[522] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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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[956] | 5 | * Copyright (C) 2003-2010 |
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[522] | 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_COST_ARBORESCENCE_H |
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| 20 | #define LEMON_MIN_COST_ARBORESCENCE_H |
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| 21 | |
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| 22 | ///\ingroup spantree |
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| 23 | ///\file |
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| 24 | ///\brief Minimum Cost Arborescence algorithm. |
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| 25 | |
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| 26 | #include <vector> |
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| 27 | |
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| 28 | #include <lemon/list_graph.h> |
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| 29 | #include <lemon/bin_heap.h> |
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| 30 | #include <lemon/assert.h> |
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| 31 | |
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| 32 | namespace lemon { |
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| 33 | |
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| 34 | |
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| 35 | /// \brief Default traits class for MinCostArborescence class. |
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| 36 | /// |
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| 37 | /// Default traits class for MinCostArborescence class. |
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[606] | 38 | /// \param GR Digraph type. |
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[672] | 39 | /// \param CM Type of the cost map. |
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[606] | 40 | template <class GR, class CM> |
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[522] | 41 | struct MinCostArborescenceDefaultTraits{ |
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| 42 | |
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| 43 | /// \brief The digraph type the algorithm runs on. |
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[606] | 44 | typedef GR Digraph; |
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[522] | 45 | |
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| 46 | /// \brief The type of the map that stores the arc costs. |
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| 47 | /// |
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| 48 | /// The type of the map that stores the arc costs. |
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[672] | 49 | /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
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[606] | 50 | typedef CM CostMap; |
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[522] | 51 | |
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| 52 | /// \brief The value type of the costs. |
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| 53 | /// |
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| 54 | /// The value type of the costs. |
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| 55 | typedef typename CostMap::Value Value; |
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| 56 | |
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| 57 | /// \brief The type of the map that stores which arcs are in the |
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| 58 | /// arborescence. |
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| 59 | /// |
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| 60 | /// The type of the map that stores which arcs are in the |
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[672] | 61 | /// arborescence. It must conform to the \ref concepts::WriteMap |
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| 62 | /// "WriteMap" concept, and its value type must be \c bool |
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| 63 | /// (or convertible). Initially it will be set to \c false on each |
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| 64 | /// arc, then it will be set on each arborescence arc once. |
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[522] | 65 | typedef typename Digraph::template ArcMap<bool> ArborescenceMap; |
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| 66 | |
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[606] | 67 | /// \brief Instantiates a \c ArborescenceMap. |
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[522] | 68 | /// |
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[606] | 69 | /// This function instantiates a \c ArborescenceMap. |
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[672] | 70 | /// \param digraph The digraph to which we would like to calculate |
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| 71 | /// the \c ArborescenceMap. |
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[522] | 72 | static ArborescenceMap *createArborescenceMap(const Digraph &digraph){ |
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| 73 | return new ArborescenceMap(digraph); |
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| 74 | } |
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| 75 | |
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[606] | 76 | /// \brief The type of the \c PredMap |
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[522] | 77 | /// |
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[672] | 78 | /// The type of the \c PredMap. It must confrom to the |
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| 79 | /// \ref concepts::WriteMap "WriteMap" concept, and its value type |
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| 80 | /// must be the \c Arc type of the digraph. |
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[522] | 81 | typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap; |
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| 82 | |
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[606] | 83 | /// \brief Instantiates a \c PredMap. |
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[522] | 84 | /// |
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[606] | 85 | /// This function instantiates a \c PredMap. |
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| 86 | /// \param digraph The digraph to which we would like to define the |
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| 87 | /// \c PredMap. |
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[522] | 88 | static PredMap *createPredMap(const Digraph &digraph){ |
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| 89 | return new PredMap(digraph); |
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| 90 | } |
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| 91 | |
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| 92 | }; |
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| 93 | |
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| 94 | /// \ingroup spantree |
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| 95 | /// |
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[631] | 96 | /// \brief Minimum Cost Arborescence algorithm class. |
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[522] | 97 | /// |
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[672] | 98 | /// This class provides an efficient implementation of the |
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[631] | 99 | /// Minimum Cost Arborescence algorithm. The arborescence is a tree |
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[522] | 100 | /// which is directed from a given source node of the digraph. One or |
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[672] | 101 | /// more sources should be given to the algorithm and it will calculate |
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| 102 | /// the minimum cost subgraph that is the union of arborescences with the |
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[522] | 103 | /// given sources and spans all the nodes which are reachable from the |
