[543] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2008 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_GOMORY_HU_TREE_H |
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| 20 | #define LEMON_GOMORY_HU_TREE_H |
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| 21 | |
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| 22 | #include <limits> |
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| 23 | |
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[544] | 24 | #include <lemon/core.h> |
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[543] | 25 | #include <lemon/preflow.h> |
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| 26 | #include <lemon/concept_check.h> |
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| 27 | #include <lemon/concepts/maps.h> |
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| 28 | |
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| 29 | /// \ingroup min_cut |
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| 30 | /// \file |
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| 31 | /// \brief Gomory-Hu cut tree in graphs. |
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| 32 | |
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| 33 | namespace lemon { |
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| 34 | |
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| 35 | /// \ingroup min_cut |
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| 36 | /// |
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| 37 | /// \brief Gomory-Hu cut tree algorithm |
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| 38 | /// |
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[546] | 39 | /// The Gomory-Hu tree is a tree on the node set of a given graph, but it |
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| 40 | /// may contain edges which are not in the original graph. It has the |
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[544] | 41 | /// property that the minimum capacity edge of the path between two nodes |
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[546] | 42 | /// in this tree has the same weight as the minimum cut in the graph |
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[544] | 43 | /// between these nodes. Moreover the components obtained by removing |
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| 44 | /// this edge from the tree determine the corresponding minimum cut. |
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| 45 | /// Therefore once this tree is computed, the minimum cut between any pair |
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| 46 | /// of nodes can easily be obtained. |
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[543] | 47 | /// |
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[544] | 48 | /// The algorithm calculates \e n-1 distinct minimum cuts (currently with |
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[596] | 49 | /// the \ref Preflow algorithm), thus it has \f$O(n^3\sqrt{e})\f$ overall |
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| 50 | /// time complexity. It calculates a rooted Gomory-Hu tree. |
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| 51 | /// The structure of the tree and the edge weights can be |
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| 52 | /// obtained using \c predNode(), \c predValue() and \c rootDist(). |
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| 53 | /// The functions \c minCutMap() and \c minCutValue() calculate |
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[546] | 54 | /// the minimum cut and the minimum cut value between any two nodes |
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| 55 | /// in the graph. You can also list (iterate on) the nodes and the |
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| 56 | /// edges of the cuts using \c MinCutNodeIt and \c MinCutEdgeIt. |
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[544] | 57 | /// |
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[546] | 58 | /// \tparam GR The type of the undirected graph the algorithm runs on. |
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[596] | 59 | /// \tparam CAP The type of the edge map containing the capacities. |
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| 60 | /// The default map type is \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
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[546] | 61 | #ifdef DOXYGEN |
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[544] | 62 | template <typename GR, |
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[546] | 63 | typename CAP> |
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| 64 | #else |
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| 65 | template <typename GR, |
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| 66 | typename CAP = typename GR::template EdgeMap<int> > |
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| 67 | #endif |
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[545] | 68 | class GomoryHu { |
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[543] | 69 | public: |
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| 70 | |
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[596] | 71 | /// The graph type of the algorithm |
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[544] | 72 | typedef GR Graph; |
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[596] | 73 | /// The capacity map type of the algorithm |
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[544] | 74 | typedef CAP Capacity; |
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[543] | 75 | /// The value type of capacities |
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| 76 | typedef typename Capacity::Value Value; |
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| 77 | |
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| 78 | private: |
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| 79 | |
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| 80 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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| 81 | |
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| 82 | const Graph& _graph; |
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| 83 | const Capacity& _capacity; |
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| 84 | |
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| 85 | Node _root; |
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| 86 | typename Graph::template NodeMap<Node>* _pred; |
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| 87 | typename Graph::template NodeMap<Value>* _weight; |
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| 88 | typename Graph::template NodeMap<int>* _order; |
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| 89 | |
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| 90 | void createStructures() { |
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| 91 | if (!_pred) { |
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| 92 | _pred = new typename Graph::template NodeMap<Node>(_graph); |
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| 93 | } |
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| 94 | if (!_weight) { |
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| 95 | _weight = new typename Graph::template NodeMap<Value>(_graph); |
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| 96 | } |
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| 97 | if (!_order) { |
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| 98 | _order = new typename Graph::template NodeMap<int>(_graph); |
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| 99 | } |
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| 100 | } |
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| 101 | |
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| 102 | void destroyStructures() { |
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| 103 | if (_pred) { |
