[409] | 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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[440] | 5 | * Copyright (C) 2003-2009 |
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[409] | 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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[596] | 34 | /// Implementation of the Hao-Orlin algorithm for finding a minimum cut |
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| 35 | /// in a digraph. |
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[409] | 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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[596] | 41 | /// \brief Hao-Orlin algorithm for finding a minimum cut in a digraph. |
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[409] | 42 | /// |
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[596] | 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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[409] | 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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[596] | 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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[409] | 50 | /// with \f$ source \f$ on the sink-side (i.e. a set |
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[596] | 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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[409] | 53 | /// minimum cut of \f$ D \f$. The algorithm is a modified |
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[596] | 54 | /// preflow push-relabel algorithm. Our implementation calculates |
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[409] | 55 | /// the minimum cut in \f$ 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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[596] | 57 | /// purpose of such algorithm is e.g. testing network reliability. |
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[409] | 58 | /// |
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[596] | 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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[559] | 69 | /// default tolerance type is \ref Tolerance "Tolerance<CAP::Value>". |
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[409] | 70 | #ifdef DOXYGEN |
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[559] | 71 | template <typename GR, typename CAP, typename TOL> |
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[409] | 72 | #else |
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[559] | 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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[409] | 76 | #endif |
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| 77 | class HaoOrlin { |
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[596] | 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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[409] | 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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[596] | 91 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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[409] | 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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[581] | 171 | (*_active)[i] = true; |
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[409] | 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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[581] | 177 | (*_next)[(*_prev)[i]] = (*_next)[i]; |
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[409] | 178 | if ((*_next)[i] != INVALID) { |
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[581] | 179 | (*_prev)[(*_next)[i]] = (*_prev)[i]; |
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[409] | 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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[581] | 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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[409] | 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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[581] | 191 | (*_active)[i] = false; |
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[409] | 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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[581] | 197 | (*_prev)[(*_next)[i]] = (*_prev)[i]; |
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[409] | 198 | if ((*_prev)[i] != INVALID) { |
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[581] | 199 | (*_next)[(*_prev)[i]] = (*_next)[i]; |
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[409] | 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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[581] | 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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[409] | 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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[581] | 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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[409] | 216 | _last[bucket] = i; |
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| 217 | } else { |
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[581] | 218 | (*_prev)[i] = INVALID; |
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[409] | 219 | _first[bucket] = i; |
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[581] | 220 | (*_next)[i] = INVALID; |
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[409] | 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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[581] | 228 | (*_excess)[n] = 0; |
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[597] | 229 | (*_source_set)[n] = false; |
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[409] | 230 | } |
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| 231 | |
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| 232 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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[581] | 233 | (*_flow)[a] = 0; |
