[2211] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[2225] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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[2553] | 5 | * Copyright (C) 2003-2008 |
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[2225] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[2211] | 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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[2340] | 23 | #include <list> |
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[2211] | 24 | #include <limits> |
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| 25 | |
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| 26 | #include <lemon/maps.h> |
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| 27 | #include <lemon/graph_utils.h> |
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[2624] | 28 | #include <lemon/tolerance.h> |
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[2211] | 29 | |
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| 30 | /// \file |
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[2376] | 31 | /// \ingroup min_cut |
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[2225] | 32 | /// \brief Implementation of the Hao-Orlin algorithm. |
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| 33 | /// |
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[2530] | 34 | /// Implementation of the Hao-Orlin algorithm class for testing network |
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[2211] | 35 | /// reliability. |
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| 36 | |
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| 37 | namespace lemon { |
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| 38 | |
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[2376] | 39 | /// \ingroup min_cut |
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[2225] | 40 | /// |
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[2228] | 41 | /// \brief %Hao-Orlin algorithm to find a minimum cut in directed graphs. |
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[2211] | 42 | /// |
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[2530] | 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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[2225] | 62 | /// |
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| 63 | /// \param _Graph 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 _Graph::EdgeMap<int>. |
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| 66 | /// \param _Tolerance is the handler of the inexact computation. The |
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[2228] | 67 | /// default type for this is Tolerance<typename CapacityMap::Value>. |
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[2211] | 68 | /// |
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| 69 | /// \author Attila Bernath and Balazs Dezso |
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[2225] | 70 | #ifdef DOXYGEN |
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| 71 | template <typename _Graph, typename _CapacityMap, typename _Tolerance> |
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| 72 | #else |
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[2211] | 73 | template <typename _Graph, |
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| 74 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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| 75 | typename _Tolerance = Tolerance<typename _CapacityMap::Value> > |
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[2225] | 76 | #endif |
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[2211] | 77 | class HaoOrlin { |
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[2530] | 78 | private: |
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[2211] | 79 | |
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| 80 | typedef _Graph Graph; |
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| 81 | typedef _CapacityMap CapacityMap; |
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| 82 | typedef _Tolerance Tolerance; |
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| 83 | |
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| 84 | typedef typename CapacityMap::Value Value; |
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| 85 | |
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[2530] | 86 | GRAPH_TYPEDEFS(typename Graph); |
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[2211] | 87 | |
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[2530] | 88 | const Graph& _graph; |
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[2211] | 89 | const CapacityMap* _capacity; |
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| 90 | |
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| 91 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
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[2530] | 92 | FlowMap* _flow; |
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[2211] | 93 | |
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[2530] | 94 | Node _source; |
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[2211] | 95 | |
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| 96 | int _node_num; |
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| 97 | |
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[2530] | 98 | // Bucketing structure |
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| 99 | std::vector<Node> _first, _last; |
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| 100 | typename Graph::template NodeMap<Node>* _next; |
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| 101 | typename Graph::template NodeMap<Node>* _prev; |
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| 102 | typename Graph::template NodeMap<bool>* _active; |
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| 103 | typename Graph::template NodeMap<int>* _bucket; |
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[2225] | 104 | |
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[2530] | 105 | std::vector<bool> _dormant; |
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[2211] | 106 | |
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[2530] | 107 | std::list<std::list<int> > _sets; |
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| 108 | std::list<int>::iterator _highest; |
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[2211] | 109 | |
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| 110 | typedef typename Graph::template NodeMap<Value> ExcessMap; |
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| 111 | ExcessMap* _excess; |
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| 112 | |
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| 113 | typedef typename Graph::template NodeMap<bool> SourceSetMap; |
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| 114 | SourceSetMap* _source_set; |
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| 115 | |
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| 116 | Value _min_cut; |
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| 117 | |
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| 118 | typedef typename Graph::template NodeMap<bool> MinCutMap; |
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| 119 | MinCutMap* _min_cut_map; |
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| 120 | |
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| 121 | Tolerance _tolerance; |
