[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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[1164] | 4 | * Copyright (C) 2005 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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| 25 | #include <lemon/maps.h> |
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[977] | 26 | #include <lemon/graph_utils.h> |
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[836] | 27 | |
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| 28 | /// \file |
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| 29 | /// \ingroup flowalgs |
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[1742] | 30 | /// \brief Implementation of the preflow algorithm. |
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[836] | 31 | |
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[921] | 32 | namespace lemon { |
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[836] | 33 | |
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[1792] | 34 | ///\ingroup flowalgs |
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| 35 | ///\brief %Preflow algorithms class. |
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| 36 | /// |
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[836] | 37 | ///This class provides an implementation of the \e preflow \e |
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| 38 | ///algorithm producing a flow of maximum value in a directed |
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[1222] | 39 | ///graph. The preflow algorithms are the fastest known max flow algorithms |
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[851] | 40 | ///up to now. The \e source node, the \e target node, the \e |
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[836] | 41 | ///capacity of the edges and the \e starting \e flow value of the |
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| 42 | ///edges should be passed to the algorithm through the |
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| 43 | ///constructor. It is possible to change these quantities using the |
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[1285] | 44 | ///functions \ref source, \ref target, \ref capacityMap and \ref |
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| 45 | ///flowMap. |
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[836] | 46 | /// |
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[921] | 47 | ///After running \ref lemon::Preflow::phase1() "phase1()" |
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| 48 | ///or \ref lemon::Preflow::run() "run()", the maximal flow |
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[836] | 49 | ///value can be obtained by calling \ref flowValue(). The minimum |
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[851] | 50 | ///value cut can be written into a <tt>bool</tt> node map by |
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| 51 | ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes |
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[836] | 52 | ///the inclusionwise minimum and maximum of the minimum value cuts, |
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| 53 | ///resp.) |
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| 54 | /// |
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| 55 | ///\param Graph The directed graph type the algorithm runs on. |
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| 56 | ///\param Num The number type of the capacities and the flow values. |
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[1222] | 57 | ///\param CapacityMap The capacity map type. |
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[836] | 58 | ///\param FlowMap The flow map type. |
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| 59 | /// |
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| 60 | ///\author Jacint Szabo |
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[1227] | 61 | ///\todo Second template parameter is superfluous |
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[836] | 62 | template <typename Graph, typename Num, |
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[1222] | 63 | typename CapacityMap=typename Graph::template EdgeMap<Num>, |
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[836] | 64 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
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| 65 | class Preflow { |
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| 66 | protected: |
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| 67 | typedef typename Graph::Node Node; |
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| 68 | typedef typename Graph::NodeIt NodeIt; |
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| 69 | typedef typename Graph::EdgeIt EdgeIt; |
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| 70 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 71 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 72 | |
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| 73 | typedef typename Graph::template NodeMap<Node> NNMap; |
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| 74 | typedef typename std::vector<Node> VecNode; |
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| 75 | |
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[1222] | 76 | const Graph* _g; |
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| 77 | Node _source; |
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| 78 | Node _target; |
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| 79 | const CapacityMap* _capacity; |
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| 80 | FlowMap* _flow; |
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| 81 | int _node_num; //the number of nodes of G |
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[836] | 82 | |
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| 83 | typename Graph::template NodeMap<int> level; |
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| 84 | typename Graph::template NodeMap<Num> excess; |
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| 85 | |
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| 86 | // constants used for heuristics |
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| 87 | static const int H0=20; |
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| 88 | static const int H1=1; |
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| 89 | |
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[1762] | 90 | public: |
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| 91 | |
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| 92 | ///\ref Exception for the case when s=t. |
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| 93 | |
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| 94 | ///\ref Exception for the case when the source equals the target. |
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| 95 | class InvalidArgument : public lemon::LogicError { |
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[836] | 96 | public: |
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[1762] | 97 | virtual const char* exceptionName() const { |
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| 98 | return "lemon::Preflow::InvalidArgument"; |
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| 99 | } |
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| 100 | }; |
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| 101 | |
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| 102 | |
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[836] | 103 | ///Indicates the property of the starting flow map. |
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[1762] | 104 | |
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[1222] | 105 | ///Indicates the property of the starting flow map. |
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| 106 | ///The meanings are as follows: |
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[836] | 107 | ///- \c ZERO_FLOW: constant zero flow |
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| 108 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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| 109 | ///the sum of the out-flows in every node except the \e source and |
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| 110 | ///the \e target. |
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| 111 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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| 112 | ///least the sum of the out-flows in every node except the \e source. |
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[911] | 113 | ///- \c NO_FLOW: indicates an unspecified edge map. \c flow will be |
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| 114 | ///set to the constant zero flow in the beginning of |
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| 115 | ///the algorithm in this case. |
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[836] | 116 | /// |
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| 117 | enum FlowEnum{ |
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| 118 | NO_FLOW, |
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| 119 | ZERO_FLOW, |
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| 120 | GEN_FLOW, |
