[2211] | 1 | /* -*- C++ -*- |
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| 2 | * lemon/hao_orlin.h - Part of LEMON, a generic C++ optimization library |
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| 3 | * |
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| 4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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| 17 | #ifndef LEMON_HAO_ORLIN_H |
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| 18 | #define LEMON_HAO_ORLIN_H |
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| 19 | |
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| 20 | #include <vector> |
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| 21 | #include <queue> |
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| 22 | #include <limits> |
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| 23 | |
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| 24 | #include <lemon/maps.h> |
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| 25 | #include <lemon/graph_utils.h> |
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| 26 | #include <lemon/graph_adaptor.h> |
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| 27 | #include <lemon/iterable_maps.h> |
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| 28 | |
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| 29 | |
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| 30 | /// \file |
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| 31 | /// \ingroup flowalgs |
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| 32 | /// Implementation of the Hao-Orlin algorithms class for testing network |
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| 33 | /// reliability. |
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| 34 | |
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| 35 | namespace lemon { |
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| 36 | |
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| 37 | /// \addtogroup flowalgs |
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| 38 | /// @{ |
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| 39 | |
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| 40 | /// %Hao-Orlin algorithm for calculate minimum cut in directed graphs. |
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| 41 | /// |
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| 42 | /// Hao-Orlin calculates the minimum cut in directed graphs. It |
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| 43 | /// separates the nodes of the graph into two disjoint sets and the |
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| 44 | /// summary of the edge capacities go from the first set to the |
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| 45 | /// second set is the minimum. The algorithm is a modified |
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| 46 | /// push-relabel preflow algorithm and it calculates the minimum cat |
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| 47 | /// in \f$ O(n^3) \f$ time. The purpose of such algorithm is testing |
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| 48 | /// network reliability. For sparse undirected graph you can use the |
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| 49 | /// algorithm of Nagamochi and Ibraki which solves the undirected |
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| 50 | /// problem in \f$ O(n^3) \f$ time. |
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| 51 | /// |
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| 52 | /// \author Attila Bernath and Balazs Dezso |
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| 53 | template <typename _Graph, |
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| 54 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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| 55 | typename _Tolerance = Tolerance<typename _CapacityMap::Value> > |
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| 56 | class HaoOrlin { |
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| 57 | protected: |
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| 58 | |
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| 59 | typedef _Graph Graph; |
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| 60 | typedef _CapacityMap CapacityMap; |
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| 61 | typedef _Tolerance Tolerance; |
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| 62 | |
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| 63 | typedef typename CapacityMap::Value Value; |
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| 64 | |
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| 65 | |
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| 66 | typedef typename Graph::Node Node; |
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| 67 | typedef typename Graph::NodeIt NodeIt; |
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| 68 | typedef typename Graph::EdgeIt EdgeIt; |
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| 69 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 70 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 71 | |
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| 72 | const Graph* _graph; |
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| 73 | const CapacityMap* _capacity; |
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| 74 | |
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| 75 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
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| 76 | |
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| 77 | FlowMap* _preflow; |
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| 78 | |
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| 79 | Node _source, _target; |
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| 80 | int _node_num; |
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| 81 | |
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| 82 | typedef ResGraphAdaptor<const Graph, Value, CapacityMap, |
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| 83 | FlowMap, Tolerance> ResGraph; |
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| 84 | typedef typename ResGraph::Node ResNode; |
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| 85 | typedef typename ResGraph::NodeIt ResNodeIt; |
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| 86 | typedef typename ResGraph::EdgeIt ResEdgeIt; |
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| 87 | typedef typename ResGraph::OutEdgeIt ResOutEdgeIt; |
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| 88 | typedef typename ResGraph::Edge ResEdge; |
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| 89 | typedef typename ResGraph::InEdgeIt ResInEdgeIt; |
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| 90 | |
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| 91 | ResGraph* _res_graph; |
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| 92 | |
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| 93 | typedef typename Graph::template NodeMap<ResEdge> CurrentArcMap; |
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| 94 | CurrentArcMap* _current_arc; |
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| 95 | |
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| 96 | |
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| 97 | typedef IterableBoolMap<Graph, Node> WakeMap; |
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| 98 | WakeMap* _wake; |
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| 99 | |
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| 100 | typedef typename Graph::template NodeMap<int> DistMap; |
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| 101 | DistMap* _dist; |
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| 102 | |
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| 103 | typedef typename Graph::template NodeMap<Value> ExcessMap; |
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| 104 | ExcessMap* _excess; |
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| 105 | |
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| 106 | typedef typename Graph::template NodeMap<bool> SourceSetMap; |
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| 107 | SourceSetMap* _source_set; |
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| 108 | |
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| 109 | std::vector<int> _level_size; |
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| 110 | |
