[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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| 5 | * Copyright (C) 2003-2006 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_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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| 23 | /// \ingroup flowalgs |
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| 24 | /// \brief Implementation of the Edmonds-Karp algorithm. |
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| 25 | |
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| 26 | #include <lemon/graph_adaptor.h> |
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| 27 | #include <lemon/tolerance.h> |
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| 28 | #include <lemon/bfs.h> |
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| 29 | |
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| 30 | namespace lemon { |
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| 31 | |
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| 32 | /// \ingroup flowalgs |
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| 33 | /// \brief Edmonds-Karp algorithms class. |
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| 34 | /// |
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| 35 | /// This class provides an implementation of the \e Edmonds-Karp \e |
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| 36 | /// algorithm producing a flow of maximum value in a directed |
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| 37 | /// graph. The Edmonds-Karp algorithm is slower than the Preflow algorithm |
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| 38 | /// but it has an advantage of the step-by-step execution control with |
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| 39 | /// feasible flow solutions. The \e source node, the \e target node, the \e |
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| 40 | /// capacity of the edges and the \e starting \e flow value of the |
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| 41 | /// edges should be passed to the algorithm through the |
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[2036] | 42 | /// constructor. |
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[2034] | 43 | /// |
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[2059] | 44 | /// The time complexity of the algorithm is \f$ O(n * e^2) \f$ in |
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| 45 | /// worst case. Always try the preflow algorithm instead of this if |
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| 46 | /// you does not have some additional reason than to compute the |
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| 47 | /// optimal flow which has \f$ O(n^3) \f$ time complexity. |
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[2034] | 48 | /// |
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| 49 | /// \param _Graph The directed graph type the algorithm runs on. |
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| 50 | /// \param _Number The number type of the capacities and the flow values. |
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| 51 | /// \param _CapacityMap The capacity map type. |
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| 52 | /// \param _FlowMap The flow map type. |
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| 53 | /// \param _Tolerance The tolerance class to handle computation problems. |
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| 54 | /// |
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| 55 | /// \author Balazs Dezso |
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[2059] | 56 | #ifdef DOXYGEN |
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| 57 | template <typename _Graph, typename _Number, |
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| 58 | typename _CapacityMap, typename _FlowMap, typename _Tolerance> |
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| 59 | #else |
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[2034] | 60 | template <typename _Graph, typename _Number, |
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| 61 | typename _CapacityMap = typename _Graph::template EdgeMap<_Number>, |
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| 62 | typename _FlowMap = typename _Graph::template EdgeMap<_Number>, |
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| 63 | typename _Tolerance = Tolerance<_Number> > |
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[2059] | 64 | #endif |
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[2034] | 65 | class EdmondsKarp { |
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| 66 | public: |
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| 67 | |
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| 68 | /// \brief \ref Exception for the case when the source equals the target. |
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| 69 | /// |
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| 70 | /// \ref Exception for the case when the source equals the target. |
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| 71 | /// |
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| 72 | class InvalidArgument : public lemon::LogicError { |
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| 73 | public: |
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| 74 | virtual const char* exceptionName() const { |
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| 75 | return "lemon::EdmondsKarp::InvalidArgument"; |
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| 76 | } |
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| 77 | }; |
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| 78 | |
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| 79 | |
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| 80 | /// \brief The graph type the algorithm runs on. |
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| 81 | typedef _Graph Graph; |
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| 82 | /// \brief The value type of the algorithms. |
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| 83 | typedef _Number Number; |
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| 84 | /// \brief The capacity map on the edges. |
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| 85 | typedef _CapacityMap CapacityMap; |
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| 86 | /// \brief The flow map on the edges. |
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| 87 | typedef _FlowMap FlowMap; |
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| 88 | /// \brief The tolerance used by the algorithm. |
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| 89 | typedef _Tolerance Tolerance; |
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| 90 | |
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| 91 | typedef ResGraphAdaptor<Graph, Number, CapacityMap, |
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| 92 | FlowMap, Tolerance> ResGraph; |
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| 93 | |
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| 94 | private: |
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| 95 | |
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| 96 | typedef typename Graph::Node Node; |
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| 97 | typedef typename Graph::Edge Edge; |
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| 98 | |
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| 99 | typedef typename Graph::NodeIt NodeIt; |
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| 100 | typedef typename Graph::EdgeIt EdgeIt; |
