[1698] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[1956] | 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) 2003-2006 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1698] | 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_TOPOLOGY_H |
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| 20 | #define LEMON_TOPOLOGY_H |
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| 21 | |
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| 22 | #include <lemon/dfs.h> |
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[1740] | 23 | #include <lemon/bfs.h> |
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[1698] | 24 | #include <lemon/graph_utils.h> |
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[1750] | 25 | #include <lemon/graph_adaptor.h> |
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| 26 | #include <lemon/maps.h> |
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[1698] | 27 | |
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| 28 | #include <lemon/concept/graph.h> |
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[1909] | 29 | #include <lemon/concept/ugraph.h> |
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[1698] | 30 | #include <lemon/concept_check.h> |
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| 31 | |
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[1750] | 32 | #include <lemon/bin_heap.h> |
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| 33 | #include <lemon/linear_heap.h> |
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| 34 | |
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| 35 | #include <stack> |
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| 36 | #include <functional> |
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| 37 | |
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| 38 | /// \ingroup topology |
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[1698] | 39 | /// \file |
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| 40 | /// \brief Topology related algorithms |
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| 41 | /// |
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| 42 | /// Topology related algorithms |
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| 43 | |
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| 44 | namespace lemon { |
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| 45 | |
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[1750] | 46 | /// \ingroup topology |
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| 47 | /// |
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| 48 | /// \brief Check that the given undirected graph is connected. |
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| 49 | /// |
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| 50 | /// Check that the given undirected graph connected. |
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| 51 | /// \param graph The undirected graph. |
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| 52 | /// \return %True when there is path between any two nodes in the graph. |
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[1807] | 53 | /// \note By definition, the empty graph is connected. |
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[1909] | 54 | template <typename UGraph> |
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| 55 | bool connected(const UGraph& graph) { |
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| 56 | checkConcept<concept::UGraph, UGraph>(); |
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| 57 | typedef typename UGraph::NodeIt NodeIt; |
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[1807] | 58 | if (NodeIt(graph) == INVALID) return true; |
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[1909] | 59 | Dfs<UGraph> dfs(graph); |
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[1750] | 60 | dfs.run(NodeIt(graph)); |
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| 61 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 62 | if (!dfs.reached(it)) { |
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| 63 | return false; |
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| 64 | } |
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| 65 | } |
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| 66 | return true; |
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| 67 | } |
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| 68 | |
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| 69 | /// \ingroup topology |
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| 70 | /// |
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| 71 | /// \brief Count the number of connected components of an undirected graph |
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| 72 | /// |
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| 73 | /// Count the number of connected components of an undirected graph |
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| 74 | /// |
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[1793] | 75 | /// \param graph The graph. It should be undirected. |
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[1750] | 76 | /// \return The number of components |
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[1807] | 77 | /// \note By definition, the empty graph consists |
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| 78 | /// of zero connected components. |
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[1909] | 79 | template <typename UGraph> |
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| 80 | int countConnectedComponents(const UGraph &graph) { |
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| 81 | checkConcept<concept::UGraph, UGraph>(); |
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| 82 | typedef typename UGraph::Node Node; |
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| 83 | typedef typename UGraph::Edge Edge; |
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[1750] | 84 | |
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| 85 | typedef NullMap<Node, Edge> PredMap; |
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| 86 | typedef NullMap<Node, int> DistMap; |
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| 87 | |
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| 88 | int compNum = 0; |
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[1909] | 89 | typename Bfs<UGraph>:: |
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[1750] | 90 | template DefPredMap<PredMap>:: |
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| 91 | template DefDistMap<DistMap>:: |
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| 92 | Create bfs(graph); |
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| 93 | |
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| 94 | PredMap predMap; |
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| 95 | bfs.predMap(predMap); |
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| 96 | |
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| 97 | DistMap distMap; |
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| 98 | bfs.distMap(distMap); |
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| 99 | |
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| 100 | bfs.init(); |
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[1909] | 101 | for(typename UGraph::NodeIt n(graph); n != INVALID; ++n) { |
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[1750] | 102 | if (!bfs.reached(n)) { |
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| 103 | bfs.addSource(n); |
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| 104 | bfs.start(); |
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| 105 | ++compNum; |
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| 106 | } |
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| 107 | } |
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| 108 | return compNum; |
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| 109 | } |
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| 110 | |