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| 122 | |
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| 123 | public: |
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| 124 | |
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[2225] | 125 | /// \brief Constructor |
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| 126 | /// |
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| 127 | /// Constructor of the algorithm class. |
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[2211] | 128 | HaoOrlin(const Graph& graph, const CapacityMap& capacity, |
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| 129 | const Tolerance& tolerance = Tolerance()) : |
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[2530] | 130 | _graph(graph), _capacity(&capacity), _flow(0), _source(), |
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| 131 | _node_num(), _first(), _last(), _next(0), _prev(0), |
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| 132 | _active(0), _bucket(0), _dormant(), _sets(), _highest(), |
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| 133 | _excess(0), _source_set(0), _min_cut(), _min_cut_map(0), |
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| 134 | _tolerance(tolerance) {} |
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[2211] | 135 | |
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| 136 | ~HaoOrlin() { |
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| 137 | if (_min_cut_map) { |
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| 138 | delete _min_cut_map; |
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| 139 | } |
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| 140 | if (_source_set) { |
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| 141 | delete _source_set; |
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| 142 | } |
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| 143 | if (_excess) { |
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| 144 | delete _excess; |
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| 145 | } |
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[2530] | 146 | if (_next) { |
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| 147 | delete _next; |
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[2211] | 148 | } |
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[2530] | 149 | if (_prev) { |
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| 150 | delete _prev; |
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[2211] | 151 | } |
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[2530] | 152 | if (_active) { |
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| 153 | delete _active; |
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| 154 | } |
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| 155 | if (_bucket) { |
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| 156 | delete _bucket; |
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| 157 | } |
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| 158 | if (_flow) { |
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| 159 | delete _flow; |
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[2211] | 160 | } |
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| 161 | } |
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| 162 | |
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| 163 | private: |
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[2530] | 164 | |
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| 165 | void activate(const Node& i) { |
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| 166 | _active->set(i, true); |
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| 167 | |
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| 168 | int bucket = (*_bucket)[i]; |
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| 169 | |
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| 170 | if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return; |
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| 171 | //unlace |
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| 172 | _next->set((*_prev)[i], (*_next)[i]); |
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| 173 | if ((*_next)[i] != INVALID) { |
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| 174 | _prev->set((*_next)[i], (*_prev)[i]); |
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| 175 | } else { |
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| 176 | _last[bucket] = (*_prev)[i]; |
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| 177 | } |
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| 178 | //lace |
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| 179 | _next->set(i, _first[bucket]); |
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| 180 | _prev->set(_first[bucket], i); |
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| 181 | _prev->set(i, INVALID); |
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| 182 | _first[bucket] = i; |
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| 183 | } |
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| 184 | |
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| 185 | void deactivate(const Node& i) { |
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| 186 | _active->set(i, false); |
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| 187 | int bucket = (*_bucket)[i]; |
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| 188 | |
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| 189 | if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return; |
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| 190 | |
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| 191 | //unlace |
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| 192 | _prev->set((*_next)[i], (*_prev)[i]); |
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| 193 | if ((*_prev)[i] != INVALID) { |
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| 194 | _next->set((*_prev)[i], (*_next)[i]); |
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| 195 | } else { |
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| 196 | _first[bucket] = (*_next)[i]; |
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| 197 | } |
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| 198 | //lace |
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| 199 | _prev->set(i, _last[bucket]); |
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| 200 | _next->set(_last[bucket], i); |
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| 201 | _next->set(i, INVALID); |
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| 202 | _last[bucket] = i; |
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| 203 | } |
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| 204 | |
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| 205 | void addItem(const Node& i, int bucket) { |
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| 206 | (*_bucket)[i] = bucket; |
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| 207 | if (_last[bucket] != INVALID) { |
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| 208 | _prev->set(i, _last[bucket]); |
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| 209 | _next->set(_last[bucket], i); |
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| 210 | _next->set(i, INVALID); |
