[590] | 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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[591] | 24 | #include <lemon/core.h> |
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[590] | 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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[593] | 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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[591] | 41 | /// property that the minimum capacity edge of the path between two nodes |
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[593] | 42 | /// in this tree has the same weight as the minimum cut in the graph |
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[591] | 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 | /// |
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| 46 | /// Therefore once this tree is computed, the minimum cut between any pair |
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| 47 | /// of nodes can easily be obtained. |
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[590] | 48 | /// |
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[591] | 49 | /// The algorithm calculates \e n-1 distinct minimum cuts (currently with |
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| 50 | /// the \ref Preflow algorithm), therefore the algorithm has |
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[590] | 51 | /// \f$(O(n^3\sqrt{e})\f$ overall time complexity. It calculates a |
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[591] | 52 | /// rooted Gomory-Hu tree, its structure and the weights can be obtained |
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| 53 | /// by \c predNode(), \c predValue() and \c rootDist(). |
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| 54 | /// |
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| 55 | /// The members \c minCutMap() and \c minCutValue() calculate |
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[593] | 56 | /// the minimum cut and the minimum cut value between any two nodes |
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| 57 | /// in the graph. You can also list (iterate on) the nodes and the |
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| 58 | /// edges of the cuts using \c MinCutNodeIt and \c MinCutEdgeIt. |
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[591] | 59 | /// |
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[593] | 60 | /// \tparam GR The type of the undirected graph the algorithm runs on. |
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| 61 | /// \tparam CAP The type of the edge map describing the edge capacities. |
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| 62 | /// It is \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>" by default. |
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| 63 | #ifdef DOXYGEN |
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[591] | 64 | template <typename GR, |
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[593] | 65 | typename CAP> |
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| 66 | #else |
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| 67 | template <typename GR, |
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| 68 | typename CAP = typename GR::template EdgeMap<int> > |
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| 69 | #endif |
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[592] | 70 | class GomoryHu { |
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[590] | 71 | public: |
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| 72 | |
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| 73 | /// The graph type |
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[591] | 74 | typedef GR Graph; |
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[593] | 75 | /// The type of the edge capacity map |
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[591] | 76 | typedef CAP Capacity; |
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[590] | 77 | /// The value type of capacities |
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| 78 | typedef typename Capacity::Value Value; |
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| 79 | |
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| 80 | private: |
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| 81 | |
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| 82 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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| 83 | |
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| 84 | const Graph& _graph; |
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| 85 | const Capacity& _capacity; |
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| 86 | |
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| 87 | Node _root; |
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| 88 | typename Graph::template NodeMap<Node>* _pred; |
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| 89 | typename Graph::template NodeMap<Value>* _weight; |
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| 90 | typename Graph::template NodeMap<int>* _order; |
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| 91 | |
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| 92 | void createStructures() { |
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| 93 | if (!_pred) { |
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| 94 | _pred = new typename Graph::template NodeMap<Node>(_graph); |
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| 95 | } |
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| 96 | if (!_weight) { |
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| 97 | _weight = new typename Graph::template NodeMap<Value>(_graph); |
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| 98 | } |
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| 99 | if (!_order) { |
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| 100 | _order = new typename Graph::template NodeMap<int>(_graph); |
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| 101 | } |
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| 102 | } |
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| 103 | |
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| 104 | void destroyStructures() { |
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| 105 | if (_pred) { |
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| 106 | delete _pred; |
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| 107 | } |
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| 108 | if (_weight) { |
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| 109 | delete _weight; |
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| 110 | } |
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| 111 | if (_order) { |
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| 112 | delete _order; |
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| 113 | } |
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| 114 | } |
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| 115 | |
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| 116 | public: |
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| 117 | |
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| 118 | /// \brief Constructor |
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| 119 | /// |
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| 120 | /// Constructor |