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| 121 | PRE_FLOW |
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| 122 | }; |
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| 123 | |
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| 124 | ///Indicates the state of the preflow algorithm. |
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| 125 | |
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[1222] | 126 | ///Indicates the state of the preflow algorithm. |
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| 127 | ///The meanings are as follows: |
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| 128 | ///- \c AFTER_NOTHING: before running the algorithm or |
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| 129 | /// at an unspecified state. |
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[836] | 130 | ///- \c AFTER_PREFLOW_PHASE_1: right after running \c phase1 |
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| 131 | ///- \c AFTER_PREFLOW_PHASE_2: after running \ref phase2() |
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| 132 | /// |
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| 133 | enum StatusEnum { |
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| 134 | AFTER_NOTHING, |
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| 135 | AFTER_PREFLOW_PHASE_1, |
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| 136 | AFTER_PREFLOW_PHASE_2 |
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| 137 | }; |
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| 138 | |
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[1762] | 139 | protected: |
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| 140 | FlowEnum flow_prop; |
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[836] | 141 | StatusEnum status; // Do not needle this flag only if necessary. |
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| 142 | |
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| 143 | public: |
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| 144 | ///The constructor of the class. |
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| 145 | |
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| 146 | ///The constructor of the class. |
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[1285] | 147 | ///\param _gr The directed graph the algorithm runs on. |
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[836] | 148 | ///\param _s The source node. |
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| 149 | ///\param _t The target node. |
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[1222] | 150 | ///\param _cap The capacity of the edges. |
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| 151 | ///\param _f The flow of the edges. |
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[836] | 152 | ///Except the graph, all of these parameters can be reset by |
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[1285] | 153 | ///calling \ref source, \ref target, \ref capacityMap and \ref |
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| 154 | ///flowMap, resp. |
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[1222] | 155 | Preflow(const Graph& _gr, Node _s, Node _t, |
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| 156 | const CapacityMap& _cap, FlowMap& _f) : |
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| 157 | _g(&_gr), _source(_s), _target(_t), _capacity(&_cap), |
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| 158 | _flow(&_f), _node_num(countNodes(_gr)), level(_gr), excess(_gr,0), |
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[1762] | 159 | flow_prop(NO_FLOW), status(AFTER_NOTHING) { |
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| 160 | if ( _source==_target ) |
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| 161 | throw InvalidArgument(); |
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| 162 | } |
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| 163 | |
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[836] | 164 | |
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| 165 | |
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| 166 | ///Runs the preflow algorithm. |
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| 167 | |
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[851] | 168 | ///Runs the preflow algorithm. |
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| 169 | /// |
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[836] | 170 | void run() { |
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| 171 | phase1(flow_prop); |
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| 172 | phase2(); |
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| 173 | } |
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| 174 | |
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| 175 | ///Runs the preflow algorithm. |
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| 176 | |
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| 177 | ///Runs the preflow algorithm. |
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| 178 | ///\pre The starting flow map must be |
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| 179 | /// - a constant zero flow if \c fp is \c ZERO_FLOW, |
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| 180 | /// - an arbitrary flow if \c fp is \c GEN_FLOW, |
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| 181 | /// - an arbitrary preflow if \c fp is \c PRE_FLOW, |
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| 182 | /// - any map if \c fp is NO_FLOW. |
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| 183 | ///If the starting flow map is a flow or a preflow then |
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| 184 | ///the algorithm terminates faster. |
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| 185 | void run(FlowEnum fp) { |
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| 186 | flow_prop=fp; |
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| 187 | run(); |
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| 188 | } |
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| 189 | |
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| 190 | ///Runs the first phase of the preflow algorithm. |
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| 191 | |
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[920] | 192 | ///The preflow algorithm consists of two phases, this method runs |
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| 193 | ///the first phase. After the first phase the maximum flow value |
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[1285] | 194 | ///and a minimum value cut can already be computed, although a |
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[920] | 195 | ///maximum flow is not yet obtained. So after calling this method |
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| 196 | ///\ref flowValue returns the value of a maximum flow and \ref |
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| 197 | ///minCut returns a minimum cut. |
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| 198 | ///\warning \ref minMinCut and \ref maxMinCut do not give minimum |
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| 199 | ///value cuts unless calling \ref phase2. |
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| 200 | ///\pre The starting flow must be |
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| 201 | ///- a constant zero flow if \c fp is \c ZERO_FLOW, |
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| 202 | ///- an arbitary flow if \c fp is \c GEN_FLOW, |
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| 203 | ///- an arbitary preflow if \c fp is \c PRE_FLOW, |
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| 204 | ///- any map if \c fp is NO_FLOW. |
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[836] | 205 | void phase1(FlowEnum fp) |
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| 206 | { |
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| 207 | flow_prop=fp; |
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| 208 | phase1(); |
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| 209 | } |
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| 210 | |
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| 211 | |
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| 212 | ///Runs the first phase of the preflow algorithm. |
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| 213 | |
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[920] | 214 | ///The preflow algorithm consists of two phases, this method runs |
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| 215 | ///the first phase. After the first phase the maximum flow value |
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[1285] | 216 | ///and a minimum value cut can already be computed, although a |
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[920] | 217 | ///maximum flow is not yet obtained. So after calling this method |
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| 218 | ///\ref flowValue returns the value of a maximum flow and \ref |
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| 219 | ///minCut returns a minimum cut. |
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[1786] | 220 | ///\warning \ref minMinCut() and \ref maxMinCut() do not |
