[906] | 1 | /* -*- C++ -*- |
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[1435] | 2 | * lemon/preflow.h - Part of LEMON, a generic C++ optimization library |
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[906] | 3 | * |
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[1875] | 4 | * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[906] | 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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[921] | 17 | #ifndef LEMON_PREFLOW_H |
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| 18 | #define LEMON_PREFLOW_H |
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[836] | 19 | |
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| 20 | #include <vector> |
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| 21 | #include <queue> |
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| 22 | |
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[1762] | 23 | #include <lemon/error.h> |
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[921] | 24 | #include <lemon/invalid.h> |
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[1835] | 25 | #include <lemon/tolerance.h> |
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[921] | 26 | #include <lemon/maps.h> |
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[977] | 27 | #include <lemon/graph_utils.h> |
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[836] | 28 | |
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| 29 | /// \file |
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| 30 | /// \ingroup flowalgs |
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[1742] | 31 | /// \brief Implementation of the preflow algorithm. |
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[836] | 32 | |
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[921] | 33 | namespace lemon { |
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[836] | 34 | |
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[1792] | 35 | ///\ingroup flowalgs |
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| 36 | ///\brief %Preflow algorithms class. |
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| 37 | /// |
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[836] | 38 | ///This class provides an implementation of the \e preflow \e |
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| 39 | ///algorithm producing a flow of maximum value in a directed |
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[1222] | 40 | ///graph. The preflow algorithms are the fastest known max flow algorithms |
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[851] | 41 | ///up to now. The \e source node, the \e target node, the \e |
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[836] | 42 | ///capacity of the edges and the \e starting \e flow value of the |
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| 43 | ///edges should be passed to the algorithm through the |
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| 44 | ///constructor. It is possible to change these quantities using the |
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[1285] | 45 | ///functions \ref source, \ref target, \ref capacityMap and \ref |
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| 46 | ///flowMap. |
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[836] | 47 | /// |
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[921] | 48 | ///After running \ref lemon::Preflow::phase1() "phase1()" |
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| 49 | ///or \ref lemon::Preflow::run() "run()", the maximal flow |
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[836] | 50 | ///value can be obtained by calling \ref flowValue(). The minimum |
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[851] | 51 | ///value cut can be written into a <tt>bool</tt> node map by |
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| 52 | ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes |
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[836] | 53 | ///the inclusionwise minimum and maximum of the minimum value cuts, |
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| 54 | ///resp.) |
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| 55 | /// |
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| 56 | ///\param Graph The directed graph type the algorithm runs on. |
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| 57 | ///\param Num The number type of the capacities and the flow values. |
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[1222] | 58 | ///\param CapacityMap The capacity map type. |
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[836] | 59 | ///\param FlowMap The flow map type. |
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| 60 | /// |
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| 61 | ///\author Jacint Szabo |
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[1227] | 62 | ///\todo Second template parameter is superfluous |
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[836] | 63 | template <typename Graph, typename Num, |
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[1222] | 64 | typename CapacityMap=typename Graph::template EdgeMap<Num>, |
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[1835] | 65 | typename FlowMap=typename Graph::template EdgeMap<Num>, |
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| 66 | typename TOL=Tolerance<Num> > |
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[836] | 67 | class Preflow { |
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| 68 | protected: |
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| 69 | typedef typename Graph::Node Node; |
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| 70 | typedef typename Graph::NodeIt NodeIt; |
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| 71 | typedef typename Graph::EdgeIt EdgeIt; |
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| 72 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 73 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 74 | |
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| 75 | typedef typename Graph::template NodeMap<Node> NNMap; |
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| 76 | typedef typename std::vector<Node> VecNode; |
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| 77 | |
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[1222] | 78 | const Graph* _g; |
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| 79 | Node _source; |
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| 80 | Node _target; |
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| 81 | const CapacityMap* _capacity; |
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| 82 | FlowMap* _flow; |
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[1835] | 83 | |
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| 84 | TOL surely; |
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| 85 | |
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[1222] | 86 | int _node_num; //the number of nodes of G |
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[836] | 87 | |
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| 88 | typename Graph::template NodeMap<int> level; |
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| 89 | typename Graph::template NodeMap<Num> excess; |
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| 90 | |
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| 91 | // constants used for heuristics |
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| 92 | static const int H0=20; |
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| 93 | static const int H1=1; |
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| 94 | |
