[425] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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| 4 | * |
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[463] | 5 | * Copyright (C) 2003-2009 |
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[425] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 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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| 19 | #ifndef LEMON_HAO_ORLIN_H |
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| 20 | #define LEMON_HAO_ORLIN_H |
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| 21 | |
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| 22 | #include <vector> |
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| 23 | #include <list> |
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| 24 | #include <limits> |
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| 25 | |
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| 26 | #include <lemon/maps.h> |
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| 27 | #include <lemon/core.h> |
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| 28 | #include <lemon/tolerance.h> |
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| 29 | |
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| 30 | /// \file |
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| 31 | /// \ingroup min_cut |
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| 32 | /// \brief Implementation of the Hao-Orlin algorithm. |
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| 33 | /// |
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[643] | 34 | /// Implementation of the Hao-Orlin algorithm for finding a minimum cut |
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| 35 | /// in a digraph. |
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[425] | 36 | |
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| 37 | namespace lemon { |
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| 38 | |
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| 39 | /// \ingroup min_cut |
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| 40 | /// |
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[643] | 41 | /// \brief Hao-Orlin algorithm for finding a minimum cut in a digraph. |
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[425] | 42 | /// |
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[643] | 43 | /// This class implements the Hao-Orlin algorithm for finding a minimum |
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| 44 | /// value cut in a directed graph \f$D=(V,A)\f$. |
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| 45 | /// It takes a fixed node \f$ source \in V \f$ and |
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[425] | 46 | /// consists of two phases: in the first phase it determines a |
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| 47 | /// minimum cut with \f$ source \f$ on the source-side (i.e. a set |
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[643] | 48 | /// \f$ X\subsetneq V \f$ with \f$ source \in X \f$ and minimal outgoing |
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| 49 | /// capacity) and in the second phase it determines a minimum cut |
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[425] | 50 | /// with \f$ source \f$ on the sink-side (i.e. a set |
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[643] | 51 | /// \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ and minimal outgoing |
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| 52 | /// capacity). Obviously, the smaller of these two cuts will be a |
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[425] | 53 | /// minimum cut of \f$ D \f$. The algorithm is a modified |
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[643] | 54 | /// preflow push-relabel algorithm. Our implementation calculates |
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[425] | 55 | /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the |
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| 56 | /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. The |
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[643] | 57 | /// purpose of such algorithm is e.g. testing network reliability. |
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[425] | 58 | /// |
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[643] | 59 | /// For an undirected graph you can run just the first phase of the |
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| 60 | /// algorithm or you can use the algorithm of Nagamochi and Ibaraki, |
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| 61 | /// which solves the undirected problem in \f$ O(nm + n^2 \log n) \f$ |
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| 62 | /// time. It is implemented in the NagamochiIbaraki algorithm class. |
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| 63 | /// |
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| 64 | /// \tparam GR The type of the digraph the algorithm runs on. |
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| 65 | /// \tparam CAP The type of the arc map containing the capacities, |
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| 66 | /// which can be any numreric type. The default map type is |
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| 67 | /// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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| 68 | /// \tparam TOL Tolerance class for handling inexact computations. The |
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[606] | 69 | /// default tolerance type is \ref Tolerance "Tolerance<CAP::Value>". |
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[425] | 70 | #ifdef DOXYGEN |
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[606] | 71 | template <typename GR, typename CAP, typename TOL> |
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[425] | 72 | #else |
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[606] | 73 | template <typename GR, |
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| 74 | typename CAP = typename GR::template ArcMap<int>, |
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| 75 | typename TOL = Tolerance<typename CAP::Value> > |
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[425] | 76 | #endif |
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| 77 | class HaoOrlin { |
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[643] | 78 | public: |
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| 79 | |
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| 80 | /// The digraph type of the algorithm |
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| 81 | typedef GR Digraph; |
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| 82 | /// The capacity map type of the algorithm |
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| 83 | typedef CAP CapacityMap; |
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| 84 | /// The tolerance type of the algorithm |
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| 85 | typedef TOL Tolerance; |
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| 86 | |
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[425] | 87 | private: |
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| 88 | |
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| 89 | typedef typename CapacityMap::Value Value; |
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| 90 | |
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[643] | 91 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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[425] | 92 | |
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| 93 | const Digraph& _graph; |