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[409] | 234 | } |
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| 235 | |
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[411] | 236 | int bucket_num = 0; |
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| 237 | std::vector<Node> queue(_node_num); |
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| 238 | int qfirst = 0, qlast = 0, qsep = 0; |
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[409] | 239 | |
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| 240 | { |
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| 241 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
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| 242 | |
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[581] | 243 | reached[_source] = true; |
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[409] | 244 | bool first_set = true; |
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| 245 | |
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| 246 | for (NodeIt t(_graph); t != INVALID; ++t) { |
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| 247 | if (reached[t]) continue; |
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| 248 | _sets.push_front(std::list<int>()); |
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[440] | 249 | |
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[411] | 250 | queue[qlast++] = t; |
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[581] | 251 | reached[t] = true; |
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[409] | 252 | |
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[411] | 253 | while (qfirst != qlast) { |
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| 254 | if (qsep == qfirst) { |
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| 255 | ++bucket_num; |
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| 256 | _sets.front().push_front(bucket_num); |
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| 257 | _dormant[bucket_num] = !first_set; |
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| 258 | _first[bucket_num] = _last[bucket_num] = INVALID; |
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| 259 | qsep = qlast; |
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| 260 | } |
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[409] | 261 | |
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[411] | 262 | Node n = queue[qfirst++]; |
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| 263 | addItem(n, bucket_num); |
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| 264 | |
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| 265 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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| 266 | Node u = _graph.source(a); |
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| 267 | if (!reached[u] && _tolerance.positive((*_capacity)[a])) { |
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[581] | 268 | reached[u] = true; |
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[411] | 269 | queue[qlast++] = u; |
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[409] | 270 | } |
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| 271 | } |
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| 272 | } |
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| 273 | first_set = false; |
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| 274 | } |
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| 275 | |
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[411] | 276 | ++bucket_num; |
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[581] | 277 | (*_bucket)[_source] = 0; |
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[409] | 278 | _dormant[0] = true; |
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| 279 | } |
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[581] | 280 | (*_source_set)[_source] = true; |
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[409] | 281 | |
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| 282 | Node target = _last[_sets.back().back()]; |
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| 283 | { |
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| 284 | for (OutArcIt a(_graph, _source); a != INVALID; ++a) { |
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| 285 | if (_tolerance.positive((*_capacity)[a])) { |
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| 286 | Node u = _graph.target(a); |
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[581] | 287 | (*_flow)[a] = (*_capacity)[a]; |
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| 288 | (*_excess)[u] += (*_capacity)[a]; |
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[409] | 289 | if (!(*_active)[u] && u != _source) { |
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| 290 | activate(u); |
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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 | if ((*_active)[target]) { |
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| 296 | deactivate(target); |
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| 297 | } |
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| 298 | |
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| 299 | _highest = _sets.back().begin(); |
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| 300 | while (_highest != _sets.back().end() && |
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| 301 | !(*_active)[_first[*_highest]]) { |
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| 302 | ++_highest; |
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| 303 | } |
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| 304 | } |
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| 305 | |
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| 306 | while (true) { |
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| 307 | while (_highest != _sets.back().end()) { |
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| 308 | Node n = _first[*_highest]; |
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| 309 | Value excess = (*_excess)[n]; |