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[606] | 104 | /// sources. The time complexity of the algorithm is O(n<sup>2</sup>+e). |
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[522] | 105 | /// |
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[672] | 106 | /// The algorithm also provides an optimal dual solution, therefore |
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[522] | 107 | /// the optimality of the solution can be checked. |
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| 108 | /// |
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[672] | 109 | /// \param GR The digraph type the algorithm runs on. |
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| 110 | /// \param CM A read-only arc map storing the costs of the |
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[522] | 111 | /// arcs. It is read once for each arc, so the map may involve in |
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[672] | 112 | /// relatively time consuming process to compute the arc costs if |
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[522] | 113 | /// it is necessary. The default map type is \ref |
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| 114 | /// concepts::Digraph::ArcMap "Digraph::ArcMap<int>". |
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[891] | 115 | /// \tparam TR The traits class that defines various types used by the |
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| 116 | /// algorithm. By default, it is \ref MinCostArborescenceDefaultTraits |
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[672] | 117 | /// "MinCostArborescenceDefaultTraits<GR, CM>". |
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[891] | 118 | /// In most cases, this parameter should not be set directly, |
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| 119 | /// consider to use the named template parameters instead. |
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[522] | 120 | #ifndef DOXYGEN |
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[672] | 121 | template <typename GR, |
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[606] | 122 | typename CM = typename GR::template ArcMap<int>, |
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| 123 | typename TR = |
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| 124 | MinCostArborescenceDefaultTraits<GR, CM> > |
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[522] | 125 | #else |
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[891] | 126 | template <typename GR, typename CM, typename TR> |
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[522] | 127 | #endif |
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| 128 | class MinCostArborescence { |
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| 129 | public: |
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| 130 | |
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[956] | 131 | /// \brief The \ref MinCostArborescenceDefaultTraits "traits class" |
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| 132 | /// of the algorithm. |
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[606] | 133 | typedef TR Traits; |
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[522] | 134 | /// The type of the underlying digraph. |
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| 135 | typedef typename Traits::Digraph Digraph; |
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| 136 | /// The type of the map that stores the arc costs. |
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| 137 | typedef typename Traits::CostMap CostMap; |
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| 138 | ///The type of the costs of the arcs. |
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| 139 | typedef typename Traits::Value Value; |
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| 140 | ///The type of the predecessor map. |
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| 141 | typedef typename Traits::PredMap PredMap; |
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| 142 | ///The type of the map that stores which arcs are in the arborescence. |
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| 143 | typedef typename Traits::ArborescenceMap ArborescenceMap; |
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| 144 | |
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| 145 | typedef MinCostArborescence Create; |
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| 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 | struct CostArc { |
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| 152 | |
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| 153 | Arc arc; |
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| 154 | Value value; |
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| 155 | |
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| 156 | CostArc() {} |
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| 157 | CostArc(Arc _arc, Value _value) : arc(_arc), value(_value) {} |
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| 158 | |
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| 159 | }; |
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| 160 | |
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| 161 | const Digraph *_digraph; |
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| 162 | const CostMap *_cost; |
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| 163 | |
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| 164 | PredMap *_pred; |
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| 165 | bool local_pred; |
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| 166 | |
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| 167 | ArborescenceMap *_arborescence; |
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| 168 | bool local_arborescence; |
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| 169 | |
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| 170 | typedef typename Digraph::template ArcMap<int> ArcOrder; |
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| 171 | ArcOrder *_arc_order; |
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| 172 | |
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| 173 | typedef typename Digraph::template NodeMap<int> NodeOrder; |
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| 174 | NodeOrder *_node_order; |
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| 175 | |
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| 176 | typedef typename Digraph::template NodeMap<CostArc> CostArcMap; |
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| 177 | CostArcMap *_cost_arcs; |
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| 178 | |
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| 179 | struct StackLevel { |
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| 180 | |
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| 181 | std::vector<CostArc> arcs; |
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| 182 | int node_level; |
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| 183 | |
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| 184 | }; |
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| 185 | |
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| 186 | std::vector<StackLevel> level_stack; |
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| 187 | std::vector<Node> queue; |
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| 188 | |
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| 189 | typedef std::vector<typename Digraph::Node> DualNodeList; |
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| 190 | |
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| 191 | DualNodeList _dual_node_list; |
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| 192 | |
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| 193 | struct DualVariable { |
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| 194 | int begin, end; |
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| 195 | Value value; |
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| 196 | |
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| 197 | DualVariable(int _begin, int _end, Value _value) |
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| 198 | : begin(_begin), end(_end), value(_value) {} |
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| 199 | |