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| 111 | int _highest_active; |
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| 112 | std::vector<std::list<Node> > _active_nodes; |
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| 113 | |
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| 114 | int _dormant_max; |
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| 115 | std::vector<std::list<Node> > _dormant; |
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| 116 | |
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| 117 | |
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| 118 | Value _min_cut; |
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| 119 | |
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| 120 | typedef typename Graph::template NodeMap<bool> MinCutMap; |
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| 121 | MinCutMap* _min_cut_map; |
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| 122 | |
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| 123 | Tolerance _tolerance; |
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| 124 | |
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| 125 | public: |
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| 126 | |
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| 127 | HaoOrlin(const Graph& graph, const CapacityMap& capacity, |
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| 128 | const Tolerance& tolerance = Tolerance()) : |
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| 129 | _graph(&graph), _capacity(&capacity), |
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| 130 | _preflow(0), _source(), _target(), _res_graph(0), _current_arc(0), |
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| 131 | _wake(0),_dist(0), _excess(0), _source_set(0), |
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| 132 | _highest_active(), _active_nodes(), _dormant_max(), _dormant(), |
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| 133 | _min_cut(), _min_cut_map(0), _tolerance(tolerance) {} |
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| 134 | |
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| 135 | ~HaoOrlin() { |
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| 136 | if (_res_graph) { |
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| 137 | delete _res_graph; |
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| 138 | } |
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| 139 | if (_min_cut_map) { |
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| 140 | delete _min_cut_map; |
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| 141 | } |
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| 142 | if (_current_arc) { |
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| 143 | delete _current_arc; |
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| 144 | } |
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| 145 | if (_source_set) { |
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| 146 | delete _source_set; |
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| 147 | } |
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| 148 | if (_excess) { |
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| 149 | delete _excess; |
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| 150 | } |
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| 151 | if (_dist) { |
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| 152 | delete _dist; |
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| 153 | } |
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| 154 | if (_wake) { |
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| 155 | delete _wake; |
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| 156 | } |
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| 157 | if (_preflow) { |
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| 158 | delete _preflow; |
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| 159 | } |
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| 160 | } |
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| 161 | |
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| 162 | private: |
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| 163 | |
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| 164 | void relabel(Node i) { |
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| 165 | int k = (*_dist)[i]; |
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| 166 | if (_level_size[k] == 1) { |
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| 167 | ++_dormant_max; |
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| 168 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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| 169 | if ((*_wake)[it] && (*_dist)[it] >= k) { |
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| 170 | (*_wake)[it] = false; |
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| 171 | _dormant[_dormant_max].push_front(it); |
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| 172 | --_level_size[(*_dist)[it]]; |
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| 173 | } |
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| 174 | } |
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| 175 | --_highest_active; |
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| 176 | } else { |
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| 177 | ResOutEdgeIt e(*_res_graph, i); |
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| 178 | while (e != INVALID && !(*_wake)[_res_graph->target(e)]) { |
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| 179 | ++e; |
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| 180 | } |
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| 181 | |
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| 182 | if (e == INVALID){ |
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| 183 | ++_dormant_max; |
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| 184 | (*_wake)[i] = false; |
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| 185 | _dormant[_dormant_max].push_front(i); |
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| 186 | --_level_size[(*_dist)[i]]; |
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| 187 | } else{ |
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| 188 | Node j = _res_graph->target(e); |
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| 189 | int new_dist = (*_dist)[j]; |
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| 190 | ++e; |
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| 191 | while (e != INVALID){ |
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| 192 | Node j = _res_graph->target(e); |
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| 193 | if ((*_wake)[j] && new_dist > (*_dist)[j]) { |
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| 194 | new_dist = (*_dist)[j]; |
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| 195 | } |
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| 196 | ++e; |
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| 197 | } |
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| 198 | --_level_size[(*_dist)[i]]; |
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| 199 | (*_dist)[i] = new_dist + 1; |
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| 200 | _highest_active = (*_dist)[i]; |
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| 201 | _active_nodes[_highest_active].push_front(i); |
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| 202 | ++_level_size[(*_dist)[i]]; |
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| 203 | _res_graph->firstOut((*_current_arc)[i], i); |
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| 204 | } |
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| 205 | } |
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| 206 | } |
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| 207 | |
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| 208 | bool selectNewSink(){ |
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| 209 | Node old_target = _target; |
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| 210 | (*_wake)[_target] = false; |
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| 211 | --_level_size[(*_dist)[_target]]; |
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| 212 | _dormant[0].push_front(_target); |
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| 213 | (*_source_set)[_target] = true; |
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| 214 | if ((int)_dormant[0].size() == _node_num){ |