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| 310 | int next_bucket = _node_num; |
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| 311 | |
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| 312 | int under_bucket; |
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| 313 | if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
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| 314 | under_bucket = -1; |
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| 315 | } else { |
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| 316 | under_bucket = *(++std::list<int>::iterator(_highest)); |
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| 317 | } |
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| 318 | |
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| 319 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
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| 320 | Node v = _graph.target(a); |
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| 321 | if (_dormant[(*_bucket)[v]]) continue; |
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| 322 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
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| 323 | if (!_tolerance.positive(rem)) continue; |
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| 324 | if ((*_bucket)[v] == under_bucket) { |
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| 325 | if (!(*_active)[v] && v != target) { |
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| 326 | activate(v); |
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| 327 | } |
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| 328 | if (!_tolerance.less(rem, excess)) { |
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[581] | 329 | (*_flow)[a] += excess; |
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| 330 | (*_excess)[v] += excess; |
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[409] | 331 | excess = 0; |
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| 332 | goto no_more_push; |
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| 333 | } else { |
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| 334 | excess -= rem; |
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[581] | 335 | (*_excess)[v] += rem; |
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| 336 | (*_flow)[a] = (*_capacity)[a]; |
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[409] | 337 | } |
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| 338 | } else if (next_bucket > (*_bucket)[v]) { |
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| 339 | next_bucket = (*_bucket)[v]; |
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| 340 | } |
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| 341 | } |
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| 342 | |
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| 343 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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| 344 | Node v = _graph.source(a); |
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| 345 | if (_dormant[(*_bucket)[v]]) continue; |
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| 346 | Value rem = (*_flow)[a]; |
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| 347 | if (!_tolerance.positive(rem)) continue; |
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| 348 | if ((*_bucket)[v] == under_bucket) { |
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| 349 | if (!(*_active)[v] && v != target) { |
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| 350 | activate(v); |
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| 351 | } |
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| 352 | if (!_tolerance.less(rem, excess)) { |
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[581] | 353 | (*_flow)[a] -= excess; |
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| 354 | (*_excess)[v] += excess; |
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[409] | 355 | excess = 0; |
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| 356 | goto no_more_push; |
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| 357 | } else { |
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| 358 | excess -= rem; |
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[581] | 359 | (*_excess)[v] += rem; |
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| 360 | (*_flow)[a] = 0; |
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[409] | 361 | } |
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| 362 | } else if (next_bucket > (*_bucket)[v]) { |
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| 363 | next_bucket = (*_bucket)[v]; |
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| 364 | } |
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| 365 | } |
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| 366 | |
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| 367 | no_more_push: |
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| 368 | |
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[581] | 369 | (*_excess)[n] = excess; |
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[409] | 370 | |
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| 371 | if (excess != 0) { |
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| 372 | if ((*_next)[n] == INVALID) { |
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| 373 | typename std::list<std::list<int> >::iterator new_set = |
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| 374 | _sets.insert(--_sets.end(), std::list<int>()); |
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| 375 | new_set->splice(new_set->end(), _sets.back(), |
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| 376 | _sets.back().begin(), ++_highest); |
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| 377 | for (std::list<int>::iterator it = new_set->begin(); |
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| 378 | it != new_set->end(); ++it) { |
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| 379 | _dormant[*it] = true; |