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| 101 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 102 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 103 | |
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| 104 | public: |
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| 105 | |
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| 106 | /// \brief The constructor of the class. |
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| 107 | /// |
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| 108 | /// The constructor of the class. |
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[2037] | 109 | /// \param graph The directed graph the algorithm runs on. |
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| 110 | /// \param source The source node. |
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| 111 | /// \param target The target node. |
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| 112 | /// \param capacity The capacity of the edges. |
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| 113 | /// \param flow The flow of the edges. |
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| 114 | /// \param tolerance Tolerance class. |
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[2034] | 115 | EdmondsKarp(const Graph& graph, Node source, Node target, |
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| 116 | const CapacityMap& capacity, FlowMap& flow, |
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| 117 | const Tolerance& tolerance = Tolerance()) |
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| 118 | : _graph(graph), _capacity(capacity), _flow(flow), |
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| 119 | _tolerance(tolerance), _resgraph(graph, capacity, flow, tolerance), |
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| 120 | _source(source), _target(target) |
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| 121 | { |
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| 122 | if (_source == _target) { |
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| 123 | throw InvalidArgument(); |
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| 124 | } |
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| 125 | } |
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| 126 | |
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| 127 | /// \brief Initializes the algorithm |
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| 128 | /// |
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| 129 | /// It sets the flow to empty flow. |
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| 130 | void init() { |
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| 131 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
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| 132 | _flow.set(it, 0); |
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| 133 | } |
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| 134 | _value = 0; |
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| 135 | } |
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| 136 | |
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| 137 | /// \brief Initializes the algorithm |
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| 138 | /// |
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| 139 | /// If the flow map initially flow this let the flow map |
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| 140 | /// unchanged but the flow value will be set by the flow |
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| 141 | /// on the outedges from the source. |
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| 142 | void flowInit() { |
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| 143 | _value = 0; |
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| 144 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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| 145 | _value += _flow[jt]; |
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| 146 | } |
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| 147 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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| 148 | _value -= _flow[jt]; |
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| 149 | } |
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| 150 | } |
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| 151 | |
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| 152 | /// \brief Initializes the algorithm |
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| 153 | /// |
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| 154 | /// If the flow map initially flow this let the flow map |
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| 155 | /// unchanged but the flow value will be set by the flow |
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| 156 | /// on the outedges from the source. It also checks that |
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| 157 | /// the flow map really contains a flow. |
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| 158 | /// \return %True when the flow map really a flow. |
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| 159 | bool checkedFlowInit() { |
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| 160 | _value = 0; |
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| 161 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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| 162 | _value += _flow[jt]; |
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| 163 | } |
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| 164 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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| 165 | _value -= _flow[jt]; |
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| 166 | } |
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| 167 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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| 168 | if (it == _source || it == _target) continue; |
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| 169 | Number outFlow = 0; |
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| 170 | for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
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| 171 | outFlow += _flow[jt]; |
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| 172 | } |
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| 173 | Number inFlow = 0; |
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| 174 | for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
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| 175 | inFlow += _flow[jt]; |
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| 176 | } |
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| 177 | if (_tolerance.different(outFlow, inFlow)) { |
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| 178 | return false; |
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| 179 | } |
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| 180 | } |
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| 181 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
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| 182 | if (_tolerance.less(_flow[it], 0)) return false; |
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| 183 | if (_tolerance.less(_capacity[it], _flow[it])) return false; |
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| 184 | } |
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| 185 | return true; |
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| 186 | } |
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| 187 | |
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| 188 | /// \brief Augment the solution on an edge shortest path. |
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| 189 | /// |
