[808] | 181 | |
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| 182 | Tolerance _tolerance; |
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| 183 | |
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[814] | 184 | // Infinite constant |
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| 185 | const LargeValue INF; |
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| 186 | |
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[808] | 187 | public: |
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| 188 | |
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| 189 | /// \name Named Template Parameters |
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| 190 | /// @{ |
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| 191 | |
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| 192 | template <typename T> |
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| 193 | struct SetLargeValueTraits : public Traits { |
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| 194 | typedef T LargeValue; |
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| 195 | typedef lemon::Tolerance<T> Tolerance; |
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| 196 | }; |
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| 197 | |
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| 198 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 199 | /// \c LargeValue type. |
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| 200 | /// |
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| 201 | /// \ref named-templ-param "Named parameter" for setting \c LargeValue |
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| 202 | /// type. It is used for internal computations in the algorithm. |
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| 203 | template <typename T> |
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| 204 | struct SetLargeValue |
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[811] | 205 | : public Howard<GR, LEN, SetLargeValueTraits<T> > { |
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| 206 | typedef Howard<GR, LEN, SetLargeValueTraits<T> > Create; |
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[808] | 207 | }; |
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| 208 | |
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| 209 | template <typename T> |
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| 210 | struct SetPathTraits : public Traits { |
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| 211 | typedef T Path; |
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| 212 | }; |
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| 213 | |
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| 214 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 215 | /// \c %Path type. |
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| 216 | /// |
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| 217 | /// \ref named-templ-param "Named parameter" for setting the \c %Path |
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| 218 | /// type of the found cycles. |
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| 219 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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| 220 | /// and it must have an \c addBack() function. |
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| 221 | template <typename T> |
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| 222 | struct SetPath |
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[811] | 223 | : public Howard<GR, LEN, SetPathTraits<T> > { |
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| 224 | typedef Howard<GR, LEN, SetPathTraits<T> > Create; |
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[808] | 225 | }; |
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[807] | 226 | |
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[808] | 227 | /// @} |
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[805] | 228 | |
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| 229 | public: |
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| 230 | |
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| 231 | /// \brief Constructor. |
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| 232 | /// |
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| 233 | /// The constructor of the class. |
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| 234 | /// |
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| 235 | /// \param digraph The digraph the algorithm runs on. |
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| 236 | /// \param length The lengths (costs) of the arcs. |
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[811] | 237 | Howard( const Digraph &digraph, |
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| 238 | const LengthMap &length ) : |
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[814] | 239 | _gr(digraph), _length(length), _best_found(false), |
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| 240 | _best_length(0), _best_size(1), _cycle_path(NULL), _local_path(false), |
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[807] | 241 | _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph), |
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[814] | 242 | _comp(digraph), _in_arcs(digraph), |
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| 243 | INF(std::numeric_limits<LargeValue>::has_infinity ? |
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| 244 | std::numeric_limits<LargeValue>::infinity() : |
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| 245 | std::numeric_limits<LargeValue>::max()) |
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[805] | 246 | {} |
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| 247 | |
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| 248 | /// Destructor. |
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[811] | 249 | ~Howard() { |
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[805] | 250 | if (_local_path) delete _cycle_path; |
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| 251 | } |
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| 252 | |
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| 253 | /// \brief Set the path structure for storing the found cycle. |
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| 254 | /// |
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| 255 | /// This function sets an external path structure for storing the |
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| 256 | /// found cycle. |
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| 257 | /// |
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| 258 | /// If you don't call this function before calling \ref run() or |
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[806] | 259 | /// \ref findMinMean(), it will allocate a local \ref Path "path" |
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[805] | 260 | /// structure. The destuctor deallocates this automatically |
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| 261 | /// allocated object, of course. |
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| 262 | /// |
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| 263 | /// \note The algorithm calls only the \ref lemon::Path::addBack() |
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| 264 | /// "addBack()" function of the given path structure. |
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| 265 | /// |
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| 266 | /// \return <tt>(*this)</tt> |
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[811] | 267 | Howard& cycle(Path &path) { |
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[805] | 268 | if (_local_path) { |
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| 269 | delete _cycle_path; |
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| 270 | _local_path = false; |
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| 271 | } |
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| 272 | _cycle_path = &path; |
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| 273 | return *this; |
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| 274 | } |
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| 275 | |
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| 276 | /// \name Execution control |
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| 277 | /// The simplest way to execute the algorithm is to call the \ref run() |
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| 278 | /// function.\n |
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[806] | 279 | /// If you only need the minimum mean length, you may call |
