[389] | 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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[440] | 5 | * Copyright (C) 2003-2009 |
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[389] | 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_PREFLOW_H |
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| 20 | #define LEMON_PREFLOW_H |
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| 21 | |
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| 22 | #include <lemon/tolerance.h> |
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| 23 | #include <lemon/elevator.h> |
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| 24 | |
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| 25 | /// \file |
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| 26 | /// \ingroup max_flow |
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| 27 | /// \brief Implementation of the preflow algorithm. |
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| 28 | |
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| 29 | namespace lemon { |
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| 30 | |
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| 31 | /// \brief Default traits class of Preflow class. |
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| 32 | /// |
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| 33 | /// Default traits class of Preflow class. |
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[492] | 34 | /// \tparam GR Digraph type. |
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| 35 | /// \tparam CM Capacity map type. |
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| 36 | template <typename GR, typename CM> |
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[389] | 37 | struct PreflowDefaultTraits { |
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| 38 | |
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[393] | 39 | /// \brief The type of the digraph the algorithm runs on. |
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[492] | 40 | typedef GR Digraph; |
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[389] | 41 | |
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| 42 | /// \brief The type of the map that stores the arc capacities. |
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| 43 | /// |
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| 44 | /// The type of the map that stores the arc capacities. |
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| 45 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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[492] | 46 | typedef CM CapacityMap; |
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[389] | 47 | |
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[393] | 48 | /// \brief The type of the flow values. |
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[389] | 49 | typedef typename CapacityMap::Value Value; |
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| 50 | |
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[393] | 51 | /// \brief The type of the map that stores the flow values. |
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[389] | 52 | /// |
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[393] | 53 | /// The type of the map that stores the flow values. |
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[389] | 54 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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| 55 | typedef typename Digraph::template ArcMap<Value> FlowMap; |
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| 56 | |
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| 57 | /// \brief Instantiates a FlowMap. |
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| 58 | /// |
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| 59 | /// This function instantiates a \ref FlowMap. |
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| 60 | /// \param digraph The digraph, to which we would like to define |
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| 61 | /// the flow map. |
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| 62 | static FlowMap* createFlowMap(const Digraph& digraph) { |
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| 63 | return new FlowMap(digraph); |
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| 64 | } |
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| 65 | |
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[393] | 66 | /// \brief The elevator type used by Preflow algorithm. |
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[389] | 67 | /// |
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| 68 | /// The elevator type used by Preflow algorithm. |
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| 69 | /// |
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| 70 | /// \sa Elevator |
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| 71 | /// \sa LinkedElevator |
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| 72 | typedef LinkedElevator<Digraph, typename Digraph::Node> Elevator; |
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| 73 | |
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| 74 | /// \brief Instantiates an Elevator. |
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| 75 | /// |
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[393] | 76 | /// This function instantiates an \ref Elevator. |
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[389] | 77 | /// \param digraph The digraph, to which we would like to define |
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| 78 | /// the elevator. |
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| 79 | /// \param max_level The maximum level of the elevator. |
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| 80 | static Elevator* createElevator(const Digraph& digraph, int max_level) { |
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| 81 | return new Elevator(digraph, max_level); |
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| 82 | } |
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| 83 | |
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| 84 | /// \brief The tolerance used by the algorithm |
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| 85 | /// |
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| 86 | /// The tolerance used by the algorithm to handle inexact computation. |
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| 87 | typedef lemon::Tolerance<Value> Tolerance; |
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| 88 | |
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| 89 | }; |
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| 90 | |
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| 91 | |
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| 92 | /// \ingroup max_flow |
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| 93 | /// |
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[393] | 94 | /// \brief %Preflow algorithm class. |
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[389] | 95 | /// |
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[393] | 96 | /// This class provides an implementation of Goldberg-Tarjan's \e preflow |
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| 97 | /// \e push-relabel algorithm producing a flow of maximum value in a |
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| 98 | /// digraph. The preflow algorithms are the fastest known maximum |
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[389] | 99 | /// flow algorithms. The current implementation use a mixture of the |
