[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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| 5 | * Copyright (C) 2003-2008 |
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| 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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| 34 | /// Implementation of the Hao-Orlin algorithm class for testing network |
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| 35 | /// reliability. |
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| 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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| 41 | /// \brief %Hao-Orlin algorithm to find a minimum cut in directed graphs. |
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| 42 | /// |
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| 43 | /// Hao-Orlin calculates a minimum cut in a directed graph |
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| 44 | /// \f$D=(V,A)\f$. It takes a fixed node \f$ source \in V \f$ and |
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| 45 | /// consists of two phases: in the first phase it determines a |
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| 46 | /// minimum cut with \f$ source \f$ on the source-side (i.e. a set |
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| 47 | /// \f$ X\subsetneq V \f$ with \f$ source \in X \f$ and minimal |
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| 48 | /// out-degree) and in the second phase it determines a minimum cut |
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| 49 | /// with \f$ source \f$ on the sink-side (i.e. a set |
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| 50 | /// \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ and minimal |
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| 51 | /// out-degree). Obviously, the smaller of these two cuts will be a |
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| 52 | /// minimum cut of \f$ D \f$. The algorithm is a modified |
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| 53 | /// push-relabel preflow algorithm and our implementation calculates |
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| 54 | /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the |
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| 55 | /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. The |
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| 56 | /// purpose of such algorithm is testing network reliability. For an |
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| 57 | /// undirected graph you can run just the first phase of the |
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| 58 | /// algorithm or you can use the algorithm of Nagamochi and Ibaraki |
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| 59 | /// which solves the undirected problem in |
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| 60 | /// \f$ O(nm + n^2 \log(n)) \f$ time: it is implemented in the |
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| 61 | /// NagamochiIbaraki algorithm class. |
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| 62 | /// |
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| 63 | /// \param _Digraph is the graph type of the algorithm. |
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| 64 | /// \param _CapacityMap is an edge map of capacities which should |
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| 65 | /// be any numreric type. The default type is _Digraph::ArcMap<int>. |
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| 66 | /// \param _Tolerance is the handler of the inexact computation. The |
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| 67 | /// default type for this is Tolerance<CapacityMap::Value>. |
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| 68 | #ifdef DOXYGEN |
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| 69 | template <typename _Digraph, typename _CapacityMap, typename _Tolerance> |
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| 70 | #else |
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| 71 | template <typename _Digraph, |
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| 72 | typename _CapacityMap = typename _Digraph::template ArcMap<int>, |
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| 73 | typename _Tolerance = Tolerance<typename _CapacityMap::Value> > |
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| 74 | #endif |
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| 75 | class HaoOrlin { |
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| 76 | private: |
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| 77 | |
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| 78 | typedef _Digraph Digraph; |
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| 79 | typedef _CapacityMap CapacityMap; |
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| 80 | typedef _Tolerance Tolerance; |
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| 81 | |
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| 82 | typedef typename CapacityMap::Value Value; |
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| 83 | |
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| 84 | TEMPLATE_GRAPH_TYPEDEFS(Digraph); |
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| 85 | |
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| 86 | const Digraph& _graph; |
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| 87 | const CapacityMap* _capacity; |
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| 88 | |
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| 89 | typedef typename Digraph::template ArcMap<Value> FlowMap; |
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| 90 | FlowMap* _flow; |
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| 91 | |
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| 92 | Node _source; |
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| 93 | |
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| 94 | int _node_num; |
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| 95 | |
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| 96 | // Bucketing structure |
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| 97 | std::vector<Node> _first, _last; |
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| 98 | typename Digraph::template NodeMap<Node>* _next; |
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| 99 | typename Digraph::template NodeMap<Node>* _prev; |
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| 100 | typename Digraph::template NodeMap<bool>* _active; |
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| 101 | typename Digraph::template NodeMap<int>* _bucket; |
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| 102 | |
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| 103 | std::vector<bool> _dormant; |
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| 104 | |
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| 105 | std::list<std::list<int> > _sets; |
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| 106 | std::list<int>::iterator _highest; |