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| 111 | /// \ingroup topology |
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| 112 | /// |
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| 113 | /// \brief Find the connected components of an undirected graph |
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| 114 | /// |
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| 115 | /// Find the connected components of an undirected graph. |
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| 116 | /// |
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[1763] | 117 | /// \image html connected_components.png |
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| 118 | /// \image latex connected_components.eps "Connected components" width=\textwidth |
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| 119 | /// |
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[1793] | 120 | /// \param graph The graph. It should be undirected. |
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| 121 | /// \retval compMap A writable node map. The values will be set from 0 to |
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[1750] | 122 | /// the number of the connected components minus one. Each values of the map |
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| 123 | /// will be set exactly once, the values of a certain component will be |
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| 124 | /// set continuously. |
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| 125 | /// \return The number of components |
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[1763] | 126 | /// |
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[1909] | 127 | template <class UGraph, class NodeMap> |
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| 128 | int connectedComponents(const UGraph &graph, NodeMap &compMap) { |
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| 129 | checkConcept<concept::UGraph, UGraph>(); |
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| 130 | typedef typename UGraph::Node Node; |
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| 131 | typedef typename UGraph::Edge Edge; |
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[1750] | 132 | checkConcept<concept::WriteMap<Node, int>, NodeMap>(); |
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| 133 | |
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| 134 | typedef NullMap<Node, Edge> PredMap; |
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| 135 | typedef NullMap<Node, int> DistMap; |
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| 136 | |
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| 137 | int compNum = 0; |
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[1909] | 138 | typename Bfs<UGraph>:: |
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[1750] | 139 | template DefPredMap<PredMap>:: |
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| 140 | template DefDistMap<DistMap>:: |
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| 141 | Create bfs(graph); |
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| 142 | |
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| 143 | PredMap predMap; |
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| 144 | bfs.predMap(predMap); |
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| 145 | |
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| 146 | DistMap distMap; |
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| 147 | bfs.distMap(distMap); |
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| 148 | |
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| 149 | bfs.init(); |
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[1909] | 150 | for(typename UGraph::NodeIt n(graph); n != INVALID; ++n) { |
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[1750] | 151 | if(!bfs.reached(n)) { |
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| 152 | bfs.addSource(n); |
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| 153 | while (!bfs.emptyQueue()) { |
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| 154 | compMap.set(bfs.nextNode(), compNum); |
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| 155 | bfs.processNextNode(); |
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| 156 | } |
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| 157 | ++compNum; |
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| 158 | } |
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| 159 | } |
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| 160 | return compNum; |
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| 161 | } |
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| 162 | |
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| 163 | namespace _topology_bits { |
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| 164 | |
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| 165 | template <typename Graph, typename Iterator > |
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| 166 | struct LeaveOrderVisitor : public DfsVisitor<Graph> { |
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| 167 | public: |
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| 168 | typedef typename Graph::Node Node; |
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| 169 | LeaveOrderVisitor(Iterator it) : _it(it) {} |
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| 170 | |
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| 171 | void leave(const Node& node) { |
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| 172 | *(_it++) = node; |
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| 173 | } |
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| 174 | |
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| 175 | private: |
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| 176 | Iterator _it; |
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| 177 | }; |
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| 178 | |
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| 179 | template <typename Graph, typename Map> |
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| 180 | struct FillMapVisitor : public DfsVisitor<Graph> { |
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| 181 | public: |
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| 182 | typedef typename Graph::Node Node; |
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| 183 | typedef typename Map::Value Value; |
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| 184 | |
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| 185 | FillMapVisitor(Map& map, Value& value) |
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| 186 | : _map(map), _value(value) {} |
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| 187 | |
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| 188 | void reach(const Node& node) { |
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| 189 | _map.set(node, _value); |
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| 190 | } |
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| 191 | private: |
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| 192 | Map& _map; |
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| 193 | Value& _value; |
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| 194 | }; |
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| 195 | |
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| 196 | template <typename Graph, typename EdgeMap> |
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| 197 | struct StronglyConnectedCutEdgesVisitor : public DfsVisitor<Graph> { |
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| 198 | public: |
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| 199 | typedef typename Graph::Node Node; |
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| 200 | typedef typename Graph::Edge Edge; |
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| 201 | |
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| 202 | StronglyConnectedCutEdgesVisitor(const Graph& graph, EdgeMap& cutMap, |
