[906] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[1956] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2006 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[906] | 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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[921] | 19 | #ifndef LEMON_PREFLOW_H |
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| 20 | #define LEMON_PREFLOW_H |
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[836] | 21 | |
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| 22 | #include <vector> |
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| 23 | #include <queue> |
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| 24 | |
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[1762] | 25 | #include <lemon/error.h> |
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[1993] | 26 | #include <lemon/bits/invalid.h> |
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[1835] | 27 | #include <lemon/tolerance.h> |
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[921] | 28 | #include <lemon/maps.h> |
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[977] | 29 | #include <lemon/graph_utils.h> |
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[836] | 30 | |
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| 31 | /// \file |
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| 32 | /// \ingroup flowalgs |
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[1742] | 33 | /// \brief Implementation of the preflow algorithm. |
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[836] | 34 | |
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[921] | 35 | namespace lemon { |
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[836] | 36 | |
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[1792] | 37 | ///\ingroup flowalgs |
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| 38 | ///\brief %Preflow algorithms class. |
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| 39 | /// |
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[836] | 40 | ///This class provides an implementation of the \e preflow \e |
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| 41 | ///algorithm producing a flow of maximum value in a directed |
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[2024] | 42 | ///graph. The preflow algorithms are the fastest known max flow algorithms. |
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| 43 | ///The \e source node, the \e target node, the \e |
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[836] | 44 | ///capacity of the edges and the \e starting \e flow value of the |
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| 45 | ///edges should be passed to the algorithm through the |
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| 46 | ///constructor. It is possible to change these quantities using the |
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[1285] | 47 | ///functions \ref source, \ref target, \ref capacityMap and \ref |
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| 48 | ///flowMap. |
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[836] | 49 | /// |
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[921] | 50 | ///After running \ref lemon::Preflow::phase1() "phase1()" |
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| 51 | ///or \ref lemon::Preflow::run() "run()", the maximal flow |
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[836] | 52 | ///value can be obtained by calling \ref flowValue(). The minimum |
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[851] | 53 | ///value cut can be written into a <tt>bool</tt> node map by |
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| 54 | ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes |
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[836] | 55 | ///the inclusionwise minimum and maximum of the minimum value cuts, |
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| 56 | ///resp.) |
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| 57 | /// |
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| 58 | ///\param Graph The directed graph type the algorithm runs on. |
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| 59 | ///\param Num The number type of the capacities and the flow values. |
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[1222] | 60 | ///\param CapacityMap The capacity map type. |
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[836] | 61 | ///\param FlowMap The flow map type. |
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[2024] | 62 | ///\param Tolerance The tolerance type. |
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[836] | 63 | /// |
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| 64 | ///\author Jacint Szabo |
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[1227] | 65 | ///\todo Second template parameter is superfluous |
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[836] | 66 | template <typename Graph, typename Num, |
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[1222] | 67 | typename CapacityMap=typename Graph::template EdgeMap<Num>, |
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[1835] | 68 | typename FlowMap=typename Graph::template EdgeMap<Num>, |
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[2019] | 69 | typename Tolerance=Tolerance<Num> > |
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[836] | 70 | class Preflow { |
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| 71 | protected: |
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| 72 | typedef typename Graph::Node Node; |
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| 73 | typedef typename Graph::NodeIt NodeIt; |
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| 74 | typedef typename Graph::EdgeIt EdgeIt; |
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| 75 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 76 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 77 | |
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| 78 | typedef typename Graph::template NodeMap<Node> NNMap; |
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| 79 | typedef typename std::vector<Node> VecNode; |
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| 80 | |
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[1222] | 81 | const Graph* _g; |
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| 82 | Node _source; |
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| 83 | Node _target; |
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| 84 | const CapacityMap* _capacity; |
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| 85 | FlowMap* _flow; |
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[1835] | 86 | |
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[2019] | 87 | Tolerance _surely; |
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[1835] | 88 | |
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[1222] | 89 | int _node_num; //the number of nodes of G |
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[836] | 90 | |
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| 91 | typename Graph::template NodeMap<int> level; |