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| 200 | }; |
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| 201 | |
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| 202 | typedef std::vector<DualVariable> DualVariables; |
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| 203 | |
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| 204 | DualVariables _dual_variables; |
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| 205 | |
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| 206 | typedef typename Digraph::template NodeMap<int> HeapCrossRef; |
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| 207 | |
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| 208 | HeapCrossRef *_heap_cross_ref; |
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| 209 | |
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| 210 | typedef BinHeap<int, HeapCrossRef> Heap; |
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| 211 | |
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| 212 | Heap *_heap; |
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| 213 | |
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| 214 | protected: |
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| 215 | |
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| 216 | MinCostArborescence() {} |
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| 217 | |
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| 218 | private: |
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| 219 | |
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| 220 | void createStructures() { |
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| 221 | if (!_pred) { |
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| 222 | local_pred = true; |
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| 223 | _pred = Traits::createPredMap(*_digraph); |
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| 224 | } |
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| 225 | if (!_arborescence) { |
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| 226 | local_arborescence = true; |
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| 227 | _arborescence = Traits::createArborescenceMap(*_digraph); |
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| 228 | } |
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| 229 | if (!_arc_order) { |
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| 230 | _arc_order = new ArcOrder(*_digraph); |
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| 231 | } |
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| 232 | if (!_node_order) { |
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| 233 | _node_order = new NodeOrder(*_digraph); |
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| 234 | } |
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| 235 | if (!_cost_arcs) { |
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| 236 | _cost_arcs = new CostArcMap(*_digraph); |
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| 237 | } |
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| 238 | if (!_heap_cross_ref) { |
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| 239 | _heap_cross_ref = new HeapCrossRef(*_digraph, -1); |
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| 240 | } |
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| 241 | if (!_heap) { |
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| 242 | _heap = new Heap(*_heap_cross_ref); |
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| 243 | } |
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| 244 | } |
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| 245 | |
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| 246 | void destroyStructures() { |
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| 247 | if (local_arborescence) { |
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| 248 | delete _arborescence; |
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| 249 | } |
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| 250 | if (local_pred) { |
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| 251 | delete _pred; |
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| 252 | } |
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| 253 | if (_arc_order) { |
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| 254 | delete _arc_order; |
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| 255 | } |
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| 256 | if (_node_order) { |
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| 257 | delete _node_order; |
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| 258 | } |
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| 259 | if (_cost_arcs) { |
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| 260 | delete _cost_arcs; |
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| 261 | } |
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| 262 | if (_heap) { |
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| 263 | delete _heap; |
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| 264 | } |
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| 265 | if (_heap_cross_ref) { |
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| 266 | delete _heap_cross_ref; |
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| 267 | } |
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| 268 | } |
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| 269 | |
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| 270 | Arc prepare(Node node) { |
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| 271 | std::vector<Node> nodes; |
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| 272 | (*_node_order)[node] = _dual_node_list.size(); |
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| 273 | StackLevel level; |
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| 274 | level.node_level = _dual_node_list.size(); |
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| 275 | _dual_node_list.push_back(node); |
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| 276 | for (InArcIt it(*_digraph, node); it != INVALID; ++it) { |
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| 277 | Arc arc = it; |
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| 278 | Node source = _digraph->source(arc); |
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| 279 | Value value = (*_cost)[it]; |
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| 280 | if (source == node || (*_node_order)[source] == -3) continue; |
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| 281 | if ((*_cost_arcs)[source].arc == INVALID) { |
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| 282 | (*_cost_arcs)[source].arc = arc; |
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| 283 | (*_cost_arcs)[source].value = value; |
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| 284 | nodes.push_back(source); |
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| 285 | } else { |
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| 286 | if ((*_cost_arcs)[source].value > value) { |
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| 287 | (*_cost_arcs)[source].arc = arc; |
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| 288 | (*_cost_arcs)[source].value = value; |
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| 289 | } |
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| 290 | } |
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| 291 | } |
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| 292 | CostArc minimum = (*_cost_arcs)[nodes[0]]; |
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| 293 | for (int i = 1; i < int(nodes.size()); ++i) { |
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| 294 | if ((*_cost_arcs)[nodes[i]].value < minimum.value) { |
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| 295 | minimum = (*_cost_arcs)[nodes[i]]; |
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| 296 | } |
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| 297 | } |
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[628] | 298 | (*_arc_order)[minimum.arc] = _dual_variables.size(); |
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[522] | 299 | DualVariable var(_dual_node_list.size() - 1, |
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| 300 | _dual_node_list.size(), minimum.value); |