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| 380 | } |
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| 381 | while (_highest != _sets.back().end() && |
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| 382 | !(*_active)[_first[*_highest]]) { |
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| 383 | ++_highest; |
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| 384 | } |
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| 385 | } else if (next_bucket == _node_num) { |
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| 386 | _first[(*_bucket)[n]] = (*_next)[n]; |
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[581] | 387 | (*_prev)[(*_next)[n]] = INVALID; |
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[409] | 388 | |
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| 389 | std::list<std::list<int> >::iterator new_set = |
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| 390 | _sets.insert(--_sets.end(), std::list<int>()); |
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| 391 | |
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| 392 | new_set->push_front(bucket_num); |
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[581] | 393 | (*_bucket)[n] = bucket_num; |
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[409] | 394 | _first[bucket_num] = _last[bucket_num] = n; |
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[581] | 395 | (*_next)[n] = INVALID; |
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| 396 | (*_prev)[n] = INVALID; |
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[409] | 397 | _dormant[bucket_num] = true; |
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| 398 | ++bucket_num; |
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| 399 | |
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| 400 | while (_highest != _sets.back().end() && |
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| 401 | !(*_active)[_first[*_highest]]) { |
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| 402 | ++_highest; |
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| 403 | } |
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| 404 | } else { |
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| 405 | _first[*_highest] = (*_next)[n]; |
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[581] | 406 | (*_prev)[(*_next)[n]] = INVALID; |
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[409] | 407 | |
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| 408 | while (next_bucket != *_highest) { |
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| 409 | --_highest; |
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| 410 | } |
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| 411 | |
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| 412 | if (_highest == _sets.back().begin()) { |
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| 413 | _sets.back().push_front(bucket_num); |
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| 414 | _dormant[bucket_num] = false; |
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| 415 | _first[bucket_num] = _last[bucket_num] = INVALID; |
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| 416 | ++bucket_num; |
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| 417 | } |
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| 418 | --_highest; |
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| 419 | |
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[581] | 420 | (*_bucket)[n] = *_highest; |
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| 421 | (*_next)[n] = _first[*_highest]; |
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[409] | 422 | if (_first[*_highest] != INVALID) { |
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[581] | 423 | (*_prev)[_first[*_highest]] = n; |
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[409] | 424 | } else { |
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| 425 | _last[*_highest] = n; |
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| 426 | } |
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| 427 | _first[*_highest] = n; |
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| 428 | } |
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| 429 | } else { |
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| 430 | |
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| 431 | deactivate(n); |
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| 432 | if (!(*_active)[_first[*_highest]]) { |
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| 433 | ++_highest; |
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| 434 | if (_highest != _sets.back().end() && |
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| 435 | !(*_active)[_first[*_highest]]) { |
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| 436 | _highest = _sets.back().end(); |
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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 | |
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| 442 | if ((*_excess)[target] < _min_cut) { |
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| 443 | _min_cut = (*_excess)[target]; |
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| 444 | for (NodeIt i(_graph); i != INVALID; ++i) { |
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[581] | 445 | (*_min_cut_map)[i] = true; |
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[409] | 446 | } |
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| 447 | for (std::list<int>::iterator it = _sets.back().begin(); |
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| 448 | it != _sets.back().end(); ++it) { |
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| 449 | Node n = _first[*it]; |
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| 450 | while (n != INVALID) { |
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[581] | 451 | (*_min_cut_map)[n] = false; |
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[409] | 452 | n = (*_next)[n]; |
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| 453 | } |
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| 454 | } |