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| 107 | |
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| 108 | typedef typename Digraph::template NodeMap<Value> ExcessMap; |
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| 109 | ExcessMap* _excess; |
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| 110 | |
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| 111 | typedef typename Digraph::template NodeMap<bool> SourceSetMap; |
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| 112 | SourceSetMap* _source_set; |
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| 113 | |
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| 114 | Value _min_cut; |
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| 115 | |
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| 116 | typedef typename Digraph::template NodeMap<bool> MinCutMap; |
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| 117 | MinCutMap* _min_cut_map; |
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| 118 | |
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| 119 | Tolerance _tolerance; |
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| 120 | |
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| 121 | public: |
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| 122 | |
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| 123 | /// \brief Constructor |
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| 124 | /// |
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| 125 | /// Constructor of the algorithm class. |
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| 126 | HaoOrlin(const Digraph& graph, const CapacityMap& capacity, |
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| 127 | const Tolerance& tolerance = Tolerance()) : |
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| 128 | _graph(graph), _capacity(&capacity), _flow(0), _source(), |
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| 129 | _node_num(), _first(), _last(), _next(0), _prev(0), |
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| 130 | _active(0), _bucket(0), _dormant(), _sets(), _highest(), |
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| 131 | _excess(0), _source_set(0), _min_cut(), _min_cut_map(0), |
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| 132 | _tolerance(tolerance) {} |
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| 133 | |
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| 134 | ~HaoOrlin() { |
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| 135 | if (_min_cut_map) { |
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| 136 | delete _min_cut_map; |
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| 137 | } |
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| 138 | if (_source_set) { |
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| 139 | delete _source_set; |
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| 140 | } |
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| 141 | if (_excess) { |
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| 142 | delete _excess; |
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| 143 | } |
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| 144 | if (_next) { |
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| 145 | delete _next; |
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| 146 | } |
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| 147 | if (_prev) { |
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| 148 | delete _prev; |
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| 149 | } |
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| 150 | if (_active) { |
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| 151 | delete _active; |
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| 152 | } |
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| 153 | if (_bucket) { |
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| 154 | delete _bucket; |
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| 155 | } |
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| 156 | if (_flow) { |
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| 157 | delete _flow; |
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| 158 | } |
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| 159 | } |
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| 160 | |
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| 161 | private: |
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| 162 | |
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| 163 | void activate(const Node& i) { |
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| 164 | _active->set(i, true); |
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| 165 | |
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| 166 | int bucket = (*_bucket)[i]; |
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| 167 | |
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| 168 | if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return; |
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| 169 | //unlace |
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| 170 | _next->set((*_prev)[i], (*_next)[i]); |
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| 171 | if ((*_next)[i] != INVALID) { |
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| 172 | _prev->set((*_next)[i], (*_prev)[i]); |
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| 173 | } else { |
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| 174 | _last[bucket] = (*_prev)[i]; |
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| 175 | } |
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| 176 | //lace |
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| 177 | _next->set(i, _first[bucket]); |
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| 178 | _prev->set(_first[bucket], i); |
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| 179 | _prev->set(i, INVALID); |
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| 180 | _first[bucket] = i; |
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| 181 | } |
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| 182 | |
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| 183 | void deactivate(const Node& i) { |
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| 184 | _active->set(i, false); |
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| 185 | int bucket = (*_bucket)[i]; |
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| 186 | |
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| 187 | if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return; |
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| 188 | |
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| 189 | //unlace |
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| 190 | _prev->set((*_next)[i], (*_prev)[i]); |
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| 191 | if ((*_prev)[i] != INVALID) { |
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| 192 | _next->set((*_prev)[i], (*_next)[i]); |
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| 193 | } else { |
