[2514] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2007 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_GOLDBERG_TARJAN_H |
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| 20 | #define LEMON_GOLDBERG_TARJAN_H |
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| 21 | |
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| 22 | #include <vector> |
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| 23 | #include <queue> |
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| 24 | |
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| 25 | #include <lemon/error.h> |
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| 26 | #include <lemon/bits/invalid.h> |
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| 27 | #include <lemon/tolerance.h> |
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| 28 | #include <lemon/maps.h> |
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| 29 | #include <lemon/graph_utils.h> |
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| 30 | #include <lemon/dynamic_tree.h> |
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| 31 | #include <limits> |
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| 32 | |
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| 33 | /// \file |
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| 34 | /// \ingroup max_flow |
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| 35 | /// \brief Implementation of the preflow algorithm. |
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| 36 | |
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| 37 | namespace lemon { |
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| 38 | |
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| 39 | /// \brief Default traits class of GoldbergTarjan class. |
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| 40 | /// |
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| 41 | /// Default traits class of GoldbergTarjan class. |
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| 42 | /// \param _Graph Graph type. |
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| 43 | /// \param _CapacityMap Type of capacity map. |
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| 44 | template <typename _Graph, typename _CapacityMap> |
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| 45 | struct GoldbergTarjanDefaultTraits { |
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| 46 | |
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| 47 | /// \brief The graph type the algorithm runs on. |
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| 48 | typedef _Graph Graph; |
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| 49 | |
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| 50 | /// \brief The type of the map that stores the edge capacities. |
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| 51 | /// |
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| 52 | /// The type of the map that stores the edge capacities. |
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| 53 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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| 54 | typedef _CapacityMap CapacityMap; |
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| 55 | |
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| 56 | /// \brief The type of the length of the edges. |
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| 57 | typedef typename CapacityMap::Value Value; |
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| 58 | |
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| 59 | /// \brief The map type that stores the flow values. |
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| 60 | /// |
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| 61 | /// The map type that stores the flow values. |
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| 62 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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| 63 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
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| 64 | |
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| 65 | /// \brief Instantiates a FlowMap. |
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| 66 | /// |
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| 67 | /// This function instantiates a \ref FlowMap. |
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| 68 | /// \param graph The graph, to which we would like to define the flow map. |
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| 69 | static FlowMap* createFlowMap(const Graph& graph) { |
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| 70 | return new FlowMap(graph); |
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| 71 | } |
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| 72 | |
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| 73 | /// \brief The eleavator type used by GoldbergTarjan algorithm. |
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| 74 | /// |
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| 75 | /// The elevator type used by GoldbergTarjan algorithm. |
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| 76 | /// |
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| 77 | /// \sa Elevator |
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| 78 | /// \sa LinkedElevator |
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| 79 | typedef LinkedElevator<Graph, typename Graph::Node> Elevator; |
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| 80 | |
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| 81 | /// \brief Instantiates an Elevator. |
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| 82 | /// |
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| 83 | /// This function instantiates a \ref Elevator. |
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| 84 | /// \param graph The graph, to which we would like to define the elevator. |
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| 85 | /// \param max_level The maximum level of the elevator. |
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| 86 | static Elevator* createElevator(const Graph& graph, int max_level) { |
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| 87 | return new Elevator(graph, max_level); |
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| 88 | } |
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| 89 | |
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| 90 | /// \brief The tolerance used by the algorithm |
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| 91 | /// |
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| 92 | /// The tolerance used by the algorithm to handle inexact computation. |
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| 93 | typedef Tolerance<Value> Tolerance; |
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| 94 | |
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| 95 | }; |
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| 96 | |
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| 97 | /// \ingroup max_flow |
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| 98 | /// \brief Goldberg-Tarjan algorithms class. |
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| 99 | /// |
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| 100 | /// This class provides an implementation of the \e GoldbergTarjan |
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| 101 | /// \e algorithm producing a flow of maximum value in a directed |
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| 102 | /// graph. The GoldbergTarjan algorithm is a theoretical improvement |
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| 103 | /// of the Goldberg's \ref Preflow "preflow" algorithm by using the \ref |