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[593] | 121 | /// \param graph The undirected graph the algorithm runs on. |
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| 122 | /// \param capacity The edge capacity map. |
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[592] | 123 | GomoryHu(const Graph& graph, const Capacity& capacity) |
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[590] | 124 | : _graph(graph), _capacity(capacity), |
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| 125 | _pred(0), _weight(0), _order(0) |
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| 126 | { |
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| 127 | checkConcept<concepts::ReadMap<Edge, Value>, Capacity>(); |
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| 128 | } |
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| 129 | |
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| 130 | |
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| 131 | /// \brief Destructor |
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| 132 | /// |
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| 133 | /// Destructor |
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[592] | 134 | ~GomoryHu() { |
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[590] | 135 | destroyStructures(); |
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| 136 | } |
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| 137 | |
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[593] | 138 | private: |
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| 139 | |
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| 140 | // Initialize the internal data structures |
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[590] | 141 | void init() { |
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| 142 | createStructures(); |
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| 143 | |
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| 144 | _root = NodeIt(_graph); |
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| 145 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 146 | _pred->set(n, _root); |
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| 147 | _order->set(n, -1); |
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| 148 | } |
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| 149 | _pred->set(_root, INVALID); |
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| 150 | _weight->set(_root, std::numeric_limits<Value>::max()); |
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| 151 | } |
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| 152 | |
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| 153 | |
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[593] | 154 | // Start the algorithm |
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[590] | 155 | void start() { |
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| 156 | Preflow<Graph, Capacity> fa(_graph, _capacity, _root, INVALID); |
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| 157 | |
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| 158 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 159 | if (n == _root) continue; |
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| 160 | |
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| 161 | Node pn = (*_pred)[n]; |
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| 162 | fa.source(n); |
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| 163 | fa.target(pn); |
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| 164 | |
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| 165 | fa.runMinCut(); |
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| 166 | |
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| 167 | _weight->set(n, fa.flowValue()); |
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| 168 | |
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| 169 | for (NodeIt nn(_graph); nn != INVALID; ++nn) { |
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| 170 | if (nn != n && fa.minCut(nn) && (*_pred)[nn] == pn) { |
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| 171 | _pred->set(nn, n); |
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| 172 | } |
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| 173 | } |
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| 174 | if ((*_pred)[pn] != INVALID && fa.minCut((*_pred)[pn])) { |
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| 175 | _pred->set(n, (*_pred)[pn]); |
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| 176 | _pred->set(pn, n); |
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| 177 | _weight->set(n, (*_weight)[pn]); |
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| 178 | _weight->set(pn, fa.flowValue()); |
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| 179 | } |
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| 180 | } |
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| 181 | |
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| 182 | _order->set(_root, 0); |
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| 183 | int index = 1; |
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| 184 | |
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| 185 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 186 | std::vector<Node> st; |
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| 187 | Node nn = n; |
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| 188 | while ((*_order)[nn] == -1) { |
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| 189 | st.push_back(nn); |
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| 190 | nn = (*_pred)[nn]; |
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| 191 | } |
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| 192 | while (!st.empty()) { |
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| 193 | _order->set(st.back(), index++); |
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| 194 | st.pop_back(); |
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| 195 | } |
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| 196 | } |
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| 197 | } |
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| 198 | |
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[593] | 199 | public: |
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| 200 | |
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[591] | 201 | ///\name Execution Control |
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| 202 | |
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| 203 | ///@{ |
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| 204 | |
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| 205 | /// \brief Run the Gomory-Hu algorithm. |
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[590] | 206 | /// |
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[591] | 207 | /// This function runs the Gomory-Hu algorithm. |
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[590] | 208 | void run() { |
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| 209 | init(); |
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| 210 | start(); |
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| 211 | } |
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[591] | 212 | |
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| 213 | /// @} |
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[590] | 214 | |