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| 455 | } |
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| 456 | |
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| 457 | { |
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| 458 | Node new_target; |
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| 459 | if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
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| 460 | if ((*_next)[target] == INVALID) { |
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| 461 | _last[(*_bucket)[target]] = (*_prev)[target]; |
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| 462 | new_target = (*_prev)[target]; |
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| 463 | } else { |
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[581] | 464 | (*_prev)[(*_next)[target]] = (*_prev)[target]; |
---|
[409] | 465 | new_target = (*_next)[target]; |
---|
| 466 | } |
---|
| 467 | if ((*_prev)[target] == INVALID) { |
---|
| 468 | _first[(*_bucket)[target]] = (*_next)[target]; |
---|
| 469 | } else { |
---|
[581] | 470 | (*_next)[(*_prev)[target]] = (*_next)[target]; |
---|
[409] | 471 | } |
---|
| 472 | } else { |
---|
| 473 | _sets.back().pop_back(); |
---|
| 474 | if (_sets.back().empty()) { |
---|
| 475 | _sets.pop_back(); |
---|
| 476 | if (_sets.empty()) |
---|
| 477 | break; |
---|
| 478 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 479 | it != _sets.back().end(); ++it) { |
---|
| 480 | _dormant[*it] = false; |
---|
| 481 | } |
---|
| 482 | } |
---|
| 483 | new_target = _last[_sets.back().back()]; |
---|
| 484 | } |
---|
| 485 | |
---|
[581] | 486 | (*_bucket)[target] = 0; |
---|
[409] | 487 | |
---|
[581] | 488 | (*_source_set)[target] = true; |
---|
[409] | 489 | for (OutArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 490 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
| 491 | if (!_tolerance.positive(rem)) continue; |
---|
| 492 | Node v = _graph.target(a); |
---|
| 493 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 494 | activate(v); |
---|
| 495 | } |
---|
[581] | 496 | (*_excess)[v] += rem; |
---|
| 497 | (*_flow)[a] = (*_capacity)[a]; |
---|
[409] | 498 | } |
---|
| 499 | |
---|
| 500 | for (InArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 501 | Value rem = (*_flow)[a]; |
---|
| 502 | if (!_tolerance.positive(rem)) continue; |
---|
| 503 | Node v = _graph.source(a); |
---|
| 504 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 505 | activate(v); |
---|
| 506 | } |
---|
[581] | 507 | (*_excess)[v] += rem; |
---|
| 508 | (*_flow)[a] = 0; |
---|
[409] | 509 | } |
---|
| 510 | |
---|
| 511 | target = new_target; |
---|
| 512 | if ((*_active)[target]) { |
---|
| 513 | deactivate(target); |
---|
| 514 | } |
---|
| 515 | |
---|
| 516 | _highest = _sets.back().begin(); |
---|
| 517 | while (_highest != _sets.back().end() && |
---|
| 518 | !(*_active)[_first[*_highest]]) { |
---|
| 519 | ++_highest; |
---|
| 520 | } |
---|
| 521 | } |
---|
| 522 | } |
---|
| 523 | } |
---|
| 524 | |
---|
| 525 | void findMinCutIn() { |
---|
| 526 | |
---|
| 527 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
[581] | 528 | (*_excess)[n] = 0; |
---|
[597] | 529 | (*_source_set)[n] = false; |
---|
[409] | 530 | } |
---|
| 531 | |
---|
| 532 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
[581] | 533 | (*_flow)[a] = 0; |
---|
[409] | 534 | } |
---|
| 535 | |
---|
[411] | 536 | int bucket_num = 0; |
---|
| 537 | std::vector<Node> queue(_node_num); |
---|
| 538 | int qfirst = 0, qlast = 0, qsep = 0; |
---|
[409] | 539 | |
---|
| 540 | { |
---|
| 541 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
---|
| 542 | |
---|
[581] | 543 | reached[_source] = true; |
---|
[409] | 544 | |
---|
| 545 | bool first_set = true; |
---|
| 546 | |
---|
| 547 | for (NodeIt t(_graph); t != INVALID; ++t) { |
---|
| 548 | if (reached[t]) continue; |
---|
| 549 | _sets.push_front(std::list<int>()); |
---|
[440] | 550 | |
---|
[411] | 551 | queue[qlast++] = t; |
---|
[581] | 552 | reached[t] = true; |
---|
[409] | 553 | |
---|
[411] | 554 | while (qfirst != qlast) { |
---|
| 555 | if (qsep == qfirst) { |
---|
| 556 | ++bucket_num; |
---|
| 557 | _sets.front().push_front(bucket_num); |
---|
| 558 | _dormant[bucket_num] = !first_set; |
---|
| 559 | _first[bucket_num] = _last[bucket_num] = INVALID; |
---|
| 560 | qsep = qlast; |
---|
| 561 | } |
---|
[409] | 562 | |
---|
[411] | 563 | Node n = queue[qfirst++]; |
---|
| 564 | addItem(n, bucket_num); |
---|
| 565 | |
---|
| 566 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
---|
| 567 | Node u = _graph.target(a); |
---|
| 568 | if (!reached[u] && _tolerance.positive((*_capacity)[a])) { |
---|
[581] | 569 | reached[u] = true; |
---|
[411] | 570 | queue[qlast++] = u; |
---|
[409] | 571 | } |
---|
| 572 | } |
---|
| 573 | } |
---|
| 574 | first_set = false; |
---|
| 575 | } |
---|
| 576 | |
---|
[411] | 577 | ++bucket_num; |
---|
[581] | 578 | (*_bucket)[_source] = 0; |
---|
[409] | 579 | _dormant[0] = true; |
---|
| 580 | } |
---|
[581] | 581 | (*_source_set)[_source] = true; |
---|
[409] | 582 | |
---|
| 583 | Node target = _last[_sets.back().back()]; |
---|
| 584 | { |
---|
| 585 | for (InArcIt a(_graph, _source); a != INVALID; ++a) { |
---|
| 586 | if (_tolerance.positive((*_capacity)[a])) { |
---|
| 587 | Node u = _graph.source(a); |
---|
[581] | 588 | (*_flow)[a] = (*_capacity)[a]; |
---|
| 589 | (*_excess)[u] += (*_capacity)[a]; |
---|
[409] | 590 | if (!(*_active)[u] && u != _source) { |
---|
| 591 | activate(u); |
---|
| 592 | } |
---|
| 593 | } |
---|
| 594 | } |
---|
| 595 | if ((*_active)[target]) { |
---|
| 596 | deactivate(target); |
---|
| 597 | } |
---|
| 598 | |
---|
| 599 | _highest = _sets.back().begin(); |
---|
| 600 | while (_highest != _sets.back().end() && |
---|
| 601 | !(*_active)[_first[*_highest]]) { |
---|
| 602 | ++_highest; |
---|
| 603 | } |
---|
| 604 | } |
---|
| 605 | |
---|
| 606 | |
---|
| 607 | while (true) { |
---|
| 608 | while (_highest != _sets.back().end()) { |
---|
| 609 | Node n = _first[*_highest]; |
---|
| 610 | Value excess = (*_excess)[n]; |