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| 104 | /// DynamicTree "dynamic tree" data structure of Sleator and Tarjan. |
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| 105 | /// |
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| 106 | /// The original preflow algorithm with \e "highest label" or \e |
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| 107 | /// FIFO heuristic has \f$O(n^3)\f$ time complexity. The current |
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| 108 | /// algorithm improved this complexity to |
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| 109 | /// \f$O(nm\log(\frac{n^2}{m}))\f$. The algorithm builds limited |
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| 110 | /// size dynamic trees on the residual graph, which can be used to |
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| 111 | /// make multilevel push operations and gives a better bound on the |
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| 112 | /// number of non-saturating pushes. |
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| 113 | /// |
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| 114 | /// \param Graph The directed graph type the algorithm runs on. |
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| 115 | /// \param CapacityMap The capacity map type. |
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| 116 | /// \param _Traits Traits class to set various data types used by |
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| 117 | /// the algorithm. The default traits class is \ref |
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| 118 | /// GoldbergTarjanDefaultTraits. See \ref |
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| 119 | /// GoldbergTarjanDefaultTraits for the documentation of a |
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| 120 | /// Goldberg-Tarjan traits class. |
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| 121 | /// |
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| 122 | /// \author Tamas Hamori and Balazs Dezso |
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| 123 | #ifdef DOXYGEN |
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| 124 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
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| 125 | #else |
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| 126 | template <typename _Graph, |
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| 127 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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| 128 | typename _Traits = |
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| 129 | GoldbergTarjanDefaultTraits<_Graph, _CapacityMap> > |
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| 130 | #endif |
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| 131 | class GoldbergTarjan { |
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| 132 | public: |
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| 133 | |
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| 134 | typedef _Traits Traits; |
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| 135 | typedef typename Traits::Graph Graph; |
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| 136 | typedef typename Traits::CapacityMap CapacityMap; |
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| 137 | typedef typename Traits::Value Value; |
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| 138 | |
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| 139 | typedef typename Traits::FlowMap FlowMap; |
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| 140 | typedef typename Traits::Elevator Elevator; |
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| 141 | typedef typename Traits::Tolerance Tolerance; |
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| 142 | |
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| 143 | protected: |
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| 144 | |
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| 145 | GRAPH_TYPEDEFS(typename Graph); |
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| 146 | |
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| 147 | typedef typename Graph::template NodeMap<Node> NodeNodeMap; |
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| 148 | typedef typename Graph::template NodeMap<int> IntNodeMap; |
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| 149 | |
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| 150 | typedef typename Graph::template NodeMap<Edge> EdgeNodeMap; |
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| 151 | typedef typename Graph::template EdgeMap<Edge> EdgeEdgeMap; |
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| 152 | |
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| 153 | typedef typename std::vector<Node> VecNode; |
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| 154 | |
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| 155 | typedef DynamicTree<Value,IntNodeMap,Tolerance> DynTree; |
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| 156 | |
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| 157 | const Graph& _graph; |
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| 158 | const CapacityMap* _capacity; |
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| 159 | int _node_num; //the number of nodes of G |
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| 160 | |
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| 161 | Node _source; |
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| 162 | Node _target; |
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| 163 | |
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| 164 | FlowMap* _flow; |
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| 165 | bool _local_flow; |
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| 166 | |
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| 167 | Elevator* _level; |
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| 168 | bool _local_level; |
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| 169 | |
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| 170 | typedef typename Graph::template NodeMap<Value> ExcessMap; |
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| 171 | ExcessMap* _excess; |
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| 172 | |
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| 173 | Tolerance _tolerance; |
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| 174 | |
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| 175 | bool _phase; |
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| 176 | |
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| 177 | // constant for treesize |
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| 178 | static const double _tree_bound = 2; |
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| 179 | int _max_tree_size; |
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| 180 | |
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| 181 | //tags for the dynamic tree |
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| 182 | DynTree *_dt; |
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| 183 | //datastructure of dyanamic tree |
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| 184 | IntNodeMap *_dt_index; |
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| 185 | //datastrucure for solution of the communication between the two class |
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| 186 | EdgeNodeMap *_dt_edges; |
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| 187 | //nodeMap for storing the outgoing edge from the node in the tree |
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| 188 | |
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| 189 | //max of the type Value |
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| 190 | const Value _max_value; |
