[906] | 1 | /* -*- C++ -*- |
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[1435] | 2 | * lemon/preflow.h - Part of LEMON, a generic C++ optimization library |
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[906] | 3 | * |
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[1875] | 4 | * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[906] | 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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[921] | 17 | #ifndef LEMON_PREFLOW_H |
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| 18 | #define LEMON_PREFLOW_H |
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[836] | 19 | |
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| 20 | #include <vector> |
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| 21 | #include <queue> |
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| 22 | |
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[1762] | 23 | #include <lemon/error.h> |
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[921] | 24 | #include <lemon/invalid.h> |
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[1835] | 25 | #include <lemon/tolerance.h> |
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[921] | 26 | #include <lemon/maps.h> |
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[977] | 27 | #include <lemon/graph_utils.h> |
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[836] | 28 | |
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| 29 | /// \file |
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| 30 | /// \ingroup flowalgs |
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[1742] | 31 | /// \brief Implementation of the preflow algorithm. |
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[836] | 32 | |
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[921] | 33 | namespace lemon { |
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[836] | 34 | |
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[1792] | 35 | ///\ingroup flowalgs |
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| 36 | ///\brief %Preflow algorithms class. |
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| 37 | /// |
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[836] | 38 | ///This class provides an implementation of the \e preflow \e |
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| 39 | ///algorithm producing a flow of maximum value in a directed |
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[1222] | 40 | ///graph. The preflow algorithms are the fastest known max flow algorithms |
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[851] | 41 | ///up to now. The \e source node, the \e target node, the \e |
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[836] | 42 | ///capacity of the edges and the \e starting \e flow value of the |
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| 43 | ///edges should be passed to the algorithm through the |
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| 44 | ///constructor. It is possible to change these quantities using the |
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[1285] | 45 | ///functions \ref source, \ref target, \ref capacityMap and \ref |
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| 46 | ///flowMap. |
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[836] | 47 | /// |
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[921] | 48 | ///After running \ref lemon::Preflow::phase1() "phase1()" |
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| 49 | ///or \ref lemon::Preflow::run() "run()", the maximal flow |
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[836] | 50 | ///value can be obtained by calling \ref flowValue(). The minimum |
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[851] | 51 | ///value cut can be written into a <tt>bool</tt> node map by |
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| 52 | ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes |
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[836] | 53 | ///the inclusionwise minimum and maximum of the minimum value cuts, |
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| 54 | ///resp.) |
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| 55 | /// |
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| 56 | ///\param Graph The directed graph type the algorithm runs on. |
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| 57 | ///\param Num The number type of the capacities and the flow values. |
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[1222] | 58 | ///\param CapacityMap The capacity map type. |
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[836] | 59 | ///\param FlowMap The flow map type. |
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| 60 | /// |
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| 61 | ///\author Jacint Szabo |
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[1227] | 62 | ///\todo Second template parameter is superfluous |
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[836] | 63 | template <typename Graph, typename Num, |
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[1222] | 64 | typename CapacityMap=typename Graph::template EdgeMap<Num>, |
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[1835] | 65 | typename FlowMap=typename Graph::template EdgeMap<Num>, |
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| 66 | typename TOL=Tolerance<Num> > |
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[836] | 67 | class Preflow { |
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| 68 | protected: |
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| 69 | typedef typename Graph::Node Node; |
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| 70 | typedef typename Graph::NodeIt NodeIt; |
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| 71 | typedef typename Graph::EdgeIt EdgeIt; |
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| 72 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 73 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 74 | |
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| 75 | typedef typename Graph::template NodeMap<Node> NNMap; |
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| 76 | typedef typename std::vector<Node> VecNode; |
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| 77 | |
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[1222] | 78 | const Graph* _g; |
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| 79 | Node _source; |
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| 80 | Node _target; |
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| 81 | const CapacityMap* _capacity; |
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| 82 | FlowMap* _flow; |
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[1835] | 83 | |
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| 84 | TOL surely; |
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| 85 | |
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[1222] | 86 | int _node_num; //the number of nodes of G |
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[836] | 87 | |
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| 88 | typename Graph::template NodeMap<int> level; |
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| 89 | typename Graph::template NodeMap<Num> excess; |
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| 90 | |
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| 91 | // constants used for heuristics |