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[1762] | 95 | public: |
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| 96 | |
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| 97 | ///\ref Exception for the case when s=t. |
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| 98 | |
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| 99 | ///\ref Exception for the case when the source equals the target. |
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| 100 | class InvalidArgument : public lemon::LogicError { |
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[836] | 101 | public: |
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[1762] | 102 | virtual const char* exceptionName() const { |
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| 103 | return "lemon::Preflow::InvalidArgument"; |
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| 104 | } |
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| 105 | }; |
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| 106 | |
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| 107 | |
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[836] | 108 | ///Indicates the property of the starting flow map. |
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[1762] | 109 | |
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[1222] | 110 | ///Indicates the property of the starting flow map. |
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| 111 | ///The meanings are as follows: |
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[836] | 112 | ///- \c ZERO_FLOW: constant zero flow |
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| 113 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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| 114 | ///the sum of the out-flows in every node except the \e source and |
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| 115 | ///the \e target. |
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| 116 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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| 117 | ///least the sum of the out-flows in every node except the \e source. |
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[911] | 118 | ///- \c NO_FLOW: indicates an unspecified edge map. \c flow will be |
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| 119 | ///set to the constant zero flow in the beginning of |
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| 120 | ///the algorithm in this case. |
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[836] | 121 | /// |
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| 122 | enum FlowEnum{ |
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| 123 | NO_FLOW, |
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| 124 | ZERO_FLOW, |
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| 125 | GEN_FLOW, |
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| 126 | PRE_FLOW |
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| 127 | }; |
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| 128 | |
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| 129 | ///Indicates the state of the preflow algorithm. |
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| 130 | |
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[1222] | 131 | ///Indicates the state of the preflow algorithm. |
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| 132 | ///The meanings are as follows: |
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| 133 | ///- \c AFTER_NOTHING: before running the algorithm or |
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| 134 | /// at an unspecified state. |
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[836] | 135 | ///- \c AFTER_PREFLOW_PHASE_1: right after running \c phase1 |
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| 136 | ///- \c AFTER_PREFLOW_PHASE_2: after running \ref phase2() |
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| 137 | /// |
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| 138 | enum StatusEnum { |
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| 139 | AFTER_NOTHING, |
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| 140 | AFTER_PREFLOW_PHASE_1, |
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| 141 | AFTER_PREFLOW_PHASE_2 |
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| 142 | }; |
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| 143 | |
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[1762] | 144 | protected: |
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| 145 | FlowEnum flow_prop; |
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[836] | 146 | StatusEnum status; // Do not needle this flag only if necessary. |
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| 147 | |
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| 148 | public: |
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| 149 | ///The constructor of the class. |
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| 150 | |
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| 151 | ///The constructor of the class. |
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[1285] | 152 | ///\param _gr The directed graph the algorithm runs on. |
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[836] | 153 | ///\param _s The source node. |
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| 154 | ///\param _t The target node. |
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[1222] | 155 | ///\param _cap The capacity of the edges. |
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| 156 | ///\param _f The flow of the edges. |
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[836] | 157 | ///Except the graph, all of these parameters can be reset by |
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[1285] | 158 | ///calling \ref source, \ref target, \ref capacityMap and \ref |
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| 159 | ///flowMap, resp. |
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[1222] | 160 | Preflow(const Graph& _gr, Node _s, Node _t, |
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[1835] | 161 | const CapacityMap& _cap, FlowMap& _f, |
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| 162 | const TOL &tol=TOL()) : |
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[1222] | 163 | _g(&_gr), _source(_s), _target(_t), _capacity(&_cap), |
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[1835] | 164 | _flow(&_f), surely(tol), |
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| 165 | _node_num(countNodes(_gr)), level(_gr), excess(_gr,0), |
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[1762] | 166 | flow_prop(NO_FLOW), status(AFTER_NOTHING) { |
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| 167 | if ( _source==_target ) |
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| 168 | throw InvalidArgument(); |
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| 169 | } |
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| 170 | |
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[836] | 171 | |
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| 172 | |
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| 173 | ///Runs the preflow algorithm. |
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| 174 | |
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[851] | 175 | ///Runs the preflow algorithm. |
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| 176 | /// |
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[836] | 177 | void run() { |
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| 178 | phase1(flow_prop); |
