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