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| 92 | static const int H0=20; |
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| 93 | static const int H1=1; |
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| 94 | |
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[1762] | 95 | public: |
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| 96 | |
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| 97 | ///\ref Exception for the case when s=t. |
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| 98 | |
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| 99 | ///\ref Exception for the case when the source equals the target. |
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| 100 | class InvalidArgument : public lemon::LogicError { |
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[836] | 101 | public: |
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[1762] | 102 | virtual const char* exceptionName() const { |
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| 103 | return "lemon::Preflow::InvalidArgument"; |
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| 104 | } |
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| 105 | }; |
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| 106 | |
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| 107 | |
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[836] | 108 | ///Indicates the property of the starting flow map. |
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[1762] | 109 | |
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[1222] | 110 | ///Indicates the property of the starting flow map. |
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[836] | 111 | /// |
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| 112 | enum FlowEnum{ |
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[1898] | 113 | ///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 | NO_FLOW, |
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[1898] | 117 | ///constant zero flow |
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[836] | 118 | ZERO_FLOW, |
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[1898] | 119 | ///any flow, i.e. the sum of the in-flows equals to |
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| 120 | ///the sum of the out-flows in every node except the \c source and |
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| 121 | ///the \c target. |
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[836] | 122 | GEN_FLOW, |
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[1898] | 123 | ///any preflow, i.e. the sum of the in-flows is at |
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| 124 | ///least the sum of the out-flows in every node except the \c source. |
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[836] | 125 | PRE_FLOW |
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| 126 | }; |
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| 127 | |
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| 128 | ///Indicates the state of the preflow algorithm. |
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| 129 | |
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[1222] | 130 | ///Indicates the state of the preflow algorithm. |
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[836] | 131 | /// |
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| 132 | enum StatusEnum { |
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[1898] | 133 | ///before running the algorithm or |
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| 134 | ///at an unspecified state. |
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[836] | 135 | AFTER_NOTHING, |
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[1898] | 136 | ///right after running \ref phase1() |
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[836] | 137 | AFTER_PREFLOW_PHASE_1, |
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[1898] | 138 | ///after running \ref phase2() |
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[836] | 139 | AFTER_PREFLOW_PHASE_2 |
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| 140 | }; |
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| 141 | |
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[1762] | 142 | protected: |
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| 143 | FlowEnum flow_prop; |
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[836] | 144 | StatusEnum status; // Do not needle this flag only if necessary. |
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| 145 | |
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| 146 | public: |
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| 147 | ///The constructor of the class. |
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| 148 | |
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| 149 | ///The constructor of the class. |
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[1285] | 150 | ///\param _gr The directed graph the algorithm runs on. |
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[836] | 151 | ///\param _s The source node. |
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| 152 | ///\param _t The target node. |
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[1222] | 153 | ///\param _cap The capacity of the edges. |
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| 154 | ///\param _f The flow of the edges. |
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[836] | 155 | ///Except the graph, all of these parameters can be reset by |
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[1285] | 156 | ///calling \ref source, \ref target, \ref capacityMap and \ref |
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| 157 | ///flowMap, resp. |
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[1222] | 158 | Preflow(const Graph& _gr, Node _s, Node _t, |
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[1835] | 159 | const CapacityMap& _cap, FlowMap& _f, |
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| 160 | const TOL &tol=TOL()) : |
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[1222] | 161 | _g(&_gr), _source(_s), _target(_t), _capacity(&_cap), |
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[1835] | 162 | _flow(&_f), surely(tol), |
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| 163 | _node_num(countNodes(_gr)), level(_gr), excess(_gr,0), |
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[1762] | 164 | flow_prop(NO_FLOW), status(AFTER_NOTHING) { |
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| 165 | if ( _source==_target ) |
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| 166 | throw InvalidArgument(); |
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| 167 | } |
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| 168 | |
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[1898] | 169 | ///Give a reference to the tolerance handler class |
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[836] | 170 | |
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[1898] | 171 | ///Give a reference to the tolerance handler class |
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| 172 | ///\sa Tolerance |
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| 173 | TOL &tolerance() { return surely; } |
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| 174 | |
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[836] | 175 | ///Runs the preflow algorithm. |