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| 179 | phase2(); |
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| 180 | } |
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| 181 | |
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| 182 | ///Runs the preflow algorithm. |
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| 183 | |
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| 184 | ///Runs the preflow algorithm. |
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| 185 | ///\pre The starting flow map must be |
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| 186 | /// - a constant zero flow if \c fp is \c ZERO_FLOW, |
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| 187 | /// - an arbitrary flow if \c fp is \c GEN_FLOW, |
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| 188 | /// - an arbitrary preflow if \c fp is \c PRE_FLOW, |
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| 189 | /// - any map if \c fp is NO_FLOW. |
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| 190 | ///If the starting flow map is a flow or a preflow then |
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| 191 | ///the algorithm terminates faster. |
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| 192 | void run(FlowEnum fp) { |
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| 193 | flow_prop=fp; |
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| 194 | run(); |
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| 195 | } |
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| 196 | |
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| 197 | ///Runs the first phase of the preflow algorithm. |
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| 198 | |
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[920] | 199 | ///The preflow algorithm consists of two phases, this method runs |
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| 200 | ///the first phase. After the first phase the maximum flow value |
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[1285] | 201 | ///and a minimum value cut can already be computed, although a |
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[920] | 202 | ///maximum flow is not yet obtained. So after calling this method |
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| 203 | ///\ref flowValue returns the value of a maximum flow and \ref |
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| 204 | ///minCut returns a minimum cut. |
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| 205 | ///\warning \ref minMinCut and \ref maxMinCut do not give minimum |
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| 206 | ///value cuts unless calling \ref phase2. |
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| 207 | ///\pre The starting flow must be |
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| 208 | ///- a constant zero flow if \c fp is \c ZERO_FLOW, |
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| 209 | ///- an arbitary flow if \c fp is \c GEN_FLOW, |
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| 210 | ///- an arbitary preflow if \c fp is \c PRE_FLOW, |
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| 211 | ///- any map if \c fp is NO_FLOW. |
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[836] | 212 | void phase1(FlowEnum fp) |
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| 213 | { |
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| 214 | flow_prop=fp; |
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| 215 | phase1(); |
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| 216 | } |
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| 217 | |
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| 218 | |
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| 219 | ///Runs the first phase of the preflow algorithm. |
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| 220 | |
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[920] | 221 | ///The preflow algorithm consists of two phases, this method runs |
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| 222 | ///the first phase. After the first phase the maximum flow value |
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[1285] | 223 | ///and a minimum value cut can already be computed, although a |
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[920] | 224 | ///maximum flow is not yet obtained. So after calling this method |
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| 225 | ///\ref flowValue returns the value of a maximum flow and \ref |
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| 226 | ///minCut returns a minimum cut. |
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[1786] | 227 | ///\warning \ref minMinCut() and \ref maxMinCut() do not |
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[911] | 228 | ///give minimum value cuts unless calling \ref phase2(). |
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[836] | 229 | void phase1() |
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| 230 | { |
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[1222] | 231 | int heur0=(int)(H0*_node_num); //time while running 'bound decrease' |
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| 232 | int heur1=(int)(H1*_node_num); //time while running 'highest label' |
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[836] | 233 | int heur=heur1; //starting time interval (#of relabels) |
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| 234 | int numrelabel=0; |
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| 235 | |
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| 236 | bool what_heur=1; |
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| 237 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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| 238 | |
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| 239 | bool end=false; |
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| 240 | //Needed for 'bound decrease', true means no active |
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| 241 | //nodes are above bound b. |
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| 242 | |
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[1222] | 243 | int k=_node_num-2; //bound on the highest level under n containing a node |
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[836] | 244 | int b=k; //bound on the highest level under n of an active node |
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| 245 | |
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[1222] | 246 | VecNode first(_node_num, INVALID); |
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| 247 | NNMap next(*_g, INVALID); |
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[836] | 248 | |
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[1222] | 249 | NNMap left(*_g, INVALID); |
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| 250 | NNMap right(*_g, INVALID); |
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| 251 | VecNode level_list(_node_num,INVALID); |
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[836] | 252 | //List of the nodes in level i<n, set to n. |
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| 253 | |
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| 254 | preflowPreproc(first, next, level_list, left, right); |
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| 255 | |
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| 256 | //Push/relabel on the highest level active nodes. |
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| 257 | while ( true ) { |
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| 258 | if ( b == 0 ) { |