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| 104 | delete _pred; |
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| 105 | } |
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| 106 | if (_weight) { |
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| 107 | delete _weight; |
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| 108 | } |
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| 109 | if (_order) { |
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| 110 | delete _order; |
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| 111 | } |
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| 112 | } |
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| 113 | |
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| 114 | public: |
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| 115 | |
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| 116 | /// \brief Constructor |
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| 117 | /// |
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[596] | 118 | /// Constructor. |
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[546] | 119 | /// \param graph The undirected graph the algorithm runs on. |
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| 120 | /// \param capacity The edge capacity map. |
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[545] | 121 | GomoryHu(const Graph& graph, const Capacity& capacity) |
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[543] | 122 | : _graph(graph), _capacity(capacity), |
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| 123 | _pred(0), _weight(0), _order(0) |
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| 124 | { |
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| 125 | checkConcept<concepts::ReadMap<Edge, Value>, Capacity>(); |
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| 126 | } |
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| 127 | |
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| 128 | |
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| 129 | /// \brief Destructor |
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| 130 | /// |
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[596] | 131 | /// Destructor. |
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[545] | 132 | ~GomoryHu() { |
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[543] | 133 | destroyStructures(); |
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| 134 | } |
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| 135 | |
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[546] | 136 | private: |
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| 137 | |
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| 138 | // Initialize the internal data structures |
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[543] | 139 | void init() { |
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| 140 | createStructures(); |
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| 141 | |
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| 142 | _root = NodeIt(_graph); |
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| 143 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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[581] | 144 | (*_pred)[n] = _root; |
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| 145 | (*_order)[n] = -1; |
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[543] | 146 | } |
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[581] | 147 | (*_pred)[_root] = INVALID; |
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| 148 | (*_weight)[_root] = std::numeric_limits<Value>::max(); |
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[543] | 149 | } |
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| 150 | |
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| 151 | |
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[546] | 152 | // Start the algorithm |
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[543] | 153 | void start() { |
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| 154 | Preflow<Graph, Capacity> fa(_graph, _capacity, _root, INVALID); |
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| 155 | |
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| 156 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 157 | if (n == _root) continue; |
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| 158 | |
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| 159 | Node pn = (*_pred)[n]; |
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| 160 | fa.source(n); |
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| 161 | fa.target(pn); |
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| 162 | |
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| 163 | fa.runMinCut(); |
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| 164 | |
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[581] | 165 | (*_weight)[n] = fa.flowValue(); |
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[543] | 166 | |
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| 167 | for (NodeIt nn(_graph); nn != INVALID; ++nn) { |
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| 168 | if (nn != n && fa.minCut(nn) && (*_pred)[nn] == pn) { |
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[581] | 169 | (*_pred)[nn] = n; |
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[543] | 170 | } |
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| 171 | } |
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| 172 | if ((*_pred)[pn] != INVALID && fa.minCut((*_pred)[pn])) { |
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[581] | 173 | (*_pred)[n] = (*_pred)[pn]; |
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| 174 | (*_pred)[pn] = n; |
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| 175 | (*_weight)[n] = (*_weight)[pn]; |
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| 176 | (*_weight)[pn] = fa.flowValue(); |
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[543] | 177 | } |
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| 178 | } |
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| 179 | |
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[581] | 180 | (*_order)[_root] = 0; |
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[543] | 181 | int index = 1; |
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| 182 | |
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| 183 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 184 | std::vector<Node> st; |
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| 185 | Node nn = n; |
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| 186 | while ((*_order)[nn] == -1) { |
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| 187 | st.push_back(nn); |
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| 188 | nn = (*_pred)[nn]; |
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| 189 | } |
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| 190 | while (!st.empty()) { |
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[581] | 191 | (*_order)[st.back()] = index++; |
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[543] | 192 | st.pop_back(); |
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| 193 | } |
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| 194 | } |
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| 195 | } |
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| 196 | |
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[546] | 197 | public: |
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| 198 | |
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[544] | 199 | ///\name Execution Control |
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| 200 | |
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| 201 | ///@{ |
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| 202 | |
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| 203 | /// \brief Run the Gomory-Hu algorithm. |
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[543] | 204 | /// |