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| 176 | |
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[851] | 177 | ///Runs the preflow algorithm. |
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| 178 | /// |
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[836] | 179 | void run() { |
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| 180 | phase1(flow_prop); |
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| 181 | phase2(); |
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| 182 | } |
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| 183 | |
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| 184 | ///Runs the preflow algorithm. |
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| 185 | |
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| 186 | ///Runs the preflow algorithm. |
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| 187 | ///\pre The starting flow map must be |
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| 188 | /// - a constant zero flow if \c fp is \c ZERO_FLOW, |
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| 189 | /// - an arbitrary flow if \c fp is \c GEN_FLOW, |
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| 190 | /// - an arbitrary preflow if \c fp is \c PRE_FLOW, |
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| 191 | /// - any map if \c fp is NO_FLOW. |
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| 192 | ///If the starting flow map is a flow or a preflow then |
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| 193 | ///the algorithm terminates faster. |
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| 194 | void run(FlowEnum fp) { |
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| 195 | flow_prop=fp; |
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| 196 | run(); |
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| 197 | } |
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| 198 | |
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| 199 | ///Runs the first phase of the preflow algorithm. |
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| 200 | |
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[920] | 201 | ///The preflow algorithm consists of two phases, this method runs |
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| 202 | ///the first phase. After the first phase the maximum flow value |
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[1285] | 203 | ///and a minimum value cut can already be computed, although a |
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[920] | 204 | ///maximum flow is not yet obtained. So after calling this method |
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| 205 | ///\ref flowValue returns the value of a maximum flow and \ref |
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| 206 | ///minCut returns a minimum cut. |
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| 207 | ///\warning \ref minMinCut and \ref maxMinCut do not give minimum |
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| 208 | ///value cuts unless calling \ref phase2. |
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| 209 | ///\pre The starting flow must be |
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| 210 | ///- a constant zero flow if \c fp is \c ZERO_FLOW, |
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| 211 | ///- an arbitary flow if \c fp is \c GEN_FLOW, |
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| 212 | ///- an arbitary preflow if \c fp is \c PRE_FLOW, |
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| 213 | ///- any map if \c fp is NO_FLOW. |
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[836] | 214 | void phase1(FlowEnum fp) |
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| 215 | { |
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| 216 | flow_prop=fp; |
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| 217 | phase1(); |
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| 218 | } |
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| 219 | |
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| 220 | |
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| 221 | ///Runs the first phase of the preflow algorithm. |
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| 222 | |
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[920] | 223 | ///The preflow algorithm consists of two phases, this method runs |
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| 224 | ///the first phase. After the first phase the maximum flow value |
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[1285] | 225 | ///and a minimum value cut can already be computed, although a |
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[920] | 226 | ///maximum flow is not yet obtained. So after calling this method |
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| 227 | ///\ref flowValue returns the value of a maximum flow and \ref |
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| 228 | ///minCut returns a minimum cut. |
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[1786] | 229 | ///\warning \ref minMinCut() and \ref maxMinCut() do not |
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[911] | 230 | ///give minimum value cuts unless calling \ref phase2(). |
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[836] | 231 | void phase1() |
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| 232 | { |
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[1222] | 233 | int heur0=(int)(H0*_node_num); //time while running 'bound decrease' |
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| 234 | int heur1=(int)(H1*_node_num); //time while running 'highest label' |
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[836] | 235 | int heur=heur1; //starting time interval (#of relabels) |
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| 236 | int numrelabel=0; |
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| 237 | |
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| 238 | bool what_heur=1; |
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| 239 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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| 240 | |
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| 241 | bool end=false; |
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| 242 | //Needed for 'bound decrease', true means no active |
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| 243 | //nodes are above bound b. |
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| 244 | |
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[1222] | 245 | int k=_node_num-2; //bound on the highest level under n containing a node |
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[836] | 246 | int b=k; //bound on the highest level under n of an active node |
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| 247 | |
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[1222] | 248 | VecNode first(_node_num, INVALID); |
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| 249 | NNMap next(*_g, INVALID); |
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[836] | 250 | |
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[1222] | 251 | NNMap left(*_g, INVALID); |
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| 252 | NNMap right(*_g, INVALID); |
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| 253 | VecNode level_list(_node_num,INVALID); |