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[911] | 221 | ///give minimum value cuts unless calling \ref phase2(). |
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[836] | 222 | void phase1() |
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| 223 | { |
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[1222] | 224 | int heur0=(int)(H0*_node_num); //time while running 'bound decrease' |
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| 225 | int heur1=(int)(H1*_node_num); //time while running 'highest label' |
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[836] | 226 | int heur=heur1; //starting time interval (#of relabels) |
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| 227 | int numrelabel=0; |
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| 228 | |
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| 229 | bool what_heur=1; |
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| 230 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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| 231 | |
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| 232 | bool end=false; |
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| 233 | //Needed for 'bound decrease', true means no active |
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| 234 | //nodes are above bound b. |
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| 235 | |
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[1222] | 236 | int k=_node_num-2; //bound on the highest level under n containing a node |
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[836] | 237 | int b=k; //bound on the highest level under n of an active node |
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| 238 | |
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[1222] | 239 | VecNode first(_node_num, INVALID); |
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| 240 | NNMap next(*_g, INVALID); |
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[836] | 241 | |
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[1222] | 242 | NNMap left(*_g, INVALID); |
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| 243 | NNMap right(*_g, INVALID); |
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| 244 | VecNode level_list(_node_num,INVALID); |
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[836] | 245 | //List of the nodes in level i<n, set to n. |
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| 246 | |
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| 247 | preflowPreproc(first, next, level_list, left, right); |
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| 248 | |
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| 249 | //Push/relabel on the highest level active nodes. |
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| 250 | while ( true ) { |
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| 251 | if ( b == 0 ) { |
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| 252 | if ( !what_heur && !end && k > 0 ) { |
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| 253 | b=k; |
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| 254 | end=true; |
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| 255 | } else break; |
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| 256 | } |
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| 257 | |
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| 258 | if ( first[b]==INVALID ) --b; |
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| 259 | else { |
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| 260 | end=false; |
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| 261 | Node w=first[b]; |
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| 262 | first[b]=next[w]; |
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| 263 | int newlevel=push(w, next, first); |
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| 264 | if ( excess[w] > 0 ) relabel(w, newlevel, first, next, level_list, |
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| 265 | left, right, b, k, what_heur); |
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| 266 | |
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| 267 | ++numrelabel; |
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| 268 | if ( numrelabel >= heur ) { |
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| 269 | numrelabel=0; |
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| 270 | if ( what_heur ) { |
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| 271 | what_heur=0; |
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| 272 | heur=heur0; |
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| 273 | end=false; |
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| 274 | } else { |
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| 275 | what_heur=1; |
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| 276 | heur=heur1; |
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| 277 | b=k; |
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| 278 | } |
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| 279 | } |
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| 280 | } |
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| 281 | } |
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| 282 | flow_prop=PRE_FLOW; |
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| 283 | status=AFTER_PREFLOW_PHASE_1; |
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| 284 | } |
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| 285 | // Heuristics: |
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| 286 | // 2 phase |
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| 287 | // gap |
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| 288 | // list 'level_list' on the nodes on level i implemented by hand |
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| 289 | // stack 'active' on the active nodes on level i |
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| 290 | // runs heuristic 'highest label' for H1*n relabels |
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[1222] | 291 | // runs heuristic 'bound decrease' for H0*n relabels, |
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| 292 | // starts with 'highest label' |
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[836] | 293 | // Parameters H0 and H1 are initialized to 20 and 1. |
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| 294 | |
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| 295 | |
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| 296 | ///Runs the second phase of the preflow algorithm. |
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| 297 | |
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| 298 | ///The preflow algorithm consists of two phases, this method runs |
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[1631] | 299 | ///the second phase. After calling \ref phase1() and then |
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| 300 | ///\ref phase2(), |
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| 301 | /// \ref flowMap() return a maximum flow, \ref flowValue |
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[920] | 302 | ///returns the value of a maximum flow, \ref minCut returns a |
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| 303 | ///minimum cut, while the methods \ref minMinCut and \ref |
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| 304 | ///maxMinCut return the inclusionwise minimum and maximum cuts of |
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| 305 | ///minimum value, resp. \pre \ref phase1 must be called before. |
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[836] | 306 | void phase2() |
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| 307 | { |
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| 308 | |
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[1222] | 309 | int k=_node_num-2; //bound on the highest level under n containing a node |
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[836] | 310 | int b=k; //bound on the highest level under n of an active node |
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| 311 | |
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| 312 | |
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[1222] | 313 | VecNode first(_node_num, INVALID); |
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| 314 | NNMap next(*_g, INVALID); |
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| 315 | level.set(_source,0); |
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[836] | 316 | std::queue<Node> bfs_queue; |
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[1222] | 317 | bfs_queue.push(_source); |
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[836] | 318 | |
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| 319 | while ( !bfs_queue.empty() ) { |
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| 320 | |
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| 321 | Node v=bfs_queue.front(); |
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| 322 | bfs_queue.pop(); |
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| 323 | int l=level[v]+1; |
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| 324 | |