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[544] | 205 | /// This function runs the Gomory-Hu algorithm. |
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[543] | 206 | void run() { |
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| 207 | init(); |
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| 208 | start(); |
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| 209 | } |
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[544] | 210 | |
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| 211 | /// @} |
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[543] | 212 | |
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[544] | 213 | ///\name Query Functions |
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| 214 | ///The results of the algorithm can be obtained using these |
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| 215 | ///functions.\n |
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[596] | 216 | ///\ref run() should be called before using them.\n |
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[546] | 217 | ///See also \ref MinCutNodeIt and \ref MinCutEdgeIt. |
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[544] | 218 | |
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| 219 | ///@{ |
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| 220 | |
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| 221 | /// \brief Return the predecessor node in the Gomory-Hu tree. |
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[543] | 222 | /// |
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[596] | 223 | /// This function returns the predecessor node of the given node |
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| 224 | /// in the Gomory-Hu tree. |
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| 225 | /// If \c node is the root of the tree, then it returns \c INVALID. |
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| 226 | /// |
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| 227 | /// \pre \ref run() must be called before using this function. |
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| 228 | Node predNode(const Node& node) const { |
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[543] | 229 | return (*_pred)[node]; |
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| 230 | } |
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| 231 | |
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[544] | 232 | /// \brief Return the weight of the predecessor edge in the |
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[543] | 233 | /// Gomory-Hu tree. |
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| 234 | /// |
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[596] | 235 | /// This function returns the weight of the predecessor edge of the |
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| 236 | /// given node in the Gomory-Hu tree. |
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| 237 | /// If \c node is the root of the tree, the result is undefined. |
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| 238 | /// |
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| 239 | /// \pre \ref run() must be called before using this function. |
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| 240 | Value predValue(const Node& node) const { |
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[543] | 241 | return (*_weight)[node]; |
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| 242 | } |
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| 243 | |
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[596] | 244 | /// \brief Return the distance from the root node in the Gomory-Hu tree. |
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| 245 | /// |
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| 246 | /// This function returns the distance of the given node from the root |
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| 247 | /// node in the Gomory-Hu tree. |
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| 248 | /// |
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| 249 | /// \pre \ref run() must be called before using this function. |
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| 250 | int rootDist(const Node& node) const { |
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| 251 | return (*_order)[node]; |
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| 252 | } |
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| 253 | |
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[544] | 254 | /// \brief Return the minimum cut value between two nodes |
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[543] | 255 | /// |
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[596] | 256 | /// This function returns the minimum cut value between the nodes |
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| 257 | /// \c s and \c t. |
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| 258 | /// It finds the nearest common ancestor of the given nodes in the |
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| 259 | /// Gomory-Hu tree and calculates the minimum weight edge on the |
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| 260 | /// paths to the ancestor. |
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| 261 | /// |
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| 262 | /// \pre \ref run() must be called before using this function. |
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[543] | 263 | Value minCutValue(const Node& s, const Node& t) const { |
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| 264 | Node sn = s, tn = t; |
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| 265 | Value value = std::numeric_limits<Value>::max(); |
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| 266 | |
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| 267 | while (sn != tn) { |
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| 268 | if ((*_order)[sn] < (*_order)[tn]) { |
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[544] | 269 | if ((*_weight)[tn] <= value) value = (*_weight)[tn]; |
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[543] | 270 | tn = (*_pred)[tn]; |
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| 271 | } else { |
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[544] | 272 | if ((*_weight)[sn] <= value) value = (*_weight)[sn]; |
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[543] | 273 | sn = (*_pred)[sn]; |
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| 274 | } |
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| 275 | } |
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| 276 | return value; |
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| 277 | } |
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| 278 | |
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[544] | 279 | /// \brief Return the minimum cut between two nodes |
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[543] | 280 | /// |
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[544] | 281 | /// This function returns the minimum cut between the nodes \c s and \c t |
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[546] | 282 | /// in the \c cutMap parameter by setting the nodes in the component of |
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| 283 | /// \c s to \c true and the other nodes to \c false. |
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[544] | 284 | /// |
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[596] | 285 | /// For higher level interfaces see MinCutNodeIt and MinCutEdgeIt. |
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| 286 | /// |
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| 287 | /// \param s The base node. |
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| 288 | /// \param t The node you want to separate from node \c s. |
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| 289 | /// \param cutMap The cut will be returned in this map. |