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| 259 | if ( !what_heur && !end && k > 0 ) { |
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| 260 | b=k; |
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| 261 | end=true; |
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| 262 | } else break; |
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| 263 | } |
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| 264 | |
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| 265 | if ( first[b]==INVALID ) --b; |
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| 266 | else { |
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| 267 | end=false; |
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| 268 | Node w=first[b]; |
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| 269 | first[b]=next[w]; |
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| 270 | int newlevel=push(w, next, first); |
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| 271 | if ( excess[w] > 0 ) relabel(w, newlevel, first, next, level_list, |
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| 272 | left, right, b, k, what_heur); |
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| 273 | |
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| 274 | ++numrelabel; |
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| 275 | if ( numrelabel >= heur ) { |
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| 276 | numrelabel=0; |
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| 277 | if ( what_heur ) { |
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| 278 | what_heur=0; |
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| 279 | heur=heur0; |
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| 280 | end=false; |
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| 281 | } else { |
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| 282 | what_heur=1; |
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| 283 | heur=heur1; |
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| 284 | b=k; |
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| 285 | } |
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| 286 | } |
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| 287 | } |
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| 288 | } |
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| 289 | flow_prop=PRE_FLOW; |
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| 290 | status=AFTER_PREFLOW_PHASE_1; |
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| 291 | } |
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| 292 | // Heuristics: |
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| 293 | // 2 phase |
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| 294 | // gap |
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| 295 | // list 'level_list' on the nodes on level i implemented by hand |
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| 296 | // stack 'active' on the active nodes on level i |
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| 297 | // runs heuristic 'highest label' for H1*n relabels |
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[1222] | 298 | // runs heuristic 'bound decrease' for H0*n relabels, |
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| 299 | // starts with 'highest label' |
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[836] | 300 | // Parameters H0 and H1 are initialized to 20 and 1. |
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| 301 | |
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| 302 | |
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| 303 | ///Runs the second phase of the preflow algorithm. |
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| 304 | |
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| 305 | ///The preflow algorithm consists of two phases, this method runs |
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[1631] | 306 | ///the second phase. After calling \ref phase1() and then |
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| 307 | ///\ref phase2(), |
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| 308 | /// \ref flowMap() return a maximum flow, \ref flowValue |
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[920] | 309 | ///returns the value of a maximum flow, \ref minCut returns a |
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| 310 | ///minimum cut, while the methods \ref minMinCut and \ref |
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| 311 | ///maxMinCut return the inclusionwise minimum and maximum cuts of |
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| 312 | ///minimum value, resp. \pre \ref phase1 must be called before. |
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[836] | 313 | void phase2() |
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| 314 | { |
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| 315 | |
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[1222] | 316 | int k=_node_num-2; //bound on the highest level under n containing a node |
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[836] | 317 | int b=k; //bound on the highest level under n of an active node |
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| 318 | |
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| 319 | |
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[1222] | 320 | VecNode first(_node_num, INVALID); |
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| 321 | NNMap next(*_g, INVALID); |
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| 322 | level.set(_source,0); |
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[836] | 323 | std::queue<Node> bfs_queue; |
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[1222] | 324 | bfs_queue.push(_source); |
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[836] | 325 | |
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| 326 | while ( !bfs_queue.empty() ) { |
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| 327 | |
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| 328 | Node v=bfs_queue.front(); |
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| 329 | bfs_queue.pop(); |
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| 330 | int l=level[v]+1; |
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| 331 | |
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[1222] | 332 | for(InEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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| 333 | if ( (*_capacity)[e] <= (*_flow)[e] ) continue; |
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| 334 | Node u=_g->source(e); |
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| 335 | if ( level[u] >= _node_num ) { |
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[836] | 336 | bfs_queue.push(u); |
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| 337 | level.set(u, l); |
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| 338 | if ( excess[u] > 0 ) { |
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| 339 | next.set(u,first[l]); |
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| 340 | first[l]=u; |
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| 341 | } |
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| 342 | } |
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| 343 | } |
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| 344 | |
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[1222] | 345 | for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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| 346 | if ( 0 >= (*_flow)[e] ) continue; |
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| 347 | Node u=_g->target(e); |