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| 194 | _first[bucket] = (*_next)[i]; |
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| 195 | } |
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| 196 | //lace |
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| 197 | _prev->set(i, _last[bucket]); |
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| 198 | _next->set(_last[bucket], i); |
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| 199 | _next->set(i, INVALID); |
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| 200 | _last[bucket] = i; |
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| 201 | } |
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| 202 | |
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| 203 | void addItem(const Node& i, int bucket) { |
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| 204 | (*_bucket)[i] = bucket; |
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| 205 | if (_last[bucket] != INVALID) { |
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| 206 | _prev->set(i, _last[bucket]); |
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| 207 | _next->set(_last[bucket], i); |
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| 208 | _next->set(i, INVALID); |
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| 209 | _last[bucket] = i; |
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| 210 | } else { |
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| 211 | _prev->set(i, INVALID); |
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| 212 | _first[bucket] = i; |
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| 213 | _next->set(i, INVALID); |
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| 214 | _last[bucket] = i; |
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| 215 | } |
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| 216 | } |
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| 217 | |
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| 218 | void findMinCutOut() { |
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| 219 | |
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| 220 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 221 | _excess->set(n, 0); |
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| 222 | } |
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| 223 | |
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| 224 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 225 | _flow->set(a, 0); |
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| 226 | } |
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| 227 | |
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[411] | 228 | int bucket_num = 0; |
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| 229 | std::vector<Node> queue(_node_num); |
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| 230 | int qfirst = 0, qlast = 0, qsep = 0; |
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[409] | 231 | |
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| 232 | { |
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| 233 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
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| 234 | |
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| 235 | reached.set(_source, true); |
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| 236 | bool first_set = true; |
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| 237 | |
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| 238 | for (NodeIt t(_graph); t != INVALID; ++t) { |
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| 239 | if (reached[t]) continue; |
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| 240 | _sets.push_front(std::list<int>()); |
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[411] | 241 | |
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| 242 | queue[qlast++] = t; |
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[409] | 243 | reached.set(t, true); |
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| 244 | |
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[411] | 245 | while (qfirst != qlast) { |
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| 246 | if (qsep == qfirst) { |
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| 247 | ++bucket_num; |
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| 248 | _sets.front().push_front(bucket_num); |
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| 249 | _dormant[bucket_num] = !first_set; |
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| 250 | _first[bucket_num] = _last[bucket_num] = INVALID; |
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| 251 | qsep = qlast; |
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| 252 | } |
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[409] | 253 | |
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[411] | 254 | Node n = queue[qfirst++]; |
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| 255 | addItem(n, bucket_num); |
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| 256 | |
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| 257 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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| 258 | Node u = _graph.source(a); |
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| 259 | if (!reached[u] && _tolerance.positive((*_capacity)[a])) { |
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| 260 | reached.set(u, true); |
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| 261 | queue[qlast++] = u; |
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[409] | 262 | } |
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| 263 | } |
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| 264 | } |
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| 265 | first_set = false; |
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| 266 | } |
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| 267 | |
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[411] | 268 | ++bucket_num; |
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[409] | 269 | _bucket->set(_source, 0); |
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| 270 | _dormant[0] = true; |
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| 271 | } |
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| 272 | _source_set->set(_source, true); |
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| 273 | |
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| 274 | Node target = _last[_sets.back().back()]; |
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| 275 | { |
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| 276 | for (OutArcIt a(_graph, _source); a != INVALID; ++a) { |
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| 277 | if (_tolerance.positive((*_capacity)[a])) { |
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| 278 | Node u = _graph.target(a); |
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| 279 | _flow->set(a, (*_capacity)[a]); |
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| 280 | _excess->set(u, (*_excess)[u] + (*_capacity)[a]); |