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| 191 | |
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| 192 | public: |
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| 193 | |
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| 194 | typedef GoldbergTarjan Create; |
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| 195 | |
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| 196 | ///\name Named template parameters |
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| 197 | |
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| 198 | ///@{ |
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| 199 | |
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| 200 | template <typename _FlowMap> |
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| 201 | struct DefFlowMapTraits : public Traits { |
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| 202 | typedef _FlowMap FlowMap; |
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| 203 | static FlowMap *createFlowMap(const Graph&) { |
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| 204 | throw UninitializedParameter(); |
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| 205 | } |
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| 206 | }; |
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| 207 | |
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| 208 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 209 | /// FlowMap type |
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| 210 | /// |
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| 211 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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| 212 | /// type |
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| 213 | template <typename _FlowMap> |
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| 214 | struct DefFlowMap |
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| 215 | : public GoldbergTarjan<Graph, CapacityMap, |
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| 216 | DefFlowMapTraits<_FlowMap> > { |
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| 217 | typedef GoldbergTarjan<Graph, CapacityMap, |
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| 218 | DefFlowMapTraits<_FlowMap> > Create; |
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| 219 | }; |
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| 220 | |
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| 221 | template <typename _Elevator> |
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| 222 | struct DefElevatorTraits : public Traits { |
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| 223 | typedef _Elevator Elevator; |
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| 224 | static Elevator *createElevator(const Graph&, int) { |
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| 225 | throw UninitializedParameter(); |
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| 226 | } |
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| 227 | }; |
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| 228 | |
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| 229 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 230 | /// Elevator type |
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| 231 | /// |
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| 232 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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| 233 | /// type |
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| 234 | template <typename _Elevator> |
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| 235 | struct DefElevator |
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| 236 | : public GoldbergTarjan<Graph, CapacityMap, |
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| 237 | DefElevatorTraits<_Elevator> > { |
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| 238 | typedef GoldbergTarjan<Graph, CapacityMap, |
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| 239 | DefElevatorTraits<_Elevator> > Create; |
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| 240 | }; |
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| 241 | |
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| 242 | template <typename _Elevator> |
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| 243 | struct DefStandardElevatorTraits : public Traits { |
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| 244 | typedef _Elevator Elevator; |
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| 245 | static Elevator *createElevator(const Graph& graph, int max_level) { |
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| 246 | return new Elevator(graph, max_level); |
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| 247 | } |
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| 248 | }; |
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| 249 | |
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| 250 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 251 | /// Elevator type |
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| 252 | /// |
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| 253 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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| 254 | /// type. The Elevator should be standard constructor interface, ie. |
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| 255 | /// the graph and the maximum level should be passed to it. |
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| 256 | template <typename _Elevator> |
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| 257 | struct DefStandardElevator |
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| 258 | : public GoldbergTarjan<Graph, CapacityMap, |
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| 259 | DefStandardElevatorTraits<_Elevator> > { |
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| 260 | typedef GoldbergTarjan<Graph, CapacityMap, |
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| 261 | DefStandardElevatorTraits<_Elevator> > Create; |
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| 262 | }; |
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| 263 | |
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| 264 | |
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| 265 | ///\ref Exception for the case when s=t. |
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| 266 | |
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| 267 | ///\ref Exception for the case when the source equals the target. |
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| 268 | class InvalidArgument : public lemon::LogicError { |
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| 269 | public: |
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| 270 | virtual const char* what() const throw() { |
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| 271 | return "lemon::GoldbergTarjan::InvalidArgument"; |
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| 272 | } |
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| 273 | }; |
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| 274 | |
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| 275 | public: |
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| 276 | |
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| 277 | /// \brief The constructor of the class. |
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| 278 | /// |
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| 279 | /// The constructor of the class. |
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| 280 | /// \param graph The directed graph the algorithm runs on. |
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| 281 | /// \param capacity The capacity of the edges. |
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| 282 | /// \param source The source node. |