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| 94 | const CapacityMap* _capacity; |
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| 95 | |
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| 96 | typedef typename Digraph::template ArcMap<Value> FlowMap; |
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| 97 | FlowMap* _flow; |
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| 98 | |
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| 99 | Node _source; |
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| 100 | |
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| 101 | int _node_num; |
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| 102 | |
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| 103 | // Bucketing structure |
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| 104 | std::vector<Node> _first, _last; |
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| 105 | typename Digraph::template NodeMap<Node>* _next; |
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| 106 | typename Digraph::template NodeMap<Node>* _prev; |
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| 107 | typename Digraph::template NodeMap<bool>* _active; |
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| 108 | typename Digraph::template NodeMap<int>* _bucket; |
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| 109 | |
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| 110 | std::vector<bool> _dormant; |
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| 111 | |
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| 112 | std::list<std::list<int> > _sets; |
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| 113 | std::list<int>::iterator _highest; |
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| 114 | |
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| 115 | typedef typename Digraph::template NodeMap<Value> ExcessMap; |
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| 116 | ExcessMap* _excess; |
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| 117 | |
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| 118 | typedef typename Digraph::template NodeMap<bool> SourceSetMap; |
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| 119 | SourceSetMap* _source_set; |
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| 120 | |
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| 121 | Value _min_cut; |
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| 122 | |
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| 123 | typedef typename Digraph::template NodeMap<bool> MinCutMap; |
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| 124 | MinCutMap* _min_cut_map; |
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| 125 | |
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| 126 | Tolerance _tolerance; |
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| 127 | |
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| 128 | public: |
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| 129 | |
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| 130 | /// \brief Constructor |
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| 131 | /// |
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| 132 | /// Constructor of the algorithm class. |
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| 133 | HaoOrlin(const Digraph& graph, const CapacityMap& capacity, |
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| 134 | const Tolerance& tolerance = Tolerance()) : |
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| 135 | _graph(graph), _capacity(&capacity), _flow(0), _source(), |
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| 136 | _node_num(), _first(), _last(), _next(0), _prev(0), |
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| 137 | _active(0), _bucket(0), _dormant(), _sets(), _highest(), |
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| 138 | _excess(0), _source_set(0), _min_cut(), _min_cut_map(0), |
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| 139 | _tolerance(tolerance) {} |
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| 140 | |
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| 141 | ~HaoOrlin() { |
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| 142 | if (_min_cut_map) { |
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| 143 | delete _min_cut_map; |
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| 144 | } |
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| 145 | if (_source_set) { |
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| 146 | delete _source_set; |
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| 147 | } |
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| 148 | if (_excess) { |
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| 149 | delete _excess; |
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| 150 | } |
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| 151 | if (_next) { |
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| 152 | delete _next; |
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| 153 | } |
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| 154 | if (_prev) { |
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| 155 | delete _prev; |
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| 156 | } |
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| 157 | if (_active) { |
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| 158 | delete _active; |
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| 159 | } |
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| 160 | if (_bucket) { |
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| 161 | delete _bucket; |
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| 162 | } |
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| 163 | if (_flow) { |
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| 164 | delete _flow; |
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| 165 | } |
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| 166 | } |
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| 167 | |
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| 168 | private: |
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| 169 | |
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| 170 | void activate(const Node& i) { |
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[628] | 171 | (*_active)[i] = true; |
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[425] | 172 | |
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| 173 | int bucket = (*_bucket)[i]; |
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| 174 | |
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| 175 | if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return; |
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| 176 | //unlace |
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[628] | 177 | (*_next)[(*_prev)[i]] = (*_next)[i]; |
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[425] | 178 | if ((*_next)[i] != INVALID) { |
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[628] | 179 | (*_prev)[(*_next)[i]] = (*_prev)[i]; |
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[425] | 180 | } else { |
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| 181 | _last[bucket] = (*_prev)[i]; |
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| 182 | } |
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| 183 | //lace |
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[628] | 184 | (*_next)[i] = _first[bucket]; |
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| 185 | (*_prev)[_first[bucket]] = i; |
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| 186 | (*_prev)[i] = INVALID; |
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[425] | 187 | _first[bucket] = i; |