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| 281 | if (!(*_active)[u] && u != _source) { |
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| 282 | activate(u); |
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| 283 | } |
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| 284 | } |
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| 285 | } |
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| 286 | |
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| 287 | if ((*_active)[target]) { |
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| 288 | deactivate(target); |
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| 289 | } |
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| 290 | |
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| 291 | _highest = _sets.back().begin(); |
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| 292 | while (_highest != _sets.back().end() && |
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| 293 | !(*_active)[_first[*_highest]]) { |
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| 294 | ++_highest; |
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| 295 | } |
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| 296 | } |
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| 297 | |
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| 298 | while (true) { |
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| 299 | while (_highest != _sets.back().end()) { |
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| 300 | Node n = _first[*_highest]; |
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| 301 | Value excess = (*_excess)[n]; |
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| 302 | int next_bucket = _node_num; |
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| 303 | |
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| 304 | int under_bucket; |
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| 305 | if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
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| 306 | under_bucket = -1; |
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| 307 | } else { |
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| 308 | under_bucket = *(++std::list<int>::iterator(_highest)); |
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| 309 | } |
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| 310 | |
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| 311 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
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| 312 | Node v = _graph.target(a); |
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| 313 | if (_dormant[(*_bucket)[v]]) continue; |
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| 314 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
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| 315 | if (!_tolerance.positive(rem)) continue; |
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| 316 | if ((*_bucket)[v] == under_bucket) { |
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| 317 | if (!(*_active)[v] && v != target) { |
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| 318 | activate(v); |
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| 319 | } |
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| 320 | if (!_tolerance.less(rem, excess)) { |
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| 321 | _flow->set(a, (*_flow)[a] + excess); |
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| 322 | _excess->set(v, (*_excess)[v] + excess); |
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| 323 | excess = 0; |
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| 324 | goto no_more_push; |
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| 325 | } else { |
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| 326 | excess -= rem; |
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| 327 | _excess->set(v, (*_excess)[v] + rem); |
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| 328 | _flow->set(a, (*_capacity)[a]); |
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| 329 | } |
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| 330 | } else if (next_bucket > (*_bucket)[v]) { |
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| 331 | next_bucket = (*_bucket)[v]; |
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| 332 | } |
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| 333 | } |
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| 334 | |
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| 335 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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| 336 | Node v = _graph.source(a); |
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| 337 | if (_dormant[(*_bucket)[v]]) continue; |
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| 338 | Value rem = (*_flow)[a]; |
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| 339 | if (!_tolerance.positive(rem)) continue; |
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| 340 | if ((*_bucket)[v] == under_bucket) { |
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| 341 | if (!(*_active)[v] && v != target) { |
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| 342 | activate(v); |
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| 343 | } |
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| 344 | if (!_tolerance.less(rem, excess)) { |
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| 345 | _flow->set(a, (*_flow)[a] - excess); |
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| 346 | _excess->set(v, (*_excess)[v] + excess); |
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| 347 | excess = 0; |
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| 348 | goto no_more_push; |
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| 349 | } else { |
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| 350 | excess -= rem; |
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| 351 | _excess->set(v, (*_excess)[v] + rem); |
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| 352 | _flow->set(a, 0); |
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| 353 | } |
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| 354 | } else if (next_bucket > (*_bucket)[v]) { |
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| 355 | next_bucket = (*_bucket)[v]; |
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| 356 | } |
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| 357 | } |
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| 358 | |
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| 359 | no_more_push: |
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| 360 | |
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| 361 | _excess->set(n, excess); |
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| 362 | |
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| 363 | if (excess != 0) { |
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| 364 | if ((*_next)[n] == INVALID) { |
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| 365 | typename std::list<std::list<int> >::iterator new_set = |