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| 283 | /// \param target The target node. |
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| 284 | /// Except the graph, all of these parameters can be reset by |
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| 285 | /// calling \ref source, \ref target, \ref capacityMap and \ref |
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| 286 | /// flowMap, resp. |
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| 287 | GoldbergTarjan(const Graph& graph, const CapacityMap& capacity, |
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| 288 | Node source, Node target) |
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| 289 | : _graph(graph), _capacity(&capacity), |
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| 290 | _node_num(), _source(source), _target(target), |
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| 291 | _flow(0), _local_flow(false), |
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| 292 | _level(0), _local_level(false), |
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| 293 | _excess(0), _tolerance(), |
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| 294 | _phase(), _max_tree_size(), |
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| 295 | _dt(0), _dt_index(0), _dt_edges(0), |
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| 296 | _max_value(std::numeric_limits<Value>::max()) { |
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| 297 | if (_source == _target) throw InvalidArgument(); |
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| 298 | } |
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| 299 | |
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| 300 | /// \brief Destrcutor. |
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| 301 | /// |
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| 302 | /// Destructor. |
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| 303 | ~GoldbergTarjan() { |
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| 304 | destroyStructures(); |
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| 305 | } |
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| 306 | |
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| 307 | /// \brief Sets the capacity map. |
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| 308 | /// |
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| 309 | /// Sets the capacity map. |
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| 310 | /// \return \c (*this) |
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| 311 | GoldbergTarjan& capacityMap(const CapacityMap& map) { |
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| 312 | _capacity = ↦ |
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| 313 | return *this; |
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| 314 | } |
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| 315 | |
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| 316 | /// \brief Sets the flow map. |
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| 317 | /// |
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| 318 | /// Sets the flow map. |
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| 319 | /// \return \c (*this) |
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| 320 | GoldbergTarjan& flowMap(FlowMap& map) { |
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| 321 | if (_local_flow) { |
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| 322 | delete _flow; |
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| 323 | _local_flow = false; |
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| 324 | } |
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| 325 | _flow = ↦ |
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| 326 | return *this; |
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| 327 | } |
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| 328 | |
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| 329 | /// \brief Returns the flow map. |
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| 330 | /// |
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| 331 | /// \return The flow map. |
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| 332 | const FlowMap& flowMap() { |
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| 333 | return *_flow; |
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| 334 | } |
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| 335 | |
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| 336 | /// \brief Sets the elevator. |
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| 337 | /// |
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| 338 | /// Sets the elevator. |
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| 339 | /// \return \c (*this) |
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| 340 | GoldbergTarjan& elevator(Elevator& elevator) { |
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| 341 | if (_local_level) { |
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| 342 | delete _level; |
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| 343 | _local_level = false; |
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| 344 | } |
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| 345 | _level = &elevator; |
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| 346 | return *this; |
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| 347 | } |
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| 348 | |
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| 349 | /// \brief Returns the elevator. |
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| 350 | /// |
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| 351 | /// \return The elevator. |
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| 352 | const Elevator& elevator() { |
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| 353 | return *_level; |
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| 354 | } |
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| 355 | |
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| 356 | /// \brief Sets the source node. |
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| 357 | /// |
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| 358 | /// Sets the source node. |
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| 359 | /// \return \c (*this) |
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| 360 | GoldbergTarjan& source(const Node& node) { |
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| 361 | _source = node; |
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| 362 | return *this; |
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| 363 | } |
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| 364 | |
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| 365 | /// \brief Sets the target node. |
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| 366 | /// |
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| 367 | /// Sets the target node. |
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| 368 | /// \return \c (*this) |
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| 369 | GoldbergTarjan& target(const Node& node) { |
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| 370 | _target = node; |
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| 371 | return *this; |
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| 372 | } |
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| 373 | |
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| 374 | /// \brief Sets the tolerance used by algorithm. |
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| 375 | /// |
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| 376 | /// Sets the tolerance used by algorithm. |