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| 100 | /// \e "highest label" and the \e "bound decrease" heuristics. |
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| 101 | /// The worst case time complexity of the algorithm is \f$O(n^2\sqrt{e})\f$. |
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| 102 | /// |
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[393] | 103 | /// The algorithm consists of two phases. After the first phase |
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| 104 | /// the maximum flow value and the minimum cut is obtained. The |
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| 105 | /// second phase constructs a feasible maximum flow on each arc. |
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[389] | 106 | /// |
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[492] | 107 | /// \tparam GR The type of the digraph the algorithm runs on. |
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| 108 | /// \tparam CM The type of the capacity map. The default map |
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| 109 | /// type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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[389] | 110 | #ifdef DOXYGEN |
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[492] | 111 | template <typename GR, typename CM, typename TR> |
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[389] | 112 | #else |
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[492] | 113 | template <typename GR, |
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| 114 | typename CM = typename GR::template ArcMap<int>, |
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| 115 | typename TR = PreflowDefaultTraits<GR, CM> > |
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[389] | 116 | #endif |
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| 117 | class Preflow { |
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| 118 | public: |
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| 119 | |
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[393] | 120 | ///The \ref PreflowDefaultTraits "traits class" of the algorithm. |
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[492] | 121 | typedef TR Traits; |
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[393] | 122 | ///The type of the digraph the algorithm runs on. |
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[389] | 123 | typedef typename Traits::Digraph Digraph; |
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[393] | 124 | ///The type of the capacity map. |
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[389] | 125 | typedef typename Traits::CapacityMap CapacityMap; |
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[393] | 126 | ///The type of the flow values. |
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[389] | 127 | typedef typename Traits::Value Value; |
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| 128 | |
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[393] | 129 | ///The type of the flow map. |
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[389] | 130 | typedef typename Traits::FlowMap FlowMap; |
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[393] | 131 | ///The type of the elevator. |
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[389] | 132 | typedef typename Traits::Elevator Elevator; |
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[393] | 133 | ///The type of the tolerance. |
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[389] | 134 | typedef typename Traits::Tolerance Tolerance; |
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| 135 | |
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| 136 | private: |
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| 137 | |
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| 138 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 139 | |
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| 140 | const Digraph& _graph; |
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| 141 | const CapacityMap* _capacity; |
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| 142 | |
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| 143 | int _node_num; |
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| 144 | |
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| 145 | Node _source, _target; |
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| 146 | |
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| 147 | FlowMap* _flow; |
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| 148 | bool _local_flow; |
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| 149 | |
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| 150 | Elevator* _level; |
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| 151 | bool _local_level; |
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| 152 | |
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| 153 | typedef typename Digraph::template NodeMap<Value> ExcessMap; |
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| 154 | ExcessMap* _excess; |
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| 155 | |
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| 156 | Tolerance _tolerance; |
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| 157 | |
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| 158 | bool _phase; |
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| 159 | |
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| 160 | |
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| 161 | void createStructures() { |
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| 162 | _node_num = countNodes(_graph); |
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| 163 | |
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| 164 | if (!_flow) { |
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| 165 | _flow = Traits::createFlowMap(_graph); |
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| 166 | _local_flow = true; |
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| 167 | } |
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| 168 | if (!_level) { |
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| 169 | _level = Traits::createElevator(_graph, _node_num); |
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| 170 | _local_level = true; |
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| 171 | } |
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| 172 | if (!_excess) { |
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| 173 | _excess = new ExcessMap(_graph); |
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| 174 | } |
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| 175 | } |
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| 176 | |
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| 177 | void destroyStructures() { |
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| 178 | if (_local_flow) { |
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| 179 | delete _flow; |
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| 180 | } |
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| 181 | if (_local_level) { |
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| 182 | delete _level; |
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| 183 | } |
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| 184 | if (_excess) { |
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| 185 | delete _excess; |
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| 186 | } |
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| 187 | } |
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| 188 | |