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[1222] | 325 | for(InEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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| 326 | if ( (*_capacity)[e] <= (*_flow)[e] ) continue; |
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| 327 | Node u=_g->source(e); |
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| 328 | if ( level[u] >= _node_num ) { |
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[836] | 329 | bfs_queue.push(u); |
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| 330 | level.set(u, l); |
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| 331 | if ( excess[u] > 0 ) { |
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| 332 | next.set(u,first[l]); |
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| 333 | first[l]=u; |
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| 334 | } |
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| 335 | } |
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| 336 | } |
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| 337 | |
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[1222] | 338 | for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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| 339 | if ( 0 >= (*_flow)[e] ) continue; |
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| 340 | Node u=_g->target(e); |
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| 341 | if ( level[u] >= _node_num ) { |
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[836] | 342 | bfs_queue.push(u); |
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| 343 | level.set(u, l); |
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| 344 | if ( excess[u] > 0 ) { |
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| 345 | next.set(u,first[l]); |
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| 346 | first[l]=u; |
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| 347 | } |
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| 348 | } |
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| 349 | } |
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| 350 | } |
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[1222] | 351 | b=_node_num-2; |
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[836] | 352 | |
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| 353 | while ( true ) { |
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| 354 | |
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| 355 | if ( b == 0 ) break; |
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| 356 | if ( first[b]==INVALID ) --b; |
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| 357 | else { |
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| 358 | Node w=first[b]; |
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| 359 | first[b]=next[w]; |
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| 360 | int newlevel=push(w,next, first); |
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| 361 | |
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| 362 | //relabel |
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| 363 | if ( excess[w] > 0 ) { |
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| 364 | level.set(w,++newlevel); |
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| 365 | next.set(w,first[newlevel]); |
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| 366 | first[newlevel]=w; |
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| 367 | b=newlevel; |
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| 368 | } |
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| 369 | } |
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| 370 | } // while(true) |
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| 371 | flow_prop=GEN_FLOW; |
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| 372 | status=AFTER_PREFLOW_PHASE_2; |
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| 373 | } |
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| 374 | |
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| 375 | /// Returns the value of the maximum flow. |
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| 376 | |
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| 377 | /// Returns the value of the maximum flow by returning the excess |
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[911] | 378 | /// of the target node \c t. This value equals to the value of |
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[836] | 379 | /// the maximum flow already after running \ref phase1. |
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| 380 | Num flowValue() const { |
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[1222] | 381 | return excess[_target]; |
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[836] | 382 | } |
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| 383 | |
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| 384 | |
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| 385 | ///Returns a minimum value cut. |
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| 386 | |
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| 387 | ///Sets \c M to the characteristic vector of a minimum value |
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| 388 | ///cut. This method can be called both after running \ref |
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| 389 | ///phase1 and \ref phase2. It is much faster after |
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[849] | 390 | ///\ref phase1. \pre M should be a bool-valued node-map. \pre |
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[911] | 391 | ///If \ref minCut() is called after \ref phase2() then M should |
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[836] | 392 | ///be initialized to false. |
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| 393 | template<typename _CutMap> |
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| 394 | void minCut(_CutMap& M) const { |
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| 395 | switch ( status ) { |
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| 396 | case AFTER_PREFLOW_PHASE_1: |
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[1222] | 397 | for(NodeIt v(*_g); v!=INVALID; ++v) { |
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| 398 | if (level[v] < _node_num) { |
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[836] | 399 | M.set(v, false); |
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| 400 | } else { |
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| 401 | M.set(v, true); |
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| 402 | } |
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| 403 | } |
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| 404 | break; |
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| 405 | case AFTER_PREFLOW_PHASE_2: |
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| 406 | minMinCut(M); |
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| 407 | break; |
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| 408 | case AFTER_NOTHING: |
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| 409 | break; |
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| 410 | } |
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| 411 | } |
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| 412 | |
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| 413 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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| 414 | |
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| 415 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 416 | ///which is inclusionwise minimum. It is computed by processing a |
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| 417 | ///bfs from the source node \c s in the residual graph. \pre M |
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| 418 | ///should be a node map of bools initialized to false. \pre \ref |
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| 419 | ///phase2 should already be run. |
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| 420 | template<typename _CutMap> |
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| 421 | void minMinCut(_CutMap& M) const { |
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| 422 | |
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| 423 | std::queue<Node> queue; |
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[1222] | 424 | M.set(_source,true); |
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[1227] | 425 | queue.push(_source); |
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[836] | 426 | |
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| 427 | while (!queue.empty()) { |
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| 428 | Node w=queue.front(); |
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| 429 | queue.pop(); |
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| 430 | |
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[1222] | 431 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 432 | Node v=_g->target(e); |
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| 433 | if (!M[v] && (*_flow)[e] < (*_capacity)[e] ) { |
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[836] | 434 | queue.push(v); |
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| 435 | M.set(v, true); |