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| 92 | typename Graph::template NodeMap<Num> excess; |
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| 93 | |
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| 94 | // constants used for heuristics |
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| 95 | static const int H0=20; |
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| 96 | static const int H1=1; |
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| 97 | |
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[1762] | 98 | public: |
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| 99 | |
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| 100 | ///\ref Exception for the case when s=t. |
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| 101 | |
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| 102 | ///\ref Exception for the case when the source equals the target. |
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| 103 | class InvalidArgument : public lemon::LogicError { |
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[836] | 104 | public: |
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[1762] | 105 | virtual const char* exceptionName() const { |
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| 106 | return "lemon::Preflow::InvalidArgument"; |
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| 107 | } |
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| 108 | }; |
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| 109 | |
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| 110 | |
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[836] | 111 | ///Indicates the property of the starting flow map. |
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[1762] | 112 | |
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[1222] | 113 | ///Indicates the property of the starting flow map. |
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[836] | 114 | /// |
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| 115 | enum FlowEnum{ |
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[1898] | 116 | ///indicates an unspecified edge map. \c flow will be |
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| 117 | ///set to the constant zero flow in the beginning of |
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| 118 | ///the algorithm in this case. |
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[836] | 119 | NO_FLOW, |
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[1898] | 120 | ///constant zero flow |
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[836] | 121 | ZERO_FLOW, |
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[1898] | 122 | ///any flow, i.e. the sum of the in-flows equals to |
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| 123 | ///the sum of the out-flows in every node except the \c source and |
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| 124 | ///the \c target. |
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[836] | 125 | GEN_FLOW, |
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[1898] | 126 | ///any preflow, i.e. the sum of the in-flows is at |
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| 127 | ///least the sum of the out-flows in every node except the \c source. |
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[836] | 128 | PRE_FLOW |
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| 129 | }; |
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| 130 | |
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| 131 | ///Indicates the state of the preflow algorithm. |
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| 132 | |
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[1222] | 133 | ///Indicates the state of the preflow algorithm. |
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[836] | 134 | /// |
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| 135 | enum StatusEnum { |
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[1898] | 136 | ///before running the algorithm or |
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| 137 | ///at an unspecified state. |
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[836] | 138 | AFTER_NOTHING, |
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[1898] | 139 | ///right after running \ref phase1() |
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[836] | 140 | AFTER_PREFLOW_PHASE_1, |
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[1898] | 141 | ///after running \ref phase2() |
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[836] | 142 | AFTER_PREFLOW_PHASE_2 |
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| 143 | }; |
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| 144 | |
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[1762] | 145 | protected: |
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| 146 | FlowEnum flow_prop; |
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[836] | 147 | StatusEnum status; // Do not needle this flag only if necessary. |
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| 148 | |
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| 149 | public: |
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| 150 | ///The constructor of the class. |
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| 151 | |
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| 152 | ///The constructor of the class. |
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[1285] | 153 | ///\param _gr The directed graph the algorithm runs on. |
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[836] | 154 | ///\param _s The source node. |
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| 155 | ///\param _t The target node. |
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[1222] | 156 | ///\param _cap The capacity of the edges. |
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| 157 | ///\param _f The flow of the edges. |
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[1953] | 158 | ///\param tol Tolerance class. |
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[836] | 159 | ///Except the graph, all of these parameters can be reset by |
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[1285] | 160 | ///calling \ref source, \ref target, \ref capacityMap and \ref |
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| 161 | ///flowMap, resp. |
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[2033] | 162 | Preflow(const Graph& _gr, Node _s, Node _t, |
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| 163 | const CapacityMap& _cap, FlowMap& _f, |
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| 164 | const Tolerance &_sr=Tolerance()) : |
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[1222] | 165 | _g(&_gr), _source(_s), _target(_t), _capacity(&_cap), |
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[2019] | 166 | _flow(&_f), _surely(_sr), |
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[1835] | 167 | _node_num(countNodes(_gr)), level(_gr), excess(_gr,0), |
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[1762] | 168 | flow_prop(NO_FLOW), status(AFTER_NOTHING) { |
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| 169 | if ( _source==_target ) |