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| 189 | public: |
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| 190 | |
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| 191 | typedef Preflow Create; |
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| 192 | |
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[393] | 193 | ///\name Named Template Parameters |
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[389] | 194 | |
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| 195 | ///@{ |
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| 196 | |
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| 197 | template <typename _FlowMap> |
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[391] | 198 | struct SetFlowMapTraits : public Traits { |
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[389] | 199 | typedef _FlowMap FlowMap; |
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| 200 | static FlowMap *createFlowMap(const Digraph&) { |
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[390] | 201 | LEMON_ASSERT(false, "FlowMap is not initialized"); |
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| 202 | return 0; // ignore warnings |
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[389] | 203 | } |
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| 204 | }; |
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| 205 | |
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| 206 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 207 | /// FlowMap type |
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| 208 | /// |
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| 209 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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[393] | 210 | /// type. |
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[389] | 211 | template <typename _FlowMap> |
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[391] | 212 | struct SetFlowMap |
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| 213 | : public Preflow<Digraph, CapacityMap, SetFlowMapTraits<_FlowMap> > { |
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[389] | 214 | typedef Preflow<Digraph, CapacityMap, |
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[391] | 215 | SetFlowMapTraits<_FlowMap> > Create; |
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[389] | 216 | }; |
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| 217 | |
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| 218 | template <typename _Elevator> |
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[391] | 219 | struct SetElevatorTraits : public Traits { |
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[389] | 220 | typedef _Elevator Elevator; |
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| 221 | static Elevator *createElevator(const Digraph&, int) { |
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[390] | 222 | LEMON_ASSERT(false, "Elevator is not initialized"); |
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| 223 | return 0; // ignore warnings |
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[389] | 224 | } |
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| 225 | }; |
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| 226 | |
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| 227 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 228 | /// Elevator type |
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| 229 | /// |
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| 230 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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[393] | 231 | /// type. If this named parameter is used, then an external |
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| 232 | /// elevator object must be passed to the algorithm using the |
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| 233 | /// \ref elevator(Elevator&) "elevator()" function before calling |
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| 234 | /// \ref run() or \ref init(). |
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| 235 | /// \sa SetStandardElevator |
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[389] | 236 | template <typename _Elevator> |
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[391] | 237 | struct SetElevator |
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| 238 | : public Preflow<Digraph, CapacityMap, SetElevatorTraits<_Elevator> > { |
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[389] | 239 | typedef Preflow<Digraph, CapacityMap, |
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[391] | 240 | SetElevatorTraits<_Elevator> > Create; |
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[389] | 241 | }; |
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| 242 | |
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| 243 | template <typename _Elevator> |
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[391] | 244 | struct SetStandardElevatorTraits : public Traits { |
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[389] | 245 | typedef _Elevator Elevator; |
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| 246 | static Elevator *createElevator(const Digraph& digraph, int max_level) { |
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| 247 | return new Elevator(digraph, max_level); |
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| 248 | } |
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| 249 | }; |
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| 250 | |
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| 251 | /// \brief \ref named-templ-param "Named parameter" for setting |
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[393] | 252 | /// Elevator type with automatic allocation |
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[389] | 253 | /// |
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| 254 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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[393] | 255 | /// type with automatic allocation. |
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| 256 | /// The Elevator should have standard constructor interface to be |
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| 257 | /// able to automatically created by the algorithm (i.e. the |
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| 258 | /// digraph and the maximum level should be passed to it). |
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| 259 | /// However an external elevator object could also be passed to the |
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| 260 | /// algorithm with the \ref elevator(Elevator&) "elevator()" function |
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| 261 | /// before calling \ref run() or \ref init(). |
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| 262 | /// \sa SetElevator |
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[389] | 263 | template <typename _Elevator> |
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[391] | 264 | struct SetStandardElevator |
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[389] | 265 | : public Preflow<Digraph, CapacityMap, |
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[391] | 266 | SetStandardElevatorTraits<_Elevator> > { |
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[389] | 267 | typedef Preflow<Digraph, CapacityMap, |
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[391] | 268 | SetStandardElevatorTraits<_Elevator> > Create; |
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[389] | 269 | }; |
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| 270 | |
