[2034] | 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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[2391] | 5 | * Copyright (C) 2003-2007 |
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[2034] | 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_EDMONDS_KARP_H |
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| 20 | #define LEMON_EDMONDS_KARP_H |
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| 21 | |
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| 22 | /// \file |
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[2376] | 23 | /// \ingroup max_flow |
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[2034] | 24 | /// \brief Implementation of the Edmonds-Karp algorithm. |
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| 25 | |
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| 26 | #include <lemon/tolerance.h> |
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[2514] | 27 | #include <vector> |
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[2034] | 28 | |
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| 29 | namespace lemon { |
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| 30 | |
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[2514] | 31 | /// \brief Default traits class of EdmondsKarp class. |
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| 32 | /// |
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| 33 | /// Default traits class of EdmondsKarp class. |
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| 34 | /// \param _Graph Graph type. |
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| 35 | /// \param _CapacityMap Type of capacity map. |
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| 36 | template <typename _Graph, typename _CapacityMap> |
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| 37 | struct EdmondsKarpDefaultTraits { |
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| 38 | |
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| 39 | /// \brief The graph type the algorithm runs on. |
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| 40 | typedef _Graph Graph; |
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| 41 | |
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| 42 | /// \brief The type of the map that stores the edge capacities. |
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| 43 | /// |
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| 44 | /// The type of the map that stores the edge capacities. |
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| 45 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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| 46 | typedef _CapacityMap CapacityMap; |
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| 47 | |
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| 48 | /// \brief The type of the length of the edges. |
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| 49 | typedef typename CapacityMap::Value Value; |
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| 50 | |
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| 51 | /// \brief The map type that stores the flow values. |
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| 52 | /// |
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| 53 | /// The map type that stores the flow values. |
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| 54 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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| 55 | typedef typename Graph::template EdgeMap<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 graph The graph, to which we would like to define the flow map. |
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| 61 | static FlowMap* createFlowMap(const Graph& graph) { |
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| 62 | return new FlowMap(graph); |
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| 63 | } |
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| 64 | |
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| 65 | /// \brief The tolerance used by the algorithm |
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| 66 | /// |
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| 67 | /// The tolerance used by the algorithm to handle inexact computation. |
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| 68 | typedef Tolerance<Value> Tolerance; |
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| 69 | |
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| 70 | }; |
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| 71 | |
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[2376] | 72 | /// \ingroup max_flow |
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[2514] | 73 | /// |
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[2034] | 74 | /// \brief Edmonds-Karp algorithms class. |
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| 75 | /// |
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| 76 | /// This class provides an implementation of the \e Edmonds-Karp \e |
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| 77 | /// algorithm producing a flow of maximum value in a directed |
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[2514] | 78 | /// graphs. The Edmonds-Karp algorithm is slower than the Preflow |
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| 79 | /// algorithm but it has an advantage of the step-by-step execution |
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| 80 | /// control with feasible flow solutions. The \e source node, the \e |
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| 81 | /// target node, the \e capacity of the edges and the \e starting \e |
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| 82 | /// flow value of the edges should be passed to the algorithm |
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| 83 | /// through the constructor. |
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[2034] | 84 | /// |
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[2514] | 85 | /// The time complexity of the algorithm is \f$ O(nm^2) \f$ in |
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[2059] | 86 | /// worst case. Always try the preflow algorithm instead of this if |
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[2113] | 87 | /// you just want to compute the optimal flow. |
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[2034] | 88 | /// |
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| 89 | /// \param _Graph The directed graph type the algorithm runs on. |
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| 90 | /// \param _CapacityMap The capacity map type. |
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[2514] | 91 | /// \param _Traits Traits class to set various data types used by |
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| 92 | /// the algorithm. The default traits class is \ref |
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| 93 | /// EdmondsKarpDefaultTraits. See \ref EdmondsKarpDefaultTraits for the |
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| 94 | /// documentation of a Edmonds-Karp traits class. |
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[2034] | 95 | /// |
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| 96 | /// \author Balazs Dezso |
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[2059] | 97 | #ifdef DOXYGEN |
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[2514] | 98 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
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| 99 | #else |
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| 100 | template <typename _Graph, |
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| 101 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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| 102 | typename _Traits = EdmondsKarpDefaultTraits<_Graph, _CapacityMap> > |
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[2059] | 103 | #endif |
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[2034] | 104 | class EdmondsKarp { |
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| 105 | public: |
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| 106 | |
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[2514] | 107 | typedef _Traits Traits; |
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| 108 | typedef typename Traits::Graph Graph; |
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| 109 | typedef typename Traits::CapacityMap CapacityMap; |
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| 110 | typedef typename Traits::Value Value; |
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| 111 | |
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| 112 | typedef typename Traits::FlowMap FlowMap; |