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| 348 | if ( level[u] >= _node_num ) { |
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[836] | 349 | bfs_queue.push(u); |
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| 350 | level.set(u, l); |
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| 351 | if ( excess[u] > 0 ) { |
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| 352 | next.set(u,first[l]); |
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| 353 | first[l]=u; |
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| 354 | } |
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| 355 | } |
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| 356 | } |
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| 357 | } |
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[1222] | 358 | b=_node_num-2; |
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[836] | 359 | |
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| 360 | while ( true ) { |
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| 361 | |
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| 362 | if ( b == 0 ) break; |
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| 363 | if ( first[b]==INVALID ) --b; |
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| 364 | else { |
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| 365 | Node w=first[b]; |
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| 366 | first[b]=next[w]; |
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| 367 | int newlevel=push(w,next, first); |
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| 368 | |
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| 369 | //relabel |
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| 370 | if ( excess[w] > 0 ) { |
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| 371 | level.set(w,++newlevel); |
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| 372 | next.set(w,first[newlevel]); |
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| 373 | first[newlevel]=w; |
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| 374 | b=newlevel; |
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| 375 | } |
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| 376 | } |
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| 377 | } // while(true) |
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| 378 | flow_prop=GEN_FLOW; |
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| 379 | status=AFTER_PREFLOW_PHASE_2; |
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| 380 | } |
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| 381 | |
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| 382 | /// Returns the value of the maximum flow. |
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| 383 | |
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| 384 | /// Returns the value of the maximum flow by returning the excess |
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[911] | 385 | /// of the target node \c t. This value equals to the value of |
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[836] | 386 | /// the maximum flow already after running \ref phase1. |
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| 387 | Num flowValue() const { |
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[1222] | 388 | return excess[_target]; |
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[836] | 389 | } |
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| 390 | |
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| 391 | |
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| 392 | ///Returns a minimum value cut. |
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| 393 | |
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| 394 | ///Sets \c M to the characteristic vector of a minimum value |
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| 395 | ///cut. This method can be called both after running \ref |
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| 396 | ///phase1 and \ref phase2. It is much faster after |
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[849] | 397 | ///\ref phase1. \pre M should be a bool-valued node-map. \pre |
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[911] | 398 | ///If \ref minCut() is called after \ref phase2() then M should |
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[836] | 399 | ///be initialized to false. |
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| 400 | template<typename _CutMap> |
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| 401 | void minCut(_CutMap& M) const { |
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| 402 | switch ( status ) { |
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| 403 | case AFTER_PREFLOW_PHASE_1: |
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[1222] | 404 | for(NodeIt v(*_g); v!=INVALID; ++v) { |
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| 405 | if (level[v] < _node_num) { |
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[836] | 406 | M.set(v, false); |
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| 407 | } else { |
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| 408 | M.set(v, true); |
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| 409 | } |
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| 410 | } |
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| 411 | break; |
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| 412 | case AFTER_PREFLOW_PHASE_2: |
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| 413 | minMinCut(M); |
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| 414 | break; |
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| 415 | case AFTER_NOTHING: |
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| 416 | break; |
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| 417 | } |
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| 418 | } |
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| 419 | |
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| 420 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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| 421 | |
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| 422 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 423 | ///which is inclusionwise minimum. It is computed by processing a |
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| 424 | ///bfs from the source node \c s in the residual graph. \pre M |
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| 425 | ///should be a node map of bools initialized to false. \pre \ref |
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| 426 | ///phase2 should already be run. |
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| 427 | template<typename _CutMap> |
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| 428 | void minMinCut(_CutMap& M) const { |
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| 429 | |
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| 430 | std::queue<Node> queue; |
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[1222] | 431 | M.set(_source,true); |
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[1227] | 432 | queue.push(_source); |
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[836] | 433 | |
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| 434 | while (!queue.empty()) { |
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| 435 | Node w=queue.front(); |
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| 436 | queue.pop(); |
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| 437 | |
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[1222] | 438 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 439 | Node v=_g->target(e); |