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| 377 | GoldbergTarjan& tolerance(const Tolerance& tolerance) const { |
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| 378 | _tolerance = tolerance; |
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| 379 | if (_dt) { |
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| 380 | _dt->tolerance(_tolerance); |
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| 381 | } |
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| 382 | return *this; |
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| 383 | } |
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| 384 | |
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| 385 | /// \brief Returns the tolerance used by algorithm. |
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| 386 | /// |
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| 387 | /// Returns the tolerance used by algorithm. |
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| 388 | const Tolerance& tolerance() const { |
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| 389 | return tolerance; |
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| 390 | } |
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| 391 | |
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| 392 | |
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| 393 | private: |
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| 394 | |
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| 395 | void createStructures() { |
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| 396 | _node_num = countNodes(_graph); |
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| 397 | |
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| 398 | _max_tree_size = (double(_node_num) * double(_node_num)) / |
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| 399 | double(countEdges(_graph)); |
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| 400 | |
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| 401 | if (!_flow) { |
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| 402 | _flow = Traits::createFlowMap(_graph); |
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| 403 | _local_flow = true; |
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| 404 | } |
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| 405 | if (!_level) { |
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| 406 | _level = Traits::createElevator(_graph, _node_num); |
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| 407 | _local_level = true; |
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| 408 | } |
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| 409 | if (!_excess) { |
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| 410 | _excess = new ExcessMap(_graph); |
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| 411 | } |
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| 412 | if (!_dt_index && !_dt) { |
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| 413 | _dt_index = new IntNodeMap(_graph); |
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| 414 | _dt = new DynTree(*_dt_index, _tolerance); |
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| 415 | } |
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| 416 | if (!_dt_edges) { |
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| 417 | _dt_edges = new EdgeNodeMap(_graph); |
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| 418 | } |
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| 419 | } |
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| 420 | |
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| 421 | void destroyStructures() { |
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| 422 | if (_local_flow) { |
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| 423 | delete _flow; |
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| 424 | } |
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| 425 | if (_local_level) { |
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| 426 | delete _level; |
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| 427 | } |
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| 428 | if (_excess) { |
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| 429 | delete _excess; |
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| 430 | } |
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| 431 | if (_dt) { |
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| 432 | delete _dt; |
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| 433 | } |
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| 434 | if (_dt_index) { |
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| 435 | delete _dt_index; |
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| 436 | } |
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| 437 | if (_dt_edges) { |
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| 438 | delete _dt_edges; |
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| 439 | } |
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| 440 | } |
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| 441 | |
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| 442 | bool sendOut(Node n, Value& excess) { |
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| 443 | |
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| 444 | Node w = _dt->findRoot(n); |
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| 445 | |
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| 446 | while (w != n) { |
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| 447 | |
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| 448 | Value rem; |
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| 449 | Node u = _dt->findCost(n, rem); |
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| 450 | |
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| 451 | if (_tolerance.positive(rem) && !_level->active(w) && w != _target) { |
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| 452 | _level->activate(w); |
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| 453 | } |
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| 454 | |
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| 455 | if (!_tolerance.less(rem, excess)) { |
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| 456 | _dt->addCost(n, - excess); |
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| 457 | _excess->set(w, (*_excess)[w] + excess); |
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| 458 | excess = 0; |
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| 459 | return true; |
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| 460 | } |
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| 461 | |
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| 462 | |
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| 463 | _dt->addCost(n, - rem); |
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| 464 | |
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| 465 | excess -= rem; |
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| 466 | _excess->set(w, (*_excess)[w] + rem); |
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| 467 | |
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| 468 | _dt->cut(u); |
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| 469 | _dt->addCost(u, _max_value); |
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| 470 | |
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| 471 | Edge e = (*_dt_edges)[u]; |
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| 472 | _dt_edges->set(u, INVALID); |
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| 473 | |
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| 474 | if (u == _graph.source(e)) { |
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| 475 | _flow->set(e, (*_capacity)[e]); |
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| 476 | } else { |