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| 203 | int& cutNum) |
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| 204 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
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| 205 | _compMap(graph), _num(0) { |
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| 206 | } |
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| 207 | |
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| 208 | void stop(const Node&) { |
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| 209 | ++_num; |
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| 210 | } |
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| 211 | |
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| 212 | void reach(const Node& node) { |
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| 213 | _compMap.set(node, _num); |
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| 214 | } |
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| 215 | |
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| 216 | void examine(const Edge& edge) { |
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| 217 | if (_compMap[_graph.source(edge)] != _compMap[_graph.target(edge)]) { |
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| 218 | _cutMap.set(edge, true); |
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| 219 | ++_cutNum; |
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| 220 | } |
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| 221 | } |
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| 222 | private: |
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| 223 | const Graph& _graph; |
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| 224 | EdgeMap& _cutMap; |
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| 225 | int& _cutNum; |
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| 226 | |
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| 227 | typename Graph::template NodeMap<int> _compMap; |
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| 228 | int _num; |
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| 229 | }; |
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| 230 | |
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| 231 | } |
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| 232 | |
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| 233 | |
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| 234 | /// \ingroup topology |
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| 235 | /// |
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| 236 | /// \brief Check that the given directed graph is strongly connected. |
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| 237 | /// |
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| 238 | /// Check that the given directed graph is strongly connected. The |
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| 239 | /// graph is strongly connected when any two nodes of the graph are |
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[1817] | 240 | /// connected with directed paths in both direction. |
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[1750] | 241 | /// \return %False when the graph is not strongly connected. |
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| 242 | /// \see connected |
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| 243 | /// |
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[1807] | 244 | /// \note By definition, the empty graph is strongly connected. |
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[1750] | 245 | template <typename Graph> |
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| 246 | bool stronglyConnected(const Graph& graph) { |
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| 247 | checkConcept<concept::StaticGraph, Graph>(); |
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[1807] | 248 | if (NodeIt(graph) == INVALID) return true; |
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[1750] | 249 | |
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| 250 | typedef typename Graph::Node Node; |
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| 251 | typedef typename Graph::NodeIt NodeIt; |
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| 252 | |
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| 253 | using namespace _topology_bits; |
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| 254 | |
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| 255 | typedef DfsVisitor<Graph> Visitor; |
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| 256 | Visitor visitor; |
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| 257 | |
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| 258 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 259 | dfs.init(); |
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| 260 | dfs.addSource(NodeIt(graph)); |
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| 261 | dfs.start(); |
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| 262 | |
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| 263 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 264 | if (!dfs.reached(it)) { |
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| 265 | return false; |
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| 266 | } |
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| 267 | } |
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| 268 | |
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| 269 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 270 | RGraph rgraph(graph); |
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| 271 | |
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| 272 | typedef DfsVisitor<Graph> RVisitor; |
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| 273 | RVisitor rvisitor; |
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| 274 | |
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| 275 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 276 | rdfs.init(); |
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| 277 | rdfs.addSource(NodeIt(graph)); |
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| 278 | rdfs.start(); |
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| 279 | |
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| 280 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 281 | if (!rdfs.reached(it)) { |
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| 282 | return false; |
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| 283 | } |
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| 284 | } |
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| 285 | |
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| 286 | return true; |
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| 287 | } |
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| 288 | |
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| 289 | /// \ingroup topology |
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| 290 | /// |
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| 291 | /// \brief Count the strongly connected components of a directed graph |
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| 292 | /// |
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| 293 | /// Count the strongly connected components of a directed graph. |
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| 294 | /// The strongly connected components are the classes of an equivalence |
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| 295 | /// relation on the nodes of the graph. Two nodes are connected with |
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| 296 | /// directed paths in both direction. |
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| 297 | /// |
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[1793] | 298 | /// \param graph The graph. |
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[1750] | 299 | /// \return The number of components |
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[1807] | 300 | /// \note By definition, the empty graph has zero |