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| 440 | if (!M[v] && (*_flow)[e] < (*_capacity)[e] ) { |
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[836] | 441 | queue.push(v); |
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| 442 | M.set(v, true); |
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| 443 | } |
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| 444 | } |
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| 445 | |
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[1222] | 446 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 447 | Node v=_g->source(e); |
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| 448 | if (!M[v] && (*_flow)[e] > 0 ) { |
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[836] | 449 | queue.push(v); |
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| 450 | M.set(v, true); |
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| 451 | } |
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| 452 | } |
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| 453 | } |
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| 454 | } |
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| 455 | |
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| 456 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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| 457 | |
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| 458 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 459 | ///which is inclusionwise maximum. It is computed by processing a |
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| 460 | ///backward bfs from the target node \c t in the residual graph. |
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[911] | 461 | ///\pre \ref phase2() or run() should already be run. |
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[836] | 462 | template<typename _CutMap> |
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| 463 | void maxMinCut(_CutMap& M) const { |
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| 464 | |
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[1222] | 465 | for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true); |
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[836] | 466 | |
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| 467 | std::queue<Node> queue; |
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| 468 | |
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[1222] | 469 | M.set(_target,false); |
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| 470 | queue.push(_target); |
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[836] | 471 | |
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| 472 | while (!queue.empty()) { |
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| 473 | Node w=queue.front(); |
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| 474 | queue.pop(); |
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| 475 | |
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[1222] | 476 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 477 | Node v=_g->source(e); |
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| 478 | if (M[v] && (*_flow)[e] < (*_capacity)[e] ) { |
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[836] | 479 | queue.push(v); |
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| 480 | M.set(v, false); |
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| 481 | } |
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| 482 | } |
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| 483 | |
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[1222] | 484 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 485 | Node v=_g->target(e); |
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| 486 | if (M[v] && (*_flow)[e] > 0 ) { |
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[836] | 487 | queue.push(v); |
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| 488 | M.set(v, false); |
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| 489 | } |
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| 490 | } |
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| 491 | } |
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| 492 | } |
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| 493 | |
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| 494 | ///Sets the source node to \c _s. |
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| 495 | |
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| 496 | ///Sets the source node to \c _s. |
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| 497 | /// |
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[1222] | 498 | void source(Node _s) { |
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| 499 | _source=_s; |
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[836] | 500 | if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW; |
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| 501 | status=AFTER_NOTHING; |
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| 502 | } |
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| 503 | |
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[1222] | 504 | ///Returns the source node. |
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| 505 | |
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| 506 | ///Returns the source node. |
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| 507 | /// |
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| 508 | Node source() const { |
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| 509 | return _source; |
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| 510 | } |
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| 511 | |
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[836] | 512 | ///Sets the target node to \c _t. |
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| 513 | |
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| 514 | ///Sets the target node to \c _t. |
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| 515 | /// |
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[1222] | 516 | void target(Node _t) { |
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| 517 | _target=_t; |
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[836] | 518 | if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW; |
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| 519 | status=AFTER_NOTHING; |
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| 520 | } |
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| 521 | |
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[1222] | 522 | ///Returns the target node. |
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| 523 | |
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| 524 | ///Returns the target node. |
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| 525 | /// |
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| 526 | Node target() const { |
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| 527 | return _target; |
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| 528 | } |
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| 529 | |
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[836] | 530 | /// Sets the edge map of the capacities to _cap. |
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| 531 | |
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| 532 | /// Sets the edge map of the capacities to _cap. |
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| 533 | /// |
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[1222] | 534 | void capacityMap(const CapacityMap& _cap) { |
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| 535 | _capacity=&_cap; |