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| 170 | throw InvalidArgument(); |
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[2033] | 171 | } |
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[1762] | 172 | |
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[1898] | 173 | ///Give a reference to the tolerance handler class |
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[836] | 174 | |
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[1898] | 175 | ///Give a reference to the tolerance handler class |
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| 176 | ///\sa Tolerance |
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[2019] | 177 | Tolerance &tolerance() { return _surely; } |
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[1898] | 178 | |
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[836] | 179 | ///Runs the preflow algorithm. |
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| 180 | |
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[851] | 181 | ///Runs the preflow algorithm. |
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| 182 | /// |
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[836] | 183 | void run() { |
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| 184 | phase1(flow_prop); |
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| 185 | phase2(); |
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| 186 | } |
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| 187 | |
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| 188 | ///Runs the preflow algorithm. |
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| 189 | |
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| 190 | ///Runs the preflow algorithm. |
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| 191 | ///\pre The starting flow map must be |
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| 192 | /// - a constant zero flow if \c fp is \c ZERO_FLOW, |
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| 193 | /// - an arbitrary flow if \c fp is \c GEN_FLOW, |
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| 194 | /// - an arbitrary preflow if \c fp is \c PRE_FLOW, |
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| 195 | /// - any map if \c fp is NO_FLOW. |
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| 196 | ///If the starting flow map is a flow or a preflow then |
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| 197 | ///the algorithm terminates faster. |
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| 198 | void run(FlowEnum fp) { |
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| 199 | flow_prop=fp; |
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| 200 | run(); |
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| 201 | } |
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| 202 | |
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| 203 | ///Runs the first phase of the preflow algorithm. |
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| 204 | |
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[920] | 205 | ///The preflow algorithm consists of two phases, this method runs |
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| 206 | ///the first phase. After the first phase the maximum flow value |
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[1285] | 207 | ///and a minimum value cut can already be computed, although a |
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[920] | 208 | ///maximum flow is not yet obtained. So after calling this method |
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| 209 | ///\ref flowValue returns the value of a maximum flow and \ref |
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| 210 | ///minCut returns a minimum cut. |
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| 211 | ///\warning \ref minMinCut and \ref maxMinCut do not give minimum |
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| 212 | ///value cuts unless calling \ref phase2. |
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| 213 | ///\pre The starting flow must be |
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| 214 | ///- a constant zero flow if \c fp is \c ZERO_FLOW, |
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| 215 | ///- an arbitary flow if \c fp is \c GEN_FLOW, |
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| 216 | ///- an arbitary preflow if \c fp is \c PRE_FLOW, |
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| 217 | ///- any map if \c fp is NO_FLOW. |
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[836] | 218 | void phase1(FlowEnum fp) |
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| 219 | { |
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| 220 | flow_prop=fp; |
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| 221 | phase1(); |
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| 222 | } |
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| 223 | |
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| 224 | |
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| 225 | ///Runs the first phase of the preflow algorithm. |
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| 226 | |
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[920] | 227 | ///The preflow algorithm consists of two phases, this method runs |
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| 228 | ///the first phase. After the first phase the maximum flow value |
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[1285] | 229 | ///and a minimum value cut can already be computed, although a |
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[920] | 230 | ///maximum flow is not yet obtained. So after calling this method |
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| 231 | ///\ref flowValue returns the value of a maximum flow and \ref |
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| 232 | ///minCut returns a minimum cut. |
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[1786] | 233 | ///\warning \ref minMinCut() and \ref maxMinCut() do not |
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[911] | 234 | ///give minimum value cuts unless calling \ref phase2(). |
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[836] | 235 | void phase1() |
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| 236 | { |
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[1222] | 237 | int heur0=(int)(H0*_node_num); //time while running 'bound decrease' |
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| 238 | int heur1=(int)(H1*_node_num); //time while running 'highest label' |
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[836] | 239 | int heur=heur1; //starting time interval (#of relabels) |
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| 240 | int numrelabel=0; |
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| 241 | |
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| 242 | bool what_heur=1; |
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| 243 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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| 244 | |
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| 245 | bool end=false; |