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| 366 | _sets.insert(--_sets.end(), std::list<int>()); |
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| 367 | new_set->splice(new_set->end(), _sets.back(), |
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| 368 | _sets.back().begin(), ++_highest); |
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| 369 | for (std::list<int>::iterator it = new_set->begin(); |
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| 370 | it != new_set->end(); ++it) { |
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| 371 | _dormant[*it] = true; |
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| 372 | } |
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| 373 | while (_highest != _sets.back().end() && |
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| 374 | !(*_active)[_first[*_highest]]) { |
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| 375 | ++_highest; |
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| 376 | } |
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| 377 | } else if (next_bucket == _node_num) { |
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| 378 | _first[(*_bucket)[n]] = (*_next)[n]; |
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| 379 | _prev->set((*_next)[n], INVALID); |
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| 380 | |
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| 381 | std::list<std::list<int> >::iterator new_set = |
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| 382 | _sets.insert(--_sets.end(), std::list<int>()); |
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| 383 | |
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| 384 | new_set->push_front(bucket_num); |
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| 385 | _bucket->set(n, bucket_num); |
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| 386 | _first[bucket_num] = _last[bucket_num] = n; |
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| 387 | _next->set(n, INVALID); |
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| 388 | _prev->set(n, INVALID); |
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| 389 | _dormant[bucket_num] = true; |
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| 390 | ++bucket_num; |
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| 391 | |
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| 392 | while (_highest != _sets.back().end() && |
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| 393 | !(*_active)[_first[*_highest]]) { |
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| 394 | ++_highest; |
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| 395 | } |
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| 396 | } else { |
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| 397 | _first[*_highest] = (*_next)[n]; |
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| 398 | _prev->set((*_next)[n], INVALID); |
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| 399 | |
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| 400 | while (next_bucket != *_highest) { |
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| 401 | --_highest; |
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| 402 | } |
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| 403 | |
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| 404 | if (_highest == _sets.back().begin()) { |
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| 405 | _sets.back().push_front(bucket_num); |
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| 406 | _dormant[bucket_num] = false; |
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| 407 | _first[bucket_num] = _last[bucket_num] = INVALID; |
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| 408 | ++bucket_num; |
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| 409 | } |
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| 410 | --_highest; |
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| 411 | |
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| 412 | _bucket->set(n, *_highest); |
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| 413 | _next->set(n, _first[*_highest]); |
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| 414 | if (_first[*_highest] != INVALID) { |
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| 415 | _prev->set(_first[*_highest], n); |
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| 416 | } else { |
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| 417 | _last[*_highest] = n; |
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| 418 | } |
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| 419 | _first[*_highest] = n; |
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| 420 | } |
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| 421 | } else { |
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| 422 | |
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| 423 | deactivate(n); |
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| 424 | if (!(*_active)[_first[*_highest]]) { |
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| 425 | ++_highest; |
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| 426 | if (_highest != _sets.back().end() && |
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| 427 | !(*_active)[_first[*_highest]]) { |
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| 428 | _highest = _sets.back().end(); |
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| 429 | } |
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| 430 | } |
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| 431 | } |
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| 432 | } |
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| 433 | |
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| 434 | if ((*_excess)[target] < _min_cut) { |
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| 435 | _min_cut = (*_excess)[target]; |
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| 436 | for (NodeIt i(_graph); i != INVALID; ++i) { |
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| 437 | _min_cut_map->set(i, true); |
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| 438 | } |
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| 439 | for (std::list<int>::iterator it = _sets.back().begin(); |
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| 440 | it != _sets.back().end(); ++it) { |
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| 441 | Node n = _first[*it]; |
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| 442 | while (n != INVALID) { |
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| 443 | _min_cut_map->set(n, false); |
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| 444 | n = (*_next)[n]; |
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| 445 | } |
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| 446 | } |
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| 447 | } |
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| 448 | |
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| 449 | { |