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[591] | 215 | ///\name Query Functions |
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| 216 | ///The results of the algorithm can be obtained using these |
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| 217 | ///functions.\n |
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[593] | 218 | ///\ref run() "run()" should be called before using them.\n |
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| 219 | ///See also \ref MinCutNodeIt and \ref MinCutEdgeIt. |
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[591] | 220 | |
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| 221 | ///@{ |
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| 222 | |
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| 223 | /// \brief Return the predecessor node in the Gomory-Hu tree. |
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[590] | 224 | /// |
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[591] | 225 | /// This function returns the predecessor node in the Gomory-Hu tree. |
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| 226 | /// If the node is |
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[590] | 227 | /// the root of the Gomory-Hu tree, then it returns \c INVALID. |
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| 228 | Node predNode(const Node& node) { |
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| 229 | return (*_pred)[node]; |
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| 230 | } |
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| 231 | |
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[591] | 232 | /// \brief Return the distance from the root node in the Gomory-Hu tree. |
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| 233 | /// |
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| 234 | /// This function returns the distance of \c node from the root node |
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| 235 | /// in the Gomory-Hu tree. |
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| 236 | int rootDist(const Node& node) { |
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| 237 | return (*_order)[node]; |
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| 238 | } |
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| 239 | |
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| 240 | /// \brief Return the weight of the predecessor edge in the |
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[590] | 241 | /// Gomory-Hu tree. |
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| 242 | /// |
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[591] | 243 | /// This function returns the weight of the predecessor edge in the |
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| 244 | /// Gomory-Hu tree. If the node is the root, the result is undefined. |
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[590] | 245 | Value predValue(const Node& node) { |
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| 246 | return (*_weight)[node]; |
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| 247 | } |
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| 248 | |
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[591] | 249 | /// \brief Return the minimum cut value between two nodes |
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[590] | 250 | /// |
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[591] | 251 | /// This function returns the minimum cut value between two nodes. The |
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[590] | 252 | /// algorithm finds the nearest common ancestor in the Gomory-Hu |
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[593] | 253 | /// tree and calculates the minimum weight edge on the paths to |
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[590] | 254 | /// the ancestor. |
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| 255 | Value minCutValue(const Node& s, const Node& t) const { |
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| 256 | Node sn = s, tn = t; |
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| 257 | Value value = std::numeric_limits<Value>::max(); |
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| 258 | |
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| 259 | while (sn != tn) { |
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| 260 | if ((*_order)[sn] < (*_order)[tn]) { |
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[591] | 261 | if ((*_weight)[tn] <= value) value = (*_weight)[tn]; |
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[590] | 262 | tn = (*_pred)[tn]; |
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| 263 | } else { |
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[591] | 264 | if ((*_weight)[sn] <= value) value = (*_weight)[sn]; |
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[590] | 265 | sn = (*_pred)[sn]; |
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| 266 | } |
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| 267 | } |
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| 268 | return value; |
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| 269 | } |
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| 270 | |
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[591] | 271 | /// \brief Return the minimum cut between two nodes |
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[590] | 272 | /// |
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[591] | 273 | /// This function returns the minimum cut between the nodes \c s and \c t |
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[593] | 274 | /// in the \c cutMap parameter by setting the nodes in the component of |
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| 275 | /// \c s to \c true and the other nodes to \c false. |
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[591] | 276 | /// |
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[593] | 277 | /// For higher level interfaces, see MinCutNodeIt and MinCutEdgeIt. |
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[590] | 278 | template <typename CutMap> |
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[593] | 279 | Value minCutMap(const Node& s, ///< The base node. |
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[591] | 280 | const Node& t, |
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[593] | 281 | ///< The node you want to separate from node \c s. |
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[591] | 282 | CutMap& cutMap |
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[593] | 283 | ///< The cut will be returned in this map. |
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| 284 | /// It must be a \c bool (or convertible) |
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| 285 | /// \ref concepts::ReadWriteMap "ReadWriteMap" |
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| 286 | /// on the graph nodes. |
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[591] | 287 | ) const { |
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[590] | 288 | Node sn = s, tn = t; |
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[591] | 289 | bool s_root=false; |
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[590] | 290 | Node rn = INVALID; |
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| 291 | Value value = std::numeric_limits<Value>::max(); |
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| 292 | |