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| 477 | _flow->set(e, 0); |
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| 478 | } |
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| 479 | |
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| 480 | w = _dt->findRoot(n); |
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| 481 | } |
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| 482 | return false; |
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| 483 | } |
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| 484 | |
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| 485 | bool sendIn(Node n, Value& excess) { |
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| 486 | |
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| 487 | Node w = _dt->findRoot(n); |
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| 488 | |
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| 489 | while (w != n) { |
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| 490 | |
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| 491 | Value rem; |
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| 492 | Node u = _dt->findCost(n, rem); |
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| 493 | |
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| 494 | if (_tolerance.positive(rem) && !_level->active(w) && w != _source) { |
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| 495 | _level->activate(w); |
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| 496 | } |
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| 497 | |
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| 498 | if (!_tolerance.less(rem, excess)) { |
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| 499 | _dt->addCost(n, - excess); |
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| 500 | _excess->set(w, (*_excess)[w] + excess); |
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| 501 | excess = 0; |
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| 502 | return true; |
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| 503 | } |
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| 504 | |
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| 505 | |
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| 506 | _dt->addCost(n, - rem); |
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| 507 | |
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| 508 | excess -= rem; |
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| 509 | _excess->set(w, (*_excess)[w] + rem); |
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| 510 | |
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| 511 | _dt->cut(u); |
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| 512 | _dt->addCost(u, _max_value); |
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| 513 | |
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| 514 | Edge e = (*_dt_edges)[u]; |
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| 515 | _dt_edges->set(u, INVALID); |
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| 516 | |
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| 517 | if (u == _graph.source(e)) { |
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| 518 | _flow->set(e, (*_capacity)[e]); |
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| 519 | } else { |
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| 520 | _flow->set(e, 0); |
---|
| 521 | } |
---|
| 522 | |
---|
| 523 | w = _dt->findRoot(n); |
---|
| 524 | } |
---|
| 525 | return false; |
---|
| 526 | } |
---|
| 527 | |
---|
| 528 | void cutChildren(Node n) { |
---|
| 529 | |
---|
| 530 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 531 | |
---|
| 532 | Node v = _graph.target(e); |
---|
| 533 | |
---|
| 534 | if ((*_dt_edges)[v] != INVALID && (*_dt_edges)[v] == e) { |
---|
| 535 | _dt->cut(v); |
---|
| 536 | _dt_edges->set(v, INVALID); |
---|
| 537 | Value rem; |
---|
| 538 | _dt->findCost(v, rem); |
---|
| 539 | _dt->addCost(v, - rem); |
---|
| 540 | _dt->addCost(v, _max_value); |
---|
| 541 | _flow->set(e, rem); |
---|
| 542 | |
---|
| 543 | } |
---|
| 544 | } |
---|
| 545 | |
---|
| 546 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 547 | |
---|
| 548 | Node v = _graph.source(e); |
---|
| 549 | |
---|
| 550 | if ((*_dt_edges)[v] != INVALID && (*_dt_edges)[v] == e) { |
---|
| 551 | _dt->cut(v); |
---|
| 552 | _dt_edges->set(v, INVALID); |
---|
| 553 | Value rem; |
---|
| 554 | _dt->findCost(v, rem); |
---|
| 555 | _dt->addCost(v, - rem); |
---|
| 556 | _dt->addCost(v, _max_value); |
---|
| 557 | _flow->set(e, (*_capacity)[e] - rem); |
---|
| 558 | |
---|
| 559 | } |
---|
| 560 | } |
---|
| 561 | } |
---|
| 562 | |
---|
| 563 | void extractTrees() { |
---|
| 564 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 565 | |
---|
| 566 | Node w = _dt->findRoot(n); |
---|
| 567 | |
---|
| 568 | while (w != n) { |
---|
| 569 | |
---|
| 570 | Value rem; |
---|
| 571 | Node u = _dt->findCost(n, rem); |
---|
| 572 | |
---|
| 573 | _dt->cut(u); |
---|
| 574 | _dt->addCost(u, - rem); |
---|
| 575 | _dt->addCost(u, _max_value); |
---|
| 576 | |
---|
| 577 | Edge e = (*_dt_edges)[u]; |
---|
| 578 | _dt_edges->set(u, INVALID); |
---|
| 579 | |
---|
| 580 | if (u == _graph.source(e)) { |
---|
| 581 | _flow->set(e, (*_capacity)[e] - rem); |
---|
| 582 | } else { |
---|
| 583 | _flow->set(e, rem); |
---|
| 584 | } |
---|
| 585 | |
---|
| 586 | w = _dt->findRoot(n); |
---|
| 587 | } |
---|
| 588 | } |
---|
| 589 | } |
---|
| 590 | |
---|
| 591 | public: |
---|
| 592 | |
---|
| 593 | /// \name Execution control The simplest way to execute the |
---|
| 594 | /// algorithm is to use one of the member functions called \c |
---|
| 595 | /// run(). |
---|
| 596 | /// \n |
---|
| 597 | /// If you need more control on initial solution or |
---|
| 598 | /// execution then you have to call one \ref init() function and then |
---|
| 599 | /// the startFirstPhase() and if you need the startSecondPhase(). |
---|
| 600 | |
---|
| 601 | ///@{ |
---|
| 602 | |
---|
| 603 | /// \brief Initializes the internal data structures. |
---|
| 604 | /// |
---|
| 605 | /// Initializes the internal data structures. |
---|
| 606 | /// |
---|
| 607 | void init() { |
---|
| 608 | createStructures(); |
---|
| 609 | |
---|
| 610 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 611 | _excess->set(n, 0); |
---|
| 612 | } |
---|
| 613 | |
---|
| 614 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 615 | _flow->set(e, 0); |
---|
| 616 | } |
---|
| 617 | |
---|
| 618 | _dt->clear(); |
---|
| 619 | for (NodeIt v(_graph); v != INVALID; ++v) { |
---|
| 620 | (*_dt_edges)[v] = INVALID; |
---|
| 621 | _dt->makeTree(v); |
---|
| 622 | _dt->addCost(v, _max_value); |
---|
| 623 | } |
---|
| 624 | |
---|
| 625 | typename Graph::template NodeMap<bool> reached(_graph, false); |
---|
| 626 | |
---|
| 627 | _level->initStart(); |
---|
| 628 | _level->initAddItem(_target); |
---|
| 629 | |
---|
| 630 | std::vector<Node> queue; |
---|
| 631 | reached.set(_source, true); |
---|
| 632 | |
---|
| 633 | queue.push_back(_target); |
---|
| 634 | reached.set(_target, true); |
---|
| 635 | while (!queue.empty()) { |
---|
| 636 | _level->initNewLevel(); |
---|
| 637 | std::vector<Node> nqueue; |
---|
| 638 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
| 639 | Node n = queue[i]; |
---|
| 640 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 641 | Node u = _graph.source(e); |
---|
| 642 | if (!reached[u] && _tolerance.positive((*_capacity)[e])) { |
---|
| 643 | reached.set(u, true); |
---|
| 644 | _level->initAddItem(u); |
---|
| 645 | nqueue.push_back(u); |
---|
| 646 | } |
---|
| 647 | } |
---|
| 648 | } |
---|
| 649 | queue.swap(nqueue); |
---|
| 650 | } |
---|
| 651 | _level->initFinish(); |
---|
| 652 | |
---|
| 653 | for (OutEdgeIt e(_graph, _source); e != INVALID; ++e) { |
---|
| 654 | if (_tolerance.positive((*_capacity)[e])) { |