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| 450 | Node new_target; |
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| 451 | if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
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| 452 | if ((*_next)[target] == INVALID) { |
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| 453 | _last[(*_bucket)[target]] = (*_prev)[target]; |
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| 454 | new_target = (*_prev)[target]; |
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| 455 | } else { |
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| 456 | _prev->set((*_next)[target], (*_prev)[target]); |
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| 457 | new_target = (*_next)[target]; |
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| 458 | } |
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| 459 | if ((*_prev)[target] == INVALID) { |
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| 460 | _first[(*_bucket)[target]] = (*_next)[target]; |
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| 461 | } else { |
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| 462 | _next->set((*_prev)[target], (*_next)[target]); |
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| 463 | } |
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| 464 | } else { |
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| 465 | _sets.back().pop_back(); |
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| 466 | if (_sets.back().empty()) { |
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| 467 | _sets.pop_back(); |
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| 468 | if (_sets.empty()) |
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| 469 | break; |
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| 470 | for (std::list<int>::iterator it = _sets.back().begin(); |
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| 471 | it != _sets.back().end(); ++it) { |
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| 472 | _dormant[*it] = false; |
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| 473 | } |
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| 474 | } |
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| 475 | new_target = _last[_sets.back().back()]; |
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| 476 | } |
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| 477 | |
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| 478 | _bucket->set(target, 0); |
---|
| 479 | |
---|
| 480 | _source_set->set(target, true); |
---|
| 481 | for (OutArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 482 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
| 483 | if (!_tolerance.positive(rem)) continue; |
---|
| 484 | Node v = _graph.target(a); |
---|
| 485 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 486 | activate(v); |
---|
| 487 | } |
---|
| 488 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 489 | _flow->set(a, (*_capacity)[a]); |
---|
| 490 | } |
---|
| 491 | |
---|
| 492 | for (InArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 493 | Value rem = (*_flow)[a]; |
---|
| 494 | if (!_tolerance.positive(rem)) continue; |
---|
| 495 | Node v = _graph.source(a); |
---|
| 496 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 497 | activate(v); |
---|
| 498 | } |
---|
| 499 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 500 | _flow->set(a, 0); |
---|
| 501 | } |
---|
| 502 | |
---|
| 503 | target = new_target; |
---|
| 504 | if ((*_active)[target]) { |
---|
| 505 | deactivate(target); |
---|
| 506 | } |
---|
| 507 | |
---|
| 508 | _highest = _sets.back().begin(); |
---|
| 509 | while (_highest != _sets.back().end() && |
---|
| 510 | !(*_active)[_first[*_highest]]) { |
---|
| 511 | ++_highest; |
---|
| 512 | } |
---|
| 513 | } |
---|
| 514 | } |
---|
| 515 | } |
---|
| 516 | |
---|
| 517 | void findMinCutIn() { |
---|
| 518 | |
---|
| 519 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 520 | _excess->set(n, 0); |
---|
| 521 | } |
---|
| 522 | |
---|
| 523 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 524 | _flow->set(a, 0); |
---|
| 525 | } |
---|
| 526 | |
---|
[411] | 527 | int bucket_num = 0; |
---|
| 528 | std::vector<Node> queue(_node_num); |
---|
| 529 | int qfirst = 0, qlast = 0, qsep = 0; |
---|
[409] | 530 | |
---|
| 531 | { |
---|
| 532 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
---|
| 533 | |
---|
| 534 | reached.set(_source, true); |
---|
| 535 | |
---|
| 536 | bool first_set = true; |
---|
| 537 | |
---|
| 538 | for (NodeIt t(_graph); t != INVALID; ++t) { |
---|
| 539 | if (reached[t]) continue; |
---|
| 540 | _sets.push_front(std::list<int>()); |
---|
[411] | 541 | |
---|
| 542 | queue[qlast++] = t; |
---|
[409] | 543 | reached.set(t, true); |
---|
| 544 | |
---|
[411] | 545 | while (qfirst != qlast) { |
---|
| 546 | if (qsep == qfirst) { |
---|
| 547 | ++bucket_num; |
---|
| 548 | _sets.front().push_front(bucket_num); |
---|
| 549 | _dormant[bucket_num] = !first_set; |
---|
| 550 | _first[bucket_num] = _last[bucket_num] = INVALID; |
---|
| 551 | qsep = qlast; |
---|
| 552 | } |
---|
[409] | 553 | |
---|
[411] | 554 | Node n = queue[qfirst++]; |
---|
| 555 | addItem(n, bucket_num); |
---|
| 556 | |
---|
| 557 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
---|
| 558 | Node u = _graph.target(a); |
---|
| 559 | if (!reached[u] && _tolerance.positive((*_capacity)[a])) { |
---|
| 560 | reached.set(u, true); |
---|
| 561 | queue[qlast++] = u; |
---|
[409] | 562 | } |
---|
| 563 | } |
---|
| 564 | } |
---|
| 565 | first_set = false; |
---|
| 566 | } |
---|
| 567 | |
---|
[411] | 568 | ++bucket_num; |
---|
[409] | 569 | _bucket->set(_source, 0); |
---|
| 570 | _dormant[0] = true; |
---|
| 571 | } |
---|
| 572 | _source_set->set(_source, true); |
---|
| 573 | |
---|
| 574 | Node target = _last[_sets.back().back()]; |
---|
| 575 | { |
---|
| 576 | for (InArcIt a(_graph, _source); a != INVALID; ++a) { |
---|
| 577 | if (_tolerance.positive((*_capacity)[a])) { |
---|
| 578 | Node u = _graph.source(a); |
---|
| 579 | _flow->set(a, (*_capacity)[a]); |
---|
| 580 | _excess->set(u, (*_excess)[u] + (*_capacity)[a]); |
---|
| 581 | if (!(*_active)[u] && u != _source) { |
---|
| 582 | activate(u); |
---|
| 583 | } |
---|
| 584 | } |
---|
| 585 | } |
---|
| 586 | if ((*_active)[target]) { |
---|
| 587 | deactivate(target); |
---|
| 588 | } |
---|
| 589 | |
---|
| 590 | _highest = _sets.back().begin(); |
---|
| 591 | while (_highest != _sets.back().end() && |
---|
| 592 | !(*_active)[_first[*_highest]]) { |
---|
| 593 | ++_highest; |
---|
| 594 | } |
---|
| 595 | } |
---|
| 596 | |
---|
| 597 | |
---|
| 598 | while (true) { |
---|
| 599 | while (_highest != _sets.back().end()) { |
---|
| 600 | Node n = _first[*_highest]; |
---|
| 601 | Value excess = (*_excess)[n]; |
---|
| 602 | int next_bucket = _node_num; |
---|
| 603 | |
---|
| 604 | int under_bucket; |
---|
| 605 | if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
---|
| 606 | under_bucket = -1; |
---|
| 607 | } else { |
---|
| 608 | under_bucket = *(++std::list<int>::iterator(_highest)); |
---|
| 609 | } |
---|
| 610 | |
---|