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| 211 | _last[bucket] = i; |
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| 212 | } else { |
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| 213 | _prev->set(i, INVALID); |
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| 214 | _first[bucket] = i; |
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| 215 | _next->set(i, INVALID); |
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| 216 | _last[bucket] = i; |
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| 217 | } |
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| 218 | } |
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[2211] | 219 | |
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[2530] | 220 | void findMinCutOut() { |
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[2225] | 221 | |
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[2530] | 222 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 223 | _excess->set(n, 0); |
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[2225] | 224 | } |
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| 225 | |
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[2530] | 226 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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| 227 | _flow->set(e, 0); |
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[2340] | 228 | } |
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| 229 | |
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[2530] | 230 | int bucket_num = 1; |
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| 231 | |
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| 232 | { |
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| 233 | typename Graph::template NodeMap<bool> reached(_graph, false); |
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| 234 | |
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| 235 | reached.set(_source, true); |
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[2340] | 236 | |
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[2530] | 237 | bool first_set = true; |
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| 238 | |
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| 239 | for (NodeIt t(_graph); t != INVALID; ++t) { |
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| 240 | if (reached[t]) continue; |
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| 241 | _sets.push_front(std::list<int>()); |
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| 242 | _sets.front().push_front(bucket_num); |
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| 243 | _dormant[bucket_num] = !first_set; |
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| 244 | |
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| 245 | _bucket->set(t, bucket_num); |
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| 246 | _first[bucket_num] = _last[bucket_num] = t; |
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| 247 | _next->set(t, INVALID); |
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| 248 | _prev->set(t, INVALID); |
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| 249 | |
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| 250 | ++bucket_num; |
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| 251 | |
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| 252 | std::vector<Node> queue; |
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| 253 | queue.push_back(t); |
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| 254 | reached.set(t, true); |
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| 255 | |
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| 256 | while (!queue.empty()) { |
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| 257 | _sets.front().push_front(bucket_num); |
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| 258 | _dormant[bucket_num] = !first_set; |
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| 259 | _first[bucket_num] = _last[bucket_num] = INVALID; |
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| 260 | |
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| 261 | std::vector<Node> nqueue; |
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| 262 | for (int i = 0; i < int(queue.size()); ++i) { |
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| 263 | Node n = queue[i]; |
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| 264 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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| 265 | Node u = _graph.source(e); |
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| 266 | if (!reached[u] && _tolerance.positive((*_capacity)[e])) { |
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| 267 | reached.set(u, true); |
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| 268 | addItem(u, bucket_num); |
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| 269 | nqueue.push_back(u); |
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| 270 | } |
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| 271 | } |
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[2225] | 272 | } |
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[2530] | 273 | queue.swap(nqueue); |
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| 274 | ++bucket_num; |
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[2225] | 275 | } |
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[2530] | 276 | _sets.front().pop_front(); |
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| 277 | --bucket_num; |
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| 278 | first_set = false; |
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[2225] | 279 | } |
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| 280 | |
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[2530] | 281 | _bucket->set(_source, 0); |
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| 282 | _dormant[0] = true; |
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| 283 | } |
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| 284 | _source_set->set(_source, true); |
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| 285 | |
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| 286 | Node target = _last[_sets.back().back()]; |
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| 287 | { |
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| 288 | for (OutEdgeIt e(_graph, _source); e != INVALID; ++e) { |
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| 289 | if (_tolerance.positive((*_capacity)[e])) { |
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| 290 | Node u = _graph.target(e); |
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| 291 | _flow->set(e, (*_capacity)[e]); |
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| 292 | _excess->set(u, (*_excess)[u] + (*_capacity)[e]); |
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| 293 | if (!(*_active)[u] && u != _source) { |
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[2624] | 294 | activate(u); |
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[2530] | 295 | } |
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[2211] | 296 | } |
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| 297 | } |
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[2624] | 298 | |
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[2530] | 299 | if ((*_active)[target]) { |