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| 280 | /// \ref findMinMean(). |
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[805] | 281 | |
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| 282 | /// @{ |
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| 283 | |
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| 284 | /// \brief Run the algorithm. |
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| 285 | /// |
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| 286 | /// This function runs the algorithm. |
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[806] | 287 | /// It can be called more than once (e.g. if the underlying digraph |
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| 288 | /// and/or the arc lengths have been modified). |
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[805] | 289 | /// |
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| 290 | /// \return \c true if a directed cycle exists in the digraph. |
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| 291 | /// |
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[806] | 292 | /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
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[805] | 293 | /// \code |
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[806] | 294 | /// return mmc.findMinMean() && mmc.findCycle(); |
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[805] | 295 | /// \endcode |
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| 296 | bool run() { |
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| 297 | return findMinMean() && findCycle(); |
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| 298 | } |
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| 299 | |
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[806] | 300 | /// \brief Find the minimum cycle mean. |
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[805] | 301 | /// |
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[806] | 302 | /// This function finds the minimum mean length of the directed |
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| 303 | /// cycles in the digraph. |
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[805] | 304 | /// |
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[806] | 305 | /// \return \c true if a directed cycle exists in the digraph. |
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| 306 | bool findMinMean() { |
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[807] | 307 | // Initialize and find strongly connected components |
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| 308 | init(); |
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| 309 | findComponents(); |
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| 310 | |
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[806] | 311 | // Find the minimum cycle mean in the components |
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[805] | 312 | for (int comp = 0; comp < _comp_num; ++comp) { |
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[807] | 313 | // Find the minimum mean cycle in the current component |
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| 314 | if (!buildPolicyGraph(comp)) continue; |
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[805] | 315 | while (true) { |
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[807] | 316 | findPolicyCycle(); |
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[805] | 317 | if (!computeNodeDistances()) break; |
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| 318 | } |
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[807] | 319 | // Update the best cycle (global minimum mean cycle) |
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[814] | 320 | if ( _curr_found && (!_best_found || |
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[807] | 321 | _curr_length * _best_size < _best_length * _curr_size) ) { |
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| 322 | _best_found = true; |
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| 323 | _best_length = _curr_length; |
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| 324 | _best_size = _curr_size; |
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| 325 | _best_node = _curr_node; |
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| 326 | } |
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[805] | 327 | } |
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[807] | 328 | return _best_found; |
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[805] | 329 | } |
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| 330 | |
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| 331 | /// \brief Find a minimum mean directed cycle. |
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| 332 | /// |
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| 333 | /// This function finds a directed cycle of minimum mean length |
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| 334 | /// in the digraph using the data computed by findMinMean(). |
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| 335 | /// |
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| 336 | /// \return \c true if a directed cycle exists in the digraph. |
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| 337 | /// |
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[806] | 338 | /// \pre \ref findMinMean() must be called before using this function. |
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[805] | 339 | bool findCycle() { |
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[807] | 340 | if (!_best_found) return false; |
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| 341 | _cycle_path->addBack(_policy[_best_node]); |
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| 342 | for ( Node v = _best_node; |
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| 343 | (v = _gr.target(_policy[v])) != _best_node; ) { |
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[805] | 344 | _cycle_path->addBack(_policy[v]); |
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| 345 | } |
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| 346 | return true; |
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| 347 | } |
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| 348 | |
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| 349 | /// @} |
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| 350 | |
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| 351 | /// \name Query Functions |
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[806] | 352 | /// The results of the algorithm can be obtained using these |
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[805] | 353 | /// functions.\n |
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| 354 | /// The algorithm should be executed before using them. |
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| 355 | |
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| 356 | /// @{ |
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| 357 | |
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| 358 | /// \brief Return the total length of the found cycle. |
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| 359 | /// |
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| 360 | /// This function returns the total length of the found cycle. |
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| 361 | /// |
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[807] | 362 | /// \pre \ref run() or \ref findMinMean() must be called before |
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[805] | 363 | /// using this function. |
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[808] | 364 | LargeValue cycleLength() const { |
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[807] | 365 | return _best_length; |
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[805] | 366 | } |
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| 367 | |
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| 368 | /// \brief Return the number of arcs on the found cycle. |
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| 369 | /// |
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| 370 | /// This function returns the number of arcs on the found cycle. |
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| 371 | /// |
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[807] | 372 | /// \pre \ref run() or \ref findMinMean() must be called before |
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[805] | 373 | /// using this function. |