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| 190 | /// Augment the solution on an edge shortest path. It search an |
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| 191 | /// edge shortest path between the source and the target |
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| 192 | /// in the residual graph with the bfs algoritm. |
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| 193 | /// Then it increase the flow on this path with the minimal residual |
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| 194 | /// capacity on the path. If there is not such path it gives back |
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| 195 | /// false. |
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| 196 | /// \return %False when the augmenting is not success so the |
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| 197 | /// current flow is a feasible and optimal solution. |
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| 198 | bool augment() { |
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| 199 | typename Bfs<ResGraph> |
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| 200 | ::template DefDistMap<NullMap<Node, int> > |
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| 201 | ::Create bfs(_resgraph); |
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| 202 | |
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| 203 | NullMap<Node, int> distMap; |
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| 204 | bfs.distMap(distMap); |
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| 205 | |
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| 206 | bfs.init(); |
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| 207 | bfs.addSource(_source); |
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| 208 | bfs.start(_target); |
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| 209 | |
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| 210 | if (!bfs.reached(_target)) { |
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| 211 | return false; |
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| 212 | } |
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| 213 | Number min = _resgraph.rescap(bfs.predEdge(_target)); |
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| 214 | for (Node it = bfs.predNode(_target); it != _source; |
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| 215 | it = bfs.predNode(it)) { |
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| 216 | if (min > _resgraph.rescap(bfs.predEdge(it))) { |
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| 217 | min = _resgraph.rescap(bfs.predEdge(it)); |
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| 218 | } |
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| 219 | } |
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| 220 | for (Node it = _target; it != _source; it = bfs.predNode(it)) { |
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| 221 | _resgraph.augment(bfs.predEdge(it), min); |
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| 222 | } |
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| 223 | _value += min; |
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| 224 | return true; |
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| 225 | } |
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| 226 | |
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| 227 | /// \brief Executes the algorithm |
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| 228 | /// |
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| 229 | /// It runs augmenting phases until the optimal solution is reached. |
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| 230 | void start() { |
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| 231 | while (augment()) {} |
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| 232 | } |
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| 233 | |
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| 234 | /// \brief Gives back the current flow value. |
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| 235 | /// |
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| 236 | /// Gives back the current flow _value. |
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| 237 | Number flowValue() const { |
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| 238 | return _value; |
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| 239 | } |
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| 240 | |
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| 241 | /// \brief runs the algorithm. |
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| 242 | /// |
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| 243 | /// It is just a shorthand for: |
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[2059] | 244 | /// |
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| 245 | ///\code |
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[2034] | 246 | /// ek.init(); |
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| 247 | /// ek.start(); |
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[2059] | 248 | ///\endcode |
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[2034] | 249 | void run() { |
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| 250 | init(); |
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| 251 | start(); |
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| 252 | } |
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| 253 | |
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| 254 | /// \brief Returns a minimum value cut. |
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| 255 | /// |
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| 256 | /// Sets \c cut to the characteristic vector of a minimum value cut |
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| 257 | /// It simply calls the minMinCut member. |
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[2037] | 258 | /// \retval cut Write node bool map. |
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[2034] | 259 | template <typename CutMap> |
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| 260 | void minCut(CutMap& cut) const { |
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| 261 | minMinCut(cut); |
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| 262 | } |
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| 263 | |
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| 264 | /// \brief Returns the inclusionwise minimum of the minimum value cuts. |
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| 265 | /// |
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| 266 | /// Sets \c cut to the characteristic vector of the minimum value cut |
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| 267 | /// which is inclusionwise minimum. It is computed by processing a |
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| 268 | /// bfs from the source node \c source in the residual graph. |
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[2037] | 269 | /// \retval cut Write node bool map. |
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[2034] | 270 | template <typename CutMap> |
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| 271 | void minMinCut(CutMap& cut) const { |
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| 272 | |
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| 273 | typename Bfs<ResGraph> |
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| 274 | ::template DefDistMap<NullMap<Node, int> > |
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| 275 | ::template DefProcessedMap<CutMap> |
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| 276 | ::Create bfs(_resgraph); |