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| 271 | /// @} |
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| 272 | |
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| 273 | protected: |
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| 274 | |
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| 275 | Preflow() {} |
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| 276 | |
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| 277 | public: |
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| 278 | |
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| 279 | |
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| 280 | /// \brief The constructor of the class. |
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| 281 | /// |
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| 282 | /// The constructor of the class. |
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| 283 | /// \param digraph The digraph the algorithm runs on. |
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| 284 | /// \param capacity The capacity of the arcs. |
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| 285 | /// \param source The source node. |
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| 286 | /// \param target The target node. |
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| 287 | Preflow(const Digraph& digraph, const CapacityMap& capacity, |
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[393] | 288 | Node source, Node target) |
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[389] | 289 | : _graph(digraph), _capacity(&capacity), |
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| 290 | _node_num(0), _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(), _phase() {} |
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| 294 | |
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[393] | 295 | /// \brief Destructor. |
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[389] | 296 | /// |
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| 297 | /// Destructor. |
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| 298 | ~Preflow() { |
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| 299 | destroyStructures(); |
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| 300 | } |
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| 301 | |
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| 302 | /// \brief Sets the capacity map. |
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| 303 | /// |
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| 304 | /// Sets the capacity map. |
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[393] | 305 | /// \return <tt>(*this)</tt> |
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[389] | 306 | Preflow& capacityMap(const CapacityMap& map) { |
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| 307 | _capacity = ↦ |
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| 308 | return *this; |
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| 309 | } |
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| 310 | |
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| 311 | /// \brief Sets the flow map. |
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| 312 | /// |
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| 313 | /// Sets the flow map. |
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[393] | 314 | /// If you don't use this function before calling \ref run() or |
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| 315 | /// \ref init(), an instance will be allocated automatically. |
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| 316 | /// The destructor deallocates this automatically allocated map, |
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| 317 | /// of course. |
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| 318 | /// \return <tt>(*this)</tt> |
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[389] | 319 | Preflow& flowMap(FlowMap& map) { |
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| 320 | if (_local_flow) { |
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| 321 | delete _flow; |
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| 322 | _local_flow = false; |
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| 323 | } |
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| 324 | _flow = ↦ |
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| 325 | return *this; |
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| 326 | } |
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| 327 | |
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[393] | 328 | /// \brief Sets the source node. |
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[389] | 329 | /// |
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[393] | 330 | /// Sets the source node. |
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| 331 | /// \return <tt>(*this)</tt> |
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| 332 | Preflow& source(const Node& node) { |
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| 333 | _source = node; |
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| 334 | return *this; |
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[389] | 335 | } |
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| 336 | |
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[393] | 337 | /// \brief Sets the target node. |
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[389] | 338 | /// |
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[393] | 339 | /// Sets the target node. |
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| 340 | /// \return <tt>(*this)</tt> |
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| 341 | Preflow& target(const Node& node) { |
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| 342 | _target = node; |
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| 343 | return *this; |
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| 344 | } |
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| 345 | |
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| 346 | /// \brief Sets the elevator used by algorithm. |
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| 347 | /// |
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| 348 | /// Sets the elevator used by algorithm. |
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| 349 | /// If you don't use this function before calling \ref run() or |
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| 350 | /// \ref init(), an instance will be allocated automatically. |
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| 351 | /// The destructor deallocates this automatically allocated elevator, |
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| 352 | /// of course. |
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| 353 | /// \return <tt>(*this)</tt> |
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[389] | 354 | Preflow& elevator(Elevator& elevator) { |
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| 355 | if (_local_level) { |
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| 356 | delete _level; |
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| 357 | _local_level = false; |
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| 358 | } |
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| 359 | _level = &elevator; |
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| 360 | return *this; |
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| 361 | } |
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| 362 | |
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[393] | 363 | /// \brief Returns a const reference to the elevator. |