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| 374 | int cycleArcNum() const { |
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[807] | 375 | return _best_size; |
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[805] | 376 | } |
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| 377 | |
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| 378 | /// \brief Return the mean length of the found cycle. |
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| 379 | /// |
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| 380 | /// This function returns the mean length of the found cycle. |
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| 381 | /// |
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[807] | 382 | /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the |
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[805] | 383 | /// following code. |
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| 384 | /// \code |
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[807] | 385 | /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum(); |
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[805] | 386 | /// \endcode |
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| 387 | /// |
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| 388 | /// \pre \ref run() or \ref findMinMean() must be called before |
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| 389 | /// using this function. |
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| 390 | double cycleMean() const { |
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[807] | 391 | return static_cast<double>(_best_length) / _best_size; |
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[805] | 392 | } |
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| 393 | |
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| 394 | /// \brief Return the found cycle. |
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| 395 | /// |
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| 396 | /// This function returns a const reference to the path structure |
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| 397 | /// storing the found cycle. |
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| 398 | /// |
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| 399 | /// \pre \ref run() or \ref findCycle() must be called before using |
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| 400 | /// this function. |
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| 401 | const Path& cycle() const { |
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| 402 | return *_cycle_path; |
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| 403 | } |
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| 404 | |
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| 405 | ///@} |
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| 406 | |
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| 407 | private: |
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| 408 | |
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[807] | 409 | // Initialize |
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| 410 | void init() { |
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| 411 | if (!_cycle_path) { |
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| 412 | _local_path = true; |
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| 413 | _cycle_path = new Path; |
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[805] | 414 | } |
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[807] | 415 | _queue.resize(countNodes(_gr)); |
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| 416 | _best_found = false; |
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| 417 | _best_length = 0; |
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| 418 | _best_size = 1; |
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| 419 | _cycle_path->clear(); |
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| 420 | } |
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| 421 | |
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| 422 | // Find strongly connected components and initialize _comp_nodes |
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| 423 | // and _in_arcs |
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| 424 | void findComponents() { |
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| 425 | _comp_num = stronglyConnectedComponents(_gr, _comp); |
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| 426 | _comp_nodes.resize(_comp_num); |
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| 427 | if (_comp_num == 1) { |
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| 428 | _comp_nodes[0].clear(); |
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| 429 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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| 430 | _comp_nodes[0].push_back(n); |
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| 431 | _in_arcs[n].clear(); |
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| 432 | for (InArcIt a(_gr, n); a != INVALID; ++a) { |
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| 433 | _in_arcs[n].push_back(a); |
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| 434 | } |
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| 435 | } |
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| 436 | } else { |
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| 437 | for (int i = 0; i < _comp_num; ++i) |
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| 438 | _comp_nodes[i].clear(); |
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| 439 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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| 440 | int k = _comp[n]; |
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| 441 | _comp_nodes[k].push_back(n); |
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| 442 | _in_arcs[n].clear(); |
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| 443 | for (InArcIt a(_gr, n); a != INVALID; ++a) { |
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| 444 | if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a); |
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| 445 | } |
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| 446 | } |
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[805] | 447 | } |
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[807] | 448 | } |
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| 449 | |
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| 450 | // Build the policy graph in the given strongly connected component |
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| 451 | // (the out-degree of every node is 1) |
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| 452 | bool buildPolicyGraph(int comp) { |
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| 453 | _nodes = &(_comp_nodes[comp]); |
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| 454 | if (_nodes->size() < 1 || |
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| 455 | (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) { |
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| 456 | return false; |
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[805] | 457 | } |
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[807] | 458 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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[814] | 459 | _dist[(*_nodes)[i]] = INF; |
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[807] | 460 | } |
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| 461 | Node u, v; |
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| 462 | Arc e; |
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| 463 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 464 | v = (*_nodes)[i]; |
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| 465 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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| 466 | e = _in_arcs[v][j]; |
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| 467 | u = _gr.source(e); |
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| 468 | if (_length[e] < _dist[u]) { |
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| 469 | _dist[u] = _length[e]; |
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| 470 | _policy[u] = e; |
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| 471 | } |
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[805] | 472 | } |
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| 473 | } |
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| 474 | return true; |
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| 475 | } |