| 611 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
---|
| 612 | Node v = _graph.source(a); |
---|
| 613 | if (_dormant[(*_bucket)[v]]) continue; |
---|
| 614 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
| 615 | if (!_tolerance.positive(rem)) continue; |
---|
| 616 | if ((*_bucket)[v] == under_bucket) { |
---|
| 617 | if (!(*_active)[v] && v != target) { |
---|
| 618 | activate(v); |
---|
| 619 | } |
---|
| 620 | if (!_tolerance.less(rem, excess)) { |
---|
| 621 | _flow->set(a, (*_flow)[a] + excess); |
---|
| 622 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 623 | excess = 0; |
---|
| 624 | goto no_more_push; |
---|
| 625 | } else { |
---|
| 626 | excess -= rem; |
---|
| 627 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 628 | _flow->set(a, (*_capacity)[a]); |
---|
| 629 | } |
---|
| 630 | } else if (next_bucket > (*_bucket)[v]) { |
---|
| 631 | next_bucket = (*_bucket)[v]; |
---|
| 632 | } |
---|
| 633 | } |
---|
| 634 | |
---|
| 635 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
---|
| 636 | Node v = _graph.target(a); |
---|
| 637 | if (_dormant[(*_bucket)[v]]) continue; |
---|
| 638 | Value rem = (*_flow)[a]; |
---|
| 639 | if (!_tolerance.positive(rem)) continue; |
---|
| 640 | if ((*_bucket)[v] == under_bucket) { |
---|
| 641 | if (!(*_active)[v] && v != target) { |
---|
| 642 | activate(v); |
---|
| 643 | } |
---|
| 644 | if (!_tolerance.less(rem, excess)) { |
---|
| 645 | _flow->set(a, (*_flow)[a] - excess); |
---|
| 646 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 647 | excess = 0; |
---|
| 648 | goto no_more_push; |
---|
| 649 | } else { |
---|
| 650 | excess -= rem; |
---|
| 651 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 652 | _flow->set(a, 0); |
---|
| 653 | } |
---|
| 654 | } else if (next_bucket > (*_bucket)[v]) { |
---|
| 655 | next_bucket = (*_bucket)[v]; |
---|
| 656 | } |
---|
| 657 | } |
---|
| 658 | |
---|
| 659 | no_more_push: |
---|
| 660 | |
---|
| 661 | _excess->set(n, excess); |
---|
| 662 | |
---|
| 663 | if (excess != 0) { |
---|
| 664 | if ((*_next)[n] == INVALID) { |
---|
| 665 | typename std::list<std::list<int> >::iterator new_set = |
---|
| 666 | _sets.insert(--_sets.end(), std::list<int>()); |
---|
| 667 | new_set->splice(new_set->end(), _sets.back(), |
---|
| 668 | _sets.back().begin(), ++_highest); |
---|
| 669 | for (std::list<int>::iterator it = new_set->begin(); |
---|
| 670 | it != new_set->end(); ++it) { |
---|
| 671 | _dormant[*it] = true; |
---|
| 672 | } |
---|
| 673 | while (_highest != _sets.back().end() && |
---|
| 674 | !(*_active)[_first[*_highest]]) { |
---|
| 675 | ++_highest; |
---|
| 676 | } |
---|
| 677 | } else if (next_bucket == _node_num) { |
---|
| 678 | _first[(*_bucket)[n]] = (*_next)[n]; |
---|
| 679 | _prev->set((*_next)[n], INVALID); |
---|
| 680 | |
---|
| 681 | std::list<std::list<int> >::iterator new_set = |
---|
| 682 | _sets.insert(--_sets.end(), std::list<int>()); |
---|
| 683 | |
---|
| 684 | new_set->push_front(bucket_num); |
---|
| 685 | _bucket->set(n, bucket_num); |
---|
| 686 | _first[bucket_num] = _last[bucket_num] = n; |
---|
| 687 | _next->set(n, INVALID); |
---|
| 688 | _prev->set(n, INVALID); |
---|
| 689 | _dormant[bucket_num] = true; |
---|
| 690 | ++bucket_num; |
---|
| 691 | |
---|
| 692 | while (_highest != _sets.back().end() && |
---|
| 693 | !(*_active)[_first[*_highest]]) { |
---|
| 694 | ++_highest; |
---|
| 695 | } |
---|
| 696 | } else { |
---|
| 697 | _first[*_highest] = (*_next)[n]; |
---|
| 698 | _prev->set((*_next)[n], INVALID); |
---|
| 699 | |
---|
| 700 | while (next_bucket != *_highest) { |
---|
| 701 | --_highest; |
---|
| 702 | } |
---|
| 703 | if (_highest == _sets.back().begin()) { |
---|
| 704 | _sets.back().push_front(bucket_num); |
---|
| 705 | _dormant[bucket_num] = false; |
---|
| 706 | _first[bucket_num] = _last[bucket_num] = INVALID; |
---|
| 707 | ++bucket_num; |
---|
| 708 | } |
---|
| 709 | --_highest; |
---|
| 710 | |
---|
| 711 | _bucket->set(n, *_highest); |
---|
| 712 | _next->set(n, _first[*_highest]); |
---|
| 713 | if (_first[*_highest] != INVALID) { |
---|
| 714 | _prev->set(_first[*_highest], n); |
---|
| 715 | } else { |
---|
| 716 | _last[*_highest] = n; |
---|
| 717 | } |
---|
| 718 | _first[*_highest] = n; |
---|
| 719 | } |
---|
| 720 | } else { |
---|
| 721 | |
---|
| 722 | deactivate(n); |
---|
| 723 | if (!(*_active)[_first[*_highest]]) { |
---|
| 724 | ++_highest; |
---|
| 725 | if (_highest != _sets.back().end() && |
---|
| 726 | !(*_active)[_first[*_highest]]) { |
---|
| 727 | _highest = _sets.back().end(); |
---|
| 728 | } |
---|
| 729 | } |
---|
| 730 | } |
---|
| 731 | } |
---|
| 732 | |
---|
| 733 | if ((*_excess)[target] < _min_cut) { |
---|
| 734 | _min_cut = (*_excess)[target]; |
---|
| 735 | for (NodeIt i(_graph); i != INVALID; ++i) { |
---|
| 736 | _min_cut_map->set(i, false); |
---|
| 737 | } |
---|
| 738 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 739 | it != _sets.back().end(); ++it) { |
---|
| 740 | Node n = _first[*it]; |
---|
| 741 | while (n != INVALID) { |
---|
| 742 | _min_cut_map->set(n, true); |
---|
| 743 | n = (*_next)[n]; |
---|
| 744 | } |
---|
| 745 | } |
---|
| 746 | } |
---|
| 747 | |
---|
| 748 | { |
---|
| 749 | Node new_target; |
---|
| 750 | if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
---|
| 751 | if ((*_next)[target] == INVALID) { |
---|
| 752 | _last[(*_bucket)[target]] = (*_prev)[target]; |
---|
| 753 | new_target = (*_prev)[target]; |
---|
| 754 | } else { |
---|
| 755 | _prev->set((*_next)[target], (*_prev)[target]); |
---|
| 756 | new_target = (*_next)[target]; |
---|
| 757 | } |
---|
| 758 | if ((*_prev)[target] == INVALID) { |
---|
| 759 | _first[(*_bucket)[target]] = (*_next)[target]; |
---|
| 760 | } else { |
---|
| 761 | _next->set((*_prev)[target], (*_next)[target]); |
---|
| 762 | } |
---|
| 763 | } else { |
---|
| 764 | _sets.back().pop_back(); |
---|
| 765 | if (_sets.back().empty()) { |
---|
| 766 | _sets.pop_back(); |
---|
| 767 | if (_sets.empty()) |
---|
| 768 | break; |
---|
| 769 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 770 | it != _sets.back().end(); ++it) { |
---|
| 771 | _dormant[*it] = false; |
---|
| 772 | } |
---|
| 773 | } |
---|
| 774 | new_target = _last[_sets.back().back()]; |
---|
| 775 | } |
---|
| 776 | |
---|
| 777 | _bucket->set(target, 0); |
---|
| 778 | |
---|
| 779 | _source_set->set(target, true); |
---|
| 780 | for (InArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 781 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
| 782 | if (!_tolerance.positive(rem)) continue; |
---|
| 783 | Node v = _graph.source(a); |
---|
| 784 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 785 | activate(v); |
---|
| 786 | } |
---|
| 787 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 788 | _flow->set(a, (*_capacity)[a]); |
---|
| 789 | } |
---|
| 790 | |
---|
| 791 | for (OutArcIt a(_graph, target); a != INVALID; ++a) { |
---|
| 792 | Value rem = (*_flow)[a]; |
---|
| 793 | if (!_tolerance.positive(rem)) continue; |
---|
| 794 | Node v = _graph.target(a); |
---|
| 795 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 796 | activate(v); |
---|
| 797 | } |
---|