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[389] | 364 | /// |
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[393] | 365 | /// Returns a const reference to the elevator. |
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| 366 | /// |
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| 367 | /// \pre Either \ref run() or \ref init() must be called before |
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| 368 | /// using this function. |
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[420] | 369 | const Elevator& elevator() const { |
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[389] | 370 | return *_level; |
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| 371 | } |
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| 372 | |
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| 373 | /// \brief Sets the tolerance used by algorithm. |
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| 374 | /// |
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| 375 | /// Sets the tolerance used by algorithm. |
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| 376 | Preflow& tolerance(const Tolerance& tolerance) const { |
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| 377 | _tolerance = tolerance; |
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| 378 | return *this; |
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| 379 | } |
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| 380 | |
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[393] | 381 | /// \brief Returns a const reference to the tolerance. |
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[389] | 382 | /// |
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[393] | 383 | /// Returns a const reference to the tolerance. |
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[389] | 384 | const Tolerance& tolerance() const { |
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| 385 | return tolerance; |
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| 386 | } |
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| 387 | |
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[393] | 388 | /// \name Execution Control |
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| 389 | /// The simplest way to execute the preflow algorithm is to use |
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| 390 | /// \ref run() or \ref runMinCut().\n |
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| 391 | /// If you need more control on the initial solution or the execution, |
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| 392 | /// first you have to call one of the \ref init() functions, then |
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| 393 | /// \ref startFirstPhase() and if you need it \ref startSecondPhase(). |
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[389] | 394 | |
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| 395 | ///@{ |
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| 396 | |
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| 397 | /// \brief Initializes the internal data structures. |
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| 398 | /// |
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[393] | 399 | /// Initializes the internal data structures and sets the initial |
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| 400 | /// flow to zero on each arc. |
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[389] | 401 | void init() { |
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| 402 | createStructures(); |
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| 403 | |
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| 404 | _phase = true; |
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| 405 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 406 | _excess->set(n, 0); |
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| 407 | } |
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| 408 | |
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| 409 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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| 410 | _flow->set(e, 0); |
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| 411 | } |
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| 412 | |
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| 413 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
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| 414 | |
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| 415 | _level->initStart(); |
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| 416 | _level->initAddItem(_target); |
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| 417 | |
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| 418 | std::vector<Node> queue; |
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| 419 | reached.set(_source, true); |
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| 420 | |
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| 421 | queue.push_back(_target); |
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| 422 | reached.set(_target, true); |
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| 423 | while (!queue.empty()) { |
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| 424 | _level->initNewLevel(); |
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| 425 | std::vector<Node> nqueue; |
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| 426 | for (int i = 0; i < int(queue.size()); ++i) { |
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| 427 | Node n = queue[i]; |
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| 428 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
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| 429 | Node u = _graph.source(e); |
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| 430 | if (!reached[u] && _tolerance.positive((*_capacity)[e])) { |
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| 431 | reached.set(u, true); |
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| 432 | _level->initAddItem(u); |
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| 433 | nqueue.push_back(u); |
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| 434 | } |
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| 435 | } |
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| 436 | } |
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| 437 | queue.swap(nqueue); |
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| 438 | } |
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| 439 | _level->initFinish(); |
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| 440 | |
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| 441 | for (OutArcIt e(_graph, _source); e != INVALID; ++e) { |
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| 442 | if (_tolerance.positive((*_capacity)[e])) { |
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| 443 | Node u = _graph.target(e); |
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| 444 | if ((*_level)[u] == _level->maxLevel()) continue; |
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| 445 | _flow->set(e, (*_capacity)[e]); |
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| 446 | _excess->set(u, (*_excess)[u] + (*_capacity)[e]); |
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| 447 | if (u != _target && !_level->active(u)) { |
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| 448 | _level->activate(u); |
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| 449 | } |
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| 450 | } |