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| 301 | /// strongly connected components. |
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[1750] | 302 | template <typename Graph> |
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| 303 | int countStronglyConnectedComponents(const Graph& graph) { |
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| 304 | checkConcept<concept::StaticGraph, Graph>(); |
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| 305 | |
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| 306 | using namespace _topology_bits; |
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| 307 | |
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| 308 | typedef typename Graph::Node Node; |
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| 309 | typedef typename Graph::Edge Edge; |
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| 310 | typedef typename Graph::NodeIt NodeIt; |
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| 311 | typedef typename Graph::EdgeIt EdgeIt; |
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| 312 | |
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| 313 | typedef std::vector<Node> Container; |
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| 314 | typedef typename Container::iterator Iterator; |
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| 315 | |
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| 316 | Container nodes(countNodes(graph)); |
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| 317 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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| 318 | Visitor visitor(nodes.begin()); |
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| 319 | |
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| 320 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 321 | dfs.init(); |
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| 322 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 323 | if (!dfs.reached(it)) { |
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| 324 | dfs.addSource(it); |
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| 325 | dfs.start(); |
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| 326 | } |
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| 327 | } |
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| 328 | |
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| 329 | typedef typename Container::reverse_iterator RIterator; |
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| 330 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 331 | |
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| 332 | RGraph rgraph(graph); |
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| 333 | |
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| 334 | typedef DfsVisitor<Graph> RVisitor; |
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| 335 | RVisitor rvisitor; |
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| 336 | |
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| 337 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 338 | |
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| 339 | int compNum = 0; |
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| 340 | |
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| 341 | rdfs.init(); |
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| 342 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 343 | if (!rdfs.reached(*it)) { |
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| 344 | rdfs.addSource(*it); |
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| 345 | rdfs.start(); |
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| 346 | ++compNum; |
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| 347 | } |
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| 348 | } |
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| 349 | return compNum; |
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| 350 | } |
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| 351 | |
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| 352 | /// \ingroup topology |
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| 353 | /// |
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| 354 | /// \brief Find the strongly connected components of a directed graph |
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| 355 | /// |
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| 356 | /// Find the strongly connected components of a directed graph. |
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| 357 | /// The strongly connected components are the classes of an equivalence |
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| 358 | /// relation on the nodes of the graph. Two nodes are in relationship |
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| 359 | /// when there are directed paths between them in both direction. |
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| 360 | /// |
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[1763] | 361 | /// \image html strongly_connected_components.png |
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| 362 | /// \image latex strongly_connected_components.eps "Strongly connected components" width=\textwidth |
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| 363 | /// |
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[1793] | 364 | /// \param graph The graph. |
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| 365 | /// \retval compMap A writable node map. The values will be set from 0 to |
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[1750] | 366 | /// the number of the strongly connected components minus one. Each values |
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| 367 | /// of the map will be set exactly once, the values of a certain component |
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| 368 | /// will be set continuously. |
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| 369 | /// \return The number of components |
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[1763] | 370 | /// |
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[1750] | 371 | template <typename Graph, typename NodeMap> |
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| 372 | int stronglyConnectedComponents(const Graph& graph, NodeMap& compMap) { |
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| 373 | checkConcept<concept::StaticGraph, Graph>(); |
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| 374 | typedef typename Graph::Node Node; |
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| 375 | typedef typename Graph::NodeIt NodeIt; |
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| 376 | checkConcept<concept::WriteMap<Node, int>, NodeMap>(); |
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| 377 | |
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| 378 | using namespace _topology_bits; |
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| 379 | |
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| 380 | typedef std::vector<Node> Container; |
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| 381 | typedef typename Container::iterator Iterator; |
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| 382 | |
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| 383 | Container nodes(countNodes(graph)); |
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| 384 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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| 385 | Visitor visitor(nodes.begin()); |
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| 386 | |
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| 387 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 388 | dfs.init(); |
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| 389 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 390 | if (!dfs.reached(it)) { |
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| 391 | dfs.addSource(it); |
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| 392 | dfs.start(); |
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| 393 | } |