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[836] | 254 | //List of the nodes in level i<n, set to n. |
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| 255 | |
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| 256 | preflowPreproc(first, next, level_list, left, right); |
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| 257 | |
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| 258 | //Push/relabel on the highest level active nodes. |
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| 259 | while ( true ) { |
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| 260 | if ( b == 0 ) { |
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| 261 | if ( !what_heur && !end && k > 0 ) { |
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| 262 | b=k; |
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| 263 | end=true; |
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| 264 | } else break; |
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| 265 | } |
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| 266 | |
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| 267 | if ( first[b]==INVALID ) --b; |
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| 268 | else { |
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| 269 | end=false; |
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| 270 | Node w=first[b]; |
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| 271 | first[b]=next[w]; |
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| 272 | int newlevel=push(w, next, first); |
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| 273 | if ( excess[w] > 0 ) relabel(w, newlevel, first, next, level_list, |
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| 274 | left, right, b, k, what_heur); |
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| 275 | |
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| 276 | ++numrelabel; |
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| 277 | if ( numrelabel >= heur ) { |
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| 278 | numrelabel=0; |
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| 279 | if ( what_heur ) { |
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| 280 | what_heur=0; |
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| 281 | heur=heur0; |
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| 282 | end=false; |
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| 283 | } else { |
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| 284 | what_heur=1; |
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| 285 | heur=heur1; |
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| 286 | b=k; |
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| 287 | } |
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| 288 | } |
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| 289 | } |
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| 290 | } |
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| 291 | flow_prop=PRE_FLOW; |
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| 292 | status=AFTER_PREFLOW_PHASE_1; |
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| 293 | } |
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| 294 | // Heuristics: |
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| 295 | // 2 phase |
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| 296 | // gap |
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| 297 | // list 'level_list' on the nodes on level i implemented by hand |
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| 298 | // stack 'active' on the active nodes on level i |
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| 299 | // runs heuristic 'highest label' for H1*n relabels |
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[1222] | 300 | // runs heuristic 'bound decrease' for H0*n relabels, |
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| 301 | // starts with 'highest label' |
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[836] | 302 | // Parameters H0 and H1 are initialized to 20 and 1. |
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| 303 | |
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| 304 | |
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| 305 | ///Runs the second phase of the preflow algorithm. |
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| 306 | |
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| 307 | ///The preflow algorithm consists of two phases, this method runs |
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[1631] | 308 | ///the second phase. After calling \ref phase1() and then |
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| 309 | ///\ref phase2(), |
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| 310 | /// \ref flowMap() return a maximum flow, \ref flowValue |
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[920] | 311 | ///returns the value of a maximum flow, \ref minCut returns a |
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| 312 | ///minimum cut, while the methods \ref minMinCut and \ref |
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| 313 | ///maxMinCut return the inclusionwise minimum and maximum cuts of |
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| 314 | ///minimum value, resp. \pre \ref phase1 must be called before. |
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[836] | 315 | void phase2() |
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| 316 | { |
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| 317 | |
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[1222] | 318 | int k=_node_num-2; //bound on the highest level under n containing a node |
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[836] | 319 | int b=k; //bound on the highest level under n of an active node |
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| 320 | |
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| 321 | |
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[1222] | 322 | VecNode first(_node_num, INVALID); |
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| 323 | NNMap next(*_g, INVALID); |
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| 324 | level.set(_source,0); |
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[836] | 325 | std::queue<Node> bfs_queue; |
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[1222] | 326 | bfs_queue.push(_source); |
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[836] | 327 | |
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| 328 | while ( !bfs_queue.empty() ) { |
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| 329 | |
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| 330 | Node v=bfs_queue.front(); |
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| 331 | bfs_queue.pop(); |
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| 332 | int l=level[v]+1; |
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| 333 | |
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[1222] | 334 | for(InEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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| 335 | if ( (*_capacity)[e] <= (*_flow)[e] ) continue; |
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| 336 | Node u=_g->source(e); |
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| 337 | if ( level[u] >= _node_num ) { |
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[836] | 338 | bfs_queue.push(u); |
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| 339 | level.set(u, l); |