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| 188 | } |
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| 189 | |
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| 190 | void deactivate(const Node& i) { |
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[628] | 191 | (*_active)[i] = false; |
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[425] | 192 | int bucket = (*_bucket)[i]; |
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| 193 | |
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| 194 | if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return; |
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| 195 | |
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| 196 | //unlace |
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[628] | 197 | (*_prev)[(*_next)[i]] = (*_prev)[i]; |
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[425] | 198 | if ((*_prev)[i] != INVALID) { |
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[628] | 199 | (*_next)[(*_prev)[i]] = (*_next)[i]; |
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[425] | 200 | } else { |
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| 201 | _first[bucket] = (*_next)[i]; |
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| 202 | } |
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| 203 | //lace |
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[628] | 204 | (*_prev)[i] = _last[bucket]; |
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| 205 | (*_next)[_last[bucket]] = i; |
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| 206 | (*_next)[i] = INVALID; |
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[425] | 207 | _last[bucket] = i; |
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| 208 | } |
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| 209 | |
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| 210 | void addItem(const Node& i, int bucket) { |
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| 211 | (*_bucket)[i] = bucket; |
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| 212 | if (_last[bucket] != INVALID) { |
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[628] | 213 | (*_prev)[i] = _last[bucket]; |
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| 214 | (*_next)[_last[bucket]] = i; |
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| 215 | (*_next)[i] = INVALID; |
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[425] | 216 | _last[bucket] = i; |
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| 217 | } else { |
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[628] | 218 | (*_prev)[i] = INVALID; |
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[425] | 219 | _first[bucket] = i; |
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[628] | 220 | (*_next)[i] = INVALID; |
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[425] | 221 | _last[bucket] = i; |
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| 222 | } |
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| 223 | } |
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| 224 | |
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| 225 | void findMinCutOut() { |
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| 226 | |
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| 227 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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[628] | 228 | (*_excess)[n] = 0; |
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[425] | 229 | } |
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| 230 | |
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| 231 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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[628] | 232 | (*_flow)[a] = 0; |
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[425] | 233 | } |
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| 234 | |
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[427] | 235 | int bucket_num = 0; |
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| 236 | std::vector<Node> queue(_node_num); |
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| 237 | int qfirst = 0, qlast = 0, qsep = 0; |
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[425] | 238 | |
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| 239 | { |
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| 240 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
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| 241 | |
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[628] | 242 | reached[_source] = true; |
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[425] | 243 | bool first_set = true; |
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| 244 | |
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| 245 | for (NodeIt t(_graph); t != INVALID; ++t) { |
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| 246 | if (reached[t]) continue; |
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| 247 | _sets.push_front(std::list<int>()); |
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[463] | 248 | |
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[427] | 249 | queue[qlast++] = t; |
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[628] | 250 | reached[t] = true; |
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[425] | 251 | |
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[427] | 252 | while (qfirst != qlast) { |
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| 253 | if (qsep == qfirst) { |
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| 254 | ++bucket_num; |
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| 255 | _sets.front().push_front(bucket_num); |
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| 256 | _dormant[bucket_num] = !first_set; |
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| 257 | _first[bucket_num] = _last[bucket_num] = INVALID; |
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| 258 | qsep = qlast; |
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| 259 | } |
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[425] | 260 | |
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[427] | 261 | Node n = queue[qfirst++]; |
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| 262 | addItem(n, bucket_num); |
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| 263 | |
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| 264 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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| 265 | Node u = _graph.source(a); |
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| 266 | if (!reached[u] && _tolerance.positive((*_capacity)[a])) { |
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[628] | 267 | reached[u] = true; |
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[427] | 268 | queue[qlast++] = u; |
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[425] | 269 | } |
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| 270 | } |
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| 271 | } |
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| 272 | first_set = false; |
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| 273 | } |
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| 274 | |
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[427] | 275 | ++bucket_num; |
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[628] | 276 | (*_bucket)[_source] = 0; |
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[425] | 277 | _dormant[0] = true; |
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| 278 | } |
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[628] | 279 | (*_source_set)[_source] = true; |
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[425] | 280 | |