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| 300 | deactivate(target); |
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| 301 | } |
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| 302 | |
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| 303 | _highest = _sets.back().begin(); |
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| 304 | while (_highest != _sets.back().end() && |
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| 305 | !(*_active)[_first[*_highest]]) { |
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| 306 | ++_highest; |
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| 307 | } |
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| 308 | } |
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| 309 | |
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| 310 | while (true) { |
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| 311 | while (_highest != _sets.back().end()) { |
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| 312 | Node n = _first[*_highest]; |
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| 313 | Value excess = (*_excess)[n]; |
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| 314 | int next_bucket = _node_num; |
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| 315 | |
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| 316 | int under_bucket; |
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| 317 | if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
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| 318 | under_bucket = -1; |
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| 319 | } else { |
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| 320 | under_bucket = *(++std::list<int>::iterator(_highest)); |
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| 321 | } |
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| 322 | |
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| 323 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
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| 324 | Node v = _graph.target(e); |
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| 325 | if (_dormant[(*_bucket)[v]]) continue; |
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| 326 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
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| 327 | if (!_tolerance.positive(rem)) continue; |
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| 328 | if ((*_bucket)[v] == under_bucket) { |
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| 329 | if (!(*_active)[v] && v != target) { |
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| 330 | activate(v); |
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| 331 | } |
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| 332 | if (!_tolerance.less(rem, excess)) { |
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| 333 | _flow->set(e, (*_flow)[e] + excess); |
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| 334 | _excess->set(v, (*_excess)[v] + excess); |
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| 335 | excess = 0; |
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| 336 | goto no_more_push; |
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| 337 | } else { |
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| 338 | excess -= rem; |
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| 339 | _excess->set(v, (*_excess)[v] + rem); |
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| 340 | _flow->set(e, (*_capacity)[e]); |
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| 341 | } |
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| 342 | } else if (next_bucket > (*_bucket)[v]) { |
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| 343 | next_bucket = (*_bucket)[v]; |
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| 344 | } |
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| 345 | } |
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| 346 | |
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| 347 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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| 348 | Node v = _graph.source(e); |
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| 349 | if (_dormant[(*_bucket)[v]]) continue; |
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| 350 | Value rem = (*_flow)[e]; |
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| 351 | if (!_tolerance.positive(rem)) continue; |
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| 352 | if ((*_bucket)[v] == under_bucket) { |
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| 353 | if (!(*_active)[v] && v != target) { |
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| 354 | activate(v); |
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| 355 | } |
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| 356 | if (!_tolerance.less(rem, excess)) { |
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| 357 | _flow->set(e, (*_flow)[e] - excess); |
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| 358 | _excess->set(v, (*_excess)[v] + excess); |
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| 359 | excess = 0; |
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| 360 | goto no_more_push; |
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| 361 | } else { |
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| 362 | excess -= rem; |
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| 363 | _excess->set(v, (*_excess)[v] + rem); |
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| 364 | _flow->set(e, 0); |
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| 365 | } |
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| 366 | } else if (next_bucket > (*_bucket)[v]) { |
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| 367 | next_bucket = (*_bucket)[v]; |
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| 368 | } |
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| 369 | } |
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| 370 | |
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| 371 | no_more_push: |
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| 372 | |
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| 373 | _excess->set(n, excess); |
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| 374 | |
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| 375 | if (excess != 0) { |
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| 376 | if ((*_next)[n] == INVALID) { |
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| 377 | typename std::list<std::list<int> >::iterator new_set = |
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| 378 | _sets.insert(--_sets.end(), std::list<int>()); |
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| 379 | new_set->splice(new_set->end(), _sets.back(), |
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| 380 | _sets.back().begin(), ++_highest); |
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| 381 | for (std::list<int>::iterator it = new_set->begin(); |
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| 382 | it != new_set->end(); ++it) { |
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| 383 | _dormant[*it] = true; |
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| 384 | } |
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| 385 | while (_highest != _sets.back().end() && |