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| 246 | //Needed for 'bound decrease', true means no active |
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| 247 | //nodes are above bound b. |
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| 248 | |
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[1222] | 249 | int k=_node_num-2; //bound on the highest level under n containing a node |
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[2024] | 250 | int b=k; //bound on the highest level under n containing an active node |
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[836] | 251 | |
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[1222] | 252 | VecNode first(_node_num, INVALID); |
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| 253 | NNMap next(*_g, INVALID); |
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[836] | 254 | |
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[1222] | 255 | NNMap left(*_g, INVALID); |
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| 256 | NNMap right(*_g, INVALID); |
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| 257 | VecNode level_list(_node_num,INVALID); |
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[836] | 258 | //List of the nodes in level i<n, set to n. |
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| 259 | |
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| 260 | preflowPreproc(first, next, level_list, left, right); |
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| 261 | |
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| 262 | //Push/relabel on the highest level active nodes. |
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| 263 | while ( true ) { |
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| 264 | if ( b == 0 ) { |
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| 265 | if ( !what_heur && !end && k > 0 ) { |
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| 266 | b=k; |
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| 267 | end=true; |
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| 268 | } else break; |
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| 269 | } |
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| 270 | |
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| 271 | if ( first[b]==INVALID ) --b; |
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| 272 | else { |
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| 273 | end=false; |
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| 274 | Node w=first[b]; |
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| 275 | first[b]=next[w]; |
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| 276 | int newlevel=push(w, next, first); |
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[2024] | 277 | if ( _surely.positive(excess[w]) ) relabel(w, newlevel, first, next, level_list, |
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[836] | 278 | left, right, b, k, what_heur); |
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| 279 | |
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| 280 | ++numrelabel; |
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| 281 | if ( numrelabel >= heur ) { |
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| 282 | numrelabel=0; |
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| 283 | if ( what_heur ) { |
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| 284 | what_heur=0; |
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| 285 | heur=heur0; |
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| 286 | end=false; |
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| 287 | } else { |
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| 288 | what_heur=1; |
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| 289 | heur=heur1; |
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| 290 | b=k; |
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| 291 | } |
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| 292 | } |
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| 293 | } |
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| 294 | } |
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| 295 | flow_prop=PRE_FLOW; |
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| 296 | status=AFTER_PREFLOW_PHASE_1; |
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| 297 | } |
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| 298 | // Heuristics: |
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| 299 | // 2 phase |
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| 300 | // gap |
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| 301 | // list 'level_list' on the nodes on level i implemented by hand |
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| 302 | // stack 'active' on the active nodes on level i |
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| 303 | // runs heuristic 'highest label' for H1*n relabels |
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[1222] | 304 | // runs heuristic 'bound decrease' for H0*n relabels, |
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| 305 | // starts with 'highest label' |
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[836] | 306 | // Parameters H0 and H1 are initialized to 20 and 1. |
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| 307 | |
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| 308 | |
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| 309 | ///Runs the second phase of the preflow algorithm. |
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| 310 | |
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| 311 | ///The preflow algorithm consists of two phases, this method runs |
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[1631] | 312 | ///the second phase. After calling \ref phase1() and then |
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| 313 | ///\ref phase2(), |
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| 314 | /// \ref flowMap() return a maximum flow, \ref flowValue |
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[920] | 315 | ///returns the value of a maximum flow, \ref minCut returns a |
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| 316 | ///minimum cut, while the methods \ref minMinCut and \ref |
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| 317 | ///maxMinCut return the inclusionwise minimum and maximum cuts of |
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| 318 | ///minimum value, resp. \pre \ref phase1 must be called before. |
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[836] | 319 | void phase2() |
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| 320 | { |
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| 321 | |
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[1222] | 322 | int k=_node_num-2; //bound on the highest level under n containing a node |
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[836] | 323 | int b=k; //bound on the highest level under n of an active node |
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| 324 | |
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| 325 | |