| 798 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 799 | _flow->set(a, 0); |
---|
| 800 | } |
---|
| 801 | |
---|
| 802 | target = new_target; |
---|
| 803 | if ((*_active)[target]) { |
---|
| 804 | deactivate(target); |
---|
| 805 | } |
---|
| 806 | |
---|
| 807 | _highest = _sets.back().begin(); |
---|
| 808 | while (_highest != _sets.back().end() && |
---|
| 809 | !(*_active)[_first[*_highest]]) { |
---|
| 810 | ++_highest; |
---|
| 811 | } |
---|
| 812 | } |
---|
| 813 | } |
---|
| 814 | } |
---|
| 815 | |
---|
| 816 | public: |
---|
| 817 | |
---|
| 818 | /// \name Execution control |
---|
| 819 | /// The simplest way to execute the algorithm is to use |
---|
| 820 | /// one of the member functions called \c run(...). |
---|
| 821 | /// \n |
---|
| 822 | /// If you need more control on the execution, |
---|
| 823 | /// first you must call \ref init(), then the \ref calculateIn() or |
---|
[412] | 824 | /// \ref calculateOut() functions. |
---|
[409] | 825 | |
---|
| 826 | /// @{ |
---|
| 827 | |
---|
| 828 | /// \brief Initializes the internal data structures. |
---|
| 829 | /// |
---|
| 830 | /// Initializes the internal data structures. It creates |
---|
| 831 | /// the maps, residual graph adaptors and some bucket structures |
---|
| 832 | /// for the algorithm. |
---|
| 833 | void init() { |
---|
| 834 | init(NodeIt(_graph)); |
---|
| 835 | } |
---|
| 836 | |
---|
| 837 | /// \brief Initializes the internal data structures. |
---|
| 838 | /// |
---|
| 839 | /// Initializes the internal data structures. It creates |
---|
| 840 | /// the maps, residual graph adaptor and some bucket structures |
---|
| 841 | /// for the algorithm. Node \c source is used as the push-relabel |
---|
| 842 | /// algorithm's source. |
---|
| 843 | void init(const Node& source) { |
---|
| 844 | _source = source; |
---|
| 845 | |
---|
| 846 | _node_num = countNodes(_graph); |
---|
| 847 | |
---|
[411] | 848 | _first.resize(_node_num); |
---|
| 849 | _last.resize(_node_num); |
---|
[409] | 850 | |
---|
[411] | 851 | _dormant.resize(_node_num); |
---|
[409] | 852 | |
---|
| 853 | if (!_flow) { |
---|
| 854 | _flow = new FlowMap(_graph); |
---|
| 855 | } |
---|
| 856 | if (!_next) { |
---|
| 857 | _next = new typename Digraph::template NodeMap<Node>(_graph); |
---|
| 858 | } |
---|
| 859 | if (!_prev) { |
---|
| 860 | _prev = new typename Digraph::template NodeMap<Node>(_graph); |
---|
| 861 | } |
---|
| 862 | if (!_active) { |
---|
| 863 | _active = new typename Digraph::template NodeMap<bool>(_graph); |
---|
| 864 | } |
---|
| 865 | if (!_bucket) { |
---|
| 866 | _bucket = new typename Digraph::template NodeMap<int>(_graph); |
---|
| 867 | } |
---|
| 868 | if (!_excess) { |
---|
| 869 | _excess = new ExcessMap(_graph); |
---|
| 870 | } |
---|
| 871 | if (!_source_set) { |
---|
| 872 | _source_set = new SourceSetMap(_graph); |
---|
| 873 | } |
---|
| 874 | if (!_min_cut_map) { |
---|
| 875 | _min_cut_map = new MinCutMap(_graph); |
---|
| 876 | } |
---|
| 877 | |
---|
| 878 | _min_cut = std::numeric_limits<Value>::max(); |
---|
| 879 | } |
---|
| 880 | |
---|
| 881 | |
---|
| 882 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
---|
| 883 | /// source-side. |
---|
| 884 | /// |
---|
| 885 | /// Calculates a minimum cut with \f$ source \f$ on the |
---|
[412] | 886 | /// source-side (i.e. a set \f$ X\subsetneq V \f$ with |
---|
| 887 | /// \f$ source \in X \f$ and minimal out-degree). |
---|
[409] | 888 | void calculateOut() { |
---|
| 889 | findMinCutOut(); |
---|
| 890 | } |
---|
| 891 | |
---|
| 892 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
---|
| 893 | /// target-side. |
---|
| 894 | /// |
---|
| 895 | /// Calculates a minimum cut with \f$ source \f$ on the |
---|
[412] | 896 | /// target-side (i.e. a set \f$ X\subsetneq V \f$ with |
---|
| 897 | /// \f$ source \in X \f$ and minimal out-degree). |
---|
[409] | 898 | void calculateIn() { |
---|
| 899 | findMinCutIn(); |
---|
| 900 | } |
---|
| 901 | |
---|
| 902 | |
---|
| 903 | /// \brief Runs the algorithm. |
---|
| 904 | /// |
---|
| 905 | /// Runs the algorithm. It finds nodes \c source and \c target |
---|
| 906 | /// arbitrarily and then calls \ref init(), \ref calculateOut() |
---|
| 907 | /// and \ref calculateIn(). |
---|
| 908 | void run() { |
---|
| 909 | init(); |
---|
| 910 | calculateOut(); |
---|
| 911 | calculateIn(); |
---|
| 912 | } |
---|
| 913 | |
---|
| 914 | /// \brief Runs the algorithm. |
---|
| 915 | /// |
---|
| 916 | /// Runs the algorithm. It uses the given \c source node, finds a |
---|
| 917 | /// proper \c target and then calls the \ref init(), \ref |
---|
| 918 | /// calculateOut() and \ref calculateIn(). |
---|
| 919 | void run(const Node& s) { |
---|
| 920 | init(s); |
---|
| 921 | calculateOut(); |
---|
| 922 | calculateIn(); |
---|
| 923 | } |
---|
| 924 | |
---|
| 925 | /// @} |
---|
| 926 | |
---|
| 927 | /// \name Query Functions |
---|
| 928 | /// The result of the %HaoOrlin algorithm |
---|
| 929 | /// can be obtained using these functions. |
---|
| 930 | /// \n |
---|
| 931 | /// Before using these functions, either \ref run(), \ref |
---|
| 932 | /// calculateOut() or \ref calculateIn() must be called. |
---|
| 933 | |
---|
| 934 | /// @{ |
---|
| 935 | |
---|
| 936 | /// \brief Returns the value of the minimum value cut. |
---|
| 937 | /// |
---|
| 938 | /// Returns the value of the minimum value cut. |
---|
| 939 | Value minCutValue() const { |
---|
| 940 | return _min_cut; |
---|
| 941 | } |
---|
| 942 | |
---|
| 943 | |
---|
| 944 | /// \brief Returns a minimum cut. |
---|
| 945 | /// |
---|
| 946 | /// Sets \c nodeMap to the characteristic vector of a minimum |
---|
| 947 | /// value cut: it will give a nonempty set \f$ X\subsetneq V \f$ |
---|
| 948 | /// with minimal out-degree (i.e. \c nodeMap will be true exactly |
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| 949 | /// for the nodes of \f$ X \f$). \pre nodeMap should be a |
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| 950 | /// bool-valued node-map. |
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| 951 | template <typename NodeMap> |
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| 952 | Value minCutMap(NodeMap& nodeMap) const { |
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| 953 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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| 954 | nodeMap.set(it, (*_min_cut_map)[it]); |
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| 955 | } |
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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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| 960 | |
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| 961 | }; //class HaoOrlin |
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| 962 | |
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| 963 | |
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| 964 | } //namespace lemon |
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| 965 | |
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| 966 | #endif //LEMON_HAO_ORLIN_H |
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