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| 301 | _dual_variables.push_back(var); |
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| 302 | for (int i = 0; i < int(nodes.size()); ++i) { |
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| 303 | (*_cost_arcs)[nodes[i]].value -= minimum.value; |
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| 304 | level.arcs.push_back((*_cost_arcs)[nodes[i]]); |
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| 305 | (*_cost_arcs)[nodes[i]].arc = INVALID; |
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| 306 | } |
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| 307 | level_stack.push_back(level); |
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| 308 | return minimum.arc; |
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| 309 | } |
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| 310 | |
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| 311 | Arc contract(Node node) { |
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| 312 | int node_bottom = bottom(node); |
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| 313 | std::vector<Node> nodes; |
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| 314 | while (!level_stack.empty() && |
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| 315 | level_stack.back().node_level >= node_bottom) { |
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| 316 | for (int i = 0; i < int(level_stack.back().arcs.size()); ++i) { |
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| 317 | Arc arc = level_stack.back().arcs[i].arc; |
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| 318 | Node source = _digraph->source(arc); |
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| 319 | Value value = level_stack.back().arcs[i].value; |
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| 320 | if ((*_node_order)[source] >= node_bottom) continue; |
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| 321 | if ((*_cost_arcs)[source].arc == INVALID) { |
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| 322 | (*_cost_arcs)[source].arc = arc; |
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| 323 | (*_cost_arcs)[source].value = value; |
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| 324 | nodes.push_back(source); |
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| 325 | } else { |
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| 326 | if ((*_cost_arcs)[source].value > value) { |
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| 327 | (*_cost_arcs)[source].arc = arc; |
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| 328 | (*_cost_arcs)[source].value = value; |
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| 329 | } |
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| 330 | } |
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| 331 | } |
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| 332 | level_stack.pop_back(); |
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| 333 | } |
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| 334 | CostArc minimum = (*_cost_arcs)[nodes[0]]; |
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| 335 | for (int i = 1; i < int(nodes.size()); ++i) { |
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| 336 | if ((*_cost_arcs)[nodes[i]].value < minimum.value) { |
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| 337 | minimum = (*_cost_arcs)[nodes[i]]; |
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| 338 | } |
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| 339 | } |
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[628] | 340 | (*_arc_order)[minimum.arc] = _dual_variables.size(); |
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[522] | 341 | DualVariable var(node_bottom, _dual_node_list.size(), minimum.value); |
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| 342 | _dual_variables.push_back(var); |
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| 343 | StackLevel level; |
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| 344 | level.node_level = node_bottom; |
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| 345 | for (int i = 0; i < int(nodes.size()); ++i) { |
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| 346 | (*_cost_arcs)[nodes[i]].value -= minimum.value; |
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| 347 | level.arcs.push_back((*_cost_arcs)[nodes[i]]); |
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| 348 | (*_cost_arcs)[nodes[i]].arc = INVALID; |
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| 349 | } |
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| 350 | level_stack.push_back(level); |
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| 351 | return minimum.arc; |
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| 352 | } |
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| 353 | |
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| 354 | int bottom(Node node) { |
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| 355 | int k = level_stack.size() - 1; |
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| 356 | while (level_stack[k].node_level > (*_node_order)[node]) { |
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| 357 | --k; |
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| 358 | } |
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| 359 | return level_stack[k].node_level; |
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| 360 | } |
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| 361 | |
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| 362 | void finalize(Arc arc) { |
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| 363 | Node node = _digraph->target(arc); |
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| 364 | _heap->push(node, (*_arc_order)[arc]); |
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| 365 | _pred->set(node, arc); |
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| 366 | while (!_heap->empty()) { |
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| 367 | Node source = _heap->top(); |
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| 368 | _heap->pop(); |
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[628] | 369 | (*_node_order)[source] = -1; |
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[522] | 370 | for (OutArcIt it(*_digraph, source); it != INVALID; ++it) { |
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| 371 | if ((*_arc_order)[it] < 0) continue; |
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| 372 | Node target = _digraph->target(it); |
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| 373 | switch(_heap->state(target)) { |
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| 374 | case Heap::PRE_HEAP: |
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| 375 | _heap->push(target, (*_arc_order)[it]); |
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| 376 | _pred->set(target, it); |
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| 377 | break; |
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| 378 | case Heap::IN_HEAP: |
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| 379 | if ((*_arc_order)[it] < (*_heap)[target]) { |
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| 380 | _heap->decrease(target, (*_arc_order)[it]); |
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| 381 | _pred->set(target, it); |
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| 382 | } |
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| 383 | break; |
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| 384 | case Heap::POST_HEAP: |
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| 385 | break; |
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| 386 | } |
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| 387 | } |
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| 388 | _arborescence->set((*_pred)[source], true); |
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| 389 | } |
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| 390 | } |
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| 391 | |
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| 392 | |
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| 393 | public: |
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| 394 | |