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| 113 | typedef typename Traits::Tolerance Tolerance; |
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| 114 | |
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[2034] | 115 | /// \brief \ref Exception for the case when the source equals the target. |
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| 116 | /// |
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| 117 | /// \ref Exception for the case when the source equals the target. |
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| 118 | /// |
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| 119 | class InvalidArgument : public lemon::LogicError { |
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| 120 | public: |
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[2151] | 121 | virtual const char* what() const throw() { |
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[2034] | 122 | return "lemon::EdmondsKarp::InvalidArgument"; |
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| 123 | } |
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| 124 | }; |
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| 125 | |
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| 126 | |
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| 127 | private: |
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| 128 | |
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[2514] | 129 | GRAPH_TYPEDEFS(typename Graph); |
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| 130 | typedef typename Graph::template NodeMap<Edge> PredMap; |
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[2034] | 131 | |
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[2514] | 132 | const Graph& _graph; |
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| 133 | const CapacityMap* _capacity; |
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| 134 | |
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| 135 | Node _source, _target; |
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| 136 | |
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| 137 | FlowMap* _flow; |
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| 138 | bool _local_flow; |
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| 139 | |
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| 140 | PredMap* _pred; |
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| 141 | std::vector<Node> _queue; |
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| 142 | |
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| 143 | Tolerance _tolerance; |
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| 144 | Value _flow_value; |
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| 145 | |
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| 146 | void createStructures() { |
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| 147 | if (!_flow) { |
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| 148 | _flow = Traits::createFlowMap(_graph); |
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| 149 | _local_flow = true; |
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| 150 | } |
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| 151 | if (!_pred) { |
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| 152 | _pred = new PredMap(_graph); |
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| 153 | } |
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| 154 | _queue.resize(countNodes(_graph)); |
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| 155 | } |
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| 156 | |
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| 157 | void destroyStructures() { |
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| 158 | if (_local_flow) { |
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| 159 | delete _flow; |
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| 160 | } |
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| 161 | if (_pred) { |
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| 162 | delete _pred; |
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| 163 | } |
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| 164 | } |
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[2034] | 165 | |
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| 166 | public: |
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| 167 | |
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[2514] | 168 | ///\name Named template parameters |
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| 169 | |
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| 170 | ///@{ |
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| 171 | |
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| 172 | template <typename _FlowMap> |
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| 173 | struct DefFlowMapTraits : public Traits { |
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| 174 | typedef _FlowMap FlowMap; |
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| 175 | static FlowMap *createFlowMap(const Graph&) { |
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| 176 | throw UninitializedParameter(); |
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| 177 | } |
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| 178 | }; |
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| 179 | |
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| 180 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 181 | /// FlowMap type |
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| 182 | /// |
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| 183 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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| 184 | /// type |
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| 185 | template <typename _FlowMap> |
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| 186 | struct DefFlowMap |
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| 187 | : public EdmondsKarp<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > { |
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| 188 | typedef EdmondsKarp<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > |
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| 189 | Create; |
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| 190 | }; |
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| 191 | |
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| 192 | |
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| 193 | /// @} |
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| 194 | |
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[2034] | 195 | /// \brief The constructor of the class. |
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| 196 | /// |
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| 197 | /// The constructor of the class. |
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[2037] | 198 | /// \param graph The directed graph the algorithm runs on. |
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[2514] | 199 | /// \param capacity The capacity of the edges. |
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[2037] | 200 | /// \param source The source node. |
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| 201 | /// \param target The target node. |
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[2514] | 202 | EdmondsKarp(const Graph& graph, const CapacityMap& capacity, |
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| 203 | Node source, Node target) |
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| 204 | : _graph(graph), _capacity(&capacity), _source(source), _target(target), |
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| 205 | _flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value() |
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[2034] | 206 | { |
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| 207 | if (_source == _target) { |
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| 208 | throw InvalidArgument(); |
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| 209 | } |
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| 210 | } |
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| 211 | |
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[2514] | 212 | /// \brief Destrcutor. |
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| 213 | /// |
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| 214 | /// Destructor. |
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| 215 | ~EdmondsKarp() { |
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| 216 | destroyStructures(); |
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| 217 | } |
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| 218 | |
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| 219 | /// \brief Sets the capacity map. |