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| 340 | if ( excess[u] > 0 ) { |
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| 341 | next.set(u,first[l]); |
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| 342 | first[l]=u; |
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| 343 | } |
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| 344 | } |
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| 345 | } |
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| 346 | |
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[1222] | 347 | for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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| 348 | if ( 0 >= (*_flow)[e] ) continue; |
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| 349 | Node u=_g->target(e); |
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| 350 | if ( level[u] >= _node_num ) { |
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[836] | 351 | bfs_queue.push(u); |
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| 352 | level.set(u, l); |
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| 353 | if ( excess[u] > 0 ) { |
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| 354 | next.set(u,first[l]); |
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| 355 | first[l]=u; |
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| 356 | } |
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| 357 | } |
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| 358 | } |
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| 359 | } |
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[1222] | 360 | b=_node_num-2; |
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[836] | 361 | |
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| 362 | while ( true ) { |
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| 363 | |
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| 364 | if ( b == 0 ) break; |
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| 365 | if ( first[b]==INVALID ) --b; |
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| 366 | else { |
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| 367 | Node w=first[b]; |
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| 368 | first[b]=next[w]; |
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| 369 | int newlevel=push(w,next, first); |
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| 370 | |
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| 371 | //relabel |
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| 372 | if ( excess[w] > 0 ) { |
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| 373 | level.set(w,++newlevel); |
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| 374 | next.set(w,first[newlevel]); |
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| 375 | first[newlevel]=w; |
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| 376 | b=newlevel; |
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| 377 | } |
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| 378 | } |
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| 379 | } // while(true) |
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| 380 | flow_prop=GEN_FLOW; |
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| 381 | status=AFTER_PREFLOW_PHASE_2; |
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| 382 | } |
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| 383 | |
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| 384 | /// Returns the value of the maximum flow. |
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| 385 | |
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| 386 | /// Returns the value of the maximum flow by returning the excess |
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[911] | 387 | /// of the target node \c t. This value equals to the value of |
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[836] | 388 | /// the maximum flow already after running \ref phase1. |
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| 389 | Num flowValue() const { |
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[1222] | 390 | return excess[_target]; |
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[836] | 391 | } |
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| 392 | |
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| 393 | |
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| 394 | ///Returns a minimum value cut. |
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| 395 | |
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| 396 | ///Sets \c M to the characteristic vector of a minimum value |
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| 397 | ///cut. This method can be called both after running \ref |
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| 398 | ///phase1 and \ref phase2. It is much faster after |
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[849] | 399 | ///\ref phase1. \pre M should be a bool-valued node-map. \pre |
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[911] | 400 | ///If \ref minCut() is called after \ref phase2() then M should |
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[836] | 401 | ///be initialized to false. |
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| 402 | template<typename _CutMap> |
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| 403 | void minCut(_CutMap& M) const { |
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| 404 | switch ( status ) { |
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| 405 | case AFTER_PREFLOW_PHASE_1: |
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[1222] | 406 | for(NodeIt v(*_g); v!=INVALID; ++v) { |
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| 407 | if (level[v] < _node_num) { |
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[836] | 408 | M.set(v, false); |
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| 409 | } else { |
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| 410 | M.set(v, true); |
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| 411 | } |
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| 412 | } |
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| 413 | break; |
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| 414 | case AFTER_PREFLOW_PHASE_2: |
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| 415 | minMinCut(M); |
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| 416 | break; |
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| 417 | case AFTER_NOTHING: |
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| 418 | break; |
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| 419 | } |
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| 420 | } |
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| 421 | |
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| 422 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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| 423 | |
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| 424 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 425 | ///which is inclusionwise minimum. It is computed by processing a |
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| 426 | ///bfs from the source node \c s in the residual graph. \pre M |
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| 427 | ///should be a node map of bools initialized to false. \pre \ref |