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[631] | 395 | /// \name Named Template Parameters |
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[522] | 396 | |
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| 397 | /// @{ |
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| 398 | |
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| 399 | template <class T> |
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[672] | 400 | struct SetArborescenceMapTraits : public Traits { |
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[522] | 401 | typedef T ArborescenceMap; |
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| 402 | static ArborescenceMap *createArborescenceMap(const Digraph &) |
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| 403 | { |
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| 404 | LEMON_ASSERT(false, "ArborescenceMap is not initialized"); |
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| 405 | return 0; // ignore warnings |
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| 406 | } |
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| 407 | }; |
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| 408 | |
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| 409 | /// \brief \ref named-templ-param "Named parameter" for |
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[672] | 410 | /// setting \c ArborescenceMap type |
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[522] | 411 | /// |
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| 412 | /// \ref named-templ-param "Named parameter" for setting |
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[672] | 413 | /// \c ArborescenceMap type. |
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| 414 | /// It must conform to the \ref concepts::WriteMap "WriteMap" concept, |
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| 415 | /// and its value type must be \c bool (or convertible). |
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| 416 | /// Initially it will be set to \c false on each arc, |
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| 417 | /// then it will be set on each arborescence arc once. |
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[522] | 418 | template <class T> |
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[672] | 419 | struct SetArborescenceMap |
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[522] | 420 | : public MinCostArborescence<Digraph, CostMap, |
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[672] | 421 | SetArborescenceMapTraits<T> > { |
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[522] | 422 | }; |
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| 423 | |
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| 424 | template <class T> |
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[672] | 425 | struct SetPredMapTraits : public Traits { |
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[522] | 426 | typedef T PredMap; |
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| 427 | static PredMap *createPredMap(const Digraph &) |
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| 428 | { |
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| 429 | LEMON_ASSERT(false, "PredMap is not initialized"); |
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[672] | 430 | return 0; // ignore warnings |
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[522] | 431 | } |
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| 432 | }; |
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| 433 | |
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| 434 | /// \brief \ref named-templ-param "Named parameter" for |
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[672] | 435 | /// setting \c PredMap type |
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[522] | 436 | /// |
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| 437 | /// \ref named-templ-param "Named parameter" for setting |
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[672] | 438 | /// \c PredMap type. |
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[956] | 439 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept, |
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[672] | 440 | /// and its value type must be the \c Arc type of the digraph. |
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[522] | 441 | template <class T> |
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[672] | 442 | struct SetPredMap |
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| 443 | : public MinCostArborescence<Digraph, CostMap, SetPredMapTraits<T> > { |
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[522] | 444 | }; |
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| 445 | |
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| 446 | /// @} |
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| 447 | |
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| 448 | /// \brief Constructor. |
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| 449 | /// |
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[606] | 450 | /// \param digraph The digraph the algorithm will run on. |
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| 451 | /// \param cost The cost map used by the algorithm. |
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[522] | 452 | MinCostArborescence(const Digraph& digraph, const CostMap& cost) |
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| 453 | : _digraph(&digraph), _cost(&cost), _pred(0), local_pred(false), |
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| 454 | _arborescence(0), local_arborescence(false), |
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| 455 | _arc_order(0), _node_order(0), _cost_arcs(0), |
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| 456 | _heap_cross_ref(0), _heap(0) {} |
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| 457 | |
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| 458 | /// \brief Destructor. |
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| 459 | ~MinCostArborescence() { |
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| 460 | destroyStructures(); |
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| 461 | } |
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| 462 | |
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| 463 | /// \brief Sets the arborescence map. |
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| 464 | /// |
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| 465 | /// Sets the arborescence map. |
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[606] | 466 | /// \return <tt>(*this)</tt> |
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[522] | 467 | MinCostArborescence& arborescenceMap(ArborescenceMap& m) { |
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| 468 | if (local_arborescence) { |
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| 469 | delete _arborescence; |
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| 470 | } |
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| 471 | local_arborescence = false; |
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| 472 | _arborescence = &m; |
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| 473 | return *this; |
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| 474 | } |
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| 475 | |
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[672] | 476 | /// \brief Sets the predecessor map. |
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[522] | 477 | /// |
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[672] | 478 | /// Sets the predecessor map. |
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[606] | 479 | /// \return <tt>(*this)</tt> |
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[522] | 480 | MinCostArborescence& predMap(PredMap& m) { |
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| 481 | if (local_pred) { |
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| 482 | delete _pred; |
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| 483 | } |
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| 484 | local_pred = false; |
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| 485 | _pred = &m; |
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| 486 | return *this; |