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| 436 | } |
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| 437 | } |
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| 438 | |
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[1222] | 439 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 440 | Node v=_g->source(e); |
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| 441 | if (!M[v] && (*_flow)[e] > 0 ) { |
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[836] | 442 | queue.push(v); |
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| 443 | M.set(v, true); |
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| 444 | } |
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| 445 | } |
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| 446 | } |
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| 447 | } |
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| 448 | |
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| 449 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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| 450 | |
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| 451 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 452 | ///which is inclusionwise maximum. It is computed by processing a |
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| 453 | ///backward bfs from the target node \c t in the residual graph. |
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[911] | 454 | ///\pre \ref phase2() or run() should already be run. |
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[836] | 455 | template<typename _CutMap> |
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| 456 | void maxMinCut(_CutMap& M) const { |
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| 457 | |
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[1222] | 458 | for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true); |
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[836] | 459 | |
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| 460 | std::queue<Node> queue; |
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| 461 | |
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[1222] | 462 | M.set(_target,false); |
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| 463 | queue.push(_target); |
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[836] | 464 | |
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| 465 | while (!queue.empty()) { |
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| 466 | Node w=queue.front(); |
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| 467 | queue.pop(); |
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| 468 | |
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[1222] | 469 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 470 | Node v=_g->source(e); |
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| 471 | if (M[v] && (*_flow)[e] < (*_capacity)[e] ) { |
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[836] | 472 | queue.push(v); |
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| 473 | M.set(v, false); |
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| 474 | } |
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| 475 | } |
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| 476 | |
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[1222] | 477 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 478 | Node v=_g->target(e); |
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| 479 | if (M[v] && (*_flow)[e] > 0 ) { |
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[836] | 480 | queue.push(v); |
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| 481 | M.set(v, false); |
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| 482 | } |
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| 483 | } |
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| 484 | } |
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| 485 | } |
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| 486 | |
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| 487 | ///Sets the source node to \c _s. |
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| 488 | |
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| 489 | ///Sets the source node to \c _s. |
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| 490 | /// |
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[1222] | 491 | void source(Node _s) { |
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| 492 | _source=_s; |
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[836] | 493 | if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW; |
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| 494 | status=AFTER_NOTHING; |
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| 495 | } |
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| 496 | |
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[1222] | 497 | ///Returns the source node. |
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| 498 | |
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| 499 | ///Returns the source node. |
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| 500 | /// |
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| 501 | Node source() const { |
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| 502 | return _source; |
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| 503 | } |
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| 504 | |
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[836] | 505 | ///Sets the target node to \c _t. |
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| 506 | |
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| 507 | ///Sets the target node to \c _t. |
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| 508 | /// |
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[1222] | 509 | void target(Node _t) { |
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| 510 | _target=_t; |
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[836] | 511 | if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW; |
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| 512 | status=AFTER_NOTHING; |
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| 513 | } |
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| 514 | |
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[1222] | 515 | ///Returns the target node. |
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| 516 | |
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| 517 | ///Returns the target node. |
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| 518 | /// |
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| 519 | Node target() const { |
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| 520 | return _target; |
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| 521 | } |
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| 522 | |
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[836] | 523 | /// Sets the edge map of the capacities to _cap. |
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| 524 | |
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| 525 | /// Sets the edge map of the capacities to _cap. |
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| 526 | /// |
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[1222] | 527 | void capacityMap(const CapacityMap& _cap) { |
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| 528 | _capacity=&_cap; |
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[836] | 529 | status=AFTER_NOTHING; |
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| 530 | } |
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[1285] | 531 | /// Returns a reference to capacity map. |
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[1222] | 532 | |
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[1285] | 533 | /// Returns a reference to capacity map. |
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[1222] | 534 | /// |
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| 535 | const CapacityMap &capacityMap() const { |
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| 536 | return *_capacity; |
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| 537 | } |
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[836] | 538 | |
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| 539 | /// Sets the edge map of the flows to _flow. |
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| 540 | |
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| 541 | /// Sets the edge map of the flows to _flow. |
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| 542 | /// |
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[1222] | 543 | void flowMap(FlowMap& _f) { |
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| 544 | _flow=&_f; |
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[836] | 545 | flow_prop=NO_FLOW; |
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| 546 | status=AFTER_NOTHING; |
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| 547 | } |
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[1222] | 548 | |
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[1285] | 549 | /// Returns a reference to flow map. |
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[836] | 550 | |
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[1285] | 551 | /// Returns a reference to flow map. |