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| 451 | } |
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| 452 | } |
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| 453 | |
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[393] | 454 | /// \brief Initializes the internal data structures using the |
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| 455 | /// given flow map. |
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[389] | 456 | /// |
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| 457 | /// Initializes the internal data structures and sets the initial |
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| 458 | /// flow to the given \c flowMap. The \c flowMap should contain a |
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[393] | 459 | /// flow or at least a preflow, i.e. at each node excluding the |
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| 460 | /// source node the incoming flow should greater or equal to the |
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[389] | 461 | /// outgoing flow. |
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[393] | 462 | /// \return \c false if the given \c flowMap is not a preflow. |
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[389] | 463 | template <typename FlowMap> |
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[392] | 464 | bool init(const FlowMap& flowMap) { |
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[389] | 465 | createStructures(); |
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| 466 | |
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| 467 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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| 468 | _flow->set(e, flowMap[e]); |
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| 469 | } |
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| 470 | |
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| 471 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 472 | Value excess = 0; |
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| 473 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
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| 474 | excess += (*_flow)[e]; |
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| 475 | } |
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| 476 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
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| 477 | excess -= (*_flow)[e]; |
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| 478 | } |
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| 479 | if (excess < 0 && n != _source) return false; |
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| 480 | _excess->set(n, excess); |
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| 481 | } |
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| 482 | |
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| 483 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
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| 484 | |
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| 485 | _level->initStart(); |
---|
| 486 | _level->initAddItem(_target); |
---|
| 487 | |
---|
| 488 | std::vector<Node> queue; |
---|
| 489 | reached.set(_source, true); |
---|
| 490 | |
---|
| 491 | queue.push_back(_target); |
---|
| 492 | reached.set(_target, true); |
---|
| 493 | while (!queue.empty()) { |
---|
| 494 | _level->initNewLevel(); |
---|
| 495 | std::vector<Node> nqueue; |
---|
| 496 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
| 497 | Node n = queue[i]; |
---|
| 498 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 499 | Node u = _graph.source(e); |
---|
| 500 | if (!reached[u] && |
---|
| 501 | _tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
---|
| 502 | reached.set(u, true); |
---|
| 503 | _level->initAddItem(u); |
---|
| 504 | nqueue.push_back(u); |
---|
| 505 | } |
---|
| 506 | } |
---|
| 507 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 508 | Node v = _graph.target(e); |
---|
| 509 | if (!reached[v] && _tolerance.positive((*_flow)[e])) { |
---|
| 510 | reached.set(v, true); |
---|
| 511 | _level->initAddItem(v); |
---|
| 512 | nqueue.push_back(v); |
---|
| 513 | } |
---|
| 514 | } |
---|
| 515 | } |
---|
| 516 | queue.swap(nqueue); |
---|
| 517 | } |
---|
| 518 | _level->initFinish(); |
---|
| 519 | |
---|
| 520 | for (OutArcIt e(_graph, _source); e != INVALID; ++e) { |
---|
| 521 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 522 | if (_tolerance.positive(rem)) { |
---|
| 523 | Node u = _graph.target(e); |
---|
| 524 | if ((*_level)[u] == _level->maxLevel()) continue; |
---|
| 525 | _flow->set(e, (*_capacity)[e]); |
---|
| 526 | _excess->set(u, (*_excess)[u] + rem); |
---|
| 527 | if (u != _target && !_level->active(u)) { |
---|
| 528 | _level->activate(u); |
---|
| 529 | } |
---|
| 530 | } |
---|
| 531 | } |
---|
| 532 | for (InArcIt e(_graph, _source); e != INVALID; ++e) { |
---|
| 533 | Value rem = (*_flow)[e]; |
---|
| 534 | if (_tolerance.positive(rem)) { |
---|
| 535 | Node v = _graph.source(e); |
---|
| 536 | if ((*_level)[v] == _level->maxLevel()) continue; |
---|
| 537 | _flow->set(e, 0); |
---|
| 538 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 539 | if (v != _target && !_level->active(v)) { |
---|
| 540 | _level->activate(v); |
---|
| 541 | } |
---|
| 542 | } |
---|
| 543 | } |
---|
| 544 | return true; |
---|
| 545 | } |
---|
| 546 | |
---|
| 547 | /// \brief Starts the first phase of the preflow algorithm. |
---|
| 548 | /// |
---|
| 549 | /// The preflow algorithm consists of two phases, this method runs |
---|
| 550 | /// the first phase. After the first phase the maximum flow value |
---|
| 551 | /// and a minimum value cut can already be computed, although a |
---|
| 552 | /// maximum flow is not yet obtained. So after calling this method |
---|
| 553 | /// \ref flowValue() returns the value of a maximum flow and \ref |
---|
| 554 | /// minCut() returns a minimum cut. |
---|
[393] | 555 | /// \pre One of the \ref init() functions must be called before |
---|
| 556 | /// using this function. |
---|
[389] | 557 | void startFirstPhase() { |
---|
| 558 | _phase = true; |
---|
| 559 | |
---|
| 560 | Node n = _level->highestActive(); |
---|
| 561 | int level = _level->highestActiveLevel(); |
---|
| 562 | while (n != INVALID) { |
---|
| 563 | int num = _node_num; |
---|
| 564 | |
---|
| 565 | while (num > 0 && n != INVALID) { |
---|
| 566 | Value excess = (*_excess)[n]; |
---|
| 567 | int new_level = _level->maxLevel(); |
---|
| 568 | |
---|
| 569 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 570 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 571 | if (!_tolerance.positive(rem)) continue; |
---|
| 572 | Node v = _graph.target(e); |
---|
| 573 | if ((*_level)[v] < level) { |
---|
| 574 | if (!_level->active(v) && v != _target) { |
---|
| 575 | _level->activate(v); |
---|
| 576 | } |
---|
| 577 | if (!_tolerance.less(rem, excess)) { |
---|
| 578 | _flow->set(e, (*_flow)[e] + excess); |
---|
| 579 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 580 | excess = 0; |
---|
| 581 | goto no_more_push_1; |
---|
| 582 | } else { |
---|
| 583 | excess -= rem; |
---|
| 584 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 585 | _flow->set(e, (*_capacity)[e]); |
---|
| 586 | } |
---|
| 587 | } else if (new_level > (*_level)[v]) { |
---|
| 588 | new_level = (*_level)[v]; |
---|
| 589 | } |
---|
| 590 | } |
---|
| 591 | |
---|
| 592 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 593 | Value rem = (*_flow)[e]; |
---|
| 594 | if (!_tolerance.positive(rem)) continue; |
---|
| 595 | Node v = _graph.source(e); |
---|
| 596 | if ((*_level)[v] < level) { |