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| 281 | Node target = _last[_sets.back().back()]; |
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| 282 | { |
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| 283 | for (OutArcIt a(_graph, _source); a != INVALID; ++a) { |
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| 284 | if (_tolerance.positive((*_capacity)[a])) { |
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| 285 | Node u = _graph.target(a); |
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[628] | 286 | (*_flow)[a] = (*_capacity)[a]; |
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| 287 | (*_excess)[u] += (*_capacity)[a]; |
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[425] | 288 | if (!(*_active)[u] && u != _source) { |
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| 289 | activate(u); |
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| 290 | } |
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| 291 | } |
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| 292 | } |
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| 293 | |
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| 294 | if ((*_active)[target]) { |
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| 295 | deactivate(target); |
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| 296 | } |
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| 297 | |
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| 298 | _highest = _sets.back().begin(); |
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| 299 | while (_highest != _sets.back().end() && |
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| 300 | !(*_active)[_first[*_highest]]) { |
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| 301 | ++_highest; |
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| 302 | } |
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| 303 | } |
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| 304 | |
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| 305 | while (true) { |
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| 306 | while (_highest != _sets.back().end()) { |
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| 307 | Node n = _first[*_highest]; |
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| 308 | Value excess = (*_excess)[n]; |
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| 309 | int next_bucket = _node_num; |
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| 310 | |
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| 311 | int under_bucket; |
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| 312 | if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
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| 313 | under_bucket = -1; |
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| 314 | } else { |
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| 315 | under_bucket = *(++std::list<int>::iterator(_highest)); |
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| 316 | } |
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| 317 | |
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| 318 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
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| 319 | Node v = _graph.target(a); |
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| 320 | if (_dormant[(*_bucket)[v]]) continue; |
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| 321 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
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| 322 | if (!_tolerance.positive(rem)) continue; |
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| 323 | if ((*_bucket)[v] == under_bucket) { |
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| 324 | if (!(*_active)[v] && v != target) { |
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| 325 | activate(v); |
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| 326 | } |
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| 327 | if (!_tolerance.less(rem, excess)) { |
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[628] | 328 | (*_flow)[a] += excess; |
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| 329 | (*_excess)[v] += excess; |
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[425] | 330 | excess = 0; |
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| 331 | goto no_more_push; |
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| 332 | } else { |
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| 333 | excess -= rem; |
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[628] | 334 | (*_excess)[v] += rem; |
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| 335 | (*_flow)[a] = (*_capacity)[a]; |
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[425] | 336 | } |
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| 337 | } else if (next_bucket > (*_bucket)[v]) { |
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| 338 | next_bucket = (*_bucket)[v]; |
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| 339 | } |
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| 340 | } |
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| 341 | |
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| 342 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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| 343 | Node v = _graph.source(a); |
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| 344 | if (_dormant[(*_bucket)[v]]) continue; |
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| 345 | Value rem = (*_flow)[a]; |
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| 346 | if (!_tolerance.positive(rem)) continue; |
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| 347 | if ((*_bucket)[v] == under_bucket) { |
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| 348 | if (!(*_active)[v] && v != target) { |
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| 349 | activate(v); |
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| 350 | } |
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| 351 | if (!_tolerance.less(rem, excess)) { |
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[628] | 352 | (*_flow)[a] -= excess; |
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| 353 | (*_excess)[v] += excess; |
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[425] | 354 | excess = 0; |
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| 355 | goto no_more_push; |
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| 356 | } else { |
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| 357 | excess -= rem; |
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[628] | 358 | (*_excess)[v] += rem; |
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| 359 | (*_flow)[a] = 0; |
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[425] | 360 | } |
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| 361 | } else if (next_bucket > (*_bucket)[v]) { |
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| 362 | next_bucket = (*_bucket)[v]; |
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| 363 | } |
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| 364 | } |
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| 365 | |
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| 366 | no_more_push: |
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| 367 | |
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[628] | 368 | (*_excess)[n] = excess; |
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[425] | 369 | |
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| 370 | if (excess != 0) { |
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| 371 | if ((*_next)[n] == INVALID) { |
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| 372 | typename std::list<std::list<int> >::iterator new_set = |