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[1222] | 552 | /// |
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| 553 | const FlowMap &flowMap() const { |
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| 554 | return *_flow; |
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| 555 | } |
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[836] | 556 | |
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| 557 | private: |
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| 558 | |
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| 559 | int push(Node w, NNMap& next, VecNode& first) { |
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| 560 | |
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| 561 | int lev=level[w]; |
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| 562 | Num exc=excess[w]; |
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[1222] | 563 | int newlevel=_node_num; //bound on the next level of w |
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[836] | 564 | |
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[1222] | 565 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 566 | if ( (*_flow)[e] >= (*_capacity)[e] ) continue; |
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| 567 | Node v=_g->target(e); |
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[836] | 568 | |
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| 569 | if( lev > level[v] ) { //Push is allowed now |
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| 570 | |
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[1222] | 571 | if ( excess[v]<=0 && v!=_target && v!=_source ) { |
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[836] | 572 | next.set(v,first[level[v]]); |
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| 573 | first[level[v]]=v; |
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| 574 | } |
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| 575 | |
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[1222] | 576 | Num cap=(*_capacity)[e]; |
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| 577 | Num flo=(*_flow)[e]; |
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[836] | 578 | Num remcap=cap-flo; |
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| 579 | |
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| 580 | if ( remcap >= exc ) { //A nonsaturating push. |
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| 581 | |
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[1222] | 582 | _flow->set(e, flo+exc); |
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[836] | 583 | excess.set(v, excess[v]+exc); |
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| 584 | exc=0; |
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| 585 | break; |
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| 586 | |
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| 587 | } else { //A saturating push. |
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[1222] | 588 | _flow->set(e, cap); |
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[836] | 589 | excess.set(v, excess[v]+remcap); |
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| 590 | exc-=remcap; |
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| 591 | } |
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| 592 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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| 593 | } //for out edges wv |
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| 594 | |
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| 595 | if ( exc > 0 ) { |
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[1222] | 596 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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[836] | 597 | |
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[1222] | 598 | if( (*_flow)[e] <= 0 ) continue; |
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| 599 | Node v=_g->source(e); |
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[836] | 600 | |
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| 601 | if( lev > level[v] ) { //Push is allowed now |
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| 602 | |
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[1222] | 603 | if ( excess[v]<=0 && v!=_target && v!=_source ) { |
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[836] | 604 | next.set(v,first[level[v]]); |
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| 605 | first[level[v]]=v; |
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| 606 | } |
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| 607 | |
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[1222] | 608 | Num flo=(*_flow)[e]; |
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[836] | 609 | |
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| 610 | if ( flo >= exc ) { //A nonsaturating push. |
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| 611 | |
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[1222] | 612 | _flow->set(e, flo-exc); |
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[836] | 613 | excess.set(v, excess[v]+exc); |
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| 614 | exc=0; |
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| 615 | break; |
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| 616 | } else { //A saturating push. |
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| 617 | |
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| 618 | excess.set(v, excess[v]+flo); |
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| 619 | exc-=flo; |
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[1222] | 620 | _flow->set(e,0); |
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[836] | 621 | } |
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| 622 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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| 623 | } //for in edges vw |
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| 624 | |
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| 625 | } // if w still has excess after the out edge for cycle |
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| 626 | |
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| 627 | excess.set(w, exc); |
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| 628 | |
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| 629 | return newlevel; |
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| 630 | } |
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| 631 | |
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| 632 | |
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| 633 | |
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| 634 | void preflowPreproc(VecNode& first, NNMap& next, |
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| 635 | VecNode& level_list, NNMap& left, NNMap& right) |
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| 636 | { |
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[1222] | 637 | for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num); |
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[836] | 638 | std::queue<Node> bfs_queue; |
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| 639 | |
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| 640 | if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) { |
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| 641 | //Reverse_bfs from t in the residual graph, |
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| 642 | //to find the starting level. |
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[1222] | 643 | level.set(_target,0); |
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| 644 | bfs_queue.push(_target); |
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[836] | 645 | |
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| 646 | while ( !bfs_queue.empty() ) { |
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| 647 | |
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| 648 | Node v=bfs_queue.front(); |
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| 649 | bfs_queue.pop(); |
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| 650 | int l=level[v]+1; |
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| 651 | |
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[1222] | 652 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
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| 653 | if ( (*_capacity)[e] <= (*_flow)[e] ) continue; |
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| 654 | Node w=_g->source(e); |
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| 655 | if ( level[w] == _node_num && w != _source ) { |
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[836] | 656 | bfs_queue.push(w); |
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| 657 | Node z=level_list[l]; |
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| 658 | if ( z!=INVALID ) left.set(z,w); |
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| 659 | right.set(w,z); |
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| 660 | level_list[l]=w; |
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| 661 | level.set(w, l); |
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| 662 | } |