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| 394 | } |
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| 395 | |
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| 396 | typedef typename Container::reverse_iterator RIterator; |
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| 397 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 398 | |
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| 399 | RGraph rgraph(graph); |
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| 400 | |
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| 401 | int compNum = 0; |
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| 402 | |
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| 403 | typedef FillMapVisitor<RGraph, NodeMap> RVisitor; |
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| 404 | RVisitor rvisitor(compMap, compNum); |
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| 405 | |
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| 406 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 407 | |
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| 408 | rdfs.init(); |
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| 409 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 410 | if (!rdfs.reached(*it)) { |
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| 411 | rdfs.addSource(*it); |
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| 412 | rdfs.start(); |
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| 413 | ++compNum; |
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| 414 | } |
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| 415 | } |
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| 416 | return compNum; |
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| 417 | } |
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| 418 | |
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| 419 | /// \ingroup topology |
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| 420 | /// |
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| 421 | /// \brief Find the cut edges of the strongly connected components. |
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| 422 | /// |
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| 423 | /// Find the cut edges of the strongly connected components. |
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| 424 | /// The strongly connected components are the classes of an equivalence |
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| 425 | /// relation on the nodes of the graph. Two nodes are in relationship |
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| 426 | /// when there are directed paths between them in both direction. |
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| 427 | /// The strongly connected components are separated by the cut edges. |
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| 428 | /// |
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[1793] | 429 | /// \param graph The graph. |
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| 430 | /// \retval cutMap A writable node map. The values will be set true when the |
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| 431 | /// edge is a cut edge. |
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[1750] | 432 | /// |
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| 433 | /// \return The number of cut edges |
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| 434 | template <typename Graph, typename EdgeMap> |
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| 435 | int stronglyConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) { |
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| 436 | checkConcept<concept::StaticGraph, Graph>(); |
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| 437 | typedef typename Graph::Node Node; |
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| 438 | typedef typename Graph::Edge Edge; |
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| 439 | typedef typename Graph::NodeIt NodeIt; |
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| 440 | checkConcept<concept::WriteMap<Edge, bool>, EdgeMap>(); |
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| 441 | |
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| 442 | using namespace _topology_bits; |
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| 443 | |
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| 444 | typedef std::vector<Node> Container; |
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| 445 | typedef typename Container::iterator Iterator; |
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| 446 | |
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| 447 | Container nodes(countNodes(graph)); |
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| 448 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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| 449 | Visitor visitor(nodes.begin()); |
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| 450 | |
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| 451 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 452 | dfs.init(); |
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| 453 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 454 | if (!dfs.reached(it)) { |
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| 455 | dfs.addSource(it); |
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| 456 | dfs.start(); |
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| 457 | } |
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| 458 | } |
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| 459 | |
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| 460 | typedef typename Container::reverse_iterator RIterator; |
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| 461 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 462 | |
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| 463 | RGraph rgraph(graph); |
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| 464 | |
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| 465 | int cutNum = 0; |
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| 466 | |
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| 467 | typedef StronglyConnectedCutEdgesVisitor<RGraph, EdgeMap> RVisitor; |
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| 468 | RVisitor rvisitor(rgraph, cutMap, cutNum); |
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| 469 | |
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| 470 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 471 | |
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| 472 | rdfs.init(); |
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| 473 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 474 | if (!rdfs.reached(*it)) { |
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| 475 | rdfs.addSource(*it); |
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| 476 | rdfs.start(); |
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| 477 | } |
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| 478 | } |
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| 479 | return cutNum; |
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| 480 | } |
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| 481 | |
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[1698] | 482 | namespace _topology_bits { |
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| 483 | |
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[1750] | 484 | template <typename Graph> |
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[1800] | 485 | class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
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[1698] | 486 | public: |
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[1750] | 487 | typedef typename Graph::Node Node; |
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| 488 | typedef typename Graph::Edge Edge; |
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[1909] | 489 | typedef typename Graph::UEdge UEdge; |