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| 487 | } |
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| 488 | |
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[631] | 489 | /// \name Execution Control |
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[522] | 490 | /// The simplest way to execute the algorithm is to use |
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| 491 | /// one of the member functions called \c run(...). \n |
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[760] | 492 | /// If you need better control on the execution, |
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| 493 | /// you have to call \ref init() first, then you can add several |
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[522] | 494 | /// source nodes with \ref addSource(). |
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| 495 | /// Finally \ref start() will perform the arborescence |
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| 496 | /// computation. |
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| 497 | |
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| 498 | ///@{ |
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| 499 | |
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| 500 | /// \brief Initializes the internal data structures. |
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| 501 | /// |
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| 502 | /// Initializes the internal data structures. |
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| 503 | /// |
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| 504 | void init() { |
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| 505 | createStructures(); |
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| 506 | _heap->clear(); |
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| 507 | for (NodeIt it(*_digraph); it != INVALID; ++it) { |
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| 508 | (*_cost_arcs)[it].arc = INVALID; |
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[628] | 509 | (*_node_order)[it] = -3; |
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| 510 | (*_heap_cross_ref)[it] = Heap::PRE_HEAP; |
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[522] | 511 | _pred->set(it, INVALID); |
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| 512 | } |
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| 513 | for (ArcIt it(*_digraph); it != INVALID; ++it) { |
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| 514 | _arborescence->set(it, false); |
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[628] | 515 | (*_arc_order)[it] = -1; |
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[522] | 516 | } |
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| 517 | _dual_node_list.clear(); |
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| 518 | _dual_variables.clear(); |
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| 519 | } |
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| 520 | |
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| 521 | /// \brief Adds a new source node. |
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| 522 | /// |
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| 523 | /// Adds a new source node to the algorithm. |
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| 524 | void addSource(Node source) { |
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| 525 | std::vector<Node> nodes; |
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| 526 | nodes.push_back(source); |
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| 527 | while (!nodes.empty()) { |
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| 528 | Node node = nodes.back(); |
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| 529 | nodes.pop_back(); |
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| 530 | for (OutArcIt it(*_digraph, node); it != INVALID; ++it) { |
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| 531 | Node target = _digraph->target(it); |
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| 532 | if ((*_node_order)[target] == -3) { |
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| 533 | (*_node_order)[target] = -2; |
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| 534 | nodes.push_back(target); |
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| 535 | queue.push_back(target); |
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| 536 | } |
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| 537 | } |
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| 538 | } |
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| 539 | (*_node_order)[source] = -1; |
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| 540 | } |
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| 541 | |
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| 542 | /// \brief Processes the next node in the priority queue. |
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| 543 | /// |
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| 544 | /// Processes the next node in the priority queue. |
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| 545 | /// |
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| 546 | /// \return The processed node. |
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| 547 | /// |
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[672] | 548 | /// \warning The queue must not be empty. |
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[522] | 549 | Node processNextNode() { |
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| 550 | Node node = queue.back(); |
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| 551 | queue.pop_back(); |
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| 552 | if ((*_node_order)[node] == -2) { |
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| 553 | Arc arc = prepare(node); |
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| 554 | Node source = _digraph->source(arc); |
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| 555 | while ((*_node_order)[source] != -1) { |
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| 556 | if ((*_node_order)[source] >= 0) { |
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| 557 | arc = contract(source); |
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| 558 | } else { |
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| 559 | arc = prepare(source); |
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| 560 | } |
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| 561 | source = _digraph->source(arc); |
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| 562 | } |
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| 563 | finalize(arc); |
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| 564 | level_stack.clear(); |
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| 565 | } |
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| 566 | return node; |
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| 567 | } |
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| 568 | |
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| 569 | /// \brief Returns the number of the nodes to be processed. |
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| 570 | /// |
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[672] | 571 | /// Returns the number of the nodes to be processed in the priority |
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| 572 | /// queue. |
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[522] | 573 | int queueSize() const { |
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| 574 | return queue.size(); |
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| 575 | } |
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| 576 | |
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| 577 | /// \brief Returns \c false if there are nodes to be processed. |
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| 578 | /// |
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| 579 | /// Returns \c false if there are nodes to be processed. |
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| 580 | bool emptyQueue() const { |
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| 581 | return queue.empty(); |
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| 582 | } |
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| 583 | |