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| 476 | |
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[807] | 477 | // Find the minimum mean cycle in the policy graph |
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| 478 | void findPolicyCycle() { |
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| 479 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 480 | _level[(*_nodes)[i]] = -1; |
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| 481 | } |
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[808] | 482 | LargeValue clength; |
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[805] | 483 | int csize; |
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| 484 | Node u, v; |
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[807] | 485 | _curr_found = false; |
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| 486 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 487 | u = (*_nodes)[i]; |
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| 488 | if (_level[u] >= 0) continue; |
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| 489 | for (; _level[u] < 0; u = _gr.target(_policy[u])) { |
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| 490 | _level[u] = i; |
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| 491 | } |
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| 492 | if (_level[u] == i) { |
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| 493 | // A cycle is found |
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| 494 | clength = _length[_policy[u]]; |
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| 495 | csize = 1; |
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| 496 | for (v = u; (v = _gr.target(_policy[v])) != u; ) { |
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| 497 | clength += _length[_policy[v]]; |
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| 498 | ++csize; |
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[805] | 499 | } |
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[807] | 500 | if ( !_curr_found || |
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| 501 | (clength * _curr_size < _curr_length * csize) ) { |
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| 502 | _curr_found = true; |
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| 503 | _curr_length = clength; |
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| 504 | _curr_size = csize; |
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| 505 | _curr_node = u; |
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[805] | 506 | } |
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| 507 | } |
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| 508 | } |
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| 509 | } |
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| 510 | |
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[807] | 511 | // Contract the policy graph and compute node distances |
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[805] | 512 | bool computeNodeDistances() { |
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[807] | 513 | // Find the component of the main cycle and compute node distances |
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| 514 | // using reverse BFS |
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| 515 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 516 | _reached[(*_nodes)[i]] = false; |
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| 517 | } |
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| 518 | _qfront = _qback = 0; |
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| 519 | _queue[0] = _curr_node; |
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| 520 | _reached[_curr_node] = true; |
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| 521 | _dist[_curr_node] = 0; |
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[805] | 522 | Node u, v; |
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[807] | 523 | Arc e; |
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| 524 | while (_qfront <= _qback) { |
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| 525 | v = _queue[_qfront++]; |
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| 526 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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| 527 | e = _in_arcs[v][j]; |
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[805] | 528 | u = _gr.source(e); |
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[807] | 529 | if (_policy[u] == e && !_reached[u]) { |
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| 530 | _reached[u] = true; |
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[808] | 531 | _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length; |
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[807] | 532 | _queue[++_qback] = u; |
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[805] | 533 | } |
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| 534 | } |
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| 535 | } |
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[807] | 536 | |
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| 537 | // Connect all other nodes to this component and compute node |
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| 538 | // distances using reverse BFS |
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| 539 | _qfront = 0; |
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| 540 | while (_qback < int(_nodes->size())-1) { |
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| 541 | v = _queue[_qfront++]; |
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| 542 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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| 543 | e = _in_arcs[v][j]; |
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| 544 | u = _gr.source(e); |
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| 545 | if (!_reached[u]) { |
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| 546 | _reached[u] = true; |
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| 547 | _policy[u] = e; |
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[808] | 548 | _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length; |
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[807] | 549 | _queue[++_qback] = u; |
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| 550 | } |
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| 551 | } |
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| 552 | } |
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| 553 | |
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| 554 | // Improve node distances |
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[805] | 555 | bool improved = false; |
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[807] | 556 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 557 | v = (*_nodes)[i]; |
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| 558 | for (int j = 0; j < int(_in_arcs[v].size()); ++j) { |
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| 559 | e = _in_arcs[v][j]; |
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| 560 | u = _gr.source(e); |
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[808] | 561 | LargeValue delta = _dist[v] + _length[e] * _curr_size - _curr_length; |
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| 562 | if (_tolerance.less(delta, _dist[u])) { |
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[807] | 563 | _dist[u] = delta; |
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| 564 | _policy[u] = e; |
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| 565 | improved = true; |
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| 566 | } |
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[805] | 567 | } |
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| 568 | } |
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| 569 | return improved; |
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| 570 | } |
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| 571 | |
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[811] | 572 | }; //class Howard |
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[805] | 573 | |
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| 574 | ///@} |
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| 575 | |
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| 576 | } //namespace lemon |
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| 577 | |
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[811] | 578 | #endif //LEMON_HOWARD_H |
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