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| 290 | /// It must be a \c bool (or convertible) \ref concepts::ReadWriteMap |
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| 291 | /// "ReadWriteMap" on the graph nodes. |
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| 292 | /// |
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| 293 | /// \return The value of the minimum cut between \c s and \c t. |
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| 294 | /// |
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| 295 | /// \pre \ref run() must be called before using this function. |
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[543] | 296 | template <typename CutMap> |
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[786] | 297 | Value minCutMap(const Node& s, |
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[544] | 298 | const Node& t, |
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| 299 | CutMap& cutMap |
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| 300 | ) const { |
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[543] | 301 | Node sn = s, tn = t; |
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[544] | 302 | bool s_root=false; |
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[543] | 303 | Node rn = INVALID; |
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| 304 | Value value = std::numeric_limits<Value>::max(); |
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| 305 | |
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| 306 | while (sn != tn) { |
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| 307 | if ((*_order)[sn] < (*_order)[tn]) { |
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[544] | 308 | if ((*_weight)[tn] <= value) { |
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[543] | 309 | rn = tn; |
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[544] | 310 | s_root = false; |
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[543] | 311 | value = (*_weight)[tn]; |
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| 312 | } |
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| 313 | tn = (*_pred)[tn]; |
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| 314 | } else { |
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[544] | 315 | if ((*_weight)[sn] <= value) { |
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[543] | 316 | rn = sn; |
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[544] | 317 | s_root = true; |
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[543] | 318 | value = (*_weight)[sn]; |
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| 319 | } |
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| 320 | sn = (*_pred)[sn]; |
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| 321 | } |
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| 322 | } |
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| 323 | |
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| 324 | typename Graph::template NodeMap<bool> reached(_graph, false); |
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[581] | 325 | reached[_root] = true; |
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[544] | 326 | cutMap.set(_root, !s_root); |
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[581] | 327 | reached[rn] = true; |
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[544] | 328 | cutMap.set(rn, s_root); |
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[543] | 329 | |
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[544] | 330 | std::vector<Node> st; |
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[543] | 331 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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[544] | 332 | st.clear(); |
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| 333 | Node nn = n; |
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[543] | 334 | while (!reached[nn]) { |
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| 335 | st.push_back(nn); |
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| 336 | nn = (*_pred)[nn]; |
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| 337 | } |
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| 338 | while (!st.empty()) { |
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| 339 | cutMap.set(st.back(), cutMap[nn]); |
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| 340 | st.pop_back(); |
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| 341 | } |
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| 342 | } |
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| 343 | |
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| 344 | return value; |
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| 345 | } |
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| 346 | |
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[544] | 347 | ///@} |
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| 348 | |
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| 349 | friend class MinCutNodeIt; |
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| 350 | |
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| 351 | /// Iterate on the nodes of a minimum cut |
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| 352 | |
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| 353 | /// This iterator class lists the nodes of a minimum cut found by |
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[596] | 354 | /// GomoryHu. Before using it, you must allocate a GomoryHu class |
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[545] | 355 | /// and call its \ref GomoryHu::run() "run()" method. |
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[544] | 356 | /// |
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| 357 | /// This example counts the nodes in the minimum cut separating \c s from |
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| 358 | /// \c t. |
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| 359 | /// \code |
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[713] | 360 | /// GomoryHu<Graph> gom(g, capacities); |
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[544] | 361 | /// gom.run(); |
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[546] | 362 | /// int cnt=0; |
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[713] | 363 | /// for(GomoryHu<Graph>::MinCutNodeIt n(gom,s,t); n!=INVALID; ++n) ++cnt; |
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[544] | 364 | /// \endcode |
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| 365 | class MinCutNodeIt |
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| 366 | { |
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| 367 | bool _side; |
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| 368 | typename Graph::NodeIt _node_it; |
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| 369 | typename Graph::template NodeMap<bool> _cut; |
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| 370 | public: |
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| 371 | /// Constructor |
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| 372 | |
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[546] | 373 | /// Constructor. |
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[544] | 374 | /// |
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[545] | 375 | MinCutNodeIt(GomoryHu const &gomory, |
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| 376 | ///< The GomoryHu class. You must call its |
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[544] | 377 | /// run() method |
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[546] | 378 | /// before initializing this iterator. |
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| 379 | const Node& s, ///< The base node. |
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[544] | 380 | const Node& t, |
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[546] | 381 | ///< The node you want to separate from node \c s. |
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[544] | 382 | bool side=true |