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| 373 | _sets.insert(--_sets.end(), std::list<int>()); |
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| 374 | new_set->splice(new_set->end(), _sets.back(), |
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| 375 | _sets.back().begin(), ++_highest); |
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| 376 | for (std::list<int>::iterator it = new_set->begin(); |
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| 377 | it != new_set->end(); ++it) { |
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| 378 | _dormant[*it] = true; |
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| 379 | } |
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| 380 | while (_highest != _sets.back().end() && |
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| 381 | !(*_active)[_first[*_highest]]) { |
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| 382 | ++_highest; |
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| 383 | } |
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| 384 | } else if (next_bucket == _node_num) { |
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| 385 | _first[(*_bucket)[n]] = (*_next)[n]; |
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[628] | 386 | (*_prev)[(*_next)[n]] = INVALID; |
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[425] | 387 | |
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| 388 | std::list<std::list<int> >::iterator new_set = |
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| 389 | _sets.insert(--_sets.end(), std::list<int>()); |
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| 390 | |
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| 391 | new_set->push_front(bucket_num); |
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[628] | 392 | (*_bucket)[n] = bucket_num; |
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[425] | 393 | _first[bucket_num] = _last[bucket_num] = n; |
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[628] | 394 | (*_next)[n] = INVALID; |
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| 395 | (*_prev)[n] = INVALID; |
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[425] | 396 | _dormant[bucket_num] = true; |
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| 397 | ++bucket_num; |
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| 398 | |
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| 399 | while (_highest != _sets.back().end() && |
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| 400 | !(*_active)[_first[*_highest]]) { |
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| 401 | ++_highest; |
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| 402 | } |
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| 403 | } else { |
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| 404 | _first[*_highest] = (*_next)[n]; |
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[628] | 405 | (*_prev)[(*_next)[n]] = INVALID; |
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[425] | 406 | |
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| 407 | while (next_bucket != *_highest) { |
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| 408 | --_highest; |
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| 409 | } |
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| 410 | |
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| 411 | if (_highest == _sets.back().begin()) { |
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| 412 | _sets.back().push_front(bucket_num); |
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| 413 | _dormant[bucket_num] = false; |
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| 414 | _first[bucket_num] = _last[bucket_num] = INVALID; |
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| 415 | ++bucket_num; |
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| 416 | } |
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| 417 | --_highest; |
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| 418 | |
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[628] | 419 | (*_bucket)[n] = *_highest; |
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| 420 | (*_next)[n] = _first[*_highest]; |
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[425] | 421 | if (_first[*_highest] != INVALID) { |
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[628] | 422 | (*_prev)[_first[*_highest]] = n; |
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[425] | 423 | } else { |
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| 424 | _last[*_highest] = n; |
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| 425 | } |
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| 426 | _first[*_highest] = n; |
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| 427 | } |
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| 428 | } else { |
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| 429 | |
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| 430 | deactivate(n); |
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| 431 | if (!(*_active)[_first[*_highest]]) { |
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| 432 | ++_highest; |
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| 433 | if (_highest != _sets.back().end() && |
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| 434 | !(*_active)[_first[*_highest]]) { |
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| 435 | _highest = _sets.back().end(); |
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| 436 | } |
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| 437 | } |
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| 438 | } |
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| 439 | } |
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| 440 | |
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| 441 | if ((*_excess)[target] < _min_cut) { |
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| 442 | _min_cut = (*_excess)[target]; |
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| 443 | for (NodeIt i(_graph); i != INVALID; ++i) { |
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[628] | 444 | (*_min_cut_map)[i] = true; |
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[425] | 445 | } |
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| 446 | for (std::list<int>::iterator it = _sets.back().begin(); |
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| 447 | it != _sets.back().end(); ++it) { |
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| 448 | Node n = _first[*it]; |
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| 449 | while (n != INVALID) { |
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[628] | 450 | (*_min_cut_map)[n] = false; |
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[425] | 451 | n = (*_next)[n]; |
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| 452 | } |
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| 453 | } |
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| 454 | } |
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| 455 | |
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| 456 | { |
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| 457 | Node new_target; |
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| 458 | if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
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| 459 | if ((*_next)[target] == INVALID) { |
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| 460 | _last[(*_bucket)[target]] = (*_prev)[target]; |
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| 461 | new_target = (*_prev)[target]; |
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| 462 | } else { |
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[628] | 463 | (*_prev)[(*_next)[target]] = (*_prev)[target]; |