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| 386 | !(*_active)[_first[*_highest]]) { |
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| 387 | ++_highest; |
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| 388 | } |
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| 389 | } else if (next_bucket == _node_num) { |
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| 390 | _first[(*_bucket)[n]] = (*_next)[n]; |
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| 391 | _prev->set((*_next)[n], INVALID); |
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| 392 | |
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| 393 | std::list<std::list<int> >::iterator new_set = |
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| 394 | _sets.insert(--_sets.end(), std::list<int>()); |
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| 395 | |
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| 396 | new_set->push_front(bucket_num); |
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| 397 | _bucket->set(n, bucket_num); |
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| 398 | _first[bucket_num] = _last[bucket_num] = n; |
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| 399 | _next->set(n, INVALID); |
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| 400 | _prev->set(n, INVALID); |
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| 401 | _dormant[bucket_num] = true; |
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| 402 | ++bucket_num; |
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| 403 | |
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| 404 | while (_highest != _sets.back().end() && |
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| 405 | !(*_active)[_first[*_highest]]) { |
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| 406 | ++_highest; |
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| 407 | } |
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| 408 | } else { |
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| 409 | _first[*_highest] = (*_next)[n]; |
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| 410 | _prev->set((*_next)[n], INVALID); |
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| 411 | |
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| 412 | while (next_bucket != *_highest) { |
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| 413 | --_highest; |
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| 414 | } |
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| 415 | |
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| 416 | if (_highest == _sets.back().begin()) { |
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| 417 | _sets.back().push_front(bucket_num); |
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| 418 | _dormant[bucket_num] = false; |
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| 419 | _first[bucket_num] = _last[bucket_num] = INVALID; |
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| 420 | ++bucket_num; |
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| 421 | } |
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| 422 | --_highest; |
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| 423 | |
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| 424 | _bucket->set(n, *_highest); |
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| 425 | _next->set(n, _first[*_highest]); |
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| 426 | if (_first[*_highest] != INVALID) { |
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| 427 | _prev->set(_first[*_highest], n); |
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| 428 | } else { |
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| 429 | _last[*_highest] = n; |
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| 430 | } |
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| 431 | _first[*_highest] = n; |
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| 432 | } |
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| 433 | } else { |
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| 434 | |
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| 435 | deactivate(n); |
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| 436 | if (!(*_active)[_first[*_highest]]) { |
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| 437 | ++_highest; |
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| 438 | if (_highest != _sets.back().end() && |
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| 439 | !(*_active)[_first[*_highest]]) { |
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| 440 | _highest = _sets.back().end(); |
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| 441 | } |
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| 442 | } |
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| 443 | } |
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| 444 | } |
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| 445 | |
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| 446 | if ((*_excess)[target] < _min_cut) { |
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| 447 | _min_cut = (*_excess)[target]; |
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| 448 | for (NodeIt i(_graph); i != INVALID; ++i) { |
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| 449 | _min_cut_map->set(i, true); |
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| 450 | } |
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| 451 | for (std::list<int>::iterator it = _sets.back().begin(); |
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| 452 | it != _sets.back().end(); ++it) { |
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| 453 | Node n = _first[*it]; |
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| 454 | while (n != INVALID) { |
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| 455 | _min_cut_map->set(n, false); |
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| 456 | n = (*_next)[n]; |
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| 457 | } |
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| 458 | } |
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| 459 | } |
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| 460 | |
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| 461 | { |
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| 462 | Node new_target; |
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[2624] | 463 | if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
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| 464 | if ((*_next)[target] == INVALID) { |
---|
| 465 | _last[(*_bucket)[target]] = (*_prev)[target]; |
---|
| 466 | new_target = (*_prev)[target]; |
---|
| 467 | } else { |
---|
| 468 | _prev->set((*_next)[target], (*_prev)[target]); |
---|
| 469 | new_target = (*_next)[target]; |
---|
| 470 | } |
---|
| 471 | if ((*_prev)[target] == INVALID) { |
---|
| 472 | _first[(*_bucket)[target]] = (*_next)[target]; |
---|
| 473 | } else { |
---|
| 474 | _next->set((*_prev)[target], (*_next)[target]); |
---|
| 475 | } |
---|
[2530] | 476 | } else { |
---|
| 477 | _sets.back().pop_back(); |
---|
| 478 | if (_sets.back().empty()) { |
---|
| 479 | _sets.pop_back(); |
---|
| 480 | if (_sets.empty()) |
---|
| 481 | break; |
---|
| 482 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 483 | it != _sets.back().end(); ++it) { |
---|
| 484 | _dormant[*it] = false; |
---|
| 485 | } |
---|
| 486 | } |