---|
| 611 | int next_bucket = _node_num; |
---|
| 612 | |
---|
| 613 | int under_bucket; |
---|
| 614 | if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
---|
| 615 | under_bucket = -1; |
---|
| 616 | } else { |
---|
| 617 | under_bucket = *(++std::list<int>::iterator(_highest)); |
---|
| 618 | } |
---|
| 619 | |
---|
| 620 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
---|
| 621 | Node v = _graph.source(a); |
---|
| 622 | if (_dormant[(*_bucket)[v]]) continue; |
---|
| 623 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
| 624 | if (!_tolerance.positive(rem)) continue; |
---|
| 625 | if ((*_bucket)[v] == under_bucket) { |
---|
| 626 | if (!(*_active)[v] && v != target) { |
---|
| 627 | activate(v); |
---|
| 628 | } |
---|
| 629 | if (!_tolerance.less(rem, excess)) { |
---|
[581] | 630 | (*_flow)[a] += excess; |
---|
| 631 | (*_excess)[v] += excess; |
---|
[409] | 632 | excess = 0; |
---|
| 633 | goto no_more_push; |
---|
| 634 | } else { |
---|
| 635 | excess -= rem; |
---|
[581] | 636 | (*_excess)[v] += rem; |
---|
| 637 | (*_flow)[a] = (*_capacity)[a]; |
---|
[409] | 638 | } |
---|
| 639 | } else if (next_bucket > (*_bucket)[v]) { |
---|
| 640 | next_bucket = (*_bucket)[v]; |
---|
| 641 | } |
---|
| 642 | } |
---|
| 643 | |
---|
| 644 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
---|
| 645 | Node v = _graph.target(a); |
---|
| 646 | if (_dormant[(*_bucket)[v]]) continue; |
---|
| 647 | Value rem = (*_flow)[a]; |
---|
| 648 | if (!_tolerance.positive(rem)) continue; |
---|
| 649 | if ((*_bucket)[v] == under_bucket) { |
---|
| 650 | if (!(*_active)[v] && v != target) { |
---|
| 651 | activate(v); |
---|
| 652 | } |
---|
| 653 | if (!_tolerance.less(rem, excess)) { |
---|
[581] | 654 | (*_flow)[a] -= excess; |
---|
| 655 | (*_excess)[v] += excess; |
---|
[409] | 656 | excess = 0; |
---|
| 657 | goto no_more_push; |
---|
| 658 | } else { |
---|
| 659 | excess -= rem; |
---|
[581] | 660 | (*_excess)[v] += rem; |
---|
| 661 | (*_flow)[a] = 0; |
---|
[409] | 662 | } |
---|
| 663 | } else if (next_bucket > (*_bucket)[v]) { |
---|
| 664 | next_bucket = (*_bucket)[v]; |
---|
| 665 | } |
---|
| 666 | } |
---|
| 667 | |
---|
| 668 | no_more_push: |
---|
| 669 | |
---|
[581] | 670 | (*_excess)[n] = excess; |
---|
[409] | 671 | |
---|
| 672 | if (excess != 0) { |
---|
| 673 | if ((*_next)[n] == INVALID) { |
---|
| 674 | typename std::list<std::list<int> >::iterator new_set = |
---|
| 675 | _sets.insert(--_sets.end(), std::list<int>()); |
---|
| 676 | new_set->splice(new_set->end(), _sets.back(), |
---|
| 677 | _sets.back().begin(), ++_highest); |
---|
| 678 | for (std::list<int>::iterator it = new_set->begin(); |
---|
| 679 | it != new_set->end(); ++it) { |
---|
| 680 | _dormant[*it] = true; |
---|
| 681 | } |
---|
| 682 | while (_highest != _sets.back().end() && |
---|
| 683 | !(*_active)[_first[*_highest]]) { |
---|
| 684 | ++_highest; |
---|
| 685 | } |
---|
| 686 | } else if (next_bucket == _node_num) { |
---|
| 687 | _first[(*_bucket)[n]] = (*_next)[n]; |
---|
[581] | 688 | (*_prev)[(*_next)[n]] = INVALID; |
---|
[409] | 689 | |
---|
| 690 | std::list<std::list<int> >::iterator new_set = |
---|
| 691 | _sets.insert(--_sets.end(), std::list<int>()); |
---|
| 692 | |
---|
| 693 | new_set->push_front(bucket_num); |
---|
[581] | 694 | (*_bucket)[n] = bucket_num; |
---|
[409] | 695 | _first[bucket_num] = _last[bucket_num] = n; |
---|
[581] | 696 | (*_next)[n] = INVALID; |
---|
| 697 | (*_prev)[n] = INVALID; |
---|
[409] | 698 | _dormant[bucket_num] = true; |
---|
| 699 | ++bucket_num; |
---|
| 700 | |
---|
| 701 | while (_highest != _sets.back().end() && |
---|
| 702 | !(*_active)[_first[*_highest]]) { |
---|
| 703 | ++_highest; |
---|
| 704 | } |
---|
| 705 | } else { |
---|
| 706 | _first[*_highest] = (*_next)[n]; |
---|
[581] | 707 | (*_prev)[(*_next)[n]] = INVALID; |
---|
[409] | 708 | |
---|
| 709 | while (next_bucket != *_highest) { |
---|
| 710 | --_highest; |
---|
| 711 | } |
---|
| 712 | if (_highest == _sets.back().begin()) { |
---|
| 713 | _sets.back().push_front(bucket_num); |
---|
| 714 | _dormant[bucket_num] = false; |
---|
| 715 | _first[bucket_num] = _last[bucket_num] = INVALID; |
---|
| 716 | ++bucket_num; |
---|
| 717 | } |
---|
| 718 | --_highest; |
---|
| 719 | |
---|
[581] | 720 | (*_bucket)[n] = *_highest; |
---|
| 721 | (*_next)[n] = _first[*_highest]; |
---|
[409] | 722 | if (_first[*_highest] != INVALID) { |
---|
[581] | 723 | (*_prev)[_first[*_highest]] = n; |
---|
[409] | 724 | } else { |
---|
| 725 | _last[*_highest] = n; |
---|
| 726 | } |
---|
| 727 | _first[*_highest] = n; |
---|
| 728 | } |
---|
| 729 | } else { |
---|
| 730 | |
---|
| 731 | deactivate(n); |
---|
| 732 | if (!(*_active)[_first[*_highest]]) { |
---|
| 733 | ++_highest; |
---|
| 734 | if (_highest != _sets.back().end() && |
---|
| 735 | !(*_active)[_first[*_highest]]) { |
---|
| 736 | _highest = _sets.back().end(); |
---|
| 737 | } |
---|
| 738 | } |
---|
| 739 | } |
---|
| 740 | } |
---|
| 741 | |
---|
| 742 | if ((*_excess)[target] < _min_cut) { |
---|
| 743 | _min_cut = (*_excess)[target]; |
---|
| 744 | for (NodeIt i(_graph); i != INVALID; ++i) { |
---|
[581] | 745 | (*_min_cut_map)[i] = false; |
---|
[409] | 746 | } |
---|
| 747 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 748 | it != _sets.back().end(); ++it) { |
---|
| 749 | Node n = _first[*it]; |
---|
| 750 | while (n != INVALID) { |
---|
[581] | 751 | (*_min_cut_map)[n] = true; |
---|
[409] | 752 | n = (*_next)[n]; |
---|
| 753 | } |
---|
| 754 | } |
---|
| 755 | } |
---|
| 756 | |
---|
| 757 | { |
---|
| 758 | Node new_target; |
---|
| 759 | if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
---|
| 760 | if ((*_next)[target] == INVALID) { |
---|
| 761 | _last[(*_bucket)[target]] = (*_prev)[target]; |
---|
| 762 | new_target = (*_prev)[target]; |
---|
| 763 | } else { |
---|
[581] | 764 | (*_prev)[(*_next)[target]] = (*_prev)[target]; |
---|
[409] | 765 | new_target = (*_next)[target]; |
---|
| 766 | } |
---|
| 767 | if ((*_prev)[target] == INVALID) { |
---|
| 768 | _first[(*_bucket)[target]] = (*_next)[target]; |
---|
| 769 | } else { |
---|