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| 428 | ///phase2 should already be run. |
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| 429 | template<typename _CutMap> |
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| 430 | void minMinCut(_CutMap& M) const { |
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| 431 | |
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| 432 | std::queue<Node> queue; |
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[1222] | 433 | M.set(_source,true); |
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[1227] | 434 | queue.push(_source); |
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[836] | 435 | |
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| 436 | while (!queue.empty()) { |
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| 437 | Node w=queue.front(); |
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| 438 | queue.pop(); |
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| 439 | |
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[1222] | 440 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 441 | Node v=_g->target(e); |
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| 442 | if (!M[v] && (*_flow)[e] < (*_capacity)[e] ) { |
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[836] | 443 | queue.push(v); |
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| 444 | M.set(v, true); |
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| 445 | } |
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| 446 | } |
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| 447 | |
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[1222] | 448 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 449 | Node v=_g->source(e); |
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| 450 | if (!M[v] && (*_flow)[e] > 0 ) { |
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[836] | 451 | queue.push(v); |
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| 452 | M.set(v, true); |
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| 453 | } |
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| 454 | } |
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| 455 | } |
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| 456 | } |
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| 457 | |
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| 458 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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| 459 | |
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| 460 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 461 | ///which is inclusionwise maximum. It is computed by processing a |
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| 462 | ///backward bfs from the target node \c t in the residual graph. |
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[911] | 463 | ///\pre \ref phase2() or run() should already be run. |
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[836] | 464 | template<typename _CutMap> |
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| 465 | void maxMinCut(_CutMap& M) const { |
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| 466 | |
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[1222] | 467 | for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true); |
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[836] | 468 | |
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| 469 | std::queue<Node> queue; |
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| 470 | |
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[1222] | 471 | M.set(_target,false); |
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| 472 | queue.push(_target); |
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[836] | 473 | |
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| 474 | while (!queue.empty()) { |
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| 475 | Node w=queue.front(); |
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| 476 | queue.pop(); |
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| 477 | |
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[1222] | 478 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 479 | Node v=_g->source(e); |
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| 480 | if (M[v] && (*_flow)[e] < (*_capacity)[e] ) { |
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[836] | 481 | queue.push(v); |
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| 482 | M.set(v, false); |
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| 483 | } |
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| 484 | } |
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| 485 | |
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[1222] | 486 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 487 | Node v=_g->target(e); |
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| 488 | if (M[v] && (*_flow)[e] > 0 ) { |
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[836] | 489 | queue.push(v); |
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| 490 | M.set(v, false); |
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| 491 | } |
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| 492 | } |
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| 493 | } |
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| 494 | } |
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| 495 | |
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| 496 | ///Sets the source node to \c _s. |
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| 497 | |
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| 498 | ///Sets the source node to \c _s. |
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| 499 | /// |
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[1222] | 500 | void source(Node _s) { |
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| 501 | _source=_s; |
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[836] | 502 | if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW; |
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| 503 | status=AFTER_NOTHING; |
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| 504 | } |
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| 505 | |
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[1222] | 506 | ///Returns the source node. |
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| 507 | |
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| 508 | ///Returns the source node. |
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| 509 | /// |
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| 510 | Node source() const { |
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| 511 | return _source; |
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| 512 | } |
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| 513 | |
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[836] | 514 | ///Sets the target node to \c _t. |
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| 515 | |
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| 516 | ///Sets the target node to \c _t. |
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| 517 | /// |
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[1222] | 518 | void target(Node _t) { |
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| 519 | _target=_t; |
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[836] | 520 | if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW; |