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| 215 | _dormant[0].clear(); |
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| 216 | return false; |
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| 217 | } |
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| 218 | |
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| 219 | bool wake_was_empty = false; |
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| 220 | |
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| 221 | if(_wake->trueNum() == 0) { |
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| 222 | while (!_dormant[_dormant_max].empty()){ |
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| 223 | (*_wake)[_dormant[_dormant_max].front()] = true; |
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| 224 | ++_level_size[(*_dist)[_dormant[_dormant_max].front()]]; |
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| 225 | _dormant[_dormant_max].pop_front(); |
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| 226 | } |
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| 227 | --_dormant_max; |
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| 228 | wake_was_empty = true; |
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| 229 | } |
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| 230 | |
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| 231 | int min_dist = std::numeric_limits<int>::max(); |
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| 232 | for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) { |
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| 233 | if (min_dist > (*_dist)[it]){ |
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| 234 | _target = it; |
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| 235 | min_dist = (*_dist)[it]; |
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| 236 | } |
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| 237 | } |
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| 238 | |
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| 239 | if (wake_was_empty){ |
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| 240 | for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) { |
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| 241 | if (_tolerance.positive((*_excess)[it])) { |
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| 242 | if ((*_wake)[it] && it != _target) { |
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| 243 | _active_nodes[(*_dist)[it]].push_front(it); |
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| 244 | } |
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| 245 | if (_highest_active < (*_dist)[it]) { |
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| 246 | _highest_active = (*_dist)[it]; |
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| 247 | } |
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| 248 | } |
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| 249 | } |
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| 250 | } |
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| 251 | |
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| 252 | for (ResOutEdgeIt e(*_res_graph, old_target); e!=INVALID; ++e){ |
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| 253 | if (!(*_source_set)[_res_graph->target(e)]){ |
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| 254 | push(e, _res_graph->rescap(e)); |
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| 255 | } |
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| 256 | } |
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| 257 | |
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| 258 | return true; |
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| 259 | } |
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| 260 | |
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| 261 | Node findActiveNode() { |
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| 262 | while (_highest_active > 0 && _active_nodes[_highest_active].empty()){ |
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| 263 | --_highest_active; |
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| 264 | } |
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| 265 | if( _highest_active > 0) { |
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| 266 | Node n = _active_nodes[_highest_active].front(); |
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| 267 | _active_nodes[_highest_active].pop_front(); |
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| 268 | return n; |
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| 269 | } else { |
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| 270 | return INVALID; |
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| 271 | } |
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| 272 | } |
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| 273 | |
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| 274 | ResEdge findAdmissibleEdge(const Node& n){ |
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| 275 | ResEdge e = (*_current_arc)[n]; |
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| 276 | while (e != INVALID && |
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| 277 | ((*_dist)[n] <= (*_dist)[_res_graph->target(e)] || |
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| 278 | !(*_wake)[_res_graph->target(e)])) { |
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| 279 | _res_graph->nextOut(e); |
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| 280 | } |
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| 281 | if (e != INVALID) { |
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| 282 | (*_current_arc)[n] = e; |
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| 283 | return e; |
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| 284 | } else { |
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| 285 | return INVALID; |
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| 286 | } |
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| 287 | } |
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| 288 | |
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| 289 | void push(ResEdge& e,const Value& delta){ |
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| 290 | _res_graph->augment(e, delta); |
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| 291 | if (!_tolerance.positive(delta)) return; |
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| 292 | |
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| 293 | (*_excess)[_res_graph->source(e)] -= delta; |
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| 294 | Node a = _res_graph->target(e); |
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| 295 | if (!_tolerance.positive((*_excess)[a]) && (*_wake)[a] && a != _target) { |
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| 296 | _active_nodes[(*_dist)[a]].push_front(a); |
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| 297 | if (_highest_active < (*_dist)[a]) { |
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| 298 | _highest_active = (*_dist)[a]; |
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| 299 | } |
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| 300 | } |
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| 301 | (*_excess)[a] += delta; |
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| 302 | } |
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| 303 | |
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| 304 | Value cutValue() { |
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| 305 | Value value = 0; |
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| 306 | for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) { |
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| 307 | for (InEdgeIt e(*_graph, it); e != INVALID; ++e) { |
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| 308 | if (!(*_wake)[_graph->source(e)]){ |
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| 309 | value += (*_capacity)[e]; |
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| 310 | } |
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| 311 | } |
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| 312 | } |
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| 313 | return value; |
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| 314 | } |
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| 315 | |
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| 316 | public: |
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| 317 | |