---|
| 655 | Node u = _graph.target(e); |
---|
| 656 | if ((*_level)[u] == _level->maxLevel()) continue; |
---|
| 657 | _flow->set(e, (*_capacity)[e]); |
---|
| 658 | _excess->set(u, (*_excess)[u] + (*_capacity)[e]); |
---|
| 659 | if (u != _target && !_level->active(u)) { |
---|
| 660 | _level->activate(u); |
---|
| 661 | } |
---|
| 662 | } |
---|
| 663 | } |
---|
| 664 | } |
---|
| 665 | |
---|
| 666 | /// \brief Starts the first phase of the preflow algorithm. |
---|
| 667 | /// |
---|
| 668 | /// The preflow algorithm consists of two phases, this method runs |
---|
| 669 | /// the first phase. After the first phase the maximum flow value |
---|
| 670 | /// and a minimum value cut can already be computed, although a |
---|
| 671 | /// maximum flow is not yet obtained. So after calling this method |
---|
| 672 | /// \ref flowValue() returns the value of a maximum flow and \ref |
---|
| 673 | /// minCut() returns a minimum cut. |
---|
| 674 | /// \pre One of the \ref init() functions should be called. |
---|
| 675 | void startFirstPhase() { |
---|
| 676 | _phase = true; |
---|
| 677 | Node n; |
---|
| 678 | |
---|
| 679 | while ((n = _level->highestActive()) != INVALID) { |
---|
| 680 | Value excess = (*_excess)[n]; |
---|
| 681 | int level = _level->highestActiveLevel(); |
---|
| 682 | int new_level = _level->maxLevel(); |
---|
| 683 | |
---|
| 684 | if (_dt->findRoot(n) != n) { |
---|
| 685 | if (sendOut(n, excess)) goto no_more_push; |
---|
| 686 | } |
---|
| 687 | |
---|
| 688 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 689 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 690 | Node v = _graph.target(e); |
---|
| 691 | |
---|
| 692 | if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue; |
---|
| 693 | |
---|
| 694 | if ((*_level)[v] < level) { |
---|
| 695 | |
---|
| 696 | if (_dt->findSize(n) + _dt->findSize(v) < |
---|
| 697 | _tree_bound * _max_tree_size) { |
---|
| 698 | _dt->addCost(n, -_max_value); |
---|
| 699 | _dt->addCost(n, rem); |
---|
| 700 | _dt->link(n, v); |
---|
| 701 | _dt_edges->set(n, e); |
---|
| 702 | if (sendOut(n, excess)) goto no_more_push; |
---|
| 703 | } else { |
---|
| 704 | if (!_level->active(v) && v != _target) { |
---|
| 705 | _level->activate(v); |
---|
| 706 | } |
---|
| 707 | if (!_tolerance.less(rem, excess)) { |
---|
| 708 | _flow->set(e, (*_flow)[e] + excess); |
---|
| 709 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 710 | excess = 0; |
---|
| 711 | goto no_more_push; |
---|
| 712 | } else { |
---|
| 713 | excess -= rem; |
---|
| 714 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 715 | _flow->set(e, (*_capacity)[e]); |
---|
| 716 | } |
---|
| 717 | } |
---|
| 718 | } else if (new_level > (*_level)[v]) { |
---|
| 719 | new_level = (*_level)[v]; |
---|
| 720 | } |
---|
| 721 | } |
---|
| 722 | |
---|
| 723 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 724 | Value rem = (*_flow)[e]; |
---|
| 725 | Node v = _graph.source(e); |
---|
| 726 | if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue; |
---|
| 727 | |
---|
| 728 | if ((*_level)[v] < level) { |
---|
| 729 | |
---|
| 730 | if (_dt->findSize(n) + _dt->findSize(v) < |
---|
| 731 | _tree_bound * _max_tree_size) { |
---|
| 732 | _dt->addCost(n, - _max_value); |
---|
| 733 | _dt->addCost(n, rem); |
---|
| 734 | _dt->link(n, v); |
---|
| 735 | _dt_edges->set(n, e); |
---|
| 736 | if (sendOut(n, excess)) goto no_more_push; |
---|
| 737 | } else { |
---|
| 738 | if (!_level->active(v) && v != _target) { |
---|
| 739 | _level->activate(v); |
---|
| 740 | } |
---|
| 741 | if (!_tolerance.less(rem, excess)) { |
---|
| 742 | _flow->set(e, (*_flow)[e] - excess); |
---|
| 743 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 744 | excess = 0; |
---|
| 745 | goto no_more_push; |
---|
| 746 | } else { |
---|
| 747 | excess -= rem; |
---|
| 748 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 749 | _flow->set(e, 0); |
---|
| 750 | } |
---|
| 751 | } |
---|
| 752 | } else if (new_level > (*_level)[v]) { |
---|
| 753 | new_level = (*_level)[v]; |
---|
| 754 | } |
---|
| 755 | } |
---|
| 756 | |
---|
| 757 | no_more_push: |
---|
| 758 | |
---|
| 759 | _excess->set(n, excess); |
---|
| 760 | |
---|
| 761 | if (excess != 0) { |
---|
| 762 | cutChildren(n); |
---|
| 763 | if (new_level + 1 < _level->maxLevel()) { |
---|
| 764 | _level->liftHighestActive(new_level + 1); |
---|
| 765 | } else { |
---|
| 766 | _level->liftHighestActiveToTop(); |
---|
| 767 | } |
---|
| 768 | if (_level->emptyLevel(level)) { |
---|
| 769 | _level->liftToTop(level); |
---|
| 770 | } |
---|
| 771 | } else { |
---|
| 772 | _level->deactivate(n); |
---|
| 773 | } |
---|
| 774 | } |
---|
| 775 | extractTrees(); |
---|
| 776 | } |
---|
| 777 | |
---|
| 778 | /// \brief Starts the second phase of the preflow algorithm. |
---|
| 779 | /// |
---|
| 780 | /// The preflow algorithm consists of two phases, this method runs |
---|
| 781 | /// the second phase. After calling \ref init() and \ref |
---|
| 782 | /// startFirstPhase() and then \ref startSecondPhase(), \ref |
---|
| 783 | /// flowMap() return a maximum flow, \ref flowValue() returns the |
---|
| 784 | /// value of a maximum flow, \ref minCut() returns a minimum cut |
---|
| 785 | /// \pre The \ref init() and startFirstPhase() functions should be |
---|
| 786 | /// called before. |
---|
| 787 | void startSecondPhase() { |
---|
| 788 | _phase = false; |
---|
| 789 | |
---|
| 790 | typename Graph::template NodeMap<bool> reached(_graph, false); |
---|
| 791 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 792 | reached.set(n, (*_level)[n] < _level->maxLevel()); |
---|
| 793 | } |
---|
| 794 | |
---|
| 795 | _level->initStart(); |
---|
| 796 | _level->initAddItem(_source); |
---|
| 797 | |
---|
| 798 | std::vector<Node> queue; |
---|
| 799 | queue.push_back(_source); |
---|
| 800 | reached.set(_source, true); |
---|
| 801 | |
---|
| 802 | while (!queue.empty()) { |
---|
| 803 | _level->initNewLevel(); |
---|
| 804 | std::vector<Node> nqueue; |
---|
| 805 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
| 806 | Node n = queue[i]; |
---|
| 807 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 808 | Node v = _graph.target(e); |
---|
| 809 | if (!reached[v] && _tolerance.positive((*_flow)[e])) { |
---|
| 810 | reached.set(v, true); |
---|
| 811 | _level->initAddItem(v); |
---|
| 812 | nqueue.push_back(v); |
---|
| 813 | } |
---|
| 814 | } |
---|
| 815 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 816 | Node u = _graph.source(e); |
---|
| 817 | if (!reached[u] && |
---|
| 818 | _tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
---|
| 819 | reached.set(u, true); |
---|
| 820 | _level->initAddItem(u); |
---|
| 821 | nqueue.push_back(u); |
---|
| 822 | } |
---|
| 823 | } |
---|
| 824 | } |
---|
| 825 | queue.swap(nqueue); |
---|
| 826 | } |
---|
| 827 | _level->initFinish(); |
---|
| 828 | |
---|
| 829 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 830 | if ((*_excess)[n] > 0 && _target != n) { |
---|
| 831 | _level->activate(n); |
---|
| 832 | } |
---|
| 833 | } |
---|
| 834 | |
---|
| 835 | Node n; |
---|
| 836 | |
---|
| 837 | while ((n = _level->highestActive()) != INVALID) { |
---|
| 838 | Value excess = (*_excess)[n]; |
---|
| 839 | int level = _level->highestActiveLevel(); |
---|
| 840 | int new_level = _level->maxLevel(); |
---|
| 841 | |
---|
| 842 | if (_dt->findRoot(n) != n) { |
---|
| 843 | if (sendIn(n, excess)) goto no_more_push; |
---|
| 844 | } |
---|
| 845 | |
---|
| 846 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 847 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 848 | Node v = _graph.target(e); |
---|
| 849 | |
---|
| 850 | if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue; |
---|
| 851 | |
---|
| 852 | if ((*_level)[v] < level) { |
---|
| 853 | |
---|
| 854 | if (_dt->findSize(n) + _dt->findSize(v) < |
---|
| 855 | _tree_bound * _max_tree_size) { |