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| 220 | /// |
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| 221 | /// Sets the capacity map. |
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| 222 | /// \return \c (*this) |
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| 223 | EdmondsKarp& capacityMap(const CapacityMap& map) { |
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| 224 | _capacity = ↦ |
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| 225 | return *this; |
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| 226 | } |
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| 227 | |
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| 228 | /// \brief Sets the flow map. |
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| 229 | /// |
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| 230 | /// Sets the flow map. |
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| 231 | /// \return \c (*this) |
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| 232 | EdmondsKarp& flowMap(FlowMap& map) { |
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| 233 | if (_local_flow) { |
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| 234 | delete _flow; |
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| 235 | _local_flow = false; |
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| 236 | } |
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| 237 | _flow = ↦ |
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| 238 | return *this; |
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| 239 | } |
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| 240 | |
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| 241 | /// \brief Returns the flow map. |
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| 242 | /// |
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| 243 | /// \return The flow map. |
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| 244 | const FlowMap& flowMap() { |
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| 245 | return *_flow; |
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| 246 | } |
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| 247 | |
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| 248 | /// \brief Sets the source node. |
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| 249 | /// |
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| 250 | /// Sets the source node. |
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| 251 | /// \return \c (*this) |
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| 252 | EdmondsKarp& source(const Node& node) { |
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| 253 | _source = node; |
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| 254 | return *this; |
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| 255 | } |
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| 256 | |
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| 257 | /// \brief Sets the target node. |
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| 258 | /// |
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| 259 | /// Sets the target node. |
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| 260 | /// \return \c (*this) |
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| 261 | EdmondsKarp& target(const Node& node) { |
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| 262 | _target = node; |
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| 263 | return *this; |
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| 264 | } |
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| 265 | |
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| 266 | /// \brief Sets the tolerance used by algorithm. |
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| 267 | /// |
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| 268 | /// Sets the tolerance used by algorithm. |
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| 269 | EdmondsKarp& tolerance(const Tolerance& tolerance) const { |
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| 270 | _tolerance = tolerance; |
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| 271 | return *this; |
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| 272 | } |
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| 273 | |
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| 274 | /// \brief Returns the tolerance used by algorithm. |
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| 275 | /// |
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| 276 | /// Returns the tolerance used by algorithm. |
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| 277 | const Tolerance& tolerance() const { |
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| 278 | return tolerance; |
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| 279 | } |
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| 280 | |
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| 281 | /// \name Execution control The simplest way to execute the |
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| 282 | /// algorithm is to use the \c run() member functions. |
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| 283 | /// \n |
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| 284 | /// If you need more control on initial solution or |
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| 285 | /// execution then you have to call one \ref init() function and then |
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| 286 | /// the start() or multiple times the \c augment() member function. |
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| 287 | |
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| 288 | ///@{ |
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| 289 | |
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[2034] | 290 | /// \brief Initializes the algorithm |
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| 291 | /// |
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| 292 | /// It sets the flow to empty flow. |
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| 293 | void init() { |
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[2514] | 294 | createStructures(); |
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[2034] | 295 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
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[2514] | 296 | _flow->set(it, 0); |
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[2034] | 297 | } |
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[2514] | 298 | _flow_value = 0; |
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[2034] | 299 | } |
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| 300 | |
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| 301 | /// \brief Initializes the algorithm |
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| 302 | /// |
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[2514] | 303 | /// Initializes the flow to the \c flowMap. The \c flowMap should |
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| 304 | /// contain a feasible flow, ie. in each node excluding the source |
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| 305 | /// and the target the incoming flow should be equal to the |
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| 306 | /// outgoing flow. |
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| 307 | template <typename FlowMap> |
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| 308 | void flowInit(const FlowMap& flowMap) { |
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| 309 | createStructures(); |
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| 310 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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| 311 | _flow->set(e, flowMap[e]); |
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| 312 | } |
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| 313 | _flow_value = 0; |
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[2034] | 314 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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[2514] | 315 | _flow_value += (*_flow)[jt]; |
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[2034] | 316 | } |
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| 317 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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[2514] | 318 | _flow_value -= (*_flow)[jt]; |
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[2034] | 319 | } |
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| 320 | } |
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| 321 | |
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| 322 | /// \brief Initializes the algorithm |