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| 663 | } |
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| 664 | |
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[1222] | 665 | for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
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| 666 | if ( 0 >= (*_flow)[e] ) continue; |
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| 667 | Node w=_g->target(e); |
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| 668 | if ( level[w] == _node_num && w != _source ) { |
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[836] | 669 | bfs_queue.push(w); |
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| 670 | Node z=level_list[l]; |
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| 671 | if ( z!=INVALID ) left.set(z,w); |
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| 672 | right.set(w,z); |
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| 673 | level_list[l]=w; |
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| 674 | level.set(w, l); |
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| 675 | } |
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| 676 | } |
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| 677 | } //while |
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| 678 | } //if |
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| 679 | |
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| 680 | |
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| 681 | switch (flow_prop) { |
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| 682 | case NO_FLOW: |
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[1222] | 683 | for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0); |
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[836] | 684 | case ZERO_FLOW: |
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[1222] | 685 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
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[836] | 686 | |
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| 687 | //Reverse_bfs from t, to find the starting level. |
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[1222] | 688 | level.set(_target,0); |
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| 689 | bfs_queue.push(_target); |
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[836] | 690 | |
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| 691 | while ( !bfs_queue.empty() ) { |
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| 692 | |
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| 693 | Node v=bfs_queue.front(); |
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| 694 | bfs_queue.pop(); |
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| 695 | int l=level[v]+1; |
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| 696 | |
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[1222] | 697 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
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| 698 | Node w=_g->source(e); |
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| 699 | if ( level[w] == _node_num && w != _source ) { |
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[836] | 700 | bfs_queue.push(w); |
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| 701 | Node z=level_list[l]; |
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| 702 | if ( z!=INVALID ) left.set(z,w); |
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| 703 | right.set(w,z); |
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| 704 | level_list[l]=w; |
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| 705 | level.set(w, l); |
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| 706 | } |
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| 707 | } |
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| 708 | } |
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| 709 | |
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| 710 | //the starting flow |
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[1222] | 711 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
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| 712 | Num c=(*_capacity)[e]; |
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[836] | 713 | if ( c <= 0 ) continue; |
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[1222] | 714 | Node w=_g->target(e); |
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| 715 | if ( level[w] < _node_num ) { |
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| 716 | if ( excess[w] <= 0 && w!=_target ) { //putting into the stack |
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[836] | 717 | next.set(w,first[level[w]]); |
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| 718 | first[level[w]]=w; |
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| 719 | } |
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[1222] | 720 | _flow->set(e, c); |
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[836] | 721 | excess.set(w, excess[w]+c); |
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| 722 | } |
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| 723 | } |
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| 724 | break; |
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| 725 | |
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| 726 | case GEN_FLOW: |
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[1222] | 727 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
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[836] | 728 | { |
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| 729 | Num exc=0; |
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[1222] | 730 | for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e]; |
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| 731 | for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e]; |
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| 732 | excess.set(_target,exc); |
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[836] | 733 | } |
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| 734 | |
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| 735 | //the starting flow |
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[1222] | 736 | for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
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| 737 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
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[836] | 738 | if ( rem <= 0 ) continue; |
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[1222] | 739 | Node w=_g->target(e); |
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| 740 | if ( level[w] < _node_num ) { |
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| 741 | if ( excess[w] <= 0 && w!=_target ) { //putting into the stack |
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[836] | 742 | next.set(w,first[level[w]]); |
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| 743 | first[level[w]]=w; |
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| 744 | } |
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[1222] | 745 | _flow->set(e, (*_capacity)[e]); |
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[836] | 746 | excess.set(w, excess[w]+rem); |
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| 747 | } |
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| 748 | } |
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| 749 | |
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[1222] | 750 | for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
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| 751 | if ( (*_flow)[e] <= 0 ) continue; |
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| 752 | Node w=_g->source(e); |
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| 753 | if ( level[w] < _node_num ) { |
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| 754 | if ( excess[w] <= 0 && w!=_target ) { |
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[836] | 755 | next.set(w,first[level[w]]); |
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| 756 | first[level[w]]=w; |
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| 757 | } |
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[1222] | 758 | excess.set(w, excess[w]+(*_flow)[e]); |
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| 759 | _flow->set(e, 0); |
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[836] | 760 | } |
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| 761 | } |
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| 762 | break; |
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| 763 | |
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| 764 | case PRE_FLOW: |
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| 765 | //the starting flow |
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[1222] | 766 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
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| 767 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
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[836] | 768 | if ( rem <= 0 ) continue; |
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[1222] | 769 | Node w=_g->target(e); |
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| 770 | if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]); |