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[1698] | 490 | |
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[1800] | 491 | CountBiNodeConnectedComponentsVisitor(const Graph& graph, int &compNum) |
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[1750] | 492 | : _graph(graph), _compNum(compNum), |
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| 493 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
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| 494 | |
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| 495 | void start(const Node& node) { |
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| 496 | _predMap.set(node, INVALID); |
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| 497 | } |
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| 498 | |
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| 499 | void reach(const Node& node) { |
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| 500 | _numMap.set(node, _num); |
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| 501 | _retMap.set(node, _num); |
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| 502 | ++_num; |
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| 503 | } |
---|
| 504 | |
---|
| 505 | void discover(const Edge& edge) { |
---|
| 506 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
| 507 | } |
---|
| 508 | |
---|
| 509 | void examine(const Edge& edge) { |
---|
| 510 | if (_graph.source(edge) == _graph.target(edge) && |
---|
| 511 | _graph.direction(edge)) { |
---|
| 512 | ++_compNum; |
---|
| 513 | return; |
---|
| 514 | } |
---|
| 515 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) { |
---|
| 516 | return; |
---|
| 517 | } |
---|
| 518 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
| 519 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
[1698] | 520 | } |
---|
| 521 | } |
---|
| 522 | |
---|
[1750] | 523 | void backtrack(const Edge& edge) { |
---|
| 524 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 525 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 526 | } |
---|
| 527 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
| 528 | ++_compNum; |
---|
| 529 | } |
---|
| 530 | } |
---|
| 531 | |
---|
| 532 | private: |
---|
| 533 | const Graph& _graph; |
---|
| 534 | int& _compNum; |
---|
| 535 | |
---|
| 536 | typename Graph::template NodeMap<int> _numMap; |
---|
| 537 | typename Graph::template NodeMap<int> _retMap; |
---|
| 538 | typename Graph::template NodeMap<Node> _predMap; |
---|
| 539 | int _num; |
---|
| 540 | }; |
---|
| 541 | |
---|
| 542 | template <typename Graph, typename EdgeMap> |
---|
[1800] | 543 | class BiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 544 | public: |
---|
| 545 | typedef typename Graph::Node Node; |
---|
| 546 | typedef typename Graph::Edge Edge; |
---|
[1909] | 547 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 548 | |
---|
[1800] | 549 | BiNodeConnectedComponentsVisitor(const Graph& graph, |
---|
[1750] | 550 | EdgeMap& compMap, int &compNum) |
---|
| 551 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
| 552 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 553 | |
---|
| 554 | void start(const Node& node) { |
---|
| 555 | _predMap.set(node, INVALID); |
---|
| 556 | } |
---|
| 557 | |
---|
| 558 | void reach(const Node& node) { |
---|
| 559 | _numMap.set(node, _num); |
---|
| 560 | _retMap.set(node, _num); |
---|
| 561 | ++_num; |
---|
| 562 | } |
---|
| 563 | |
---|
| 564 | void discover(const Edge& edge) { |
---|
| 565 | Node target = _graph.target(edge); |
---|
| 566 | _predMap.set(target, edge); |
---|
| 567 | _edgeStack.push(edge); |
---|
| 568 | } |
---|
| 569 | |
---|
| 570 | void examine(const Edge& edge) { |
---|
| 571 | Node source = _graph.source(edge); |
---|
| 572 | Node target = _graph.target(edge); |
---|
| 573 | if (source == target && _graph.direction(edge)) { |
---|
| 574 | _compMap.set(edge, _compNum); |
---|
| 575 | ++_compNum; |
---|
| 576 | return; |
---|
| 577 | } |
---|
| 578 | if (_numMap[target] < _numMap[source]) { |
---|
| 579 | if (_predMap[source] != _graph.oppositeEdge(edge)) { |
---|
| 580 | _edgeStack.push(edge); |
---|
| 581 | } |
---|
| 582 | } |
---|
| 583 | if (_predMap[source] != INVALID && |
---|
| 584 | target == _graph.source(_predMap[source])) { |
---|
| 585 | return; |
---|
| 586 | } |
---|
| 587 | if (_retMap[source] > _numMap[target]) { |
---|
| 588 | _retMap.set(source, _numMap[target]); |
---|
| 589 | } |
---|
| 590 | } |
---|
| 591 | |
---|
| 592 | void backtrack(const Edge& edge) { |
---|
| 593 | Node source = _graph.source(edge); |
---|
| 594 | Node target = _graph.target(edge); |
---|
| 595 | if (_retMap[source] > _retMap[target]) { |
---|
| 596 | _retMap.set(source, _retMap[target]); |
---|
| 597 | } |
---|
| 598 | if (_numMap[source] <= _retMap[target]) { |
---|
| 599 | while (_edgeStack.top() != edge) { |
---|
| 600 | _compMap.set(_edgeStack.top(), _compNum); |
---|
| 601 | _edgeStack.pop(); |
---|
| 602 | } |
---|
| 603 | _compMap.set(edge, _compNum); |
---|
| 604 | _edgeStack.pop(); |
---|
| 605 | ++_compNum; |
---|
| 606 | } |
---|
| 607 | } |
---|
| 608 | |
---|
| 609 | private: |
---|
| 610 | const Graph& _graph; |
---|
| 611 | EdgeMap& _compMap; |
---|
| 612 | int& _compNum; |
---|
| 613 | |
---|
| 614 | typename Graph::template NodeMap<int> _numMap; |
---|
| 615 | typename Graph::template NodeMap<int> _retMap; |
---|
| 616 | typename Graph::template NodeMap<Edge> _predMap; |
---|
[1909] | 617 | std::stack<UEdge> _edgeStack; |
---|
[1750] | 618 | int _num; |
---|
| 619 | }; |
---|
| 620 | |
---|
| 621 | |
---|
| 622 | template <typename Graph, typename NodeMap> |
---|
[1800] | 623 | class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 624 | public: |
---|
| 625 | typedef typename Graph::Node Node; |
---|
| 626 | typedef typename Graph::Edge Edge; |
---|
[1909] | 627 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 628 | |
---|
[1800] | 629 | BiNodeConnectedCutNodesVisitor(const Graph& graph, NodeMap& cutMap, |
---|
[1750] | 630 | int& cutNum) |
---|
| 631 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
| 632 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 633 | |
---|
| 634 | void start(const Node& node) { |
---|
| 635 | _predMap.set(node, INVALID); |
---|
| 636 | rootCut = false; |
---|
| 637 | } |
---|
| 638 | |
---|
| 639 | void reach(const Node& node) { |
---|
| 640 | _numMap.set(node, _num); |
---|
| 641 | _retMap.set(node, _num); |
---|
| 642 | ++_num; |
---|
| 643 | } |
---|
| 644 | |
---|
| 645 | void discover(const Edge& edge) { |
---|
| 646 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
| 647 | } |
---|
| 648 | |
---|
| 649 | void examine(const Edge& edge) { |
---|
| 650 | if (_graph.source(edge) == _graph.target(edge) && |
---|
| 651 | _graph.direction(edge)) { |
---|
| 652 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 653 | _cutMap.set(_graph.source(edge), true); |
---|
| 654 | ++_cutNum; |
---|
| 655 | } |
---|
| 656 | return; |
---|
| 657 | } |
---|
| 658 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) return; |
---|
| 659 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
| 660 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
| 661 | } |
---|
| 662 | } |
---|
| 663 | |
---|
| 664 | void backtrack(const Edge& edge) { |
---|
| 665 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 666 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 667 | } |
---|
| 668 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
| 669 | if (_predMap[_graph.source(edge)] != INVALID) { |
---|
| 670 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 671 | _cutMap.set(_graph.source(edge), true); |
---|
| 672 | ++_cutNum; |
---|
| 673 | } |
---|
| 674 | } else if (rootCut) { |
---|
| 675 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 676 | _cutMap.set(_graph.source(edge), true); |
---|
| 677 | ++_cutNum; |
---|
| 678 | } |
---|
| 679 | } else { |
---|
| 680 | rootCut = true; |
---|
| 681 | } |
---|
| 682 | } |
---|
| 683 | } |
---|
| 684 | |
---|
| 685 | private: |
---|
| 686 | const Graph& _graph; |
---|
| 687 | NodeMap& _cutMap; |
---|
| 688 | int& _cutNum; |
---|
| 689 | |
---|