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[1222] | 326 | VecNode first(_node_num, INVALID); |
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| 327 | NNMap next(*_g, INVALID); |
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| 328 | level.set(_source,0); |
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[836] | 329 | std::queue<Node> bfs_queue; |
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[1222] | 330 | bfs_queue.push(_source); |
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[836] | 331 | |
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| 332 | while ( !bfs_queue.empty() ) { |
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| 333 | |
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| 334 | Node v=bfs_queue.front(); |
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| 335 | bfs_queue.pop(); |
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| 336 | int l=level[v]+1; |
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| 337 | |
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[1222] | 338 | for(InEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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[2024] | 339 | if ( !_surely.less((*_flow)[e], (*_capacity)[e]) ) continue; |
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[1222] | 340 | Node u=_g->source(e); |
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| 341 | if ( level[u] >= _node_num ) { |
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[836] | 342 | bfs_queue.push(u); |
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| 343 | level.set(u, l); |
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[2024] | 344 | if ( _surely.positive(excess[u]) ) { |
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[836] | 345 | next.set(u,first[l]); |
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| 346 | first[l]=u; |
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| 347 | } |
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| 348 | } |
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| 349 | } |
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| 350 | |
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[1222] | 351 | for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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[2024] | 352 | if ( !_surely.positive((*_flow)[e]) ) continue; |
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[1222] | 353 | Node u=_g->target(e); |
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| 354 | if ( level[u] >= _node_num ) { |
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[836] | 355 | bfs_queue.push(u); |
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| 356 | level.set(u, l); |
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[2024] | 357 | if ( _surely.positive(excess[u]) ) { |
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[836] | 358 | next.set(u,first[l]); |
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| 359 | first[l]=u; |
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| 360 | } |
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| 361 | } |
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| 362 | } |
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| 363 | } |
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[1222] | 364 | b=_node_num-2; |
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[836] | 365 | |
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| 366 | while ( true ) { |
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| 367 | |
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| 368 | if ( b == 0 ) break; |
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| 369 | if ( first[b]==INVALID ) --b; |
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| 370 | else { |
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| 371 | Node w=first[b]; |
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| 372 | first[b]=next[w]; |
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| 373 | int newlevel=push(w,next, first); |
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| 374 | |
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| 375 | //relabel |
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[2024] | 376 | if ( _surely.positive(excess[w]) ) { |
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[836] | 377 | level.set(w,++newlevel); |
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| 378 | next.set(w,first[newlevel]); |
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| 379 | first[newlevel]=w; |
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| 380 | b=newlevel; |
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| 381 | } |
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| 382 | } |
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| 383 | } // while(true) |
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| 384 | flow_prop=GEN_FLOW; |
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| 385 | status=AFTER_PREFLOW_PHASE_2; |
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| 386 | } |
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| 387 | |
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| 388 | /// Returns the value of the maximum flow. |
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| 389 | |
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| 390 | /// Returns the value of the maximum flow by returning the excess |
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[911] | 391 | /// of the target node \c t. This value equals to the value of |
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[836] | 392 | /// the maximum flow already after running \ref phase1. |
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| 393 | Num flowValue() const { |
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[1222] | 394 | return excess[_target]; |
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[836] | 395 | } |
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| 396 | |
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| 397 | |
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| 398 | ///Returns a minimum value cut. |
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| 399 | |
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| 400 | ///Sets \c M to the characteristic vector of a minimum value |
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| 401 | ///cut. This method can be called both after running \ref |
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| 402 | ///phase1 and \ref phase2. It is much faster after |
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[849] | 403 | ///\ref phase1. \pre M should be a bool-valued node-map. \pre |
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[911] | 404 | ///If \ref minCut() is called after \ref phase2() then M should |
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[836] | 405 | ///be initialized to false. |
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| 406 | template<typename _CutMap> |
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| 407 | void minCut(_CutMap& M) const { |
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| 408 | switch ( status ) { |