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| 293 | while (sn != tn) { |
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| 294 | if ((*_order)[sn] < (*_order)[tn]) { |
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[591] | 295 | if ((*_weight)[tn] <= value) { |
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[590] | 296 | rn = tn; |
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[591] | 297 | s_root = false; |
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[590] | 298 | value = (*_weight)[tn]; |
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| 299 | } |
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| 300 | tn = (*_pred)[tn]; |
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| 301 | } else { |
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[591] | 302 | if ((*_weight)[sn] <= value) { |
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[590] | 303 | rn = sn; |
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[591] | 304 | s_root = true; |
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[590] | 305 | value = (*_weight)[sn]; |
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| 306 | } |
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| 307 | sn = (*_pred)[sn]; |
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| 308 | } |
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| 309 | } |
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| 310 | |
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| 311 | typename Graph::template NodeMap<bool> reached(_graph, false); |
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| 312 | reached.set(_root, true); |
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[591] | 313 | cutMap.set(_root, !s_root); |
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[590] | 314 | reached.set(rn, true); |
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[591] | 315 | cutMap.set(rn, s_root); |
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[590] | 316 | |
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[591] | 317 | std::vector<Node> st; |
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[590] | 318 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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[591] | 319 | st.clear(); |
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| 320 | Node nn = n; |
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[590] | 321 | while (!reached[nn]) { |
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| 322 | st.push_back(nn); |
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| 323 | nn = (*_pred)[nn]; |
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| 324 | } |
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| 325 | while (!st.empty()) { |
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| 326 | cutMap.set(st.back(), cutMap[nn]); |
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| 327 | st.pop_back(); |
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| 328 | } |
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| 329 | } |
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| 330 | |
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| 331 | return value; |
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| 332 | } |
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| 333 | |
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[591] | 334 | ///@} |
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| 335 | |
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| 336 | friend class MinCutNodeIt; |
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| 337 | |
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| 338 | /// Iterate on the nodes of a minimum cut |
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| 339 | |
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| 340 | /// This iterator class lists the nodes of a minimum cut found by |
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[592] | 341 | /// GomoryHu. Before using it, you must allocate a GomoryHu class, |
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| 342 | /// and call its \ref GomoryHu::run() "run()" method. |
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[591] | 343 | /// |
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| 344 | /// This example counts the nodes in the minimum cut separating \c s from |
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| 345 | /// \c t. |
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| 346 | /// \code |
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[592] | 347 | /// GomoruHu<Graph> gom(g, capacities); |
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[591] | 348 | /// gom.run(); |
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[593] | 349 | /// int cnt=0; |
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| 350 | /// for(GomoruHu<Graph>::MinCutNodeIt n(gom,s,t); n!=INVALID; ++n) ++cnt; |
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[591] | 351 | /// \endcode |
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| 352 | class MinCutNodeIt |
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| 353 | { |
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| 354 | bool _side; |
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| 355 | typename Graph::NodeIt _node_it; |
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| 356 | typename Graph::template NodeMap<bool> _cut; |
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| 357 | public: |
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| 358 | /// Constructor |
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| 359 | |
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[593] | 360 | /// Constructor. |
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[591] | 361 | /// |
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[592] | 362 | MinCutNodeIt(GomoryHu const &gomory, |
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| 363 | ///< The GomoryHu class. You must call its |
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[591] | 364 | /// run() method |
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[593] | 365 | /// before initializing this iterator. |
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| 366 | const Node& s, ///< The base node. |
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[591] | 367 | const Node& t, |
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[593] | 368 | ///< The node you want to separate from node \c s. |
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[591] | 369 | bool side=true |
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| 370 | ///< If it is \c true (default) then the iterator lists |
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| 371 | /// the nodes of the component containing \c s, |
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| 372 | /// otherwise it lists the other component. |
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| 373 | /// \note As the minimum cut is not always unique, |
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| 374 | /// \code |
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| 375 | /// MinCutNodeIt(gomory, s, t, true); |
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| 376 | /// \endcode |
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| 377 | /// and |
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| 378 | /// \code |
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| 379 | /// MinCutNodeIt(gomory, t, s, false); |