| 690 | typename Graph::template NodeMap<int> _numMap; |
---|
| 691 | typename Graph::template NodeMap<int> _retMap; |
---|
| 692 | typename Graph::template NodeMap<Node> _predMap; |
---|
[1909] | 693 | std::stack<UEdge> _edgeStack; |
---|
[1750] | 694 | int _num; |
---|
| 695 | bool rootCut; |
---|
| 696 | }; |
---|
| 697 | |
---|
| 698 | } |
---|
| 699 | |
---|
[1909] | 700 | template <typename UGraph> |
---|
| 701 | int countBiNodeConnectedComponents(const UGraph& graph); |
---|
[1750] | 702 | |
---|
| 703 | /// \ingroup topology |
---|
| 704 | /// |
---|
[1767] | 705 | /// \brief Checks the graph is bi-node-connected. |
---|
[1750] | 706 | /// |
---|
[1767] | 707 | /// This function checks that the undirected graph is bi-node-connected |
---|
| 708 | /// graph. The graph is bi-node-connected if any two undirected edge is |
---|
[1750] | 709 | /// on same circle. |
---|
| 710 | /// |
---|
| 711 | /// \param graph The graph. |
---|
[1767] | 712 | /// \return %True when the graph bi-node-connected. |
---|
[1750] | 713 | /// \todo Make it faster. |
---|
[1909] | 714 | template <typename UGraph> |
---|
| 715 | bool biNodeConnected(const UGraph& graph) { |
---|
[1800] | 716 | return countBiNodeConnectedComponents(graph) == 1; |
---|
[1750] | 717 | } |
---|
| 718 | |
---|
| 719 | /// \ingroup topology |
---|
| 720 | /// |
---|
| 721 | /// \brief Count the biconnected components. |
---|
| 722 | /// |
---|
[1767] | 723 | /// This function finds the bi-node-connected components in an undirected |
---|
[1750] | 724 | /// graph. The biconnected components are the classes of an equivalence |
---|
| 725 | /// relation on the undirected edges. Two undirected edge is in relationship |
---|
| 726 | /// when they are on same circle. |
---|
| 727 | /// |
---|
| 728 | /// \param graph The graph. |
---|
| 729 | /// \return The number of components. |
---|
[1909] | 730 | template <typename UGraph> |
---|
| 731 | int countBiNodeConnectedComponents(const UGraph& graph) { |
---|
| 732 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 733 | typedef typename UGraph::NodeIt NodeIt; |
---|
[1750] | 734 | |
---|
| 735 | using namespace _topology_bits; |
---|
| 736 | |
---|
[1909] | 737 | typedef CountBiNodeConnectedComponentsVisitor<UGraph> Visitor; |
---|
[1750] | 738 | |
---|
| 739 | int compNum = 0; |
---|
| 740 | Visitor visitor(graph, compNum); |
---|
| 741 | |
---|
[1909] | 742 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 743 | dfs.init(); |
---|
| 744 | |
---|
| 745 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 746 | if (!dfs.reached(it)) { |
---|
| 747 | dfs.addSource(it); |
---|
| 748 | dfs.start(); |
---|
| 749 | } |
---|
| 750 | } |
---|
| 751 | return compNum; |
---|
| 752 | } |
---|
| 753 | |
---|
| 754 | /// \ingroup topology |
---|
| 755 | /// |
---|
[1767] | 756 | /// \brief Find the bi-node-connected components. |
---|
[1750] | 757 | /// |
---|
[1767] | 758 | /// This function finds the bi-node-connected components in an undirected |
---|
| 759 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
[1750] | 760 | /// relation on the undirected edges. Two undirected edge are in relationship |
---|
| 761 | /// when they are on same circle. |
---|
| 762 | /// |
---|
[1763] | 763 | /// \image html node_biconnected_components.png |
---|
[1767] | 764 | /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth |
---|
[1763] | 765 | /// |
---|
[1750] | 766 | /// \param graph The graph. |
---|
[1909] | 767 | /// \retval compMap A writable uedge map. The values will be set from 0 |
---|
[1793] | 768 | /// to the number of the biconnected components minus one. Each values |
---|
[1750] | 769 | /// of the map will be set exactly once, the values of a certain component |
---|
| 770 | /// will be set continuously. |
---|
| 771 | /// \return The number of components. |
---|
[1763] | 772 | /// |
---|
[1909] | 773 | template <typename UGraph, typename UEdgeMap> |
---|
| 774 | int biNodeConnectedComponents(const UGraph& graph, |
---|
| 775 | UEdgeMap& compMap) { |
---|
| 776 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 777 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 778 | typedef typename UGraph::UEdge UEdge; |
---|
| 779 | checkConcept<concept::WriteMap<UEdge, int>, UEdgeMap>(); |
---|
[1750] | 780 | |
---|
| 781 | using namespace _topology_bits; |
---|
| 782 | |
---|
[1909] | 783 | typedef BiNodeConnectedComponentsVisitor<UGraph, UEdgeMap> Visitor; |
---|
[1750] | 784 | |
---|
| 785 | int compNum = 0; |
---|
| 786 | Visitor visitor(graph, compMap, compNum); |
---|
| 787 | |
---|
[1909] | 788 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 789 | dfs.init(); |
---|
| 790 | |
---|
| 791 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 792 | if (!dfs.reached(it)) { |
---|
| 793 | dfs.addSource(it); |
---|
| 794 | dfs.start(); |
---|
| 795 | } |
---|
| 796 | } |
---|
| 797 | return compNum; |
---|
| 798 | } |
---|
| 799 | |
---|
| 800 | /// \ingroup topology |
---|
| 801 | /// |
---|
[1767] | 802 | /// \brief Find the bi-node-connected cut nodes. |
---|
[1750] | 803 | /// |
---|
[1767] | 804 | /// This function finds the bi-node-connected cut nodes in an undirected |
---|
| 805 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
[1750] | 806 | /// relation on the undirected edges. Two undirected edges are in |
---|
| 807 | /// relationship when they are on same circle. The biconnected components |
---|
| 808 | /// are separted by nodes which are the cut nodes of the components. |
---|
| 809 | /// |
---|
| 810 | /// \param graph The graph. |
---|
[1793] | 811 | /// \retval cutMap A writable edge map. The values will be set true when |
---|
[1750] | 812 | /// the node separate two or more components. |
---|
| 813 | /// \return The number of the cut nodes. |
---|
[1909] | 814 | template <typename UGraph, typename NodeMap> |
---|
| 815 | int biNodeConnectedCutNodes(const UGraph& graph, NodeMap& cutMap) { |
---|
| 816 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 817 | typedef typename UGraph::Node Node; |
---|
| 818 | typedef typename UGraph::NodeIt NodeIt; |
---|
[1750] | 819 | checkConcept<concept::WriteMap<Node, bool>, NodeMap>(); |
---|
| 820 | |
---|
| 821 | using namespace _topology_bits; |
---|
| 822 | |
---|
[1909] | 823 | typedef BiNodeConnectedCutNodesVisitor<UGraph, NodeMap> Visitor; |
---|
[1750] | 824 | |
---|
| 825 | int cutNum = 0; |
---|
| 826 | Visitor visitor(graph, cutMap, cutNum); |
---|
| 827 | |
---|
[1909] | 828 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 829 | dfs.init(); |
---|
| 830 | |
---|
| 831 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 832 | if (!dfs.reached(it)) { |
---|
| 833 | dfs.addSource(it); |
---|
| 834 | dfs.start(); |
---|
| 835 | } |
---|
| 836 | } |
---|
| 837 | return cutNum; |
---|
| 838 | } |
---|
| 839 | |
---|
| 840 | namespace _topology_bits { |
---|
| 841 | |
---|
| 842 | template <typename Graph> |
---|
[1800] | 843 | class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 844 | public: |
---|
| 845 | typedef typename Graph::Node Node; |
---|
| 846 | typedef typename Graph::Edge Edge; |
---|
[1909] | 847 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 848 | |
---|
[1800] | 849 | CountBiEdgeConnectedComponentsVisitor(const Graph& graph, int &compNum) |
---|
[1750] | 850 | : _graph(graph), _compNum(compNum), |
---|
| 851 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 852 | |
---|
| 853 | void start(const Node& node) { |
---|
| 854 | _predMap.set(node, INVALID); |
---|
| 855 | } |
---|
| 856 | |
---|
| 857 | void reach(const Node& node) { |
---|
| 858 | _numMap.set(node, _num); |
---|
| 859 | _retMap.set(node, _num); |
---|
| 860 | ++_num; |
---|
| 861 | } |
---|
| 862 | |
---|
| 863 | void leave(const Node& node) { |
---|
| 864 | if (_numMap[node] <= _retMap[node]) { |
---|
| 865 | ++_compNum; |
---|
| 866 | } |
---|
| 867 | } |
---|
| 868 | |
---|
| 869 | void discover(const Edge& edge) { |
---|
| 870 | _predMap.set(_graph.target(edge), edge); |
---|
| 871 | } |
---|
| 872 | |
---|
| 873 | void examine(const Edge& edge) { |
---|
| 874 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