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| 409 | case AFTER_PREFLOW_PHASE_1: |
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[1222] | 410 | for(NodeIt v(*_g); v!=INVALID; ++v) { |
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| 411 | if (level[v] < _node_num) { |
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[836] | 412 | M.set(v, false); |
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| 413 | } else { |
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| 414 | M.set(v, true); |
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| 415 | } |
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| 416 | } |
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| 417 | break; |
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| 418 | case AFTER_PREFLOW_PHASE_2: |
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| 419 | minMinCut(M); |
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| 420 | break; |
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| 421 | case AFTER_NOTHING: |
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| 422 | break; |
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| 423 | } |
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| 424 | } |
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| 425 | |
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| 426 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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| 427 | |
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| 428 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 429 | ///which is inclusionwise minimum. It is computed by processing a |
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| 430 | ///bfs from the source node \c s in the residual graph. \pre M |
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| 431 | ///should be a node map of bools initialized to false. \pre \ref |
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| 432 | ///phase2 should already be run. |
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| 433 | template<typename _CutMap> |
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| 434 | void minMinCut(_CutMap& M) const { |
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| 435 | |
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| 436 | std::queue<Node> queue; |
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[1222] | 437 | M.set(_source,true); |
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[1227] | 438 | queue.push(_source); |
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[836] | 439 | |
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| 440 | while (!queue.empty()) { |
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| 441 | Node w=queue.front(); |
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| 442 | queue.pop(); |
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| 443 | |
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[1222] | 444 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 445 | Node v=_g->target(e); |
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[2024] | 446 | if (!M[v] && _surely.less((*_flow)[e] , (*_capacity)[e]) ) { |
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[836] | 447 | queue.push(v); |
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| 448 | M.set(v, true); |
---|
| 449 | } |
---|
| 450 | } |
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| 451 | |
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[1222] | 452 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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| 453 | Node v=_g->source(e); |
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[2024] | 454 | if (!M[v] && _surely.positive((*_flow)[e]) ) { |
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[836] | 455 | queue.push(v); |
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| 456 | M.set(v, true); |
---|
| 457 | } |
---|
| 458 | } |
---|
| 459 | } |
---|
| 460 | } |
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| 461 | |
---|
| 462 | ///Returns the inclusionwise maximum of the minimum value cuts. |
---|
| 463 | |
---|
| 464 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 465 | ///which is inclusionwise maximum. It is computed by processing a |
---|
| 466 | ///backward bfs from the target node \c t in the residual graph. |
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[911] | 467 | ///\pre \ref phase2() or run() should already be run. |
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[836] | 468 | template<typename _CutMap> |
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| 469 | void maxMinCut(_CutMap& M) const { |
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| 470 | |
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[1222] | 471 | for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true); |
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[836] | 472 | |
---|
| 473 | std::queue<Node> queue; |
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| 474 | |
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[1222] | 475 | M.set(_target,false); |
---|
| 476 | queue.push(_target); |
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[836] | 477 | |
---|
| 478 | while (!queue.empty()) { |
---|
| 479 | Node w=queue.front(); |
---|
| 480 | queue.pop(); |
---|
| 481 | |
---|
[1222] | 482 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
| 483 | Node v=_g->source(e); |
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[2024] | 484 | if (M[v] && _surely.less((*_flow)[e], (*_capacity)[e]) ) { |
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[836] | 485 | queue.push(v); |
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| 486 | M.set(v, false); |
---|
| 487 | } |
---|
| 488 | } |
---|
| 489 | |
---|
[1222] | 490 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
| 491 | Node v=_g->target(e); |
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[2024] | 492 | if (M[v] && _surely.positive((*_flow)[e]) ) { |
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[836] | 493 | queue.push(v); |
---|
| 494 | M.set(v, false); |
---|
| 495 | } |
---|
| 496 | } |
---|
| 497 | } |
---|
| 498 | } |
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| 499 | |
---|
| 500 | ///Sets the source node to \c _s. |
---|
| 501 | |
---|
| 502 | ///Sets the source node to \c _s. |
---|
| 503 | /// |
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[1222] | 504 | void source(Node _s) { |
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| 505 | _source=_s; |
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[836] | 506 | if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW; |
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| 507 | status=AFTER_NOTHING; |
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| 508 | } |
---|
| 509 | |
---|
[1222] | 510 | ///Returns the source node. |
---|
| 511 | |
---|
| 512 | ///Returns the source node. |
---|
| 513 | /// |
---|
| 514 | Node source() const { |
---|
| 515 | return _source; |
---|
| 516 | } |
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| 517 | |
---|
[836] | 518 | ///Sets the target node to \c _t. |
---|
| 519 | |
---|
| 520 | ///Sets the target node to \c _t. |