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[425] | 464 | new_target = (*_next)[target]; |
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| 465 | } |
---|
| 466 | if ((*_prev)[target] == INVALID) { |
---|
| 467 | _first[(*_bucket)[target]] = (*_next)[target]; |
---|
| 468 | } else { |
---|
[628] | 469 | (*_next)[(*_prev)[target]] = (*_next)[target]; |
---|
[425] | 470 | } |
---|
| 471 | } else { |
---|
| 472 | _sets.back().pop_back(); |
---|
| 473 | if (_sets.back().empty()) { |
---|
| 474 | _sets.pop_back(); |
---|
| 475 | if (_sets.empty()) |
---|
| 476 | break; |
---|
| 477 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 478 | it != _sets.back().end(); ++it) { |
---|
| 479 | _dormant[*it] = false; |
---|
| 480 | } |
---|
| 481 | } |
---|
| 482 | new_target = _last[_sets.back().back()]; |
---|
| 483 | } |
---|
| 484 | |
---|
[628] | 485 | (*_bucket)[target] = 0; |
---|
[425] | 486 | |
---|
[628] | 487 | (*_source_set)[target] = true; |
---|
[425] | 488 | for (OutArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 489 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
| 490 | if (!_tolerance.positive(rem)) continue; |
---|
| 491 | Node v = _graph.target(a); |
---|
| 492 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 493 | activate(v); |
---|
| 494 | } |
---|
[628] | 495 | (*_excess)[v] += rem; |
---|
| 496 | (*_flow)[a] = (*_capacity)[a]; |
---|
[425] | 497 | } |
---|
| 498 | |
---|
| 499 | for (InArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 500 | Value rem = (*_flow)[a]; |
---|
| 501 | if (!_tolerance.positive(rem)) continue; |
---|
| 502 | Node v = _graph.source(a); |
---|
| 503 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 504 | activate(v); |
---|
| 505 | } |
---|
[628] | 506 | (*_excess)[v] += rem; |
---|
| 507 | (*_flow)[a] = 0; |
---|
[425] | 508 | } |
---|
| 509 | |
---|
| 510 | target = new_target; |
---|
| 511 | if ((*_active)[target]) { |
---|
| 512 | deactivate(target); |
---|
| 513 | } |
---|
| 514 | |
---|
| 515 | _highest = _sets.back().begin(); |
---|
| 516 | while (_highest != _sets.back().end() && |
---|
| 517 | !(*_active)[_first[*_highest]]) { |
---|
| 518 | ++_highest; |
---|
| 519 | } |
---|
| 520 | } |
---|
| 521 | } |
---|
| 522 | } |
---|
| 523 | |
---|
| 524 | void findMinCutIn() { |
---|
| 525 | |
---|
| 526 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
[628] | 527 | (*_excess)[n] = 0; |
---|
[425] | 528 | } |
---|
| 529 | |
---|
| 530 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
[628] | 531 | (*_flow)[a] = 0; |
---|
[425] | 532 | } |
---|
| 533 | |
---|
[427] | 534 | int bucket_num = 0; |
---|
| 535 | std::vector<Node> queue(_node_num); |
---|
| 536 | int qfirst = 0, qlast = 0, qsep = 0; |
---|
[425] | 537 | |
---|
| 538 | { |
---|
| 539 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
---|
| 540 | |
---|
[628] | 541 | reached[_source] = true; |
---|
[425] | 542 | |
---|
| 543 | bool first_set = true; |
---|
| 544 | |
---|
| 545 | for (NodeIt t(_graph); t != INVALID; ++t) { |
---|
| 546 | if (reached[t]) continue; |
---|
| 547 | _sets.push_front(std::list<int>()); |
---|
[463] | 548 | |
---|
[427] | 549 | queue[qlast++] = t; |
---|
[628] | 550 | reached[t] = true; |
---|
[425] | 551 | |
---|
[427] | 552 | while (qfirst != qlast) { |
---|
| 553 | if (qsep == qfirst) { |
---|
| 554 | ++bucket_num; |
---|
| 555 | _sets.front().push_front(bucket_num); |
---|
| 556 | _dormant[bucket_num] = !first_set; |
---|
| 557 | _first[bucket_num] = _last[bucket_num] = INVALID; |
---|
| 558 | qsep = qlast; |
---|
| 559 | } |
---|
[425] | 560 | |
---|
[427] | 561 | Node n = queue[qfirst++]; |
---|
| 562 | addItem(n, bucket_num); |
---|
| 563 | |
---|
| 564 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
---|
| 565 | Node u = _graph.target(a); |
---|
| 566 | if (!reached[u] && _tolerance.positive((*_capacity)[a])) { |
---|
[628] | 567 | reached[u] = true; |
---|
[427] | 568 | queue[qlast++] = u; |
---|
[425] | 569 | } |
---|
| 570 | } |
---|
| 571 | } |
---|
| 572 | first_set = false; |
---|
| 573 | } |
---|
| 574 | |
---|
[427] | 575 | ++bucket_num; |
---|
[628] | 576 | (*_bucket)[_source] = 0; |
---|
[425] | 577 | _dormant[0] = true; |
---|
| 578 | } |
---|
[628] | 579 | (*_source_set)[_source] = true; |
---|
[425] | 580 | |
---|
| 581 | Node target = _last[_sets.back().back()]; |
---|
| 582 | { |
---|
| 583 | for (InArcIt a(_graph, _source); a != INVALID; ++a) { |
---|
| 584 | if (_tolerance.positive((*_capacity)[a])) { |
---|
| 585 | Node u = _graph.source(a); |
---|
[628] | 586 | (*_flow)[a] = (*_capacity)[a]; |
---|
| 587 | (*_excess)[u] += (*_capacity)[a]; |
---|
[425] | 588 | if (!(*_active)[u] && u != _source) { |
---|
| 589 | activate(u); |
---|
| 590 | } |
---|
| 591 | } |
---|
| 592 | } |
---|
| 593 | if ((*_active)[target]) { |
---|
| 594 | deactivate(target); |
---|
| 595 | } |
---|
| 596 | |
---|
| 597 | _highest = _sets.back().begin(); |
---|
| 598 | while (_highest != _sets.back().end() && |
---|
| 599 | !(*_active)[_first[*_highest]]) { |
---|
| 600 | ++_highest; |
---|
| 601 | } |
---|
| 602 | } |
---|
| 603 | |
---|
| 604 | |
---|
| 605 | while (true) { |
---|
| 606 | while (_highest != _sets.back().end()) { |
---|
| 607 | Node n = _first[*_highest]; |
---|
| 608 | Value excess = (*_excess)[n]; |
---|
| 609 | int next_bucket = _node_num; |
---|
| 610 | |
---|
| 611 | int under_bucket; |
---|
| 612 | if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
---|
| 613 | under_bucket = -1; |
---|
| 614 | } else { |
---|
| 615 | under_bucket = *(++std::list<int>::iterator(_highest)); |
---|
| 616 | } |
---|
| 617 | |
---|
| 618 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
---|
| 619 | Node v = _graph.source(a); |
---|
| 620 | if (_dormant[(*_bucket)[v]]) continue; |
---|
| 621 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
| 622 | if (!_tolerance.positive(rem)) continue; |
---|
| 623 | if ((*_bucket)[v] == under_bucket) { |
---|
| 624 | if (!(*_active)[v] && v != target) { |
---|
| 625 | activate(v); |
---|
| 626 | } |
---|
| 627 | if (!_tolerance.less(rem, excess)) { |
---|
[628] | 628 | (*_flow)[a] += excess; |
---|
| 629 | (*_excess)[v] += excess; |
---|
[425] | 630 | excess = 0; |
---|
| 631 | goto no_more_push; |
---|
| 632 | } else { |
---|
| 633 | excess -= rem; |
---|
[628] | 634 | (*_excess)[v] += rem; |
---|
| 635 | (*_flow)[a] = (*_capacity)[a]; |
---|
[425] | 636 | } |
---|
| 637 | } else if (next_bucket > (*_bucket)[v]) { |
---|
| 638 | next_bucket = (*_bucket)[v]; |
---|
| 639 | } |
---|
| 640 | } |
---|
| 641 | |
---|
| 642 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
---|
| 643 | Node v = _graph.target(a); |
---|
| 644 | if (_dormant[(*_bucket)[v]]) continue; |
---|
| 645 | Value rem = (*_flow)[a]; |
---|
| 646 | if (!_tolerance.positive(rem)) continue; |
---|
| 647 | if ((*_bucket)[v] == under_bucket) { |
---|
| 648 | if (!(*_active)[v] && v != target) { |
---|
| 649 | activate(v); |
---|
| 650 | } |
---|
| 651 | if (!_tolerance.less(rem, excess)) { |
---|
[628] | 652 | (*_flow)[a] -= excess; |
---|
| 653 | (*_excess)[v] += excess; |
---|
[425] | 654 | excess = 0; |
---|
| 655 | goto no_more_push; |
---|
| 656 | } else { |
---|
| 657 | excess -= rem; |
---|
[628] | 658 | (*_excess)[v] += rem; |
---|
| 659 | (*_flow)[a] = 0; |
---|
[425] | 660 | } |
---|
| 661 | } else if (next_bucket > (*_bucket)[v]) { |
---|
| 662 | next_bucket = (*_bucket)[v]; |
---|
| 663 | } |
---|
| 664 | } |
---|
| 665 | |
---|
| 666 | no_more_push: |
---|
| 667 | |
---|
[628] | 668 | (*_excess)[n] = excess; |
---|
[425] | 669 | |
---|
| 670 | if (excess != 0) { |
---|
| 671 | if ((*_next)[n] == INVALID) { |
---|
| 672 | typename std::list<std::list<int> >::iterator new_set = |
---|
| 673 | _sets.insert(--_sets.end(), std::list<int>()); |