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| 584 | /// \brief Executes the algorithm. |
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| 585 | /// |
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| 586 | /// Executes the algorithm. |
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| 587 | /// |
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| 588 | /// \pre init() must be called and at least one node should be added |
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| 589 | /// with addSource() before using this function. |
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| 590 | /// |
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| 591 | ///\note mca.start() is just a shortcut of the following code. |
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| 592 | ///\code |
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| 593 | ///while (!mca.emptyQueue()) { |
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| 594 | /// mca.processNextNode(); |
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| 595 | ///} |
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| 596 | ///\endcode |
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| 597 | void start() { |
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| 598 | while (!emptyQueue()) { |
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| 599 | processNextNode(); |
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| 600 | } |
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| 601 | } |
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| 602 | |
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| 603 | /// \brief Runs %MinCostArborescence algorithm from node \c s. |
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| 604 | /// |
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| 605 | /// This method runs the %MinCostArborescence algorithm from |
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| 606 | /// a root node \c s. |
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| 607 | /// |
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| 608 | /// \note mca.run(s) is just a shortcut of the following code. |
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| 609 | /// \code |
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| 610 | /// mca.init(); |
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| 611 | /// mca.addSource(s); |
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| 612 | /// mca.start(); |
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| 613 | /// \endcode |
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[672] | 614 | void run(Node s) { |
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[522] | 615 | init(); |
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[672] | 616 | addSource(s); |
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[522] | 617 | start(); |
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| 618 | } |
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| 619 | |
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| 620 | ///@} |
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| 621 | |
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[672] | 622 | /// \name Query Functions |
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| 623 | /// The result of the %MinCostArborescence algorithm can be obtained |
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| 624 | /// using these functions.\n |
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| 625 | /// Either run() or start() must be called before using them. |
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| 626 | |
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| 627 | /// @{ |
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| 628 | |
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| 629 | /// \brief Returns the cost of the arborescence. |
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| 630 | /// |
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| 631 | /// Returns the cost of the arborescence. |
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| 632 | Value arborescenceCost() const { |
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| 633 | Value sum = 0; |
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| 634 | for (ArcIt it(*_digraph); it != INVALID; ++it) { |
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| 635 | if (arborescence(it)) { |
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| 636 | sum += (*_cost)[it]; |
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| 637 | } |
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| 638 | } |
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| 639 | return sum; |
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| 640 | } |
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| 641 | |
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| 642 | /// \brief Returns \c true if the arc is in the arborescence. |
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| 643 | /// |
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| 644 | /// Returns \c true if the given arc is in the arborescence. |
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| 645 | /// \param arc An arc of the digraph. |
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| 646 | /// \pre \ref run() must be called before using this function. |
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| 647 | bool arborescence(Arc arc) const { |
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| 648 | return (*_pred)[_digraph->target(arc)] == arc; |
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| 649 | } |
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| 650 | |
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| 651 | /// \brief Returns a const reference to the arborescence map. |
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| 652 | /// |
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| 653 | /// Returns a const reference to the arborescence map. |
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| 654 | /// \pre \ref run() must be called before using this function. |
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| 655 | const ArborescenceMap& arborescenceMap() const { |
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| 656 | return *_arborescence; |
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| 657 | } |
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| 658 | |
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| 659 | /// \brief Returns the predecessor arc of the given node. |
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| 660 | /// |
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| 661 | /// Returns the predecessor arc of the given node. |
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| 662 | /// \pre \ref run() must be called before using this function. |
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| 663 | Arc pred(Node node) const { |
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| 664 | return (*_pred)[node]; |
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| 665 | } |
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| 666 | |
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| 667 | /// \brief Returns a const reference to the pred map. |
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| 668 | /// |
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| 669 | /// Returns a const reference to the pred map. |
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| 670 | /// \pre \ref run() must be called before using this function. |
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| 671 | const PredMap& predMap() const { |
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| 672 | return *_pred; |
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| 673 | } |
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| 674 | |
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| 675 | /// \brief Indicates that a node is reachable from the sources. |
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| 676 | /// |
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| 677 | /// Indicates that a node is reachable from the sources. |
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| 678 | bool reached(Node node) const { |