---|
| 521 | /// |
---|
[1222] | 522 | void target(Node _t) { |
---|
| 523 | _target=_t; |
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[836] | 524 | if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW; |
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| 525 | status=AFTER_NOTHING; |
---|
| 526 | } |
---|
| 527 | |
---|
[1222] | 528 | ///Returns the target node. |
---|
| 529 | |
---|
| 530 | ///Returns the target node. |
---|
| 531 | /// |
---|
| 532 | Node target() const { |
---|
| 533 | return _target; |
---|
| 534 | } |
---|
| 535 | |
---|
[836] | 536 | /// Sets the edge map of the capacities to _cap. |
---|
| 537 | |
---|
| 538 | /// Sets the edge map of the capacities to _cap. |
---|
| 539 | /// |
---|
[1222] | 540 | void capacityMap(const CapacityMap& _cap) { |
---|
| 541 | _capacity=&_cap; |
---|
[836] | 542 | status=AFTER_NOTHING; |
---|
| 543 | } |
---|
[1285] | 544 | /// Returns a reference to capacity map. |
---|
[1222] | 545 | |
---|
[1285] | 546 | /// Returns a reference to capacity map. |
---|
[1222] | 547 | /// |
---|
| 548 | const CapacityMap &capacityMap() const { |
---|
| 549 | return *_capacity; |
---|
| 550 | } |
---|
[836] | 551 | |
---|
| 552 | /// Sets the edge map of the flows to _flow. |
---|
| 553 | |
---|
| 554 | /// Sets the edge map of the flows to _flow. |
---|
| 555 | /// |
---|
[1222] | 556 | void flowMap(FlowMap& _f) { |
---|
| 557 | _flow=&_f; |
---|
[836] | 558 | flow_prop=NO_FLOW; |
---|
| 559 | status=AFTER_NOTHING; |
---|
| 560 | } |
---|
[1222] | 561 | |
---|
[1285] | 562 | /// Returns a reference to flow map. |
---|
[836] | 563 | |
---|
[1285] | 564 | /// Returns a reference to flow map. |
---|
[1222] | 565 | /// |
---|
| 566 | const FlowMap &flowMap() const { |
---|
| 567 | return *_flow; |
---|
| 568 | } |
---|
[836] | 569 | |
---|
| 570 | private: |
---|
| 571 | |
---|
| 572 | int push(Node w, NNMap& next, VecNode& first) { |
---|
| 573 | |
---|
| 574 | int lev=level[w]; |
---|
| 575 | Num exc=excess[w]; |
---|
[1222] | 576 | int newlevel=_node_num; //bound on the next level of w |
---|
[836] | 577 | |
---|
[1222] | 578 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
[2024] | 579 | if ( !_surely.less((*_flow)[e], (*_capacity)[e]) ) continue; |
---|
[1222] | 580 | Node v=_g->target(e); |
---|
[2024] | 581 | |
---|
[836] | 582 | if( lev > level[v] ) { //Push is allowed now |
---|
| 583 | |
---|
[2024] | 584 | if ( !_surely.positive(excess[v]) && v!=_target && v!=_source ) { |
---|
[836] | 585 | next.set(v,first[level[v]]); |
---|
| 586 | first[level[v]]=v; |
---|
| 587 | } |
---|
| 588 | |
---|
[1222] | 589 | Num cap=(*_capacity)[e]; |
---|
| 590 | Num flo=(*_flow)[e]; |
---|
[836] | 591 | Num remcap=cap-flo; |
---|
| 592 | |
---|
[2024] | 593 | if ( ! _surely.less(remcap, exc) ) { //A nonsaturating push. |
---|
[836] | 594 | |
---|
[1222] | 595 | _flow->set(e, flo+exc); |
---|
[836] | 596 | excess.set(v, excess[v]+exc); |
---|
| 597 | exc=0; |
---|
| 598 | break; |
---|
| 599 | |
---|
| 600 | } else { //A saturating push. |
---|
[1222] | 601 | _flow->set(e, cap); |
---|
[836] | 602 | excess.set(v, excess[v]+remcap); |
---|
| 603 | exc-=remcap; |
---|
| 604 | } |
---|
| 605 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
| 606 | } //for out edges wv |
---|
| 607 | |
---|
[2024] | 608 | if ( _surely.positive(exc) ) { |
---|
[1222] | 609 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
[836] | 610 | |
---|
[2024] | 611 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
[1222] | 612 | Node v=_g->source(e); |
---|
[2024] | 613 | |
---|
[836] | 614 | if( lev > level[v] ) { //Push is allowed now |
---|
| 615 | |
---|
[2024] | 616 | if ( !_surely.positive(excess[v]) && v!=_target && v!=_source ) { |
---|
[836] | 617 | next.set(v,first[level[v]]); |
---|
| 618 | first[level[v]]=v; |
---|
| 619 | } |
---|
| 620 | |
---|
[1222] | 621 | Num flo=(*_flow)[e]; |
---|
[836] | 622 | |
---|
[2024] | 623 | if ( !_surely.less(flo, exc) ) { //A nonsaturating push. |
---|
[836] | 624 | |
---|
[1222] | 625 | _flow->set(e, flo-exc); |
---|
[836] | 626 | excess.set(v, excess[v]+exc); |
---|
| 627 | exc=0; |
---|
| 628 | break; |
---|
| 629 | } else { //A saturating push. |
---|
| 630 | |
---|
| 631 | excess.set(v, excess[v]+flo); |
---|
| 632 | exc-=flo; |
---|
[1222] | 633 | _flow->set(e,0); |
---|
[836] | 634 | } |
---|
| 635 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
| 636 | } //for in edges vw |
---|
| 637 | |
---|
| 638 | } // if w still has excess after the out edge for cycle |
---|
| 639 | |
---|
| 640 | excess.set(w, exc); |
---|
| 641 | |
---|
| 642 | return newlevel; |
---|
| 643 | } |
---|
| 644 | |
---|
| 645 | |
---|
| 646 | |
---|
| 647 | void preflowPreproc(VecNode& first, NNMap& next, |
---|
| 648 | VecNode& level_list, NNMap& left, NNMap& right) |
---|
| 649 | { |
---|
[1222] | 650 | for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num); |
---|
[836] | 651 | std::queue<Node> bfs_queue; |
---|
| 652 | |
---|
| 653 | if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) { |
---|
| 654 | //Reverse_bfs from t in the residual graph, |
---|
| 655 | //to find the starting level. |
---|
[1222] | 656 | level.set(_target,0); |
---|
| 657 | bfs_queue.push(_target); |
---|
[836] | 658 | |
---|
| 659 | while ( !bfs_queue.empty() ) { |
---|
| 660 | |
---|
| 661 | Node v=bfs_queue.front(); |
---|
| 662 | bfs_queue.pop(); |
---|
| 663 | int l=level[v]+1; |
---|
| 664 | |
---|
[1222] | 665 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
[2024] | 666 | if ( !_surely.less((*_flow)[e],(*_capacity)[e]) ) continue; |
---|
[1222] | 667 | Node w=_g->source(e); |
---|
| 668 | if ( level[w] == _node_num && w != _source ) { |
---|
[836] | 669 | bfs_queue.push(w); |
---|
| 670 | Node z=level_list[l]; |
---|
| 671 | if ( z!=INVALID ) left.set(z,w); |
---|
| 672 | right.set(w,z); |
---|
| 673 | level_list[l]=w; |
---|
| 674 | level.set(w, l); |
---|
| 675 | } |
---|
| 676 | } |
---|
| 677 | |
---|
[1222] | 678 | for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
[2024] | 679 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
[1222] | 680 | Node w=_g->target(e); |
---|
| 681 | if ( level[w] == _node_num && w != _source ) { |
---|
[836] | 682 | bfs_queue.push(w); |
---|
| 683 | Node z=level_list[l]; |
---|
| 684 | if ( z!=INVALID ) left.set(z,w); |
---|
| 685 | right.set(w,z); |
---|
| 686 | level_list[l]=w; |
---|
| 687 | level.set(w, l); |
---|
| 688 | } |
---|
| 689 | } |
---|
| 690 | } //while |
---|
| 691 | } //if |
---|
| 692 | |
---|
| 693 | |
---|
| 694 | switch (flow_prop) { |
---|
| 695 | case NO_FLOW: |
---|
[1222] | 696 | for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0); |
---|
[836] | 697 | case ZERO_FLOW: |
---|
[1222] | 698 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
[836] | 699 | |
---|
| 700 | //Reverse_bfs from t, to find the starting level. |
---|
[1222] | 701 | level.set(_target,0); |
---|
| 702 | bfs_queue.push(_target); |
---|
[836] | 703 | |
---|
| 704 | while ( !bfs_queue.empty() ) { |
---|
| 705 | |
---|
| 706 | Node v=bfs_queue.front(); |
---|
| 707 | bfs_queue.pop(); |
---|
| 708 | int l=level[v]+1; |
---|
| 709 | |
---|
[1222] | 710 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