---|
| 597 | if (!_level->active(v) && v != _target) { |
---|
| 598 | _level->activate(v); |
---|
| 599 | } |
---|
| 600 | if (!_tolerance.less(rem, excess)) { |
---|
| 601 | _flow->set(e, (*_flow)[e] - excess); |
---|
| 602 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 603 | excess = 0; |
---|
| 604 | goto no_more_push_1; |
---|
| 605 | } else { |
---|
| 606 | excess -= rem; |
---|
| 607 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 608 | _flow->set(e, 0); |
---|
| 609 | } |
---|
| 610 | } else if (new_level > (*_level)[v]) { |
---|
| 611 | new_level = (*_level)[v]; |
---|
| 612 | } |
---|
| 613 | } |
---|
| 614 | |
---|
| 615 | no_more_push_1: |
---|
| 616 | |
---|
| 617 | _excess->set(n, excess); |
---|
| 618 | |
---|
| 619 | if (excess != 0) { |
---|
| 620 | if (new_level + 1 < _level->maxLevel()) { |
---|
| 621 | _level->liftHighestActive(new_level + 1); |
---|
| 622 | } else { |
---|
| 623 | _level->liftHighestActiveToTop(); |
---|
| 624 | } |
---|
| 625 | if (_level->emptyLevel(level)) { |
---|
| 626 | _level->liftToTop(level); |
---|
| 627 | } |
---|
| 628 | } else { |
---|
| 629 | _level->deactivate(n); |
---|
| 630 | } |
---|
| 631 | |
---|
| 632 | n = _level->highestActive(); |
---|
| 633 | level = _level->highestActiveLevel(); |
---|
| 634 | --num; |
---|
| 635 | } |
---|
| 636 | |
---|
| 637 | num = _node_num * 20; |
---|
| 638 | while (num > 0 && n != INVALID) { |
---|
| 639 | Value excess = (*_excess)[n]; |
---|
| 640 | int new_level = _level->maxLevel(); |
---|
| 641 | |
---|
| 642 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 643 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 644 | if (!_tolerance.positive(rem)) continue; |
---|
| 645 | Node v = _graph.target(e); |
---|
| 646 | if ((*_level)[v] < level) { |
---|
| 647 | if (!_level->active(v) && v != _target) { |
---|
| 648 | _level->activate(v); |
---|
| 649 | } |
---|
| 650 | if (!_tolerance.less(rem, excess)) { |
---|
| 651 | _flow->set(e, (*_flow)[e] + excess); |
---|
| 652 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 653 | excess = 0; |
---|
| 654 | goto no_more_push_2; |
---|
| 655 | } else { |
---|
| 656 | excess -= rem; |
---|
| 657 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 658 | _flow->set(e, (*_capacity)[e]); |
---|
| 659 | } |
---|
| 660 | } else if (new_level > (*_level)[v]) { |
---|
| 661 | new_level = (*_level)[v]; |
---|
| 662 | } |
---|
| 663 | } |
---|
| 664 | |
---|
| 665 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 666 | Value rem = (*_flow)[e]; |
---|
| 667 | if (!_tolerance.positive(rem)) continue; |
---|
| 668 | Node v = _graph.source(e); |
---|
| 669 | if ((*_level)[v] < level) { |
---|
| 670 | if (!_level->active(v) && v != _target) { |
---|
| 671 | _level->activate(v); |
---|
| 672 | } |
---|
| 673 | if (!_tolerance.less(rem, excess)) { |
---|
| 674 | _flow->set(e, (*_flow)[e] - excess); |
---|
| 675 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 676 | excess = 0; |
---|
| 677 | goto no_more_push_2; |
---|
| 678 | } else { |
---|
| 679 | excess -= rem; |
---|
| 680 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 681 | _flow->set(e, 0); |
---|
| 682 | } |
---|
| 683 | } else if (new_level > (*_level)[v]) { |
---|
| 684 | new_level = (*_level)[v]; |
---|
| 685 | } |
---|
| 686 | } |
---|
| 687 | |
---|
| 688 | no_more_push_2: |
---|
| 689 | |
---|
| 690 | _excess->set(n, excess); |
---|
| 691 | |
---|
| 692 | if (excess != 0) { |
---|
| 693 | if (new_level + 1 < _level->maxLevel()) { |
---|
| 694 | _level->liftActiveOn(level, new_level + 1); |
---|
| 695 | } else { |
---|
| 696 | _level->liftActiveToTop(level); |
---|
| 697 | } |
---|
| 698 | if (_level->emptyLevel(level)) { |
---|
| 699 | _level->liftToTop(level); |
---|
| 700 | } |
---|
| 701 | } else { |
---|
| 702 | _level->deactivate(n); |
---|
| 703 | } |
---|
| 704 | |
---|
| 705 | while (level >= 0 && _level->activeFree(level)) { |
---|
| 706 | --level; |
---|
| 707 | } |
---|
| 708 | if (level == -1) { |
---|
| 709 | n = _level->highestActive(); |
---|
| 710 | level = _level->highestActiveLevel(); |
---|
| 711 | } else { |
---|
| 712 | n = _level->activeOn(level); |
---|
| 713 | } |
---|
| 714 | --num; |
---|
| 715 | } |
---|
| 716 | } |
---|
| 717 | } |
---|
| 718 | |
---|
| 719 | /// \brief Starts the second phase of the preflow algorithm. |
---|
| 720 | /// |
---|
| 721 | /// The preflow algorithm consists of two phases, this method runs |
---|
[393] | 722 | /// the second phase. After calling one of the \ref init() functions |
---|
| 723 | /// and \ref startFirstPhase() and then \ref startSecondPhase(), |
---|
| 724 | /// \ref flowMap() returns a maximum flow, \ref flowValue() returns the |
---|
[389] | 725 | /// value of a maximum flow, \ref minCut() returns a minimum cut |
---|
[393] | 726 | /// \pre One of the \ref init() functions and \ref startFirstPhase() |
---|
| 727 | /// must be called before using this function. |
---|
[389] | 728 | void startSecondPhase() { |
---|
| 729 | _phase = false; |
---|
| 730 | |
---|
| 731 | typename Digraph::template NodeMap<bool> reached(_graph); |
---|
| 732 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 733 | reached.set(n, (*_level)[n] < _level->maxLevel()); |
---|
| 734 | } |
---|
| 735 | |
---|
| 736 | _level->initStart(); |
---|
| 737 | _level->initAddItem(_source); |
---|
| 738 | |
---|
| 739 | std::vector<Node> queue; |
---|
| 740 | queue.push_back(_source); |
---|
| 741 | reached.set(_source, true); |
---|
| 742 | |
---|
| 743 | while (!queue.empty()) { |
---|
| 744 | _level->initNewLevel(); |
---|
| 745 | std::vector<Node> nqueue; |
---|
| 746 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
| 747 | Node n = queue[i]; |
---|
| 748 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 749 | Node v = _graph.target(e); |
---|
| 750 | if (!reached[v] && _tolerance.positive((*_flow)[e])) { |
---|
| 751 | reached.set(v, true); |
---|
| 752 | _level->initAddItem(v); |
---|
| 753 | nqueue.push_back(v); |
---|
| 754 | } |
---|
| 755 | } |
---|
| 756 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 757 | Node u = _graph.source(e); |
---|
| 758 | if (!reached[u] && |
---|
| 759 | _tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
---|
| 760 | reached.set(u, true); |
---|
| 761 | _level->initAddItem(u); |
---|
| 762 | nqueue.push_back(u); |
---|
| 763 | } |
---|
| 764 | } |
---|
| 765 | } |
---|
| 766 | queue.swap(nqueue); |
---|
| 767 | } |
---|
| 768 | _level->initFinish(); |
---|
| 769 | |
---|
| 770 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 771 | if (!reached[n]) { |
---|
| 772 | _level->dirtyTopButOne(n); |
---|
| 773 | } else if ((*_excess)[n] > 0 && _target != n) { |
---|
| 774 | _level->activate(n); |
---|
| 775 | } |
---|
| 776 | } |
---|
| 777 | |
---|
| 778 | Node n; |
---|
| 779 | while ((n = _level->highestActive()) != INVALID) { |
---|
| 780 | Value excess = (*_excess)[n]; |
---|
| 781 | int level = _level->highestActiveLevel(); |
---|
| 782 | int new_level = _level->maxLevel(); |
---|
| 783 | |
---|
| 784 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 785 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 786 | if (!_tolerance.positive(rem)) continue; |
---|
| 787 | Node v = _graph.target(e); |
---|
| 788 | if ((*_level)[v] < level) { |
---|
| 789 | if (!_level->active(v) && v != _source) { |
---|
| 790 | _level->activate(v); |
---|
| 791 | } |
---|
| 792 | if (!_tolerance.less(rem, excess)) { |
---|
| 793 | _flow->set(e, (*_flow)[e] + excess); |
---|
| 794 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 795 | excess = 0; |
---|
| 796 | goto no_more_push; |
---|
| 797 | } else { |
---|
| 798 | excess -= rem; |
---|