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| 521 | status=AFTER_NOTHING; |
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| 522 | } |
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| 523 | |
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[1222] | 524 | ///Returns the target node. |
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| 525 | |
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| 526 | ///Returns the target node. |
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| 527 | /// |
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| 528 | Node target() const { |
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| 529 | return _target; |
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| 530 | } |
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| 531 | |
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[836] | 532 | /// Sets the edge map of the capacities to _cap. |
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| 533 | |
---|
| 534 | /// Sets the edge map of the capacities to _cap. |
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| 535 | /// |
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[1222] | 536 | void capacityMap(const CapacityMap& _cap) { |
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| 537 | _capacity=&_cap; |
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[836] | 538 | status=AFTER_NOTHING; |
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| 539 | } |
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[1285] | 540 | /// Returns a reference to capacity map. |
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[1222] | 541 | |
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[1285] | 542 | /// Returns a reference to capacity map. |
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[1222] | 543 | /// |
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| 544 | const CapacityMap &capacityMap() const { |
---|
| 545 | return *_capacity; |
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| 546 | } |
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[836] | 547 | |
---|
| 548 | /// Sets the edge map of the flows to _flow. |
---|
| 549 | |
---|
| 550 | /// Sets the edge map of the flows to _flow. |
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| 551 | /// |
---|
[1222] | 552 | void flowMap(FlowMap& _f) { |
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| 553 | _flow=&_f; |
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[836] | 554 | flow_prop=NO_FLOW; |
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| 555 | status=AFTER_NOTHING; |
---|
| 556 | } |
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[1222] | 557 | |
---|
[1285] | 558 | /// Returns a reference to flow map. |
---|
[836] | 559 | |
---|
[1285] | 560 | /// Returns a reference to flow map. |
---|
[1222] | 561 | /// |
---|
| 562 | const FlowMap &flowMap() const { |
---|
| 563 | return *_flow; |
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| 564 | } |
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[836] | 565 | |
---|
| 566 | private: |
---|
| 567 | |
---|
| 568 | int push(Node w, NNMap& next, VecNode& first) { |
---|
| 569 | |
---|
| 570 | int lev=level[w]; |
---|
| 571 | Num exc=excess[w]; |
---|
[1222] | 572 | int newlevel=_node_num; //bound on the next level of w |
---|
[836] | 573 | |
---|
[1222] | 574 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
| 575 | if ( (*_flow)[e] >= (*_capacity)[e] ) continue; |
---|
| 576 | Node v=_g->target(e); |
---|
[836] | 577 | |
---|
| 578 | if( lev > level[v] ) { //Push is allowed now |
---|
| 579 | |
---|
[1222] | 580 | if ( excess[v]<=0 && v!=_target && v!=_source ) { |
---|
[836] | 581 | next.set(v,first[level[v]]); |
---|
| 582 | first[level[v]]=v; |
---|
| 583 | } |
---|
| 584 | |
---|
[1222] | 585 | Num cap=(*_capacity)[e]; |
---|
| 586 | Num flo=(*_flow)[e]; |
---|
[836] | 587 | Num remcap=cap-flo; |
---|
| 588 | |
---|
| 589 | if ( remcap >= exc ) { //A nonsaturating push. |
---|
| 590 | |
---|
[1222] | 591 | _flow->set(e, flo+exc); |
---|
[836] | 592 | excess.set(v, excess[v]+exc); |
---|
| 593 | exc=0; |
---|
| 594 | break; |
---|
| 595 | |
---|
| 596 | } else { //A saturating push. |
---|
[1222] | 597 | _flow->set(e, cap); |
---|
[836] | 598 | excess.set(v, excess[v]+remcap); |
---|
| 599 | exc-=remcap; |
---|
| 600 | } |
---|
| 601 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
| 602 | } //for out edges wv |
---|
| 603 | |
---|
| 604 | if ( exc > 0 ) { |
---|
[1222] | 605 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
[836] | 606 | |
---|
[1222] | 607 | if( (*_flow)[e] <= 0 ) continue; |
---|
| 608 | Node v=_g->source(e); |
---|
[836] | 609 | |
---|
| 610 | if( lev > level[v] ) { //Push is allowed now |
---|
| 611 | |
---|
[1222] | 612 | if ( excess[v]<=0 && v!=_target && v!=_source ) { |
---|
[836] | 613 | next.set(v,first[level[v]]); |
---|
| 614 | first[level[v]]=v; |
---|
| 615 | } |
---|
| 616 | |
---|
[1222] | 617 | Num flo=(*_flow)[e]; |
---|
[836] | 618 | |
---|
| 619 | if ( flo >= exc ) { //A nonsaturating push. |
---|
| 620 | |
---|
[1222] | 621 | _flow->set(e, flo-exc); |
---|
[836] | 622 | excess.set(v, excess[v]+exc); |
---|
| 623 | exc=0; |
---|
| 624 | break; |
---|
| 625 | } else { //A saturating push. |
---|
| 626 | |
---|
| 627 | excess.set(v, excess[v]+flo); |
---|
| 628 | exc-=flo; |
---|
[1222] | 629 | _flow->set(e,0); |
---|
[836] | 630 | } |
---|
| 631 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
| 632 | } //for in edges vw |
---|
| 633 | |
---|
| 634 | } // if w still has excess after the out edge for cycle |
---|
| 635 | |
---|
| 636 | excess.set(w, exc); |
---|
| 637 | |
---|
| 638 | return newlevel; |
---|
| 639 | } |
---|
| 640 | |
---|
| 641 | |
---|
| 642 | |
---|
| 643 | void preflowPreproc(VecNode& first, NNMap& next, |
---|
| 644 | VecNode& level_list, NNMap& left, NNMap& right) |
---|
| 645 | { |
---|
[1222] | 646 | for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num); |
---|
[836] | 647 | std::queue<Node> bfs_queue; |
---|
| 648 | |
---|
| 649 | if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) { |
---|
| 650 | //Reverse_bfs from t in the residual graph, |
---|
| 651 | //to find the starting level. |
---|
[1222] | 652 | level.set(_target,0); |
---|
| 653 | bfs_queue.push(_target); |
---|
[836] | 654 | |
---|
| 655 | while ( !bfs_queue.empty() ) { |
---|
| 656 | |
---|
| 657 | Node v=bfs_queue.front(); |
---|
| 658 | bfs_queue.pop(); |
---|
| 659 | int l=level[v]+1; |
---|
| 660 | |
---|
[1222] | 661 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
| 662 | if ( (*_capacity)[e] <= (*_flow)[e] ) continue; |
---|
| 663 | Node w=_g->source(e); |
---|
| 664 | if ( level[w] == _node_num && w != _source ) { |
---|
[836] | 665 | bfs_queue.push(w); |
---|
| 666 | Node z=level_list[l]; |
---|
| 667 | if ( z!=INVALID ) left.set(z,w); |
---|
| 668 | right.set(w,z); |
---|
| 669 | level_list[l]=w; |
---|
| 670 | level.set(w, l); |
---|
| 671 | } |
---|
| 672 | } |
---|
| 673 | |
---|
[1222] | 674 | for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
| 675 | if ( 0 >= (*_flow)[e] ) continue; |
---|
| 676 | Node w=_g->target(e); |
---|
| 677 | if ( level[w] == _node_num && w != _source ) { |
---|
[836] | 678 | bfs_queue.push(w); |
---|
| 679 | Node z=level_list[l]; |
---|
| 680 | if ( z!=INVALID ) left.set(z,w); |
---|
| 681 | right.set(w,z); |
---|
| 682 | level_list[l]=w; |
---|
| 683 | level.set(w, l); |
---|
| 684 | } |
---|
| 685 | } |
---|
| 686 | } //while |
---|
| 687 | } //if |
---|