| 711 | Node w=_g->source(e); |
---|
| 712 | if ( level[w] == _node_num && w != _source ) { |
---|
[836] | 713 | bfs_queue.push(w); |
---|
| 714 | Node z=level_list[l]; |
---|
| 715 | if ( z!=INVALID ) left.set(z,w); |
---|
| 716 | right.set(w,z); |
---|
| 717 | level_list[l]=w; |
---|
| 718 | level.set(w, l); |
---|
| 719 | } |
---|
| 720 | } |
---|
| 721 | } |
---|
| 722 | |
---|
| 723 | //the starting flow |
---|
[1222] | 724 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
| 725 | Num c=(*_capacity)[e]; |
---|
[2024] | 726 | if ( !_surely.positive(c) ) continue; |
---|
[1222] | 727 | Node w=_g->target(e); |
---|
| 728 | if ( level[w] < _node_num ) { |
---|
[2024] | 729 | if ( !_surely.positive(excess[w]) && w!=_target ) { //putting into the stack |
---|
[836] | 730 | next.set(w,first[level[w]]); |
---|
| 731 | first[level[w]]=w; |
---|
| 732 | } |
---|
[1222] | 733 | _flow->set(e, c); |
---|
[836] | 734 | excess.set(w, excess[w]+c); |
---|
| 735 | } |
---|
| 736 | } |
---|
| 737 | break; |
---|
| 738 | |
---|
| 739 | case GEN_FLOW: |
---|
[1222] | 740 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
[836] | 741 | { |
---|
| 742 | Num exc=0; |
---|
[1222] | 743 | for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
| 744 | for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
| 745 | excess.set(_target,exc); |
---|
[836] | 746 | } |
---|
| 747 | |
---|
| 748 | //the starting flow |
---|
[1222] | 749 | for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
| 750 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
[2024] | 751 | if ( !_surely.positive(rem) ) continue; |
---|
[1222] | 752 | Node w=_g->target(e); |
---|
| 753 | if ( level[w] < _node_num ) { |
---|
[2024] | 754 | if ( !_surely.positive(excess[w]) && w!=_target ) { //putting into the stack |
---|
[836] | 755 | next.set(w,first[level[w]]); |
---|
| 756 | first[level[w]]=w; |
---|
| 757 | } |
---|
[1222] | 758 | _flow->set(e, (*_capacity)[e]); |
---|
[836] | 759 | excess.set(w, excess[w]+rem); |
---|
| 760 | } |
---|
| 761 | } |
---|
| 762 | |
---|
[1222] | 763 | for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
[2024] | 764 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
[1222] | 765 | Node w=_g->source(e); |
---|
| 766 | if ( level[w] < _node_num ) { |
---|
[2024] | 767 | if ( !_surely.positive(excess[w]) && w!=_target ) { |
---|
[836] | 768 | next.set(w,first[level[w]]); |
---|
| 769 | first[level[w]]=w; |
---|
| 770 | } |
---|
[1222] | 771 | excess.set(w, excess[w]+(*_flow)[e]); |
---|
| 772 | _flow->set(e, 0); |
---|
[836] | 773 | } |
---|
| 774 | } |
---|
| 775 | break; |
---|
| 776 | |
---|
| 777 | case PRE_FLOW: |
---|
| 778 | //the starting flow |
---|
[1222] | 779 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
| 780 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
[2024] | 781 | if ( !_surely.positive(rem) ) continue; |
---|
[1222] | 782 | Node w=_g->target(e); |
---|
| 783 | if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]); |
---|
[836] | 784 | } |
---|
| 785 | |
---|
[1222] | 786 | for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
[2024] | 787 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
[1222] | 788 | Node w=_g->source(e); |
---|
| 789 | if ( level[w] < _node_num ) _flow->set(e, 0); |
---|
[836] | 790 | } |
---|
| 791 | |
---|
| 792 | //computing the excess |
---|
[1222] | 793 | for(NodeIt w(*_g); w!=INVALID; ++w) { |
---|
[836] | 794 | Num exc=0; |
---|
[1222] | 795 | for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
| 796 | for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
[836] | 797 | excess.set(w,exc); |
---|
| 798 | |
---|
| 799 | //putting the active nodes into the stack |
---|
| 800 | int lev=level[w]; |
---|
[2024] | 801 | if ( _surely.positive(exc) && lev < _node_num && Node(w) != _target ) { |
---|
[836] | 802 | next.set(w,first[lev]); |
---|
| 803 | first[lev]=w; |
---|
| 804 | } |
---|
| 805 | } |
---|
| 806 | break; |
---|
| 807 | } //switch |
---|
| 808 | } //preflowPreproc |
---|
| 809 | |
---|
| 810 | |
---|
| 811 | void relabel(Node w, int newlevel, VecNode& first, NNMap& next, |
---|
| 812 | VecNode& level_list, NNMap& left, |
---|
| 813 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
| 814 | { |
---|
| 815 | |
---|
| 816 | int lev=level[w]; |
---|
| 817 | |
---|
| 818 | Node right_n=right[w]; |
---|
| 819 | Node left_n=left[w]; |
---|
| 820 | |
---|
| 821 | //unlacing starts |
---|
| 822 | if ( right_n!=INVALID ) { |
---|
| 823 | if ( left_n!=INVALID ) { |
---|
| 824 | right.set(left_n, right_n); |
---|
| 825 | left.set(right_n, left_n); |
---|
| 826 | } else { |
---|
| 827 | level_list[lev]=right_n; |
---|
| 828 | left.set(right_n, INVALID); |
---|
| 829 | } |
---|
| 830 | } else { |
---|
| 831 | if ( left_n!=INVALID ) { |
---|
| 832 | right.set(left_n, INVALID); |
---|
| 833 | } else { |
---|
| 834 | level_list[lev]=INVALID; |
---|
| 835 | } |
---|
| 836 | } |
---|
| 837 | //unlacing ends |
---|
| 838 | |
---|
| 839 | if ( level_list[lev]==INVALID ) { |
---|
| 840 | |
---|
| 841 | //gapping starts |
---|
| 842 | for (int i=lev; i!=k ; ) { |
---|
| 843 | Node v=level_list[++i]; |
---|
| 844 | while ( v!=INVALID ) { |
---|
[1222] | 845 | level.set(v,_node_num); |
---|
[836] | 846 | v=right[v]; |
---|
| 847 | } |
---|
| 848 | level_list[i]=INVALID; |
---|
| 849 | if ( !what_heur ) first[i]=INVALID; |
---|
| 850 | } |
---|
| 851 | |
---|
[1222] | 852 | level.set(w,_node_num); |
---|
[836] | 853 | b=lev-1; |
---|
| 854 | k=b; |
---|
| 855 | //gapping ends |
---|
| 856 | |
---|
| 857 | } else { |
---|
| 858 | |
---|
[1222] | 859 | if ( newlevel == _node_num ) level.set(w,_node_num); |
---|
[836] | 860 | else { |
---|
| 861 | level.set(w,++newlevel); |
---|
| 862 | next.set(w,first[newlevel]); |
---|
| 863 | first[newlevel]=w; |
---|
| 864 | if ( what_heur ) b=newlevel; |
---|
| 865 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
| 866 | Node z=level_list[newlevel]; |
---|
| 867 | if ( z!=INVALID ) left.set(z,w); |
---|
| 868 | right.set(w,z); |
---|
| 869 | left.set(w,INVALID); |
---|
| 870 | level_list[newlevel]=w; |
---|
| 871 | } |
---|
| 872 | } |
---|
| 873 | } //relabel |
---|
| 874 | |
---|
| 875 | }; |
---|
[1227] | 876 | |
---|
[1792] | 877 | ///\ingroup flowalgs |
---|
| 878 | ///\brief Function type interface for Preflow algorithm. |
---|
| 879 | /// |
---|
[1227] | 880 | ///Function type interface for Preflow algorithm. |
---|
| 881 | ///\sa Preflow |
---|
| 882 | template<class GR, class CM, class FM> |
---|
| 883 | Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g, |
---|
| 884 | typename GR::Node source, |
---|
| 885 | typename GR::Node target, |
---|
| 886 | const CM &cap, |
---|
| 887 | FM &flow |
---|
| 888 | ) |
---|
| 889 | { |
---|
| 890 | return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow); |
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| 891 | } |
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| 892 | |
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[921] | 893 | } //namespace lemon |
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[836] | 894 | |
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[921] | 895 | #endif //LEMON_PREFLOW_H |
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