---|
| 487 | new_target = _last[_sets.back().back()]; |
---|
| 488 | } |
---|
| 489 | |
---|
| 490 | _bucket->set(target, 0); |
---|
| 491 | |
---|
| 492 | _source_set->set(target, true); |
---|
| 493 | for (OutEdgeIt e(_graph, target); e != INVALID; ++e) { |
---|
| 494 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 495 | if (!_tolerance.positive(rem)) continue; |
---|
| 496 | Node v = _graph.target(e); |
---|
| 497 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 498 | activate(v); |
---|
| 499 | } |
---|
| 500 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 501 | _flow->set(e, (*_capacity)[e]); |
---|
| 502 | } |
---|
| 503 | |
---|
| 504 | for (InEdgeIt e(_graph, target); e != INVALID; ++e) { |
---|
| 505 | Value rem = (*_flow)[e]; |
---|
| 506 | if (!_tolerance.positive(rem)) continue; |
---|
| 507 | Node v = _graph.source(e); |
---|
| 508 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 509 | activate(v); |
---|
| 510 | } |
---|
| 511 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 512 | _flow->set(e, 0); |
---|
| 513 | } |
---|
| 514 | |
---|
| 515 | target = new_target; |
---|
| 516 | if ((*_active)[target]) { |
---|
| 517 | deactivate(target); |
---|
| 518 | } |
---|
| 519 | |
---|
| 520 | _highest = _sets.back().begin(); |
---|
| 521 | while (_highest != _sets.back().end() && |
---|
| 522 | !(*_active)[_first[*_highest]]) { |
---|
| 523 | ++_highest; |
---|
| 524 | } |
---|
| 525 | } |
---|
| 526 | } |
---|
| 527 | } |
---|
| 528 | |
---|
| 529 | void findMinCutIn() { |
---|
| 530 | |
---|
| 531 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 532 | _excess->set(n, 0); |
---|
| 533 | } |
---|
| 534 | |
---|
| 535 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 536 | _flow->set(e, 0); |
---|
| 537 | } |
---|
| 538 | |
---|
| 539 | int bucket_num = 1; |
---|
| 540 | |
---|
| 541 | { |
---|
| 542 | typename Graph::template NodeMap<bool> reached(_graph, false); |
---|
| 543 | |
---|
| 544 | reached.set(_source, true); |
---|
| 545 | |
---|
| 546 | bool first_set = true; |
---|
| 547 | |
---|
| 548 | for (NodeIt t(_graph); t != INVALID; ++t) { |
---|
| 549 | if (reached[t]) continue; |
---|
| 550 | _sets.push_front(std::list<int>()); |
---|
| 551 | _sets.front().push_front(bucket_num); |
---|
| 552 | _dormant[bucket_num] = !first_set; |
---|
| 553 | |
---|
| 554 | _bucket->set(t, bucket_num); |
---|
| 555 | _first[bucket_num] = _last[bucket_num] = t; |
---|
| 556 | _next->set(t, INVALID); |
---|
| 557 | _prev->set(t, INVALID); |
---|
| 558 | |
---|
| 559 | ++bucket_num; |
---|
| 560 | |
---|
| 561 | std::vector<Node> queue; |
---|
| 562 | queue.push_back(t); |
---|
| 563 | reached.set(t, true); |
---|
| 564 | |
---|
| 565 | while (!queue.empty()) { |
---|
| 566 | _sets.front().push_front(bucket_num); |
---|
| 567 | _dormant[bucket_num] = !first_set; |
---|
| 568 | _first[bucket_num] = _last[bucket_num] = INVALID; |
---|
| 569 | |
---|
| 570 | std::vector<Node> nqueue; |
---|
| 571 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
| 572 | Node n = queue[i]; |
---|
| 573 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 574 | Node u = _graph.target(e); |
---|
| 575 | if (!reached[u] && _tolerance.positive((*_capacity)[e])) { |
---|
| 576 | reached.set(u, true); |
---|
| 577 | addItem(u, bucket_num); |
---|
| 578 | nqueue.push_back(u); |
---|
| 579 | } |
---|
| 580 | } |
---|
| 581 | } |
---|
| 582 | queue.swap(nqueue); |
---|
| 583 | ++bucket_num; |
---|
| 584 | } |
---|
| 585 | _sets.front().pop_front(); |
---|
| 586 | --bucket_num; |
---|
| 587 | first_set = false; |
---|
| 588 | } |
---|
| 589 | |
---|
| 590 | _bucket->set(_source, 0); |
---|
| 591 | _dormant[0] = true; |
---|
| 592 | } |
---|
| 593 | _source_set->set(_source, true); |
---|
| 594 | |
---|
| 595 | Node target = _last[_sets.back().back()]; |
---|
| 596 | { |
---|
| 597 | for (InEdgeIt e(_graph, _source); e != INVALID; ++e) { |
---|
| 598 | if (_tolerance.positive((*_capacity)[e])) { |
---|
| 599 | Node u = _graph.source(e); |
---|
| 600 | _flow->set(e, (*_capacity)[e]); |
---|
| 601 | _excess->set(u, (*_excess)[u] + (*_capacity)[e]); |
---|
| 602 | if (!(*_active)[u] && u != _source) { |
---|
| 603 | activate(u); |
---|
| 604 | } |
---|
| 605 | } |
---|
| 606 | } |
---|
| 607 | if ((*_active)[target]) { |
---|
| 608 | deactivate(target); |
---|
| 609 | } |
---|
| 610 | |
---|
| 611 | _highest = _sets.back().begin(); |
---|
| 612 | while (_highest != _sets.back().end() && |
---|
| 613 | !(*_active)[_first[*_highest]]) { |
---|
| 614 | ++_highest; |
---|
| 615 | } |
---|
| 616 | } |
---|
| 617 | |
---|
| 618 | |
---|
| 619 | while (true) { |
---|
| 620 | while (_highest != _sets.back().end()) { |
---|
| 621 | Node n = _first[*_highest]; |
---|
| 622 | Value excess = (*_excess)[n]; |
---|
| 623 | int next_bucket = _node_num; |
---|
| 624 | |
---|
| 625 | int under_bucket; |
---|
| 626 | if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
---|
| 627 | under_bucket = -1; |
---|
| 628 | } else { |
---|
| 629 | under_bucket = *(++std::list<int>::iterator(_highest)); |
---|
| 630 | } |
---|
| 631 | |
---|
| 632 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 633 | Node v = _graph.source(e); |
---|
| 634 | if (_dormant[(*_bucket)[v]]) continue; |
---|
| 635 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 636 | if (!_tolerance.positive(rem)) continue; |
---|
| 637 | if ((*_bucket)[v] == under_bucket) { |
---|
| 638 | if (!(*_active)[v] && v != target) { |
---|
| 639 | activate(v); |
---|
| 640 | } |
---|
| 641 | if (!_tolerance.less(rem, excess)) { |
---|
| 642 | _flow->set(e, (*_flow)[e] + excess); |
---|
| 643 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 644 | excess = 0; |
---|
| 645 | goto no_more_push; |
---|
| 646 | } else { |
---|
| 647 | excess -= rem; |
---|
| 648 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 649 | _flow->set(e, (*_capacity)[e]); |
---|
| 650 | } |
---|
| 651 | } else if (next_bucket > (*_bucket)[v]) { |
---|
| 652 | next_bucket = (*_bucket)[v]; |
---|
| 653 | } |
---|
| 654 | } |
---|
| 655 | |
---|
| 656 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 657 | Node v = _graph.target(e); |
---|
| 658 | if (_dormant[(*_bucket)[v]]) continue; |
---|
| 659 | Value rem = (*_flow)[e]; |
---|
| 660 | if (!_tolerance.positive(rem)) continue; |
---|
| 661 | if ((*_bucket)[v] == under_bucket) { |
---|
| 662 | if (!(*_active)[v] && v != target) { |
---|
| 663 | activate(v); |
---|
| 664 | } |
---|
| 665 | if (!_tolerance.less(rem, excess)) { |
---|
| 666 | _flow->set(e, (*_flow)[e] - excess); |
---|
| 667 | _excess->set(v, (*_excess)[v] + excess); |
---|
| 668 | excess = 0; |
---|
| 669 | goto no_more_push; |
---|
| 670 | } else { |
---|
| 671 | excess -= rem; |
---|
| 672 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 673 | _flow->set(e, 0); |
---|
| 674 | } |
---|
| 675 | } else if (next_bucket > (*_bucket)[v]) { |
---|
| 676 | next_bucket = (*_bucket)[v]; |
---|
| 677 | } |
---|
| 678 | } |
---|
| 679 | |
---|
| 680 | no_more_push: |
---|
| 681 | |
---|
| 682 | _excess->set(n, excess); |
---|
| 683 | |
---|
| 684 | if (excess != 0) { |
---|
| 685 | if ((*_next)[n] == INVALID) { |
---|
| 686 | typename std::list<std::list<int> >::iterator new_set = |
---|
| 687 | _sets.insert(--_sets.end(), std::list<int>()); |
---|
| 688 | new_set->splice(new_set->end(), _sets.back(), |
---|
| 689 | _sets.back().begin(), ++_highest); |
---|
| 690 | for (std::list<int>::iterator it = new_set->begin(); |