| 799 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 800 | _flow->set(e, (*_capacity)[e]); |
---|
| 801 | } |
---|
| 802 | } else if (new_level > (*_level)[v]) { |
---|
| 803 | new_level = (*_level)[v]; |
---|
| 804 | } |
---|
| 805 | } |
---|
| 806 | |
---|
| 807 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 808 | Value rem = (*_flow)[e]; |
---|
| 809 | if (!_tolerance.positive(rem)) continue; |
---|
| 810 | Node v = _graph.source(e); |
---|
| 811 | if ((*_level)[v] < level) { |
---|
| 812 | if (!_level->active(v) && v != _source) { |
---|
| 813 | _level->activate(v); |
---|
| 814 | } |
---|
| 815 | if (!_tolerance.less(rem, excess)) { |
---|
| 816 | _flow->set(e, (*_flow)[e] - excess); |
---|
| 817 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 818 | excess = 0; |
---|
| 819 | goto no_more_push; |
---|
| 820 | } else { |
---|
| 821 | excess -= rem; |
---|
| 822 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 823 | _flow->set(e, 0); |
---|
| 824 | } |
---|
| 825 | } else if (new_level > (*_level)[v]) { |
---|
| 826 | new_level = (*_level)[v]; |
---|
| 827 | } |
---|
| 828 | } |
---|
| 829 | |
---|
| 830 | no_more_push: |
---|
| 831 | |
---|
| 832 | _excess->set(n, excess); |
---|
| 833 | |
---|
| 834 | if (excess != 0) { |
---|
| 835 | if (new_level + 1 < _level->maxLevel()) { |
---|
| 836 | _level->liftHighestActive(new_level + 1); |
---|
| 837 | } else { |
---|
| 838 | // Calculation error |
---|
| 839 | _level->liftHighestActiveToTop(); |
---|
| 840 | } |
---|
| 841 | if (_level->emptyLevel(level)) { |
---|
| 842 | // Calculation error |
---|
| 843 | _level->liftToTop(level); |
---|
| 844 | } |
---|
| 845 | } else { |
---|
| 846 | _level->deactivate(n); |
---|
| 847 | } |
---|
| 848 | |
---|
| 849 | } |
---|
| 850 | } |
---|
| 851 | |
---|
| 852 | /// \brief Runs the preflow algorithm. |
---|
| 853 | /// |
---|
| 854 | /// Runs the preflow algorithm. |
---|
| 855 | /// \note pf.run() is just a shortcut of the following code. |
---|
| 856 | /// \code |
---|
| 857 | /// pf.init(); |
---|
| 858 | /// pf.startFirstPhase(); |
---|
| 859 | /// pf.startSecondPhase(); |
---|
| 860 | /// \endcode |
---|
| 861 | void run() { |
---|
| 862 | init(); |
---|
| 863 | startFirstPhase(); |
---|
| 864 | startSecondPhase(); |
---|
| 865 | } |
---|
| 866 | |
---|
| 867 | /// \brief Runs the preflow algorithm to compute the minimum cut. |
---|
| 868 | /// |
---|
| 869 | /// Runs the preflow algorithm to compute the minimum cut. |
---|
| 870 | /// \note pf.runMinCut() is just a shortcut of the following code. |
---|
| 871 | /// \code |
---|
| 872 | /// pf.init(); |
---|
| 873 | /// pf.startFirstPhase(); |
---|
| 874 | /// \endcode |
---|
| 875 | void runMinCut() { |
---|
| 876 | init(); |
---|
| 877 | startFirstPhase(); |
---|
| 878 | } |
---|
| 879 | |
---|
| 880 | /// @} |
---|
| 881 | |
---|
| 882 | /// \name Query Functions |
---|
[393] | 883 | /// The results of the preflow algorithm can be obtained using these |
---|
[389] | 884 | /// functions.\n |
---|
[393] | 885 | /// Either one of the \ref run() "run*()" functions or one of the |
---|
| 886 | /// \ref startFirstPhase() "start*()" functions should be called |
---|
| 887 | /// before using them. |
---|
[389] | 888 | |
---|
| 889 | ///@{ |
---|
| 890 | |
---|
| 891 | /// \brief Returns the value of the maximum flow. |
---|
| 892 | /// |
---|
| 893 | /// Returns the value of the maximum flow by returning the excess |
---|
[393] | 894 | /// of the target node. This value equals to the value of |
---|
| 895 | /// the maximum flow already after the first phase of the algorithm. |
---|
| 896 | /// |
---|
| 897 | /// \pre Either \ref run() or \ref init() must be called before |
---|
| 898 | /// using this function. |
---|
[389] | 899 | Value flowValue() const { |
---|
| 900 | return (*_excess)[_target]; |
---|
| 901 | } |
---|
| 902 | |
---|
[393] | 903 | /// \brief Returns the flow on the given arc. |
---|
[389] | 904 | /// |
---|
[393] | 905 | /// Returns the flow on the given arc. This method can |
---|
| 906 | /// be called after the second phase of the algorithm. |
---|
| 907 | /// |
---|
| 908 | /// \pre Either \ref run() or \ref init() must be called before |
---|
| 909 | /// using this function. |
---|
| 910 | Value flow(const Arc& arc) const { |
---|
| 911 | return (*_flow)[arc]; |
---|
| 912 | } |
---|
| 913 | |
---|
| 914 | /// \brief Returns a const reference to the flow map. |
---|
| 915 | /// |
---|
| 916 | /// Returns a const reference to the arc map storing the found flow. |
---|
| 917 | /// This method can be called after the second phase of the algorithm. |
---|
| 918 | /// |
---|
| 919 | /// \pre Either \ref run() or \ref init() must be called before |
---|
| 920 | /// using this function. |
---|
[420] | 921 | const FlowMap& flowMap() const { |
---|
[393] | 922 | return *_flow; |
---|
| 923 | } |
---|
| 924 | |
---|
| 925 | /// \brief Returns \c true when the node is on the source side of the |
---|
| 926 | /// minimum cut. |
---|
| 927 | /// |
---|
| 928 | /// Returns true when the node is on the source side of the found |
---|
| 929 | /// minimum cut. This method can be called both after running \ref |
---|
[389] | 930 | /// startFirstPhase() and \ref startSecondPhase(). |
---|
[393] | 931 | /// |
---|
| 932 | /// \pre Either \ref run() or \ref init() must be called before |
---|
| 933 | /// using this function. |
---|
[389] | 934 | bool minCut(const Node& node) const { |
---|
| 935 | return ((*_level)[node] == _level->maxLevel()) == _phase; |
---|
| 936 | } |
---|
| 937 | |
---|
[393] | 938 | /// \brief Gives back a minimum value cut. |
---|
[389] | 939 | /// |
---|
[393] | 940 | /// Sets \c cutMap to the characteristic vector of a minimum value |
---|
| 941 | /// cut. \c cutMap should be a \ref concepts::WriteMap "writable" |
---|
| 942 | /// node map with \c bool (or convertible) value type. |
---|
| 943 | /// |
---|
| 944 | /// This method can be called both after running \ref startFirstPhase() |
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| 945 | /// and \ref startSecondPhase(). The result after the second phase |
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| 946 | /// could be slightly different if inexact computation is used. |
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| 947 | /// |
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| 948 | /// \note This function calls \ref minCut() for each node, so it runs in |
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| 949 | /// \f$O(n)\f$ time. |
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| 950 | /// |
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| 951 | /// \pre Either \ref run() or \ref init() must be called before |
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| 952 | /// using this function. |
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[389] | 953 | template <typename CutMap> |
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| 954 | void minCutMap(CutMap& cutMap) const { |
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| 955 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 956 | cutMap.set(n, minCut(n)); |
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| 957 | } |
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| 958 | } |
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| 959 | |
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| 960 | /// @} |
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| 961 | }; |
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| 962 | } |
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| 963 | |
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| 964 | #endif |
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