---|
| 674 | new_set->splice(new_set->end(), _sets.back(), |
---|
| 675 | _sets.back().begin(), ++_highest); |
---|
| 676 | for (std::list<int>::iterator it = new_set->begin(); |
---|
| 677 | it != new_set->end(); ++it) { |
---|
| 678 | _dormant[*it] = true; |
---|
| 679 | } |
---|
| 680 | while (_highest != _sets.back().end() && |
---|
| 681 | !(*_active)[_first[*_highest]]) { |
---|
| 682 | ++_highest; |
---|
| 683 | } |
---|
| 684 | } else if (next_bucket == _node_num) { |
---|
| 685 | _first[(*_bucket)[n]] = (*_next)[n]; |
---|
[628] | 686 | (*_prev)[(*_next)[n]] = INVALID; |
---|
[425] | 687 | |
---|
| 688 | std::list<std::list<int> >::iterator new_set = |
---|
| 689 | _sets.insert(--_sets.end(), std::list<int>()); |
---|
| 690 | |
---|
| 691 | new_set->push_front(bucket_num); |
---|
[628] | 692 | (*_bucket)[n] = bucket_num; |
---|
[425] | 693 | _first[bucket_num] = _last[bucket_num] = n; |
---|
[628] | 694 | (*_next)[n] = INVALID; |
---|
| 695 | (*_prev)[n] = INVALID; |
---|
[425] | 696 | _dormant[bucket_num] = true; |
---|
| 697 | ++bucket_num; |
---|
| 698 | |
---|
| 699 | while (_highest != _sets.back().end() && |
---|
| 700 | !(*_active)[_first[*_highest]]) { |
---|
| 701 | ++_highest; |
---|
| 702 | } |
---|
| 703 | } else { |
---|
| 704 | _first[*_highest] = (*_next)[n]; |
---|
[628] | 705 | (*_prev)[(*_next)[n]] = INVALID; |
---|
[425] | 706 | |
---|
| 707 | while (next_bucket != *_highest) { |
---|
| 708 | --_highest; |
---|
| 709 | } |
---|
| 710 | if (_highest == _sets.back().begin()) { |
---|
| 711 | _sets.back().push_front(bucket_num); |
---|
| 712 | _dormant[bucket_num] = false; |
---|
| 713 | _first[bucket_num] = _last[bucket_num] = INVALID; |
---|
| 714 | ++bucket_num; |
---|
| 715 | } |
---|
| 716 | --_highest; |
---|
| 717 | |
---|
[628] | 718 | (*_bucket)[n] = *_highest; |
---|
| 719 | (*_next)[n] = _first[*_highest]; |
---|
[425] | 720 | if (_first[*_highest] != INVALID) { |
---|
[628] | 721 | (*_prev)[_first[*_highest]] = n; |
---|
[425] | 722 | } else { |
---|
| 723 | _last[*_highest] = n; |
---|
| 724 | } |
---|
| 725 | _first[*_highest] = n; |
---|
| 726 | } |
---|
| 727 | } else { |
---|
| 728 | |
---|
| 729 | deactivate(n); |
---|
| 730 | if (!(*_active)[_first[*_highest]]) { |
---|
| 731 | ++_highest; |
---|
| 732 | if (_highest != _sets.back().end() && |
---|
| 733 | !(*_active)[_first[*_highest]]) { |
---|
| 734 | _highest = _sets.back().end(); |
---|
| 735 | } |
---|
| 736 | } |
---|
| 737 | } |
---|
| 738 | } |
---|
| 739 | |
---|
| 740 | if ((*_excess)[target] < _min_cut) { |
---|
| 741 | _min_cut = (*_excess)[target]; |
---|
| 742 | for (NodeIt i(_graph); i != INVALID; ++i) { |
---|
[628] | 743 | (*_min_cut_map)[i] = false; |
---|
[425] | 744 | } |
---|
| 745 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 746 | it != _sets.back().end(); ++it) { |
---|
| 747 | Node n = _first[*it]; |
---|
| 748 | while (n != INVALID) { |
---|
[628] | 749 | (*_min_cut_map)[n] = true; |
---|
[425] | 750 | n = (*_next)[n]; |
---|
| 751 | } |
---|
| 752 | } |
---|
| 753 | } |
---|
| 754 | |
---|
| 755 | { |
---|
| 756 | Node new_target; |
---|
| 757 | if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
---|
| 758 | if ((*_next)[target] == INVALID) { |
---|
| 759 | _last[(*_bucket)[target]] = (*_prev)[target]; |
---|
| 760 | new_target = (*_prev)[target]; |
---|
| 761 | } else { |
---|
[628] | 762 | (*_prev)[(*_next)[target]] = (*_prev)[target]; |
---|
[425] | 763 | new_target = (*_next)[target]; |
---|
| 764 | } |
---|
| 765 | if ((*_prev)[target] == INVALID) { |
---|
| 766 | _first[(*_bucket)[target]] = (*_next)[target]; |
---|
| 767 | } else { |
---|
[628] | 768 | (*_next)[(*_prev)[target]] = (*_next)[target]; |
---|
[425] | 769 | } |
---|
| 770 | } else { |
---|
| 771 | _sets.back().pop_back(); |
---|
| 772 | if (_sets.back().empty()) { |
---|
| 773 | _sets.pop_back(); |
---|
| 774 | if (_sets.empty()) |
---|
| 775 | break; |
---|
| 776 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 777 | it != _sets.back().end(); ++it) { |
---|
| 778 | _dormant[*it] = false; |
---|
| 779 | } |
---|
| 780 | } |
---|
| 781 | new_target = _last[_sets.back().back()]; |
---|
| 782 | } |
---|
| 783 | |
---|
[628] | 784 | (*_bucket)[target] = 0; |
---|
[425] | 785 | |
---|
[628] | 786 | (*_source_set)[target] = true; |
---|
[425] | 787 | for (InArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 788 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
| 789 | if (!_tolerance.positive(rem)) continue; |
---|
| 790 | Node v = _graph.source(a); |
---|
| 791 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 792 | activate(v); |
---|
| 793 | } |
---|
[628] | 794 | (*_excess)[v] += rem; |
---|
| 795 | (*_flow)[a] = (*_capacity)[a]; |
---|
[425] | 796 | } |
---|
| 797 | |
---|
| 798 | for (OutArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 799 | Value rem = (*_flow)[a]; |
---|
| 800 | if (!_tolerance.positive(rem)) continue; |
---|
| 801 | Node v = _graph.target(a); |
---|
| 802 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 803 | activate(v); |
---|
| 804 | } |
---|
[628] | 805 | (*_excess)[v] += rem; |
---|
| 806 | (*_flow)[a] = 0; |
---|
[425] | 807 | } |
---|
| 808 | |
---|
| 809 | target = new_target; |
---|
| 810 | if ((*_active)[target]) { |
---|
| 811 | deactivate(target); |
---|
| 812 | } |
---|
| 813 | |
---|
| 814 | _highest = _sets.back().begin(); |
---|
| 815 | while (_highest != _sets.back().end() && |
---|
| 816 | !(*_active)[_first[*_highest]]) { |
---|
| 817 | ++_highest; |
---|
| 818 | } |
---|
| 819 | } |
---|
| 820 | } |
---|
| 821 | } |
---|
| 822 | |
---|
| 823 | public: |
---|
| 824 | |
---|
[643] | 825 | /// \name Execution Control |
---|
[425] | 826 | /// The simplest way to execute the algorithm is to use |
---|
[606] | 827 | /// one of the member functions called \ref run(). |
---|
[425] | 828 | /// \n |
---|
[643] | 829 | /// If you need better control on the execution, |
---|
| 830 | /// you have to call one of the \ref init() functions first, then |
---|
| 831 | /// \ref calculateOut() and/or \ref calculateIn(). |
---|
[425] | 832 | |
---|
| 833 | /// @{ |
---|
| 834 | |
---|
[643] | 835 | /// \brief Initialize the internal data structures. |
---|
[425] | 836 | /// |
---|
[643] | 837 | /// This function initializes the internal data structures. It creates |
---|
| 838 | /// the maps and some bucket structures for the algorithm. |
---|
| 839 | /// The first node is used as the source node for the push-relabel |
---|
| 840 | /// algorithm. |
---|
[425] | 841 | void init() { |
---|
| 842 | init(NodeIt(_graph)); |
---|
| 843 | } |
---|
| 844 | |
---|
[643] | 845 | /// \brief Initialize the internal data structures. |
---|
[425] | 846 | /// |
---|
[643] | 847 | /// This function initializes the internal data structures. It creates |
---|
| 848 | /// the maps and some bucket structures for the algorithm. |
---|
| 849 | /// The given node is used as the source node for the push-relabel |
---|
| 850 | /// algorithm. |
---|
[425] | 851 | void init(const Node& source) { |
---|
| 852 | _source = source; |
---|
| 853 | |
---|
| 854 | _node_num = countNodes(_graph); |
---|
| 855 | |
---|
[427] | 856 | _first.resize(_node_num); |
---|
| 857 | _last.resize(_node_num); |
---|
[425] | 858 | |
---|
[427] | 859 | _dormant.resize(_node_num); |
---|
[425] | 860 | |
---|
| 861 | if (!_flow) { |
---|
| 862 | _flow = new FlowMap(_graph); |
---|
| 863 | } |
---|
| 864 | if (!_next) { |
---|
| 865 | _next = new typename Digraph::template NodeMap<Node>(_graph); |
---|
| 866 | } |
---|
| 867 | if (!_prev) { |
---|
| 868 | _prev = new typename Digraph::template NodeMap<Node>(_graph); |
---|
| 869 | } |
---|
| 870 | if (!_active) { |
---|
| 871 | _active = new typename Digraph::template NodeMap<bool>(_graph); |
---|
| 872 | } |
---|
| 873 | if (!_bucket) { |
