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