---|
| 691 | it != new_set->end(); ++it) { |
---|
| 692 | _dormant[*it] = true; |
---|
| 693 | } |
---|
| 694 | while (_highest != _sets.back().end() && |
---|
| 695 | !(*_active)[_first[*_highest]]) { |
---|
| 696 | ++_highest; |
---|
| 697 | } |
---|
| 698 | } else if (next_bucket == _node_num) { |
---|
| 699 | _first[(*_bucket)[n]] = (*_next)[n]; |
---|
| 700 | _prev->set((*_next)[n], INVALID); |
---|
| 701 | |
---|
| 702 | std::list<std::list<int> >::iterator new_set = |
---|
| 703 | _sets.insert(--_sets.end(), std::list<int>()); |
---|
| 704 | |
---|
| 705 | new_set->push_front(bucket_num); |
---|
| 706 | _bucket->set(n, bucket_num); |
---|
| 707 | _first[bucket_num] = _last[bucket_num] = n; |
---|
| 708 | _next->set(n, INVALID); |
---|
| 709 | _prev->set(n, INVALID); |
---|
| 710 | _dormant[bucket_num] = true; |
---|
| 711 | ++bucket_num; |
---|
| 712 | |
---|
| 713 | while (_highest != _sets.back().end() && |
---|
| 714 | !(*_active)[_first[*_highest]]) { |
---|
| 715 | ++_highest; |
---|
| 716 | } |
---|
| 717 | } else { |
---|
| 718 | _first[*_highest] = (*_next)[n]; |
---|
| 719 | _prev->set((*_next)[n], INVALID); |
---|
| 720 | |
---|
| 721 | while (next_bucket != *_highest) { |
---|
| 722 | --_highest; |
---|
| 723 | } |
---|
| 724 | if (_highest == _sets.back().begin()) { |
---|
| 725 | _sets.back().push_front(bucket_num); |
---|
| 726 | _dormant[bucket_num] = false; |
---|
| 727 | _first[bucket_num] = _last[bucket_num] = INVALID; |
---|
| 728 | ++bucket_num; |
---|
| 729 | } |
---|
| 730 | --_highest; |
---|
| 731 | |
---|
| 732 | _bucket->set(n, *_highest); |
---|
| 733 | _next->set(n, _first[*_highest]); |
---|
| 734 | if (_first[*_highest] != INVALID) { |
---|
| 735 | _prev->set(_first[*_highest], n); |
---|
| 736 | } else { |
---|
| 737 | _last[*_highest] = n; |
---|
| 738 | } |
---|
| 739 | _first[*_highest] = n; |
---|
| 740 | } |
---|
| 741 | } else { |
---|
| 742 | |
---|
| 743 | deactivate(n); |
---|
| 744 | if (!(*_active)[_first[*_highest]]) { |
---|
| 745 | ++_highest; |
---|
| 746 | if (_highest != _sets.back().end() && |
---|
| 747 | !(*_active)[_first[*_highest]]) { |
---|
| 748 | _highest = _sets.back().end(); |
---|
| 749 | } |
---|
| 750 | } |
---|
| 751 | } |
---|
| 752 | } |
---|
| 753 | |
---|
| 754 | if ((*_excess)[target] < _min_cut) { |
---|
| 755 | _min_cut = (*_excess)[target]; |
---|
| 756 | for (NodeIt i(_graph); i != INVALID; ++i) { |
---|
| 757 | _min_cut_map->set(i, false); |
---|
| 758 | } |
---|
| 759 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 760 | it != _sets.back().end(); ++it) { |
---|
| 761 | Node n = _first[*it]; |
---|
| 762 | while (n != INVALID) { |
---|
| 763 | _min_cut_map->set(n, true); |
---|
| 764 | n = (*_next)[n]; |
---|
| 765 | } |
---|
| 766 | } |
---|
| 767 | } |
---|
| 768 | |
---|
| 769 | { |
---|
| 770 | Node new_target; |
---|
[2624] | 771 | if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
---|
| 772 | if ((*_next)[target] == INVALID) { |
---|
| 773 | _last[(*_bucket)[target]] = (*_prev)[target]; |
---|
| 774 | new_target = (*_prev)[target]; |
---|
| 775 | } else { |
---|
| 776 | _prev->set((*_next)[target], (*_prev)[target]); |
---|
| 777 | new_target = (*_next)[target]; |
---|
| 778 | } |
---|
| 779 | if ((*_prev)[target] == INVALID) { |
---|
| 780 | _first[(*_bucket)[target]] = (*_next)[target]; |
---|
| 781 | } else { |
---|
| 782 | _next->set((*_prev)[target], (*_next)[target]); |
---|
| 783 | } |
---|
[2530] | 784 | } else { |
---|
| 785 | _sets.back().pop_back(); |
---|
| 786 | if (_sets.back().empty()) { |
---|
| 787 | _sets.pop_back(); |
---|
| 788 | if (_sets.empty()) |
---|
| 789 | break; |
---|
| 790 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
| 791 | it != _sets.back().end(); ++it) { |
---|
| 792 | _dormant[*it] = false; |
---|
| 793 | } |
---|
| 794 | } |
---|
| 795 | new_target = _last[_sets.back().back()]; |
---|
| 796 | } |
---|
| 797 | |
---|
| 798 | _bucket->set(target, 0); |
---|
| 799 | |
---|
| 800 | _source_set->set(target, true); |
---|
| 801 | for (InEdgeIt e(_graph, target); e != INVALID; ++e) { |
---|
| 802 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 803 | if (!_tolerance.positive(rem)) continue; |
---|
| 804 | Node v = _graph.source(e); |
---|
| 805 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 806 | activate(v); |
---|
| 807 | } |
---|
| 808 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 809 | _flow->set(e, (*_capacity)[e]); |
---|
| 810 | } |
---|
| 811 | |
---|
| 812 | for (OutEdgeIt e(_graph, target); e != INVALID; ++e) { |
---|
| 813 | Value rem = (*_flow)[e]; |
---|
| 814 | if (!_tolerance.positive(rem)) continue; |
---|
| 815 | Node v = _graph.target(e); |
---|
| 816 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
| 817 | activate(v); |
---|
| 818 | } |
---|
| 819 | _excess->set(v, (*_excess)[v] + rem); |
---|
| 820 | _flow->set(e, 0); |
---|
| 821 | } |
---|
| 822 | |
---|
| 823 | target = new_target; |
---|
| 824 | if ((*_active)[target]) { |
---|
| 825 | deactivate(target); |
---|
| 826 | } |
---|
| 827 | |
---|
| 828 | _highest = _sets.back().begin(); |
---|
| 829 | while (_highest != _sets.back().end() && |
---|
| 830 | !(*_active)[_first[*_highest]]) { |
---|
| 831 | ++_highest; |
---|
| 832 | } |
---|
[2211] | 833 | } |
---|
| 834 | } |
---|
| 835 | } |
---|
| 836 | |
---|
| 837 | public: |
---|
| 838 | |
---|
[2225] | 839 | /// \name Execution control |
---|
| 840 | /// The simplest way to execute the algorithm is to use |
---|
| 841 | /// one of the member functions called \c run(...). |
---|
| 842 | /// \n |
---|
| 843 | /// If you need more control on the execution, |
---|
| 844 | /// first you must call \ref init(), then the \ref calculateIn() or |
---|
| 845 | /// \ref calculateIn() functions. |
---|
| 846 | |
---|
| 847 | /// @{ |
---|
| 848 | |
---|
[2211] | 849 | /// \brief Initializes the internal data structures. |
---|
| 850 | /// |
---|
| 851 | /// Initializes the internal data structures. It creates |
---|
[2225] | 852 | /// the maps, residual graph adaptors and some bucket structures |
---|
[2211] | 853 | /// for the algorithm. |
---|
| 854 | void init() { |
---|
[2530] | 855 | init(NodeIt(_graph)); |
---|
[2211] | 856 | } |
---|
| 857 | |
---|
| 858 | /// \brief Initializes the internal data structures. |
---|
| 859 | /// |
---|
| 860 | /// Initializes the internal data structures. It creates |
---|
| 861 | /// the maps, residual graph adaptor and some bucket structures |
---|
[2228] | 862 | /// for the algorithm. Node \c source is used as the push-relabel |
---|
[2211] | 863 | /// algorithm's source. |
---|
| 864 | void init(const Node& source) { |
---|
| 865 | _source = source; |
---|
[2530] | 866 | |
---|
| 867 | _node_num = countNodes(_graph); |
---|
| 868 | |
---|
[2624] | 869 | _first.resize(_node_num + 1); |
---|
| 870 | _last.resize(_node_num + 1); |
---|
[2211] | 871 | |
---|
[2624] | 872 | _dormant.resize(_node_num + 1); |
---|
[2211] | 873 | |
---|
[2530] | 874 | if (!_flow) { |
---|
| 875 | _flow = new FlowMap(_graph); |
---|
[2211] | 876 | } |
---|
[2530] | 877 | if (!_next) { |
---|
| 878 | _next = new typename Graph::template NodeMap<Node>(_graph); |
---|
[2211] | 879 | } |
---|
[2530] | 880 | if (!_prev) { |
---|
| 881 | _prev = new typename Graph::template NodeMap<Node>(_graph); |
---|
| 882 | } |
---|
| 883 | if (!_active) { |
---|
| 884 | _active = new typename Graph::template NodeMap<bool>(_graph); |