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| 383 | ///< If it is \c true (default) then the iterator lists |
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| 384 | /// the nodes of the component containing \c s, |
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| 385 | /// otherwise it lists the other component. |
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| 386 | /// \note As the minimum cut is not always unique, |
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| 387 | /// \code |
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| 388 | /// MinCutNodeIt(gomory, s, t, true); |
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| 389 | /// \endcode |
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| 390 | /// and |
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| 391 | /// \code |
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| 392 | /// MinCutNodeIt(gomory, t, s, false); |
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| 393 | /// \endcode |
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| 394 | /// does not necessarily give the same set of nodes. |
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[786] | 395 | /// However, it is ensured that |
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[544] | 396 | /// \code |
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| 397 | /// MinCutNodeIt(gomory, s, t, true); |
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| 398 | /// \endcode |
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| 399 | /// and |
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| 400 | /// \code |
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| 401 | /// MinCutNodeIt(gomory, s, t, false); |
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| 402 | /// \endcode |
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| 403 | /// together list each node exactly once. |
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| 404 | ) |
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| 405 | : _side(side), _cut(gomory._graph) |
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| 406 | { |
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| 407 | gomory.minCutMap(s,t,_cut); |
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| 408 | for(_node_it=typename Graph::NodeIt(gomory._graph); |
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| 409 | _node_it!=INVALID && _cut[_node_it]!=_side; |
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| 410 | ++_node_it) {} |
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| 411 | } |
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[546] | 412 | /// Conversion to \c Node |
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[544] | 413 | |
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[546] | 414 | /// Conversion to \c Node. |
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[544] | 415 | /// |
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| 416 | operator typename Graph::Node() const |
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| 417 | { |
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| 418 | return _node_it; |
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| 419 | } |
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| 420 | bool operator==(Invalid) { return _node_it==INVALID; } |
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| 421 | bool operator!=(Invalid) { return _node_it!=INVALID; } |
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| 422 | /// Next node |
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| 423 | |
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[546] | 424 | /// Next node. |
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[544] | 425 | /// |
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| 426 | MinCutNodeIt &operator++() |
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| 427 | { |
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| 428 | for(++_node_it;_node_it!=INVALID&&_cut[_node_it]!=_side;++_node_it) {} |
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| 429 | return *this; |
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| 430 | } |
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| 431 | /// Postfix incrementation |
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| 432 | |
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[546] | 433 | /// Postfix incrementation. |
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[544] | 434 | /// |
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| 435 | /// \warning This incrementation |
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[546] | 436 | /// returns a \c Node, not a \c MinCutNodeIt, as one may |
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[544] | 437 | /// expect. |
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| 438 | typename Graph::Node operator++(int) |
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| 439 | { |
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| 440 | typename Graph::Node n=*this; |
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| 441 | ++(*this); |
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| 442 | return n; |
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| 443 | } |
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| 444 | }; |
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| 445 | |
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| 446 | friend class MinCutEdgeIt; |
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| 447 | |
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| 448 | /// Iterate on the edges of a minimum cut |
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| 449 | |
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| 450 | /// This iterator class lists the edges of a minimum cut found by |
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[596] | 451 | /// GomoryHu. Before using it, you must allocate a GomoryHu class |
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[545] | 452 | /// and call its \ref GomoryHu::run() "run()" method. |
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[544] | 453 | /// |
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| 454 | /// This example computes the value of the minimum cut separating \c s from |
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| 455 | /// \c t. |
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| 456 | /// \code |
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[713] | 457 | /// GomoryHu<Graph> gom(g, capacities); |
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[544] | 458 | /// gom.run(); |
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| 459 | /// int value=0; |
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[713] | 460 | /// for(GomoryHu<Graph>::MinCutEdgeIt e(gom,s,t); e!=INVALID; ++e) |
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[544] | 461 | /// value+=capacities[e]; |
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| 462 | /// \endcode |
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[596] | 463 | /// The result will be the same as the value returned by |
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| 464 | /// \ref GomoryHu::minCutValue() "gom.minCutValue(s,t)". |
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[544] | 465 | class MinCutEdgeIt |
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| 466 | { |
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| 467 | bool _side; |
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| 468 | const Graph &_graph; |
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| 469 | typename Graph::NodeIt _node_it; |
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| 470 | typename Graph::OutArcIt _arc_it; |
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| 471 | typename Graph::template NodeMap<bool> _cut; |
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| 472 | void step() |
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| 473 | { |
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| 474 | ++_arc_it; |