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| 380 | /// \endcode |
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| 381 | /// does not necessarily give the same set of nodes. |
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| 382 | /// However it is ensured that |
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| 383 | /// \code |
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| 384 | /// MinCutNodeIt(gomory, s, t, true); |
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| 385 | /// \endcode |
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| 386 | /// and |
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| 387 | /// \code |
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| 388 | /// MinCutNodeIt(gomory, s, t, false); |
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| 389 | /// \endcode |
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| 390 | /// together list each node exactly once. |
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| 391 | ) |
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| 392 | : _side(side), _cut(gomory._graph) |
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| 393 | { |
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| 394 | gomory.minCutMap(s,t,_cut); |
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| 395 | for(_node_it=typename Graph::NodeIt(gomory._graph); |
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| 396 | _node_it!=INVALID && _cut[_node_it]!=_side; |
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| 397 | ++_node_it) {} |
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| 398 | } |
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[593] | 399 | /// Conversion to \c Node |
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[591] | 400 | |
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[593] | 401 | /// Conversion to \c Node. |
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[591] | 402 | /// |
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| 403 | operator typename Graph::Node() const |
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| 404 | { |
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| 405 | return _node_it; |
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| 406 | } |
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| 407 | bool operator==(Invalid) { return _node_it==INVALID; } |
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| 408 | bool operator!=(Invalid) { return _node_it!=INVALID; } |
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| 409 | /// Next node |
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| 410 | |
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[593] | 411 | /// Next node. |
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[591] | 412 | /// |
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| 413 | MinCutNodeIt &operator++() |
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| 414 | { |
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| 415 | for(++_node_it;_node_it!=INVALID&&_cut[_node_it]!=_side;++_node_it) {} |
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| 416 | return *this; |
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| 417 | } |
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| 418 | /// Postfix incrementation |
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| 419 | |
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[593] | 420 | /// Postfix incrementation. |
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[591] | 421 | /// |
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| 422 | /// \warning This incrementation |
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[593] | 423 | /// returns a \c Node, not a \c MinCutNodeIt, as one may |
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[591] | 424 | /// expect. |
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| 425 | typename Graph::Node operator++(int) |
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| 426 | { |
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| 427 | typename Graph::Node n=*this; |
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| 428 | ++(*this); |
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| 429 | return n; |
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| 430 | } |
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| 431 | }; |
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| 432 | |
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| 433 | friend class MinCutEdgeIt; |
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| 434 | |
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| 435 | /// Iterate on the edges of a minimum cut |
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| 436 | |
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| 437 | /// This iterator class lists the edges of a minimum cut found by |
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[592] | 438 | /// GomoryHu. Before using it, you must allocate a GomoryHu class, |
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| 439 | /// and call its \ref GomoryHu::run() "run()" method. |
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[591] | 440 | /// |
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| 441 | /// This example computes the value of the minimum cut separating \c s from |
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| 442 | /// \c t. |
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| 443 | /// \code |
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[592] | 444 | /// GomoruHu<Graph> gom(g, capacities); |
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[591] | 445 | /// gom.run(); |
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| 446 | /// int value=0; |
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[593] | 447 | /// for(GomoruHu<Graph>::MinCutEdgeIt e(gom,s,t); e!=INVALID; ++e) |
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[591] | 448 | /// value+=capacities[e]; |
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| 449 | /// \endcode |
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| 450 | /// the result will be the same as it is returned by |
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[593] | 451 | /// \ref GomoryHu::minCutValue() "gom.minCutValue(s,t)" |
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[591] | 452 | class MinCutEdgeIt |
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| 453 | { |
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| 454 | bool _side; |
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| 455 | const Graph &_graph; |
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| 456 | typename Graph::NodeIt _node_it; |
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| 457 | typename Graph::OutArcIt _arc_it; |
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| 458 | typename Graph::template NodeMap<bool> _cut; |
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| 459 | void step() |
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| 460 | { |
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| 461 | ++_arc_it; |
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| 462 | while(_node_it!=INVALID && _arc_it==INVALID) |
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| 463 | { |
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| 464 | for(++_node_it;_node_it!=INVALID&&!_cut[_node_it];++_node_it) {} |