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| 318 | /// \brief Initializes the internal data structures. |
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| 319 | /// |
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| 320 | /// Initializes the internal data structures. It creates |
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| 321 | /// the maps, residual graph adaptor and some bucket structures |
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| 322 | /// for the algorithm. |
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| 323 | void init() { |
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| 324 | init(NodeIt(*_graph)); |
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| 325 | } |
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| 326 | |
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| 327 | /// \brief Initializes the internal data structures. |
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| 328 | /// |
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| 329 | /// Initializes the internal data structures. It creates |
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| 330 | /// the maps, residual graph adaptor and some bucket structures |
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| 331 | /// for the algorithm. The \c source node is used as the push-relabel |
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| 332 | /// algorithm's source. |
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| 333 | void init(const Node& source) { |
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| 334 | _source = source; |
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| 335 | _node_num = countNodes(*_graph); |
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| 336 | |
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| 337 | _dormant.resize(_node_num); |
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| 338 | _level_size.resize(_node_num, 0); |
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| 339 | _active_nodes.resize(_node_num); |
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| 340 | |
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| 341 | if (!_preflow) { |
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| 342 | _preflow = new FlowMap(*_graph); |
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| 343 | } |
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| 344 | if (!_wake) { |
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| 345 | _wake = new WakeMap(*_graph); |
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| 346 | } |
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| 347 | if (!_dist) { |
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| 348 | _dist = new DistMap(*_graph); |
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| 349 | } |
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| 350 | if (!_excess) { |
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| 351 | _excess = new ExcessMap(*_graph); |
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| 352 | } |
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| 353 | if (!_source_set) { |
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| 354 | _source_set = new SourceSetMap(*_graph); |
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| 355 | } |
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| 356 | if (!_current_arc) { |
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| 357 | _current_arc = new CurrentArcMap(*_graph); |
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| 358 | } |
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| 359 | if (!_min_cut_map) { |
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| 360 | _min_cut_map = new MinCutMap(*_graph); |
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| 361 | } |
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| 362 | if (!_res_graph) { |
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| 363 | _res_graph = new ResGraph(*_graph, *_capacity, *_preflow); |
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| 364 | } |
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| 365 | |
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| 366 | _min_cut = std::numeric_limits<Value>::max(); |
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| 367 | } |
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| 368 | |
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| 369 | |
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| 370 | /// \brief Calculates the minimum cut with the \c source node |
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| 371 | /// in the first partition. |
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| 372 | /// |
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| 373 | /// Calculates the minimum cut with the \c source node |
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| 374 | /// in the first partition. |
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| 375 | void calculateOut() { |
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| 376 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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| 377 | if (it != _source) { |
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| 378 | calculateOut(it); |
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| 379 | return; |
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| 380 | } |
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| 381 | } |
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| 382 | } |
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| 383 | |
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| 384 | /// \brief Calculates the minimum cut with the \c source node |
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| 385 | /// in the first partition. |
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| 386 | /// |
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| 387 | /// Calculates the minimum cut with the \c source node |
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| 388 | /// in the first partition. The \c target is the initial target |
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| 389 | /// for the push-relabel algorithm. |
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| 390 | void calculateOut(const Node& target) { |
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| 391 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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| 392 | (*_wake)[it] = true; |
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| 393 | (*_dist)[it] = 1; |
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| 394 | (*_excess)[it] = 0; |
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| 395 | (*_source_set)[it] = false; |
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| 396 | |
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| 397 | _res_graph->firstOut((*_current_arc)[it], it); |
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| 398 | } |
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| 399 | |
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| 400 | _target = target; |
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| 401 | (*_dist)[target] = 0; |
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| 402 | |
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| 403 | for (ResOutEdgeIt it(*_res_graph, _source); it != INVALID; ++it) { |
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| 404 | push(it, _res_graph->rescap(it)); |
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| 405 | } |
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| 406 | |
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| 407 | _dormant[0].push_front(_source); |
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| 408 | (*_source_set)[_source] = true; |
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| 409 | _dormant_max = 0; |
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| 410 | (*_wake)[_source]=false; |
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| 411 | |
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| 412 | _level_size[0] = 1; |
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| 413 | _level_size[1] = _node_num - 1; |
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| 414 | |
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| 415 | do { |
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| 416 | Node n; |
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| 417 | while ((n = findActiveNode()) != INVALID) { |
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| 418 | ResEdge e; |