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| 323 | /// |
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[2514] | 324 | /// Initializes the flow to the \c flowMap. The \c flowMap should |
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| 325 | /// contain a feasible flow, ie. in each node excluding the source |
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| 326 | /// and the target the incoming flow should be equal to the |
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| 327 | /// outgoing flow. |
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| 328 | /// \return %False when the given flowMap does not contain |
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| 329 | /// feasible flow. |
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| 330 | template <typename FlowMap> |
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| 331 | bool checkedFlowInit(const FlowMap& flowMap) { |
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| 332 | createStructures(); |
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| 333 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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| 334 | _flow->set(e, flowMap[e]); |
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[2034] | 335 | } |
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| 336 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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| 337 | if (it == _source || it == _target) continue; |
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[2514] | 338 | Value outFlow = 0; |
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[2034] | 339 | for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
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[2514] | 340 | outFlow += (*_flow)[jt]; |
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[2034] | 341 | } |
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[2514] | 342 | Value inFlow = 0; |
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[2034] | 343 | for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
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[2514] | 344 | inFlow += (*_flow)[jt]; |
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[2034] | 345 | } |
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| 346 | if (_tolerance.different(outFlow, inFlow)) { |
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| 347 | return false; |
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| 348 | } |
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| 349 | } |
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| 350 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
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[2514] | 351 | if (_tolerance.less((*_flow)[it], 0)) return false; |
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| 352 | if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false; |
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| 353 | } |
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| 354 | _flow_value = 0; |
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| 355 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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| 356 | _flow_value += (*_flow)[jt]; |
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| 357 | } |
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| 358 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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| 359 | _flow_value -= (*_flow)[jt]; |
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[2034] | 360 | } |
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| 361 | return true; |
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| 362 | } |
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| 363 | |
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| 364 | /// \brief Augment the solution on an edge shortest path. |
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| 365 | /// |
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| 366 | /// Augment the solution on an edge shortest path. It search an |
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| 367 | /// edge shortest path between the source and the target |
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| 368 | /// in the residual graph with the bfs algoritm. |
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| 369 | /// Then it increase the flow on this path with the minimal residual |
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| 370 | /// capacity on the path. If there is not such path it gives back |
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| 371 | /// false. |
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| 372 | /// \return %False when the augmenting is not success so the |
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| 373 | /// current flow is a feasible and optimal solution. |
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| 374 | bool augment() { |
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[2514] | 375 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 376 | _pred->set(n, INVALID); |
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| 377 | } |
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| 378 | |
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| 379 | int first = 0, last = 1; |
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| 380 | |
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| 381 | _queue[0] = _source; |
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| 382 | _pred->set(_source, OutEdgeIt(_graph, _source)); |
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[2034] | 383 | |
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[2514] | 384 | while (first != last && (*_pred)[_target] == INVALID) { |
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| 385 | Node n = _queue[first++]; |
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| 386 | |
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| 387 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
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| 388 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
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| 389 | Node t = _graph.target(e); |
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| 390 | if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) { |
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| 391 | _pred->set(t, e); |
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| 392 | _queue[last++] = t; |
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| 393 | } |
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| 394 | } |
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| 395 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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| 396 | Value rem = (*_flow)[e]; |
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| 397 | Node t = _graph.source(e); |
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| 398 | if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) { |
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| 399 | _pred->set(t, e); |
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| 400 | _queue[last++] = t; |
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| 401 | } |
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| 402 | } |
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| 403 | } |
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[2034] | 404 | |
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[2514] | 405 | if ((*_pred)[_target] != INVALID) { |
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| 406 | Node n = _target; |
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| 407 | Edge e = (*_pred)[n]; |
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| 408 | |
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| 409 | Value prem = (*_capacity)[e] - (*_flow)[e]; |
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| 410 | n = _graph.source(e); |
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| 411 | while (n != _source) { |
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| 412 | e = (*_pred)[n]; |
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| 413 | if (_graph.target(e) == n) { |
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| 414 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
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| 415 | if (rem < prem) prem = rem; |
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| 416 | n = _graph.source(e); |
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| 417 | } else { |
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| 418 | Value rem = (*_flow)[e]; |
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| 419 | if (rem < prem) prem = rem; |