---|
| 874 | _bucket = new typename Digraph::template NodeMap<int>(_graph); |
---|
| 875 | } |
---|
| 876 | if (!_excess) { |
---|
| 877 | _excess = new ExcessMap(_graph); |
---|
| 878 | } |
---|
| 879 | if (!_source_set) { |
---|
| 880 | _source_set = new SourceSetMap(_graph); |
---|
| 881 | } |
---|
| 882 | if (!_min_cut_map) { |
---|
| 883 | _min_cut_map = new MinCutMap(_graph); |
---|
| 884 | } |
---|
| 885 | |
---|
| 886 | _min_cut = std::numeric_limits<Value>::max(); |
---|
| 887 | } |
---|
| 888 | |
---|
| 889 | |
---|
[643] | 890 | /// \brief Calculate a minimum cut with \f$ source \f$ on the |
---|
[425] | 891 | /// source-side. |
---|
| 892 | /// |
---|
[643] | 893 | /// This function calculates a minimum cut with \f$ source \f$ on the |
---|
[428] | 894 | /// source-side (i.e. a set \f$ X\subsetneq V \f$ with |
---|
[643] | 895 | /// \f$ source \in X \f$ and minimal outgoing capacity). |
---|
| 896 | /// |
---|
| 897 | /// \pre \ref init() must be called before using this function. |
---|
[425] | 898 | void calculateOut() { |
---|
| 899 | findMinCutOut(); |
---|
| 900 | } |
---|
| 901 | |
---|
[643] | 902 | /// \brief Calculate a minimum cut with \f$ source \f$ on the |
---|
| 903 | /// sink-side. |
---|
[425] | 904 | /// |
---|
[643] | 905 | /// This function calculates a minimum cut with \f$ source \f$ on the |
---|
| 906 | /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with |
---|
| 907 | /// \f$ source \notin X \f$ and minimal outgoing capacity). |
---|
| 908 | /// |
---|
| 909 | /// \pre \ref init() must be called before using this function. |
---|
[425] | 910 | void calculateIn() { |
---|
| 911 | findMinCutIn(); |
---|
| 912 | } |
---|
| 913 | |
---|
| 914 | |
---|
[643] | 915 | /// \brief Run the algorithm. |
---|
[425] | 916 | /// |
---|
[643] | 917 | /// This function runs the algorithm. It finds nodes \c source and |
---|
| 918 | /// \c target arbitrarily and then calls \ref init(), \ref calculateOut() |
---|
[425] | 919 | /// and \ref calculateIn(). |
---|
| 920 | void run() { |
---|
| 921 | init(); |
---|
| 922 | calculateOut(); |
---|
| 923 | calculateIn(); |
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| 924 | } |
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| 925 | |
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[643] | 926 | /// \brief Run the algorithm. |
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[425] | 927 | /// |
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[643] | 928 | /// This function runs the algorithm. It uses the given \c source node, |
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| 929 | /// finds a proper \c target node and then calls the \ref init(), |
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| 930 | /// \ref calculateOut() and \ref calculateIn(). |
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[425] | 931 | void run(const Node& s) { |
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| 932 | init(s); |
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| 933 | calculateOut(); |
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| 934 | calculateIn(); |
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| 935 | } |
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| 936 | |
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| 937 | /// @} |
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| 938 | |
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| 939 | /// \name Query Functions |
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| 940 | /// The result of the %HaoOrlin algorithm |
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[643] | 941 | /// can be obtained using these functions.\n |
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| 942 | /// \ref run(), \ref calculateOut() or \ref calculateIn() |
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| 943 | /// should be called before using them. |
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[425] | 944 | |
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| 945 | /// @{ |
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| 946 | |
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[643] | 947 | /// \brief Return the value of the minimum cut. |
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[425] | 948 | /// |
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[643] | 949 | /// This function returns the value of the minimum cut. |
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| 950 | /// |
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| 951 | /// \pre \ref run(), \ref calculateOut() or \ref calculateIn() |
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| 952 | /// must be called before using this function. |
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[425] | 953 | Value minCutValue() const { |
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| 954 | return _min_cut; |
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| 955 | } |
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| 956 | |
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| 957 | |
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[643] | 958 | /// \brief Return a minimum cut. |
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[425] | 959 | /// |
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[643] | 960 | /// This function sets \c cutMap to the characteristic vector of a |
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| 961 | /// minimum value cut: it will give a non-empty set \f$ X\subsetneq V \f$ |
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| 962 | /// with minimal outgoing capacity (i.e. \c cutMap will be \c true exactly |
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| 963 | /// for the nodes of \f$ X \f$). |
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| 964 | /// |
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| 965 | /// \param cutMap A \ref concepts::WriteMap "writable" node map with |
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| 966 | /// \c bool (or convertible) value type. |
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| 967 | /// |
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| 968 | /// \return The value of the minimum cut. |
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| 969 | /// |
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| 970 | /// \pre \ref run(), \ref calculateOut() or \ref calculateIn() |
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| 971 | /// must be called before using this function. |
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| 972 | template <typename CutMap> |
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| 973 | Value minCutMap(CutMap& cutMap) const { |
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[425] | 974 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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[643] | 975 | cutMap.set(it, (*_min_cut_map)[it]); |
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[425] | 976 | } |
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| 977 | return _min_cut; |
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| 978 | } |
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| 979 | |
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| 980 | /// @} |
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| 981 | |
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| 982 | }; //class HaoOrlin |
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| 983 | |
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| 984 | } //namespace lemon |
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| 985 | |
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| 986 | #endif //LEMON_HAO_ORLIN_H |
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