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[836] | 771 | } |
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| 772 | |
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[1222] | 773 | for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
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| 774 | if ( (*_flow)[e] <= 0 ) continue; |
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| 775 | Node w=_g->source(e); |
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| 776 | if ( level[w] < _node_num ) _flow->set(e, 0); |
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[836] | 777 | } |
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| 778 | |
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| 779 | //computing the excess |
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[1222] | 780 | for(NodeIt w(*_g); w!=INVALID; ++w) { |
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[836] | 781 | Num exc=0; |
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[1222] | 782 | for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e]; |
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| 783 | for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e]; |
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[836] | 784 | excess.set(w,exc); |
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| 785 | |
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| 786 | //putting the active nodes into the stack |
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| 787 | int lev=level[w]; |
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[1222] | 788 | if ( exc > 0 && lev < _node_num && Node(w) != _target ) { |
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[836] | 789 | next.set(w,first[lev]); |
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| 790 | first[lev]=w; |
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| 791 | } |
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| 792 | } |
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| 793 | break; |
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| 794 | } //switch |
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| 795 | } //preflowPreproc |
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| 796 | |
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| 797 | |
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| 798 | void relabel(Node w, int newlevel, VecNode& first, NNMap& next, |
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| 799 | VecNode& level_list, NNMap& left, |
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| 800 | NNMap& right, int& b, int& k, bool what_heur ) |
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| 801 | { |
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| 802 | |
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| 803 | int lev=level[w]; |
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| 804 | |
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| 805 | Node right_n=right[w]; |
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| 806 | Node left_n=left[w]; |
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| 807 | |
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| 808 | //unlacing starts |
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| 809 | if ( right_n!=INVALID ) { |
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| 810 | if ( left_n!=INVALID ) { |
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| 811 | right.set(left_n, right_n); |
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| 812 | left.set(right_n, left_n); |
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| 813 | } else { |
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| 814 | level_list[lev]=right_n; |
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| 815 | left.set(right_n, INVALID); |
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| 816 | } |
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| 817 | } else { |
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| 818 | if ( left_n!=INVALID ) { |
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| 819 | right.set(left_n, INVALID); |
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| 820 | } else { |
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| 821 | level_list[lev]=INVALID; |
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| 822 | } |
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| 823 | } |
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| 824 | //unlacing ends |
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| 825 | |
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| 826 | if ( level_list[lev]==INVALID ) { |
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| 827 | |
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| 828 | //gapping starts |
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| 829 | for (int i=lev; i!=k ; ) { |
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| 830 | Node v=level_list[++i]; |
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| 831 | while ( v!=INVALID ) { |
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[1222] | 832 | level.set(v,_node_num); |
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[836] | 833 | v=right[v]; |
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| 834 | } |
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| 835 | level_list[i]=INVALID; |
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| 836 | if ( !what_heur ) first[i]=INVALID; |
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| 837 | } |
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| 838 | |
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[1222] | 839 | level.set(w,_node_num); |
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[836] | 840 | b=lev-1; |
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| 841 | k=b; |
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| 842 | //gapping ends |
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| 843 | |
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| 844 | } else { |
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| 845 | |
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[1222] | 846 | if ( newlevel == _node_num ) level.set(w,_node_num); |
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[836] | 847 | else { |
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| 848 | level.set(w,++newlevel); |
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| 849 | next.set(w,first[newlevel]); |
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| 850 | first[newlevel]=w; |
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| 851 | if ( what_heur ) b=newlevel; |
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| 852 | if ( k < newlevel ) ++k; //now k=newlevel |
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| 853 | Node z=level_list[newlevel]; |
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| 854 | if ( z!=INVALID ) left.set(z,w); |
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| 855 | right.set(w,z); |
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| 856 | left.set(w,INVALID); |
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| 857 | level_list[newlevel]=w; |
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| 858 | } |
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| 859 | } |
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| 860 | } //relabel |
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| 861 | |
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| 862 | }; |
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[1227] | 863 | |
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[1792] | 864 | ///\ingroup flowalgs |
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| 865 | ///\brief Function type interface for Preflow algorithm. |
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| 866 | /// |
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[1227] | 867 | ///Function type interface for Preflow algorithm. |
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| 868 | ///\sa Preflow |
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| 869 | template<class GR, class CM, class FM> |
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| 870 | Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g, |
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| 871 | typename GR::Node source, |
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| 872 | typename GR::Node target, |
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| 873 | const CM &cap, |
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| 874 | FM &flow |
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| 875 | ) |
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| 876 | { |
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| 877 | return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow); |
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| 878 | } |
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| 879 | |
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[921] | 880 | } //namespace lemon |
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[836] | 881 | |
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[921] | 882 | #endif //LEMON_PREFLOW_H |
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