[581] | 770 | (*_next)[(*_prev)[target]] = (*_next)[target]; |
---|
[409] | 771 | } |
---|
| 772 | } else { |
---|
| 773 | _sets.back().pop_back(); |
---|
| 774 | if (_sets.back().empty()) { |
---|
| 775 | _sets.pop_back(); |
---|
| 776 | if (_sets.empty()) |
---|
| 777 | break; |
---|
| 778 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 779 | it != _sets.back().end(); ++it) { |
---|
| 780 | _dormant[*it] = false; |
---|
| 781 | } |
---|
| 782 | } |
---|
| 783 | new_target = _last[_sets.back().back()]; |
---|
| 784 | } |
---|
| 785 | |
---|
[581] | 786 | (*_bucket)[target] = 0; |
---|
[409] | 787 | |
---|
[581] | 788 | (*_source_set)[target] = true; |
---|
[409] | 789 | for (InArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 790 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
| 791 | if (!_tolerance.positive(rem)) continue; |
---|
| 792 | Node v = _graph.source(a); |
---|
| 793 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 794 | activate(v); |
---|
| 795 | } |
---|
[581] | 796 | (*_excess)[v] += rem; |
---|
| 797 | (*_flow)[a] = (*_capacity)[a]; |
---|
[409] | 798 | } |
---|
| 799 | |
---|
| 800 | for (OutArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 801 | Value rem = (*_flow)[a]; |
---|
| 802 | if (!_tolerance.positive(rem)) continue; |
---|
| 803 | Node v = _graph.target(a); |
---|
| 804 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 805 | activate(v); |
---|
| 806 | } |
---|
[581] | 807 | (*_excess)[v] += rem; |
---|
| 808 | (*_flow)[a] = 0; |
---|
[409] | 809 | } |
---|
| 810 | |
---|
| 811 | target = new_target; |
---|
| 812 | if ((*_active)[target]) { |
---|
| 813 | deactivate(target); |
---|
| 814 | } |
---|
| 815 | |
---|
| 816 | _highest = _sets.back().begin(); |
---|
| 817 | while (_highest != _sets.back().end() && |
---|
| 818 | !(*_active)[_first[*_highest]]) { |
---|
| 819 | ++_highest; |
---|
| 820 | } |
---|
| 821 | } |
---|
| 822 | } |
---|
| 823 | } |
---|
| 824 | |
---|
| 825 | public: |
---|
| 826 | |
---|
[596] | 827 | /// \name Execution Control |
---|
[409] | 828 | /// The simplest way to execute the algorithm is to use |
---|
[559] | 829 | /// one of the member functions called \ref run(). |
---|
[409] | 830 | /// \n |
---|
[596] | 831 | /// If you need better control on the execution, |
---|
| 832 | /// you have to call one of the \ref init() functions first, then |
---|
| 833 | /// \ref calculateOut() and/or \ref calculateIn(). |
---|
[409] | 834 | |
---|
| 835 | /// @{ |
---|
| 836 | |
---|
[596] | 837 | /// \brief Initialize the internal data structures. |
---|
[409] | 838 | /// |
---|
[596] | 839 | /// This function initializes the internal data structures. It creates |
---|
| 840 | /// the maps and some bucket structures for the algorithm. |
---|
| 841 | /// The first node is used as the source node for the push-relabel |
---|
| 842 | /// algorithm. |
---|
[409] | 843 | void init() { |
---|
| 844 | init(NodeIt(_graph)); |
---|
| 845 | } |
---|
| 846 | |
---|
[596] | 847 | /// \brief Initialize the internal data structures. |
---|
[409] | 848 | /// |
---|
[596] | 849 | /// This function initializes the internal data structures. It creates |
---|
| 850 | /// the maps and some bucket structures for the algorithm. |
---|
| 851 | /// The given node is used as the source node for the push-relabel |
---|
| 852 | /// algorithm. |
---|
[409] | 853 | void init(const Node& source) { |
---|
| 854 | _source = source; |
---|
| 855 | |
---|
| 856 | _node_num = countNodes(_graph); |
---|
| 857 | |
---|
[411] | 858 | _first.resize(_node_num); |
---|
| 859 | _last.resize(_node_num); |
---|
[409] | 860 | |
---|
[411] | 861 | _dormant.resize(_node_num); |
---|
[409] | 862 | |
---|
| 863 | if (!_flow) { |
---|
| 864 | _flow = new FlowMap(_graph); |
---|
| 865 | } |
---|
| 866 | if (!_next) { |
---|
| 867 | _next = new typename Digraph::template NodeMap<Node>(_graph); |
---|
| 868 | } |
---|
| 869 | if (!_prev) { |
---|
| 870 | _prev = new typename Digraph::template NodeMap<Node>(_graph); |
---|
| 871 | } |
---|
| 872 | if (!_active) { |
---|
| 873 | _active = new typename Digraph::template NodeMap<bool>(_graph); |
---|
| 874 | } |
---|
| 875 | if (!_bucket) { |
---|
| 876 | _bucket = new typename Digraph::template NodeMap<int>(_graph); |
---|
| 877 | } |
---|
| 878 | if (!_excess) { |
---|
| 879 | _excess = new ExcessMap(_graph); |
---|
| 880 | } |
---|
| 881 | if (!_source_set) { |
---|
| 882 | _source_set = new SourceSetMap(_graph); |
---|
| 883 | } |
---|
| 884 | if (!_min_cut_map) { |
---|
| 885 | _min_cut_map = new MinCutMap(_graph); |
---|
| 886 | } |
---|
| 887 | |
---|
| 888 | _min_cut = std::numeric_limits<Value>::max(); |
---|
| 889 | } |
---|
| 890 | |
---|
| 891 | |
---|
[596] | 892 | /// \brief Calculate a minimum cut with \f$ source \f$ on the |
---|
[409] | 893 | /// source-side. |
---|
| 894 | /// |
---|
[596] | 895 | /// This function calculates a minimum cut with \f$ source \f$ on the |
---|
[412] | 896 | /// source-side (i.e. a set \f$ X\subsetneq V \f$ with |
---|
[596] | 897 | /// \f$ source \in X \f$ and minimal outgoing capacity). |
---|
| 898 | /// |
---|
| 899 | /// \pre \ref init() must be called before using this function. |
---|
[409] | 900 | void calculateOut() { |
---|
| 901 | findMinCutOut(); |
---|
| 902 | } |
---|
| 903 | |
---|
[596] | 904 | /// \brief Calculate a minimum cut with \f$ source \f$ on the |
---|
| 905 | /// sink-side. |
---|
[409] | 906 | /// |
---|
[596] | 907 | /// This function calculates a minimum cut with \f$ source \f$ on the |
---|
| 908 | /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with |
---|
| 909 | /// \f$ source \notin X \f$ and minimal outgoing capacity). |
---|
| 910 | /// |
---|
| 911 | /// \pre \ref init() must be called before using this function. |
---|
[409] | 912 | void calculateIn() { |
---|
| 913 | findMinCutIn(); |
---|
| 914 | } |
---|
| 915 | |
---|
| 916 | |
---|
[596] | 917 | /// \brief Run the algorithm. |
---|
[409] | 918 | /// |
---|
[596] | 919 | /// This function runs the algorithm. It finds nodes \c source and |
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| 920 | /// \c target arbitrarily and then calls \ref init(), \ref calculateOut() |