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[836] | 536 | status=AFTER_NOTHING; |
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| 537 | } |
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[1285] | 538 | /// Returns a reference to capacity map. |
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[1222] | 539 | |
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[1285] | 540 | /// Returns a reference to capacity map. |
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[1222] | 541 | /// |
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| 542 | const CapacityMap &capacityMap() const { |
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| 543 | return *_capacity; |
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| 544 | } |
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[836] | 545 | |
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| 546 | /// Sets the edge map of the flows to _flow. |
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| 547 | |
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| 548 | /// Sets the edge map of the flows to _flow. |
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| 549 | /// |
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[1222] | 550 | void flowMap(FlowMap& _f) { |
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| 551 | _flow=&_f; |
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[836] | 552 | flow_prop=NO_FLOW; |
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| 553 | status=AFTER_NOTHING; |
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| 554 | } |
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[1222] | 555 | |
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[1285] | 556 | /// Returns a reference to flow map. |
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[836] | 557 | |
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[1285] | 558 | /// Returns a reference to flow map. |
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[1222] | 559 | /// |
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| 560 | const FlowMap &flowMap() const { |
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| 561 | return *_flow; |
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| 562 | } |
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[836] | 563 | |
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| 564 | private: |
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| 565 | |
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| 566 | int push(Node w, NNMap& next, VecNode& first) { |
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| 567 | |
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| 568 | int lev=level[w]; |
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| 569 | Num exc=excess[w]; |
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[1222] | 570 | int newlevel=_node_num; //bound on the next level of w |
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[836] | 571 | |
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[1222] | 572 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 573 | if ( (*_flow)[e] >= (*_capacity)[e] ) continue; |
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| 574 | Node v=_g->target(e); |
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[836] | 575 | |
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| 576 | if( lev > level[v] ) { //Push is allowed now |
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| 577 | |
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[1222] | 578 | if ( excess[v]<=0 && v!=_target && v!=_source ) { |
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[836] | 579 | next.set(v,first[level[v]]); |
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| 580 | first[level[v]]=v; |
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| 581 | } |
---|
| 582 | |
---|
[1222] | 583 | Num cap=(*_capacity)[e]; |
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| 584 | Num flo=(*_flow)[e]; |
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[836] | 585 | Num remcap=cap-flo; |
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| 586 | |
---|
| 587 | if ( remcap >= exc ) { //A nonsaturating push. |
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| 588 | |
---|
[1222] | 589 | _flow->set(e, flo+exc); |
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[836] | 590 | excess.set(v, excess[v]+exc); |
---|
| 591 | exc=0; |
---|
| 592 | break; |
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| 593 | |
---|
| 594 | } else { //A saturating push. |
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[1222] | 595 | _flow->set(e, cap); |
---|
[836] | 596 | excess.set(v, excess[v]+remcap); |
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| 597 | exc-=remcap; |
---|
| 598 | } |
---|
| 599 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
| 600 | } //for out edges wv |
---|
| 601 | |
---|
| 602 | if ( exc > 0 ) { |
---|
[1222] | 603 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
[836] | 604 | |
---|
[1222] | 605 | if( (*_flow)[e] <= 0 ) continue; |
---|
| 606 | Node v=_g->source(e); |
---|
[836] | 607 | |
---|
| 608 | if( lev > level[v] ) { //Push is allowed now |
---|
| 609 | |
---|
[1222] | 610 | if ( excess[v]<=0 && v!=_target && v!=_source ) { |
---|
[836] | 611 | next.set(v,first[level[v]]); |
---|
| 612 | first[level[v]]=v; |
---|
| 613 | } |
---|
| 614 | |
---|
[1222] | 615 | Num flo=(*_flow)[e]; |
---|
[836] | 616 | |
---|
| 617 | if ( flo >= exc ) { //A nonsaturating push. |
---|
| 618 | |
---|
[1222] | 619 | _flow->set(e, flo-exc); |
---|
[836] | 620 | excess.set(v, excess[v]+exc); |
---|
| 621 | exc=0; |
---|
| 622 | break; |
---|
| 623 | } else { //A saturating push. |
---|
| 624 | |
---|
| 625 | excess.set(v, excess[v]+flo); |
---|
| 626 | exc-=flo; |
---|
[1222] | 627 | _flow->set(e,0); |
---|
[836] | 628 | } |
---|
| 629 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
| 630 | } //for in edges vw |
---|
| 631 | |
---|
| 632 | } // if w still has excess after the out edge for cycle |
---|
| 633 | |
---|
| 634 | excess.set(w, exc); |
---|
| 635 | |
---|
| 636 | return newlevel; |
---|
| 637 | } |
---|
| 638 | |
---|
| 639 | |
---|
| 640 | |
---|
| 641 | void preflowPreproc(VecNode& first, NNMap& next, |
---|
| 642 | VecNode& level_list, NNMap& left, NNMap& right) |
---|
| 643 | { |
---|
[1222] | 644 | for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num); |
---|
[836] | 645 | std::queue<Node> bfs_queue; |
---|
| 646 | |
---|
| 647 | if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) { |
---|
| 648 | //Reverse_bfs from t in the residual graph, |
---|
| 649 | //to find the starting level. |
---|
[1222] | 650 | level.set(_target,0); |
---|
| 651 | bfs_queue.push(_target); |
---|
[836] | 652 | |
---|
| 653 | while ( !bfs_queue.empty() ) { |
---|
| 654 | |
---|
| 655 | Node v=bfs_queue.front(); |
---|
| 656 | bfs_queue.pop(); |
---|
| 657 | int l=level[v]+1; |
---|
| 658 | |
---|
[1222] | 659 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
| 660 | if ( (*_capacity)[e] <= (*_flow)[e] ) continue; |
---|
| 661 | Node w=_g->source(e); |
---|
| 662 | if ( level[w] == _node_num && w != _source ) { |
---|
[836] | 663 | bfs_queue.push(w); |
---|
| 664 | Node z=level_list[l]; |
---|
| 665 | if ( z!=INVALID ) left.set(z,w); |
---|
| 666 | right.set(w,z); |
---|
| 667 | level_list[l]=w; |
---|
| 668 | level.set(w, l); |
---|
| 669 | } |
---|
| 670 | } |
---|
| 671 | |
---|
[1222] | 672 | for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
| 673 | if ( 0 >= (*_flow)[e] ) continue; |
---|
| 674 | Node w=_g->target(e); |
---|
| 675 | if ( level[w] == _node_num && w != _source ) { |
---|
[836] | 676 | bfs_queue.push(w); |
---|
| 677 | Node z=level_list[l]; |