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| 277 | |
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| 278 | NullMap<Node, int> distMap; |
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| 279 | bfs.distMap(distMap); |
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| 280 | |
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| 281 | bfs.processedMap(cut); |
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| 282 | |
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| 283 | bfs.run(_source); |
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| 284 | } |
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| 285 | |
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| 286 | /// \brief Returns the inclusionwise minimum of the minimum value cuts. |
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| 287 | /// |
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| 288 | /// Sets \c cut to the characteristic vector of the minimum value cut |
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| 289 | /// which is inclusionwise minimum. It is computed by processing a |
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| 290 | /// bfs from the source node \c source in the residual graph. |
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[2037] | 291 | /// \retval cut Write node bool map. |
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[2034] | 292 | template <typename CutMap> |
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| 293 | void maxMinCut(CutMap& cut) const { |
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| 294 | |
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| 295 | typedef RevGraphAdaptor<const ResGraph> RevGraph; |
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| 296 | |
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| 297 | RevGraph revgraph(_resgraph); |
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| 298 | |
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| 299 | typename Bfs<RevGraph> |
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| 300 | ::template DefDistMap<NullMap<Node, int> > |
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| 301 | ::template DefPredMap<NullMap<Node, Edge> > |
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| 302 | ::template DefProcessedMap<NotWriteMap<CutMap> > |
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| 303 | ::Create bfs(revgraph); |
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| 304 | |
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| 305 | NullMap<Node, int> distMap; |
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| 306 | bfs.distMap(distMap); |
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| 307 | |
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| 308 | NullMap<Node, Edge> predMap; |
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| 309 | bfs.predMap(predMap); |
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| 310 | |
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| 311 | NotWriteMap<CutMap> notcut(cut); |
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| 312 | bfs.processedMap(notcut); |
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| 313 | |
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| 314 | bfs.run(_target); |
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| 315 | } |
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| 316 | |
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| 317 | /// \brief Returns the source node. |
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| 318 | /// |
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| 319 | /// Returns the source node. |
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| 320 | /// |
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| 321 | Node source() const { |
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| 322 | return _source; |
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| 323 | } |
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| 324 | |
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| 325 | /// \brief Returns the target node. |
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| 326 | /// |
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| 327 | /// Returns the target node. |
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| 328 | /// |
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| 329 | Node target() const { |
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| 330 | return _target; |
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| 331 | } |
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| 332 | |
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| 333 | /// \brief Returns a reference to capacity map. |
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| 334 | /// |
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| 335 | /// Returns a reference to capacity map. |
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| 336 | /// |
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| 337 | const CapacityMap &capacityMap() const { |
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| 338 | return *_capacity; |
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| 339 | } |
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| 340 | |
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| 341 | /// \brief Returns a reference to flow map. |
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| 342 | /// |
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| 343 | /// Returns a reference to flow map. |
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| 344 | /// |
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| 345 | const FlowMap &flowMap() const { |
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| 346 | return *_flow; |
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| 347 | } |
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| 348 | |
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[2036] | 349 | /// \brief Returns the tolerance used by algorithm. |
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| 350 | /// |
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| 351 | /// Returns the tolerance used by algorithm. |
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| 352 | const Tolerance& tolerance() const { |
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| 353 | return tolerance; |
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| 354 | } |
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| 355 | |
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[2034] | 356 | private: |
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| 357 | |
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| 358 | const Graph& _graph; |
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| 359 | const CapacityMap& _capacity; |
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| 360 | FlowMap& _flow; |
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| 361 | Tolerance _tolerance; |
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| 362 | |
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| 363 | ResGraph _resgraph; |
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| 364 | Node _source, _target; |
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| 365 | Number _value; |
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| 366 | |
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| 367 | }; |
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| 368 | |
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| 369 | } |
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| 370 | |
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| 371 | #endif |
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