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