---|
| 856 | _dt->addCost(n, -_max_value); |
---|
| 857 | _dt->addCost(n, rem); |
---|
| 858 | _dt->link(n, v); |
---|
| 859 | _dt_edges->set(n, e); |
---|
| 860 | if (sendIn(n, excess)) goto no_more_push; |
---|
| 861 | } else { |
---|
| 862 | if (!_level->active(v) && v != _source) { |
---|
| 863 | _level->activate(v); |
---|
| 864 | } |
---|
| 865 | if (!_tolerance.less(rem, excess)) { |
---|
| 866 | _flow->set(e, (*_flow)[e] + excess); |
---|
| 867 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 868 | excess = 0; |
---|
| 869 | goto no_more_push; |
---|
| 870 | } else { |
---|
| 871 | excess -= rem; |
---|
| 872 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 873 | _flow->set(e, (*_capacity)[e]); |
---|
| 874 | } |
---|
| 875 | } |
---|
| 876 | } else if (new_level > (*_level)[v]) { |
---|
| 877 | new_level = (*_level)[v]; |
---|
| 878 | } |
---|
| 879 | } |
---|
| 880 | |
---|
| 881 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 882 | Value rem = (*_flow)[e]; |
---|
| 883 | Node v = _graph.source(e); |
---|
| 884 | if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue; |
---|
| 885 | |
---|
| 886 | if ((*_level)[v] < level) { |
---|
| 887 | |
---|
| 888 | if (_dt->findSize(n) + _dt->findSize(v) < |
---|
| 889 | _tree_bound * _max_tree_size) { |
---|
| 890 | _dt->addCost(n, - _max_value); |
---|
| 891 | _dt->addCost(n, rem); |
---|
| 892 | _dt->link(n, v); |
---|
| 893 | _dt_edges->set(n, e); |
---|
| 894 | if (sendIn(n, excess)) goto no_more_push; |
---|
| 895 | } else { |
---|
| 896 | if (!_level->active(v) && v != _source) { |
---|
| 897 | _level->activate(v); |
---|
| 898 | } |
---|
| 899 | if (!_tolerance.less(rem, excess)) { |
---|
| 900 | _flow->set(e, (*_flow)[e] - excess); |
---|
| 901 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 902 | excess = 0; |
---|
| 903 | goto no_more_push; |
---|
| 904 | } else { |
---|
| 905 | excess -= rem; |
---|
| 906 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 907 | _flow->set(e, 0); |
---|
| 908 | } |
---|
| 909 | } |
---|
| 910 | } else if (new_level > (*_level)[v]) { |
---|
| 911 | new_level = (*_level)[v]; |
---|
| 912 | } |
---|
| 913 | } |
---|
| 914 | |
---|
| 915 | no_more_push: |
---|
| 916 | |
---|
| 917 | _excess->set(n, excess); |
---|
| 918 | |
---|
| 919 | if (excess != 0) { |
---|
| 920 | cutChildren(n); |
---|
| 921 | if (new_level + 1 < _level->maxLevel()) { |
---|
| 922 | _level->liftHighestActive(new_level + 1); |
---|
| 923 | } else { |
---|
| 924 | _level->liftHighestActiveToTop(); |
---|
| 925 | } |
---|
| 926 | if (_level->emptyLevel(level)) { |
---|
| 927 | _level->liftToTop(level); |
---|
| 928 | } |
---|
| 929 | } else { |
---|
| 930 | _level->deactivate(n); |
---|
| 931 | } |
---|
| 932 | } |
---|
| 933 | extractTrees(); |
---|
| 934 | } |
---|
| 935 | |
---|
| 936 | /// \brief Runs the Goldberg-Tarjan algorithm. |
---|
| 937 | /// |
---|
| 938 | /// Runs the Goldberg-Tarjan algorithm. |
---|
| 939 | /// \note pf.run() is just a shortcut of the following code. |
---|
| 940 | /// \code |
---|
| 941 | /// pf.init(); |
---|
| 942 | /// pf.startFirstPhase(); |
---|
| 943 | /// pf.startSecondPhase(); |
---|
| 944 | /// \endcode |
---|
| 945 | void run() { |
---|
| 946 | init(); |
---|
| 947 | startFirstPhase(); |
---|
| 948 | startSecondPhase(); |
---|
| 949 | } |
---|
| 950 | |
---|
| 951 | /// \brief Runs the Goldberg-Tarjan algorithm to compute the minimum cut. |
---|
| 952 | /// |
---|
| 953 | /// Runs the Goldberg-Tarjan algorithm to compute the minimum cut. |
---|
| 954 | /// \note pf.runMinCut() is just a shortcut of the following code. |
---|
| 955 | /// \code |
---|
| 956 | /// pf.init(); |
---|
| 957 | /// pf.startFirstPhase(); |
---|
| 958 | /// \endcode |
---|
| 959 | void runMinCut() { |
---|
| 960 | init(); |
---|
| 961 | startFirstPhase(); |
---|
| 962 | } |
---|
| 963 | |
---|
| 964 | /// @} |
---|
| 965 | |
---|
| 966 | /// \name Query Functions |
---|
| 967 | /// The result of the %Dijkstra algorithm can be obtained using these |
---|
| 968 | /// functions.\n |
---|
| 969 | /// Before the use of these functions, |
---|
| 970 | /// either run() or start() must be called. |
---|
| 971 | |
---|
| 972 | ///@{ |
---|
| 973 | |
---|
| 974 | /// \brief Returns the value of the maximum flow. |
---|
| 975 | /// |
---|
| 976 | /// Returns the value of the maximum flow by returning the excess |
---|
| 977 | /// of the target node \c t. This value equals to the value of |
---|
| 978 | /// the maximum flow already after the first phase. |
---|
| 979 | Value flowValue() const { |
---|
| 980 | return (*_excess)[_target]; |
---|
| 981 | } |
---|
| 982 | |
---|
| 983 | /// \brief Returns true when the node is on the source side of minimum cut. |
---|
| 984 | /// |
---|
| 985 | /// Returns true when the node is on the source side of minimum |
---|
| 986 | /// cut. This method can be called both after running \ref |
---|
| 987 | /// startFirstPhase() and \ref startSecondPhase(). |
---|
| 988 | bool minCut(const Node& node) const { |
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| 989 | return ((*_level)[node] == _level->maxLevel()) == _phase; |
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| 990 | } |
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| 991 | |
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| 992 | /// \brief Returns a minimum value cut. |
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| 993 | /// |
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| 994 | /// Sets the \c cutMap to the characteristic vector of a minimum value |
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| 995 | /// cut. This method can be called both after running \ref |
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| 996 | /// startFirstPhase() and \ref startSecondPhase(). The result after second |
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| 997 | /// phase could be changed slightly if inexact computation is used. |
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| 998 | /// \pre The \c cutMap should be a bool-valued node-map. |
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| 999 | template <typename CutMap> |
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| 1000 | void minCutMap(CutMap& cutMap) const { |
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| 1001 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 1002 | cutMap.set(n, minCut(n)); |
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| 1003 | } |
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| 1004 | } |
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| 1005 | |
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| 1006 | /// \brief Returns the flow on the edge. |
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| 1007 | /// |
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| 1008 | /// Sets the \c flowMap to the flow on the edges. This method can |
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| 1009 | /// be called after the second phase of algorithm. |
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| 1010 | Value flow(const Edge& edge) const { |
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| 1011 | return (*_flow)[edge]; |
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| 1012 | } |
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| 1013 | |
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| 1014 | /// @} |
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| 1015 | |
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| 1016 | }; |
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| 1017 | |
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| 1018 | } //namespace lemon |
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| 1019 | |
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| 1020 | #endif |
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