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| 465 | if(_node_it!=INVALID) |
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| 466 | _arc_it=typename Graph::OutArcIt(_graph,_node_it); |
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| 467 | } |
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| 468 | } |
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| 469 | |
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| 470 | public: |
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[592] | 471 | MinCutEdgeIt(GomoryHu const &gomory, |
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| 472 | ///< The GomoryHu class. You must call its |
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[591] | 473 | /// run() method |
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[593] | 474 | /// before initializing this iterator. |
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| 475 | const Node& s, ///< The base node. |
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[591] | 476 | const Node& t, |
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[593] | 477 | ///< The node you want to separate from node \c s. |
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[591] | 478 | bool side=true |
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| 479 | ///< If it is \c true (default) then the listed arcs |
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| 480 | /// will be oriented from the |
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| 481 | /// the nodes of the component containing \c s, |
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| 482 | /// otherwise they will be oriented in the opposite |
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| 483 | /// direction. |
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| 484 | ) |
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| 485 | : _graph(gomory._graph), _cut(_graph) |
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| 486 | { |
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| 487 | gomory.minCutMap(s,t,_cut); |
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| 488 | if(!side) |
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| 489 | for(typename Graph::NodeIt n(_graph);n!=INVALID;++n) |
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| 490 | _cut[n]=!_cut[n]; |
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| 491 | |
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| 492 | for(_node_it=typename Graph::NodeIt(_graph); |
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| 493 | _node_it!=INVALID && !_cut[_node_it]; |
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| 494 | ++_node_it) {} |
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| 495 | _arc_it = _node_it!=INVALID ? |
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| 496 | typename Graph::OutArcIt(_graph,_node_it) : INVALID; |
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| 497 | while(_node_it!=INVALID && _arc_it == INVALID) |
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| 498 | { |
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| 499 | for(++_node_it; _node_it!=INVALID&&!_cut[_node_it]; ++_node_it) {} |
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| 500 | if(_node_it!=INVALID) |
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| 501 | _arc_it= typename Graph::OutArcIt(_graph,_node_it); |
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| 502 | } |
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| 503 | while(_arc_it!=INVALID && _cut[_graph.target(_arc_it)]) step(); |
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| 504 | } |
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[593] | 505 | /// Conversion to \c Arc |
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[591] | 506 | |
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[593] | 507 | /// Conversion to \c Arc. |
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[591] | 508 | /// |
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| 509 | operator typename Graph::Arc() const |
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| 510 | { |
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| 511 | return _arc_it; |
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| 512 | } |
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[593] | 513 | /// Conversion to \c Edge |
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[591] | 514 | |
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[593] | 515 | /// Conversion to \c Edge. |
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[591] | 516 | /// |
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| 517 | operator typename Graph::Edge() const |
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| 518 | { |
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| 519 | return _arc_it; |
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| 520 | } |
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| 521 | bool operator==(Invalid) { return _node_it==INVALID; } |
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| 522 | bool operator!=(Invalid) { return _node_it!=INVALID; } |
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| 523 | /// Next edge |
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| 524 | |
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[593] | 525 | /// Next edge. |
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[591] | 526 | /// |
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| 527 | MinCutEdgeIt &operator++() |
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| 528 | { |
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| 529 | step(); |
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| 530 | while(_arc_it!=INVALID && _cut[_graph.target(_arc_it)]) step(); |
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| 531 | return *this; |
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| 532 | } |
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| 533 | /// Postfix incrementation |
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| 534 | |
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[593] | 535 | /// Postfix incrementation. |
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[591] | 536 | /// |
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| 537 | /// \warning This incrementation |
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[593] | 538 | /// returns an \c Arc, not a \c MinCutEdgeIt, as one may expect. |
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[591] | 539 | typename Graph::Arc operator++(int) |
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| 540 | { |
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| 541 | typename Graph::Arc e=*this; |
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| 542 | ++(*this); |
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| 543 | return e; |
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| 544 | } |
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| 545 | }; |
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| 546 | |
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[590] | 547 | }; |
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| 548 | |
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| 549 | } |
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| 550 | |
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| 551 | #endif |
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