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| 475 | while(_node_it!=INVALID && _arc_it==INVALID) |
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| 476 | { |
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| 477 | for(++_node_it;_node_it!=INVALID&&!_cut[_node_it];++_node_it) {} |
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| 478 | if(_node_it!=INVALID) |
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| 479 | _arc_it=typename Graph::OutArcIt(_graph,_node_it); |
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| 480 | } |
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| 481 | } |
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| 482 | |
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| 483 | public: |
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[596] | 484 | /// Constructor |
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| 485 | |
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| 486 | /// Constructor. |
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| 487 | /// |
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[545] | 488 | MinCutEdgeIt(GomoryHu const &gomory, |
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| 489 | ///< The GomoryHu class. You must call its |
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[544] | 490 | /// run() method |
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[546] | 491 | /// before initializing this iterator. |
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| 492 | const Node& s, ///< The base node. |
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[544] | 493 | const Node& t, |
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[546] | 494 | ///< The node you want to separate from node \c s. |
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[544] | 495 | bool side=true |
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| 496 | ///< If it is \c true (default) then the listed arcs |
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| 497 | /// will be oriented from the |
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[596] | 498 | /// nodes of the component containing \c s, |
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[544] | 499 | /// otherwise they will be oriented in the opposite |
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| 500 | /// direction. |
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| 501 | ) |
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| 502 | : _graph(gomory._graph), _cut(_graph) |
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| 503 | { |
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| 504 | gomory.minCutMap(s,t,_cut); |
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| 505 | if(!side) |
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| 506 | for(typename Graph::NodeIt n(_graph);n!=INVALID;++n) |
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| 507 | _cut[n]=!_cut[n]; |
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| 508 | |
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| 509 | for(_node_it=typename Graph::NodeIt(_graph); |
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| 510 | _node_it!=INVALID && !_cut[_node_it]; |
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| 511 | ++_node_it) {} |
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| 512 | _arc_it = _node_it!=INVALID ? |
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| 513 | typename Graph::OutArcIt(_graph,_node_it) : INVALID; |
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| 514 | while(_node_it!=INVALID && _arc_it == INVALID) |
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| 515 | { |
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| 516 | for(++_node_it; _node_it!=INVALID&&!_cut[_node_it]; ++_node_it) {} |
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| 517 | if(_node_it!=INVALID) |
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| 518 | _arc_it= typename Graph::OutArcIt(_graph,_node_it); |
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| 519 | } |
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| 520 | while(_arc_it!=INVALID && _cut[_graph.target(_arc_it)]) step(); |
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| 521 | } |
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[546] | 522 | /// Conversion to \c Arc |
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[544] | 523 | |
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[546] | 524 | /// Conversion to \c Arc. |
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[544] | 525 | /// |
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| 526 | operator typename Graph::Arc() const |
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| 527 | { |
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| 528 | return _arc_it; |
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| 529 | } |
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[546] | 530 | /// Conversion to \c Edge |
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[544] | 531 | |
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[546] | 532 | /// Conversion to \c Edge. |
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[544] | 533 | /// |
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| 534 | operator typename Graph::Edge() const |
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| 535 | { |
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| 536 | return _arc_it; |
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| 537 | } |
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| 538 | bool operator==(Invalid) { return _node_it==INVALID; } |
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| 539 | bool operator!=(Invalid) { return _node_it!=INVALID; } |
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| 540 | /// Next edge |
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| 541 | |
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[546] | 542 | /// Next edge. |
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[544] | 543 | /// |
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| 544 | MinCutEdgeIt &operator++() |
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| 545 | { |
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| 546 | step(); |
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| 547 | while(_arc_it!=INVALID && _cut[_graph.target(_arc_it)]) step(); |
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| 548 | return *this; |
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| 549 | } |
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| 550 | /// Postfix incrementation |
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| 551 | |
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[546] | 552 | /// Postfix incrementation. |
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[544] | 553 | /// |
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| 554 | /// \warning This incrementation |
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[546] | 555 | /// returns an \c Arc, not a \c MinCutEdgeIt, as one may expect. |
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[544] | 556 | typename Graph::Arc operator++(int) |
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| 557 | { |
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| 558 | typename Graph::Arc e=*this; |
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| 559 | ++(*this); |
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| 560 | return e; |
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| 561 | } |
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| 562 | }; |
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| 563 | |
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[543] | 564 | }; |
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| 565 | |
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| 566 | } |
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| 567 | |
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| 568 | #endif |
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