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[409] | 921 | /// and \ref calculateIn(). |
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| 922 | void run() { |
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| 923 | init(); |
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| 924 | calculateOut(); |
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| 925 | calculateIn(); |
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| 926 | } |
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| 927 | |
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[596] | 928 | /// \brief Run the algorithm. |
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[409] | 929 | /// |
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[596] | 930 | /// This function runs the algorithm. It uses the given \c source node, |
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| 931 | /// finds a proper \c target node and then calls the \ref init(), |
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| 932 | /// \ref calculateOut() and \ref calculateIn(). |
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[409] | 933 | void run(const Node& s) { |
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| 934 | init(s); |
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| 935 | calculateOut(); |
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| 936 | calculateIn(); |
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| 937 | } |
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| 938 | |
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| 939 | /// @} |
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| 940 | |
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| 941 | /// \name Query Functions |
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| 942 | /// The result of the %HaoOrlin algorithm |
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[596] | 943 | /// can be obtained using these functions.\n |
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| 944 | /// \ref run(), \ref calculateOut() or \ref calculateIn() |
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| 945 | /// should be called before using them. |
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[409] | 946 | |
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| 947 | /// @{ |
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| 948 | |
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[596] | 949 | /// \brief Return the value of the minimum cut. |
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[409] | 950 | /// |
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[596] | 951 | /// This function returns the value of the minimum cut. |
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| 952 | /// |
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| 953 | /// \pre \ref run(), \ref calculateOut() or \ref calculateIn() |
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| 954 | /// must be called before using this function. |
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[409] | 955 | Value minCutValue() const { |
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| 956 | return _min_cut; |
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| 957 | } |
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| 958 | |
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| 959 | |
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[596] | 960 | /// \brief Return a minimum cut. |
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[409] | 961 | /// |
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[596] | 962 | /// This function sets \c cutMap to the characteristic vector of a |
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| 963 | /// minimum value cut: it will give a non-empty set \f$ X\subsetneq V \f$ |
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| 964 | /// with minimal outgoing capacity (i.e. \c cutMap will be \c true exactly |
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| 965 | /// for the nodes of \f$ X \f$). |
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| 966 | /// |
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| 967 | /// \param cutMap A \ref concepts::WriteMap "writable" node map with |
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| 968 | /// \c bool (or convertible) value type. |
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| 969 | /// |
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| 970 | /// \return The value of the minimum cut. |
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| 971 | /// |
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| 972 | /// \pre \ref run(), \ref calculateOut() or \ref calculateIn() |
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| 973 | /// must be called before using this function. |
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| 974 | template <typename CutMap> |
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| 975 | Value minCutMap(CutMap& cutMap) const { |
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[409] | 976 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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[596] | 977 | cutMap.set(it, (*_min_cut_map)[it]); |
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[409] | 978 | } |
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| 979 | return _min_cut; |
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| 980 | } |
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| 981 | |
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| 982 | /// @} |
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| 983 | |
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| 984 | }; //class HaoOrlin |
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| 985 | |
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| 986 | } //namespace lemon |
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| 987 | |
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| 988 | #endif //LEMON_HAO_ORLIN_H |
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