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| 420 | n = _graph.target(e); |
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| 421 | } |
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| 422 | } |
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| 423 | |
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| 424 | n = _target; |
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| 425 | e = (*_pred)[n]; |
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| 426 | |
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| 427 | _flow->set(e, (*_flow)[e] + prem); |
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| 428 | n = _graph.source(e); |
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| 429 | while (n != _source) { |
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| 430 | e = (*_pred)[n]; |
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| 431 | if (_graph.target(e) == n) { |
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| 432 | _flow->set(e, (*_flow)[e] + prem); |
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| 433 | n = _graph.source(e); |
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| 434 | } else { |
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| 435 | _flow->set(e, (*_flow)[e] - prem); |
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| 436 | n = _graph.target(e); |
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| 437 | } |
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| 438 | } |
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| 439 | |
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| 440 | _flow_value += prem; |
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| 441 | return true; |
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| 442 | } else { |
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| 443 | return false; |
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[2034] | 444 | } |
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| 445 | } |
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| 446 | |
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| 447 | /// \brief Executes the algorithm |
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| 448 | /// |
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| 449 | /// It runs augmenting phases until the optimal solution is reached. |
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| 450 | void start() { |
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| 451 | while (augment()) {} |
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| 452 | } |
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| 453 | |
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| 454 | /// \brief runs the algorithm. |
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| 455 | /// |
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| 456 | /// It is just a shorthand for: |
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[2059] | 457 | /// |
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| 458 | ///\code |
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[2034] | 459 | /// ek.init(); |
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| 460 | /// ek.start(); |
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[2059] | 461 | ///\endcode |
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[2034] | 462 | void run() { |
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| 463 | init(); |
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| 464 | start(); |
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| 465 | } |
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| 466 | |
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[2514] | 467 | /// @} |
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| 468 | |
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| 469 | /// \name Query Functions |
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[2522] | 470 | /// The result of the Edmonds-Karp algorithm can be obtained using these |
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[2514] | 471 | /// functions.\n |
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| 472 | /// Before the use of these functions, |
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| 473 | /// either run() or start() must be called. |
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| 474 | |
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| 475 | ///@{ |
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| 476 | |
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| 477 | /// \brief Returns the value of the maximum flow. |
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| 478 | /// |
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| 479 | /// Returns the value of the maximum flow by returning the excess |
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| 480 | /// of the target node \c t. This value equals to the value of |
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| 481 | /// the maximum flow already after the first phase. |
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| 482 | Value flowValue() const { |
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| 483 | return _flow_value; |
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| 484 | } |
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| 485 | |
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| 486 | |
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| 487 | /// \brief Returns the flow on the edge. |
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| 488 | /// |
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| 489 | /// Sets the \c flowMap to the flow on the edges. This method can |
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| 490 | /// be called after the second phase of algorithm. |
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| 491 | Value flow(const Edge& edge) const { |
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| 492 | return (*_flow)[edge]; |
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| 493 | } |
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| 494 | |
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| 495 | /// \brief Returns true when the node is on the source side of minimum cut. |
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| 496 | /// |
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| 497 | |
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| 498 | /// Returns true when the node is on the source side of minimum |
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| 499 | /// cut. This method can be called both after running \ref |
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| 500 | /// startFirstPhase() and \ref startSecondPhase(). |
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| 501 | bool minCut(const Node& node) const { |
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| 502 | return (*_pred)[node] != INVALID; |
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| 503 | } |
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| 504 | |
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[2034] | 505 | /// \brief Returns a minimum value cut. |
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| 506 | /// |
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| 507 | /// Sets \c cut to the characteristic vector of a minimum value cut |
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| 508 | /// It simply calls the minMinCut member. |
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[2037] | 509 | /// \retval cut Write node bool map. |
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[2034] | 510 | template <typename CutMap> |
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[2514] | 511 | void minCutMap(CutMap& cutMap) const { |
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| 512 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 513 | cutMap.set(n, (*_pred)[n] != INVALID); |
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| 514 | } |
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| 515 | cutMap.set(_source, true); |
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| 516 | } |
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[2034] | 517 | |
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[2514] | 518 | /// @} |
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[2034] | 519 | |
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| 520 | }; |
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| 521 | |
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| 522 | } |
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| 523 | |
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| 524 | #endif |
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