---|
| 678 | if ( z!=INVALID ) left.set(z,w); |
---|
| 679 | right.set(w,z); |
---|
| 680 | level_list[l]=w; |
---|
| 681 | level.set(w, l); |
---|
| 682 | } |
---|
| 683 | } |
---|
| 684 | } //while |
---|
| 685 | } //if |
---|
| 686 | |
---|
| 687 | |
---|
| 688 | switch (flow_prop) { |
---|
| 689 | case NO_FLOW: |
---|
[1222] | 690 | for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0); |
---|
[836] | 691 | case ZERO_FLOW: |
---|
[1222] | 692 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
[836] | 693 | |
---|
| 694 | //Reverse_bfs from t, to find the starting level. |
---|
[1222] | 695 | level.set(_target,0); |
---|
| 696 | bfs_queue.push(_target); |
---|
[836] | 697 | |
---|
| 698 | while ( !bfs_queue.empty() ) { |
---|
| 699 | |
---|
| 700 | Node v=bfs_queue.front(); |
---|
| 701 | bfs_queue.pop(); |
---|
| 702 | int l=level[v]+1; |
---|
| 703 | |
---|
[1222] | 704 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
| 705 | Node w=_g->source(e); |
---|
| 706 | if ( level[w] == _node_num && w != _source ) { |
---|
[836] | 707 | bfs_queue.push(w); |
---|
| 708 | Node z=level_list[l]; |
---|
| 709 | if ( z!=INVALID ) left.set(z,w); |
---|
| 710 | right.set(w,z); |
---|
| 711 | level_list[l]=w; |
---|
| 712 | level.set(w, l); |
---|
| 713 | } |
---|
| 714 | } |
---|
| 715 | } |
---|
| 716 | |
---|
| 717 | //the starting flow |
---|
[1222] | 718 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
| 719 | Num c=(*_capacity)[e]; |
---|
[836] | 720 | if ( c <= 0 ) continue; |
---|
[1222] | 721 | Node w=_g->target(e); |
---|
| 722 | if ( level[w] < _node_num ) { |
---|
| 723 | if ( excess[w] <= 0 && w!=_target ) { //putting into the stack |
---|
[836] | 724 | next.set(w,first[level[w]]); |
---|
| 725 | first[level[w]]=w; |
---|
| 726 | } |
---|
[1222] | 727 | _flow->set(e, c); |
---|
[836] | 728 | excess.set(w, excess[w]+c); |
---|
| 729 | } |
---|
| 730 | } |
---|
| 731 | break; |
---|
| 732 | |
---|
| 733 | case GEN_FLOW: |
---|
[1222] | 734 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
[836] | 735 | { |
---|
| 736 | Num exc=0; |
---|
[1222] | 737 | for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
| 738 | for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
| 739 | excess.set(_target,exc); |
---|
[836] | 740 | } |
---|
| 741 | |
---|
| 742 | //the starting flow |
---|
[1222] | 743 | for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
| 744 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
[836] | 745 | if ( rem <= 0 ) continue; |
---|
[1222] | 746 | Node w=_g->target(e); |
---|
| 747 | if ( level[w] < _node_num ) { |
---|
| 748 | if ( excess[w] <= 0 && w!=_target ) { //putting into the stack |
---|
[836] | 749 | next.set(w,first[level[w]]); |
---|
| 750 | first[level[w]]=w; |
---|
| 751 | } |
---|
[1222] | 752 | _flow->set(e, (*_capacity)[e]); |
---|
[836] | 753 | excess.set(w, excess[w]+rem); |
---|
| 754 | } |
---|
| 755 | } |
---|
| 756 | |
---|
[1222] | 757 | for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
| 758 | if ( (*_flow)[e] <= 0 ) continue; |
---|
| 759 | Node w=_g->source(e); |
---|
| 760 | if ( level[w] < _node_num ) { |
---|
| 761 | if ( excess[w] <= 0 && w!=_target ) { |
---|
[836] | 762 | next.set(w,first[level[w]]); |
---|
| 763 | first[level[w]]=w; |
---|
| 764 | } |
---|
[1222] | 765 | excess.set(w, excess[w]+(*_flow)[e]); |
---|
| 766 | _flow->set(e, 0); |
---|
[836] | 767 | } |
---|
| 768 | } |
---|
| 769 | break; |
---|
| 770 | |
---|
| 771 | case PRE_FLOW: |
---|
| 772 | //the starting flow |
---|
[1222] | 773 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
| 774 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
[836] | 775 | if ( rem <= 0 ) continue; |
---|
[1222] | 776 | Node w=_g->target(e); |
---|
| 777 | if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]); |
---|
[836] | 778 | } |
---|
| 779 | |
---|
[1222] | 780 | for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
| 781 | if ( (*_flow)[e] <= 0 ) continue; |
---|
| 782 | Node w=_g->source(e); |
---|
| 783 | if ( level[w] < _node_num ) _flow->set(e, 0); |
---|
[836] | 784 | } |
---|
| 785 | |
---|
| 786 | //computing the excess |
---|
[1222] | 787 | for(NodeIt w(*_g); w!=INVALID; ++w) { |
---|
[836] | 788 | Num exc=0; |
---|
[1222] | 789 | for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
| 790 | for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
[836] | 791 | excess.set(w,exc); |
---|
| 792 | |
---|
| 793 | //putting the active nodes into the stack |
---|
| 794 | int lev=level[w]; |
---|
[1222] | 795 | if ( exc > 0 && lev < _node_num && Node(w) != _target ) { |
---|
[836] | 796 | next.set(w,first[lev]); |
---|
| 797 | first[lev]=w; |
---|
| 798 | } |
---|
| 799 | } |
---|
| 800 | break; |
---|
| 801 | } //switch |
---|
| 802 | } //preflowPreproc |
---|
| 803 | |
---|
| 804 | |
---|
| 805 | void relabel(Node w, int newlevel, VecNode& first, NNMap& next, |
---|
| 806 | VecNode& level_list, NNMap& left, |
---|
| 807 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
| 808 | { |
---|
| 809 | |
---|
| 810 | int lev=level[w]; |
---|
| 811 | |
---|
| 812 | Node right_n=right[w]; |
---|
| 813 | Node left_n=left[w]; |
---|
| 814 | |
---|
| 815 | //unlacing starts |
---|
| 816 | if ( right_n!=INVALID ) { |
---|
| 817 | if ( left_n!=INVALID ) { |
---|
| 818 | right.set(left_n, right_n); |
---|
| 819 | left.set(right_n, left_n); |
---|
| 820 | } else { |
---|
| 821 | level_list[lev]=right_n; |
---|
| 822 | left.set(right_n, INVALID); |
---|
| 823 | } |
---|
| 824 | } else { |
---|
| 825 | if ( left_n!=INVALID ) { |
---|
| 826 | right.set(left_n, INVALID); |
---|
| 827 | } else { |
---|
| 828 | level_list[lev]=INVALID; |
---|
| 829 | } |
---|
| 830 | } |
---|
| 831 | //unlacing ends |
---|
| 832 | |
---|
| 833 | if ( level_list[lev]==INVALID ) { |
---|
| 834 | |
---|
| 835 | //gapping starts |
---|
| 836 | for (int i=lev; i!=k ; ) { |
---|
| 837 | Node v=level_list[++i]; |
---|
| 838 | while ( v!=INVALID ) { |
---|
[1222] | 839 | level.set(v,_node_num); |
---|
[836] | 840 | v=right[v]; |
---|
| 841 | } |
---|
| 842 | level_list[i]=INVALID; |
---|
| 843 | if ( !what_heur ) first[i]=INVALID; |
---|
| 844 | } |
---|
| 845 | |
---|
[1222] | 846 | level.set(w,_node_num); |
---|
[836] | 847 | b=lev-1; |
---|
| 848 | k=b; |
---|
| 849 | //gapping ends |
---|
| 850 | |
---|
| 851 | } else { |
---|
| 852 | |
---|
[1222] | 853 | if ( newlevel == _node_num ) level.set(w,_node_num); |
---|
[836] | 854 | else { |
---|
| 855 | level.set(w,++newlevel); |
---|
| 856 | next.set(w,first[newlevel]); |
---|
| 857 | first[newlevel]=w; |
---|
| 858 | if ( what_heur ) b=newlevel; |
---|
| 859 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
| 860 | Node z=level_list[newlevel]; |
---|
| 861 | if ( z!=INVALID ) left.set(z,w); |
---|
| 862 | right.set(w,z); |
---|
| 863 | left.set(w,INVALID); |
---|
| 864 | level_list[newlevel]=w; |
---|
| 865 | } |
---|
| 866 | } |
---|
| 867 | } //relabel |
---|
| 868 | |
---|
| 869 | }; |
---|
[1227] | 870 | |
---|
[1792] | 871 | ///\ingroup flowalgs |
---|
| 872 | ///\brief Function type interface for Preflow algorithm. |
---|
| 873 | /// |
---|
[1227] | 874 | ///Function type interface for Preflow algorithm. |
---|
| 875 | ///\sa Preflow |
---|
| 876 | template<class GR, class CM, class FM> |
---|
| 877 | Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g, |
---|
| 878 | typename GR::Node source, |
---|
| 879 | typename GR::Node target, |
---|
| 880 | const CM &cap, |
---|
| 881 | FM &flow |
---|
| 882 | ) |
---|
| 883 | { |
---|
| 884 | return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow); |
---|
| 885 | } |
---|
| 886 | |
---|
[921] | 887 | } //namespace lemon |
---|
[836] | 888 | |
---|
[921] | 889 | #endif //LEMON_PREFLOW_H |
---|