---|
| 885 | } |
---|
| 886 | if (!_bucket) { |
---|
| 887 | _bucket = new typename Graph::template NodeMap<int>(_graph); |
---|
[2211] | 888 | } |
---|
| 889 | if (!_excess) { |
---|
[2530] | 890 | _excess = new ExcessMap(_graph); |
---|
[2211] | 891 | } |
---|
| 892 | if (!_source_set) { |
---|
[2530] | 893 | _source_set = new SourceSetMap(_graph); |
---|
[2225] | 894 | } |
---|
[2211] | 895 | if (!_min_cut_map) { |
---|
[2530] | 896 | _min_cut_map = new MinCutMap(_graph); |
---|
[2211] | 897 | } |
---|
| 898 | |
---|
| 899 | _min_cut = std::numeric_limits<Value>::max(); |
---|
| 900 | } |
---|
| 901 | |
---|
| 902 | |
---|
[2228] | 903 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
---|
| 904 | /// source-side. |
---|
[2211] | 905 | /// |
---|
[2530] | 906 | /// Calculates a minimum cut with \f$ source \f$ on the |
---|
| 907 | /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source |
---|
| 908 | /// \in X \f$ and minimal out-degree). |
---|
[2211] | 909 | void calculateOut() { |
---|
[2530] | 910 | findMinCutOut(); |
---|
[2211] | 911 | } |
---|
| 912 | |
---|
[2228] | 913 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
---|
[2530] | 914 | /// target-side. |
---|
[2211] | 915 | /// |
---|
[2530] | 916 | /// Calculates a minimum cut with \f$ source \f$ on the |
---|
| 917 | /// target-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source |
---|
| 918 | /// \in X \f$ and minimal out-degree). |
---|
| 919 | void calculateIn() { |
---|
| 920 | findMinCutIn(); |
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[2211] | 921 | } |
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| 922 | |
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[2225] | 923 | |
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| 924 | /// \brief Runs the algorithm. |
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| 925 | /// |
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[2228] | 926 | /// Runs the algorithm. It finds nodes \c source and \c target |
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| 927 | /// arbitrarily and then calls \ref init(), \ref calculateOut() |
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| 928 | /// and \ref calculateIn(). |
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[2211] | 929 | void run() { |
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| 930 | init(); |
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[2530] | 931 | calculateOut(); |
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| 932 | calculateIn(); |
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[2211] | 933 | } |
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| 934 | |
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[2225] | 935 | /// \brief Runs the algorithm. |
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| 936 | /// |
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[2228] | 937 | /// Runs the algorithm. It uses the given \c source node, finds a |
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| 938 | /// proper \c target and then calls the \ref init(), \ref |
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| 939 | /// calculateOut() and \ref calculateIn(). |
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[2211] | 940 | void run(const Node& s) { |
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| 941 | init(s); |
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[2530] | 942 | calculateOut(); |
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| 943 | calculateIn(); |
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[2211] | 944 | } |
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[2225] | 945 | |
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| 946 | /// @} |
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[2211] | 947 | |
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[2275] | 948 | /// \name Query Functions |
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| 949 | /// The result of the %HaoOrlin algorithm |
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[2225] | 950 | /// can be obtained using these functions. |
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| 951 | /// \n |
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[2275] | 952 | /// Before using these functions, either \ref run(), \ref |
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[2225] | 953 | /// calculateOut() or \ref calculateIn() must be called. |
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| 954 | |
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| 955 | /// @{ |
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| 956 | |
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| 957 | /// \brief Returns the value of the minimum value cut. |
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[2211] | 958 | /// |
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[2225] | 959 | /// Returns the value of the minimum value cut. |
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[2211] | 960 | Value minCut() const { |
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| 961 | return _min_cut; |
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| 962 | } |
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| 963 | |
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| 964 | |
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[2228] | 965 | /// \brief Returns a minimum cut. |
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[2211] | 966 | /// |
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| 967 | /// Sets \c nodeMap to the characteristic vector of a minimum |
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[2228] | 968 | /// value cut: it will give a nonempty set \f$ X\subsetneq V \f$ |
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| 969 | /// with minimal out-degree (i.e. \c nodeMap will be true exactly |
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[2275] | 970 | /// for the nodes of \f$ X \f$). \pre nodeMap should be a |
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[2228] | 971 | /// bool-valued node-map. |
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[2211] | 972 | template <typename NodeMap> |
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| 973 | Value minCut(NodeMap& nodeMap) const { |
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[2530] | 974 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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[2211] | 975 | nodeMap.set(it, (*_min_cut_map)[it]); |
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| 976 | } |
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| 977 | return minCut(); |
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| 978 | } |
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[2225] | 979 | |
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| 980 | /// @} |
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[2211] | 981 | |
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| 982 | }; //class HaoOrlin |
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| 983 | |
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| 984 | |
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| 985 | } //namespace lemon |
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| 986 | |
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| 987 | #endif //LEMON_HAO_ORLIN_H |
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