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| 419 | while (_tolerance.positive((*_excess)[n]) && |
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| 420 | (e = findAdmissibleEdge(n)) != INVALID){ |
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| 421 | Value delta; |
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| 422 | if ((*_excess)[n] < _res_graph->rescap(e)) { |
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| 423 | delta = (*_excess)[n]; |
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| 424 | } else { |
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| 425 | delta = _res_graph->rescap(e); |
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| 426 | _res_graph->nextOut((*_current_arc)[n]); |
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| 427 | } |
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| 428 | if (!_tolerance.positive(delta)) continue; |
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| 429 | _res_graph->augment(e, delta); |
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| 430 | (*_excess)[_res_graph->source(e)] -= delta; |
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| 431 | Node a = _res_graph->target(e); |
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| 432 | if (!_tolerance.positive((*_excess)[a]) && a != _target) { |
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| 433 | _active_nodes[(*_dist)[a]].push_front(a); |
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| 434 | } |
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| 435 | (*_excess)[a] += delta; |
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| 436 | } |
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| 437 | if (_tolerance.positive((*_excess)[n])) { |
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| 438 | relabel(n); |
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| 439 | } |
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| 440 | } |
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| 441 | |
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| 442 | Value current_value = cutValue(); |
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| 443 | if (_min_cut > current_value){ |
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| 444 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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| 445 | _min_cut_map->set(it, !(*_wake)[it]); |
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| 446 | } |
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| 447 | |
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| 448 | _min_cut = current_value; |
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| 449 | } |
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| 450 | |
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| 451 | } while (selectNewSink()); |
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| 452 | } |
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| 453 | |
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| 454 | void calculateIn() { |
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| 455 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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| 456 | if (it != _source) { |
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| 457 | calculateIn(it); |
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| 458 | return; |
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| 459 | } |
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| 460 | } |
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| 461 | } |
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| 462 | |
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| 463 | void run() { |
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| 464 | init(); |
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| 465 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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| 466 | if (it != _source) { |
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| 467 | startOut(it); |
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| 468 | // startIn(it); |
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| 469 | return; |
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| 470 | } |
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| 471 | } |
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| 472 | } |
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| 473 | |
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| 474 | void run(const Node& s) { |
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| 475 | init(s); |
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| 476 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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| 477 | if (it != _source) { |
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| 478 | startOut(it); |
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| 479 | // startIn(it); |
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| 480 | return; |
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| 481 | } |
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| 482 | } |
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| 483 | } |
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| 484 | |
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| 485 | void run(const Node& s, const Node& t) { |
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| 486 | init(s); |
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| 487 | startOut(t); |
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| 488 | startIn(t); |
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| 489 | } |
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| 490 | |
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| 491 | /// \brief Returns the value of the minimum value cut with node \c |
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| 492 | /// source on the source side. |
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| 493 | /// |
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| 494 | /// Returns the value of the minimum value cut with node \c source |
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| 495 | /// on the source side. This function can be called after running |
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| 496 | /// \ref findMinCut. |
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| 497 | Value minCut() const { |
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| 498 | return _min_cut; |
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| 499 | } |
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| 500 | |
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| 501 | |
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| 502 | /// \brief Returns a minimum value cut. |
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| 503 | /// |
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| 504 | /// Sets \c nodeMap to the characteristic vector of a minimum |
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| 505 | /// value cut with node \c source on the source side. This |
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| 506 | /// function can be called after running \ref findMinCut. |
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| 507 | /// \pre nodeMap should be a bool-valued node-map. |
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| 508 | template <typename NodeMap> |
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| 509 | Value minCut(NodeMap& nodeMap) const { |
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| 510 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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| 511 | nodeMap.set(it, (*_min_cut_map)[it]); |
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| 512 | } |
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| 513 | return minCut(); |
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| 514 | } |
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| 515 | |
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| 516 | }; //class HaoOrlin |
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| 517 | |
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| 518 | |
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| 519 | } //namespace lemon |
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| 520 | |
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| 521 | #endif //LEMON_HAO_ORLIN_H |
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