| 688 | |
---|
| 689 | |
---|
| 690 | switch (flow_prop) { |
---|
| 691 | case NO_FLOW: |
---|
[1222] | 692 | for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0); |
---|
[836] | 693 | case ZERO_FLOW: |
---|
[1222] | 694 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
[836] | 695 | |
---|
| 696 | //Reverse_bfs from t, to find the starting level. |
---|
[1222] | 697 | level.set(_target,0); |
---|
| 698 | bfs_queue.push(_target); |
---|
[836] | 699 | |
---|
| 700 | while ( !bfs_queue.empty() ) { |
---|
| 701 | |
---|
| 702 | Node v=bfs_queue.front(); |
---|
| 703 | bfs_queue.pop(); |
---|
| 704 | int l=level[v]+1; |
---|
| 705 | |
---|
[1222] | 706 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
| 707 | Node w=_g->source(e); |
---|
| 708 | if ( level[w] == _node_num && w != _source ) { |
---|
[836] | 709 | bfs_queue.push(w); |
---|
| 710 | Node z=level_list[l]; |
---|
| 711 | if ( z!=INVALID ) left.set(z,w); |
---|
| 712 | right.set(w,z); |
---|
| 713 | level_list[l]=w; |
---|
| 714 | level.set(w, l); |
---|
| 715 | } |
---|
| 716 | } |
---|
| 717 | } |
---|
| 718 | |
---|
| 719 | //the starting flow |
---|
[1222] | 720 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
| 721 | Num c=(*_capacity)[e]; |
---|
[836] | 722 | if ( c <= 0 ) continue; |
---|
[1222] | 723 | Node w=_g->target(e); |
---|
| 724 | if ( level[w] < _node_num ) { |
---|
| 725 | if ( excess[w] <= 0 && w!=_target ) { //putting into the stack |
---|
[836] | 726 | next.set(w,first[level[w]]); |
---|
| 727 | first[level[w]]=w; |
---|
| 728 | } |
---|
[1222] | 729 | _flow->set(e, c); |
---|
[836] | 730 | excess.set(w, excess[w]+c); |
---|
| 731 | } |
---|
| 732 | } |
---|
| 733 | break; |
---|
| 734 | |
---|
| 735 | case GEN_FLOW: |
---|
[1222] | 736 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
[836] | 737 | { |
---|
| 738 | Num exc=0; |
---|
[1222] | 739 | for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
| 740 | for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
| 741 | excess.set(_target,exc); |
---|
[836] | 742 | } |
---|
| 743 | |
---|
| 744 | //the starting flow |
---|
[1222] | 745 | for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
| 746 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
[836] | 747 | if ( rem <= 0 ) continue; |
---|
[1222] | 748 | Node w=_g->target(e); |
---|
| 749 | if ( level[w] < _node_num ) { |
---|
| 750 | if ( excess[w] <= 0 && w!=_target ) { //putting into the stack |
---|
[836] | 751 | next.set(w,first[level[w]]); |
---|
| 752 | first[level[w]]=w; |
---|
| 753 | } |
---|
[1222] | 754 | _flow->set(e, (*_capacity)[e]); |
---|
[836] | 755 | excess.set(w, excess[w]+rem); |
---|
| 756 | } |
---|
| 757 | } |
---|
| 758 | |
---|
[1222] | 759 | for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
| 760 | if ( (*_flow)[e] <= 0 ) continue; |
---|
| 761 | Node w=_g->source(e); |
---|
| 762 | if ( level[w] < _node_num ) { |
---|
| 763 | if ( excess[w] <= 0 && w!=_target ) { |
---|
[836] | 764 | next.set(w,first[level[w]]); |
---|
| 765 | first[level[w]]=w; |
---|
| 766 | } |
---|
[1222] | 767 | excess.set(w, excess[w]+(*_flow)[e]); |
---|
| 768 | _flow->set(e, 0); |
---|
[836] | 769 | } |
---|
| 770 | } |
---|
| 771 | break; |
---|
| 772 | |
---|
| 773 | case PRE_FLOW: |
---|
| 774 | //the starting flow |
---|
[1222] | 775 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
| 776 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
[836] | 777 | if ( rem <= 0 ) continue; |
---|
[1222] | 778 | Node w=_g->target(e); |
---|
| 779 | if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]); |
---|
[836] | 780 | } |
---|
| 781 | |
---|
[1222] | 782 | for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
| 783 | if ( (*_flow)[e] <= 0 ) continue; |
---|
| 784 | Node w=_g->source(e); |
---|
| 785 | if ( level[w] < _node_num ) _flow->set(e, 0); |
---|
[836] | 786 | } |
---|
| 787 | |
---|
| 788 | //computing the excess |
---|
[1222] | 789 | for(NodeIt w(*_g); w!=INVALID; ++w) { |
---|
[836] | 790 | Num exc=0; |
---|
[1222] | 791 | for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
| 792 | for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
[836] | 793 | excess.set(w,exc); |
---|
| 794 | |
---|
| 795 | //putting the active nodes into the stack |
---|
| 796 | int lev=level[w]; |
---|
[1222] | 797 | if ( exc > 0 && lev < _node_num && Node(w) != _target ) { |
---|
[836] | 798 | next.set(w,first[lev]); |
---|
| 799 | first[lev]=w; |
---|
| 800 | } |
---|
| 801 | } |
---|
| 802 | break; |
---|
| 803 | } //switch |
---|
| 804 | } //preflowPreproc |
---|
| 805 | |
---|
| 806 | |
---|
| 807 | void relabel(Node w, int newlevel, VecNode& first, NNMap& next, |
---|
| 808 | VecNode& level_list, NNMap& left, |
---|
| 809 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
| 810 | { |
---|
| 811 | |
---|
| 812 | int lev=level[w]; |
---|
| 813 | |
---|
| 814 | Node right_n=right[w]; |
---|
| 815 | Node left_n=left[w]; |
---|
| 816 | |
---|
| 817 | //unlacing starts |
---|
| 818 | if ( right_n!=INVALID ) { |
---|
| 819 | if ( left_n!=INVALID ) { |
---|
| 820 | right.set(left_n, right_n); |
---|
| 821 | left.set(right_n, left_n); |
---|
| 822 | } else { |
---|
| 823 | level_list[lev]=right_n; |
---|
| 824 | left.set(right_n, INVALID); |
---|
| 825 | } |
---|
| 826 | } else { |
---|
| 827 | if ( left_n!=INVALID ) { |
---|
| 828 | right.set(left_n, INVALID); |
---|
| 829 | } else { |
---|
| 830 | level_list[lev]=INVALID; |
---|
| 831 | } |
---|
| 832 | } |
---|
| 833 | //unlacing ends |
---|
| 834 | |
---|
| 835 | if ( level_list[lev]==INVALID ) { |
---|
| 836 | |
---|
| 837 | //gapping starts |
---|
| 838 | for (int i=lev; i!=k ; ) { |
---|
| 839 | Node v=level_list[++i]; |
---|
| 840 | while ( v!=INVALID ) { |
---|
[1222] | 841 | level.set(v,_node_num); |
---|
[836] | 842 | v=right[v]; |
---|
| 843 | } |
---|
| 844 | level_list[i]=INVALID; |
---|
| 845 | if ( !what_heur ) first[i]=INVALID; |
---|
| 846 | } |
---|
| 847 | |
---|
[1222] | 848 | level.set(w,_node_num); |
---|
[836] | 849 | b=lev-1; |
---|
| 850 | k=b; |
---|
| 851 | //gapping ends |
---|
| 852 | |
---|
| 853 | } else { |
---|
| 854 | |
---|
[1222] | 855 | if ( newlevel == _node_num ) level.set(w,_node_num); |
---|
[836] | 856 | else { |
---|
| 857 | level.set(w,++newlevel); |
---|
| 858 | next.set(w,first[newlevel]); |
---|
| 859 | first[newlevel]=w; |
---|
| 860 | if ( what_heur ) b=newlevel; |
---|
| 861 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
| 862 | Node z=level_list[newlevel]; |
---|
| 863 | if ( z!=INVALID ) left.set(z,w); |
---|
| 864 | right.set(w,z); |
---|
| 865 | left.set(w,INVALID); |
---|
| 866 | level_list[newlevel]=w; |
---|
| 867 | } |
---|
| 868 | } |
---|
| 869 | } //relabel |
---|
| 870 | |
---|
| 871 | }; |
---|
[1227] | 872 | |
---|
[1792] | 873 | ///\ingroup flowalgs |
---|
| 874 | ///\brief Function type interface for Preflow algorithm. |
---|
| 875 | /// |
---|
[1227] | 876 | ///Function type interface for Preflow algorithm. |
---|
| 877 | ///\sa Preflow |
---|
| 878 | template<class GR, class CM, class FM> |
---|
| 879 | Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g, |
---|
| 880 | typename GR::Node source, |
---|
| 881 | typename GR::Node target, |
---|
| 882 | const CM &cap, |
---|
| 883 | FM &flow |
---|
| 884 | ) |
---|
| 885 | { |
---|
| 886 | return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow); |
---|
| 887 | } |
---|
| 888 | |
---|
[921] | 889 | } //namespace lemon |
---|
[836] | 890 | |
---|
[921] | 891 | #endif //LEMON_PREFLOW_H |
---|