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| 679 | return (*_node_order)[node] != -3; |
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| 680 | } |
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| 681 | |
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| 682 | /// \brief Indicates that a node is processed. |
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| 683 | /// |
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| 684 | /// Indicates that a node is processed. The arborescence path exists |
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| 685 | /// from the source to the given node. |
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| 686 | bool processed(Node node) const { |
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| 687 | return (*_node_order)[node] == -1; |
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| 688 | } |
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| 689 | |
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| 690 | /// \brief Returns the number of the dual variables in basis. |
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| 691 | /// |
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| 692 | /// Returns the number of the dual variables in basis. |
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| 693 | int dualNum() const { |
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| 694 | return _dual_variables.size(); |
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| 695 | } |
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| 696 | |
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| 697 | /// \brief Returns the value of the dual solution. |
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| 698 | /// |
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| 699 | /// Returns the value of the dual solution. It should be |
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| 700 | /// equal to the arborescence value. |
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| 701 | Value dualValue() const { |
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| 702 | Value sum = 0; |
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| 703 | for (int i = 0; i < int(_dual_variables.size()); ++i) { |
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| 704 | sum += _dual_variables[i].value; |
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| 705 | } |
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| 706 | return sum; |
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| 707 | } |
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| 708 | |
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| 709 | /// \brief Returns the number of the nodes in the dual variable. |
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| 710 | /// |
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| 711 | /// Returns the number of the nodes in the dual variable. |
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| 712 | int dualSize(int k) const { |
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| 713 | return _dual_variables[k].end - _dual_variables[k].begin; |
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| 714 | } |
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| 715 | |
---|
| 716 | /// \brief Returns the value of the dual variable. |
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| 717 | /// |
---|
| 718 | /// Returns the the value of the dual variable. |
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| 719 | Value dualValue(int k) const { |
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| 720 | return _dual_variables[k].value; |
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| 721 | } |
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| 722 | |
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| 723 | /// \brief LEMON iterator for getting a dual variable. |
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| 724 | /// |
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| 725 | /// This class provides a common style LEMON iterator for getting a |
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| 726 | /// dual variable of \ref MinCostArborescence algorithm. |
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| 727 | /// It iterates over a subset of the nodes. |
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| 728 | class DualIt { |
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| 729 | public: |
---|
| 730 | |
---|
| 731 | /// \brief Constructor. |
---|
| 732 | /// |
---|
| 733 | /// Constructor for getting the nodeset of the dual variable |
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| 734 | /// of \ref MinCostArborescence algorithm. |
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| 735 | DualIt(const MinCostArborescence& algorithm, int variable) |
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| 736 | : _algorithm(&algorithm) |
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| 737 | { |
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| 738 | _index = _algorithm->_dual_variables[variable].begin; |
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| 739 | _last = _algorithm->_dual_variables[variable].end; |
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| 740 | } |
---|
| 741 | |
---|
| 742 | /// \brief Conversion to \c Node. |
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| 743 | /// |
---|
| 744 | /// Conversion to \c Node. |
---|
| 745 | operator Node() const { |
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| 746 | return _algorithm->_dual_node_list[_index]; |
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| 747 | } |
---|
| 748 | |
---|
| 749 | /// \brief Increment operator. |
---|
| 750 | /// |
---|
| 751 | /// Increment operator. |
---|
| 752 | DualIt& operator++() { |
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| 753 | ++_index; |
---|
| 754 | return *this; |
---|
| 755 | } |
---|
| 756 | |
---|
| 757 | /// \brief Validity checking |
---|
| 758 | /// |
---|
| 759 | /// Checks whether the iterator is invalid. |
---|
| 760 | bool operator==(Invalid) const { |
---|
| 761 | return _index == _last; |
---|
| 762 | } |
---|
| 763 | |
---|
| 764 | /// \brief Validity checking |
---|
| 765 | /// |
---|
| 766 | /// Checks whether the iterator is valid. |
---|
| 767 | bool operator!=(Invalid) const { |
---|
| 768 | return _index != _last; |
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| 769 | } |
---|
| 770 | |
---|
| 771 | private: |
---|
| 772 | const MinCostArborescence* _algorithm; |
---|
| 773 | int _index, _last; |
---|
| 774 | }; |
---|
| 775 | |
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| 776 | /// @} |
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| 777 | |
---|
[522] | 778 | }; |
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| 779 | |
---|
| 780 | /// \ingroup spantree |
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| 781 | /// |
---|
| 782 | /// \brief Function type interface for MinCostArborescence algorithm. |
---|
| 783 | /// |
---|
| 784 | /// Function type interface for MinCostArborescence algorithm. |
---|
[672] | 785 | /// \param digraph The digraph the algorithm runs on. |
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| 786 | /// \param cost An arc map storing the costs. |
---|
| 787 | /// \param source The source node of the arborescence. |
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| 788 | /// \retval arborescence An arc map with \c bool (or convertible) value |
---|
| 789 | /// type that stores the arborescence. |
---|
| 790 | /// \return The total cost of the arborescence. |
---|
[522] | 791 | /// |
---|
| 792 | /// \sa MinCostArborescence |
---|
| 793 | template <typename Digraph, typename CostMap, typename ArborescenceMap> |
---|
| 794 | typename CostMap::Value minCostArborescence(const Digraph& digraph, |
---|
| 795 | const CostMap& cost, |
---|
| 796 | typename Digraph::Node source, |
---|
| 797 | ArborescenceMap& arborescence) { |
---|
| 798 | typename MinCostArborescence<Digraph, CostMap> |
---|
[672] | 799 | ::template SetArborescenceMap<ArborescenceMap> |
---|
[522] | 800 | ::Create mca(digraph, cost); |
---|
| 801 | mca.arborescenceMap(arborescence); |
---|
| 802 | mca.run(source); |
---|
[672] | 803 | return mca.arborescenceCost(); |
---|
[522] | 804 | } |
---|
| 805 | |
---|
| 806 | } |
---|
| 807 | |
---|
| 808 | #endif |
---|