| 875 | return; |
---|
| 876 | } |
---|
| 877 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 878 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 879 | } |
---|
| 880 | } |
---|
| 881 | |
---|
| 882 | void backtrack(const Edge& edge) { |
---|
| 883 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 884 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 885 | } |
---|
| 886 | } |
---|
| 887 | |
---|
| 888 | private: |
---|
| 889 | const Graph& _graph; |
---|
| 890 | int& _compNum; |
---|
| 891 | |
---|
| 892 | typename Graph::template NodeMap<int> _numMap; |
---|
| 893 | typename Graph::template NodeMap<int> _retMap; |
---|
| 894 | typename Graph::template NodeMap<Edge> _predMap; |
---|
| 895 | int _num; |
---|
| 896 | }; |
---|
| 897 | |
---|
| 898 | template <typename Graph, typename NodeMap> |
---|
[1800] | 899 | class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 900 | public: |
---|
| 901 | typedef typename Graph::Node Node; |
---|
| 902 | typedef typename Graph::Edge Edge; |
---|
[1909] | 903 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 904 | |
---|
[1800] | 905 | BiEdgeConnectedComponentsVisitor(const Graph& graph, |
---|
[1750] | 906 | NodeMap& compMap, int &compNum) |
---|
| 907 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
| 908 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 909 | |
---|
| 910 | void start(const Node& node) { |
---|
| 911 | _predMap.set(node, INVALID); |
---|
| 912 | } |
---|
| 913 | |
---|
| 914 | void reach(const Node& node) { |
---|
| 915 | _numMap.set(node, _num); |
---|
| 916 | _retMap.set(node, _num); |
---|
| 917 | _nodeStack.push(node); |
---|
| 918 | ++_num; |
---|
| 919 | } |
---|
| 920 | |
---|
| 921 | void leave(const Node& node) { |
---|
| 922 | if (_numMap[node] <= _retMap[node]) { |
---|
| 923 | while (_nodeStack.top() != node) { |
---|
| 924 | _compMap.set(_nodeStack.top(), _compNum); |
---|
| 925 | _nodeStack.pop(); |
---|
| 926 | } |
---|
| 927 | _compMap.set(node, _compNum); |
---|
| 928 | _nodeStack.pop(); |
---|
| 929 | ++_compNum; |
---|
| 930 | } |
---|
| 931 | } |
---|
| 932 | |
---|
| 933 | void discover(const Edge& edge) { |
---|
| 934 | _predMap.set(_graph.target(edge), edge); |
---|
| 935 | } |
---|
| 936 | |
---|
| 937 | void examine(const Edge& edge) { |
---|
| 938 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
| 939 | return; |
---|
| 940 | } |
---|
| 941 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 942 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 943 | } |
---|
| 944 | } |
---|
| 945 | |
---|
| 946 | void backtrack(const Edge& edge) { |
---|
| 947 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 948 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 949 | } |
---|
| 950 | } |
---|
| 951 | |
---|
| 952 | private: |
---|
| 953 | const Graph& _graph; |
---|
| 954 | NodeMap& _compMap; |
---|
| 955 | int& _compNum; |
---|
| 956 | |
---|
| 957 | typename Graph::template NodeMap<int> _numMap; |
---|
| 958 | typename Graph::template NodeMap<int> _retMap; |
---|
| 959 | typename Graph::template NodeMap<Edge> _predMap; |
---|
| 960 | std::stack<Node> _nodeStack; |
---|
| 961 | int _num; |
---|
| 962 | }; |
---|
| 963 | |
---|
| 964 | |
---|
| 965 | template <typename Graph, typename EdgeMap> |
---|
[1800] | 966 | class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 967 | public: |
---|
| 968 | typedef typename Graph::Node Node; |
---|
| 969 | typedef typename Graph::Edge Edge; |
---|
[1909] | 970 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 971 | |
---|
[1800] | 972 | BiEdgeConnectedCutEdgesVisitor(const Graph& graph, |
---|
[1750] | 973 | EdgeMap& cutMap, int &cutNum) |
---|
| 974 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
| 975 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 976 | |
---|
| 977 | void start(const Node& node) { |
---|
| 978 | _predMap[node] = INVALID; |
---|
| 979 | } |
---|
| 980 | |
---|
| 981 | void reach(const Node& node) { |
---|
| 982 | _numMap.set(node, _num); |
---|
| 983 | _retMap.set(node, _num); |
---|
| 984 | ++_num; |
---|
| 985 | } |
---|
| 986 | |
---|
| 987 | void leave(const Node& node) { |
---|
| 988 | if (_numMap[node] <= _retMap[node]) { |
---|
| 989 | if (_predMap[node] != INVALID) { |
---|
| 990 | _cutMap.set(_predMap[node], true); |
---|
| 991 | ++_cutNum; |
---|
| 992 | } |
---|
| 993 | } |
---|
| 994 | } |
---|
| 995 | |
---|
| 996 | void discover(const Edge& edge) { |
---|
| 997 | _predMap.set(_graph.target(edge), edge); |
---|
| 998 | } |
---|
| 999 | |
---|
| 1000 | void examine(const Edge& edge) { |
---|
| 1001 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
| 1002 | return; |
---|
| 1003 | } |
---|
| 1004 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1005 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1006 | } |
---|
| 1007 | } |
---|
| 1008 | |
---|
| 1009 | void backtrack(const Edge& edge) { |
---|
| 1010 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1011 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1012 | } |
---|
| 1013 | } |
---|
| 1014 | |
---|
| 1015 | private: |
---|
| 1016 | const Graph& _graph; |
---|
| 1017 | EdgeMap& _cutMap; |
---|
| 1018 | int& _cutNum; |
---|
| 1019 | |
---|
| 1020 | typename Graph::template NodeMap<int> _numMap; |
---|
| 1021 | typename Graph::template NodeMap<int> _retMap; |
---|
| 1022 | typename Graph::template NodeMap<Edge> _predMap; |
---|
| 1023 | int _num; |
---|
| 1024 | }; |
---|
| 1025 | } |
---|
| 1026 | |
---|
[1909] | 1027 | template <typename UGraph> |
---|
| 1028 | int countbiEdgeConnectedComponents(const UGraph& graph); |
---|
[1750] | 1029 | |
---|
| 1030 | /// \ingroup topology |
---|
| 1031 | /// |
---|
[1767] | 1032 | /// \brief Checks that the graph is bi-edge-connected. |
---|
[1750] | 1033 | /// |
---|
[1767] | 1034 | /// This function checks that the graph is bi-edge-connected. The undirected |
---|
| 1035 | /// graph is bi-edge-connected when any two nodes are connected with two |
---|
[1750] | 1036 | /// edge-disjoint paths. |
---|
| 1037 | /// |
---|
| 1038 | /// \param graph The undirected graph. |
---|
| 1039 | /// \return The number of components. |
---|
| 1040 | /// \todo Make it faster. |
---|
[1909] | 1041 | template <typename UGraph> |
---|
| 1042 | bool biEdgeConnected(const UGraph& graph) { |
---|
[1800] | 1043 | return countBiEdgeConnectedComponents(graph) == 1; |
---|
[1750] | 1044 | } |
---|
| 1045 | |
---|
| 1046 | /// \ingroup topology |
---|
| 1047 | /// |
---|
[1767] | 1048 | /// \brief Count the bi-edge-connected components. |
---|
[1750] | 1049 | /// |
---|
[1767] | 1050 | /// This function count the bi-edge-connected components in an undirected |
---|
| 1051 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
[1750] | 1052 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
| 1053 | /// connected with at least two edge-disjoint paths. |
---|
| 1054 | /// |
---|
| 1055 | /// \param graph The undirected graph. |
---|
| 1056 | /// \return The number of components. |
---|
[1909] | 1057 | template <typename UGraph> |
---|
| 1058 | int countBiEdgeConnectedComponents(const UGraph& graph) { |
---|
| 1059 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 1060 | typedef typename UGraph::NodeIt NodeIt; |
---|
[1750] | 1061 | |
---|
| 1062 | using namespace _topology_bits; |
---|
| 1063 | |
---|
[1909] | 1064 | typedef CountBiEdgeConnectedComponentsVisitor<UGraph> Visitor; |
---|
[1750] | 1065 | |
---|
| 1066 | int compNum = 0; |
---|
| 1067 | Visitor visitor(graph, compNum); |
---|
| 1068 | |
---|
[1909] | 1069 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 1070 | dfs.init(); |
---|
| 1071 | |
---|
| 1072 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1073 | if (!dfs.reached(it)) { |
---|
| 1074 | dfs.addSource(it); |
---|
| 1075 | dfs.start(); |
---|
| 1076 | } |
---|
| 1077 | } |
---|
| 1078 | return compNum; |
---|
| 1079 | } |
---|
| 1080 | |
---|
| 1081 | /// \ingroup topology |
---|
| 1082 | /// |
---|
[1767] | 1083 | /// \brief Find the bi-edge-connected components. |
---|
[1750] | 1084 | /// |
---|
[1767] | 1085 | /// This function finds the bi-edge-connected components in an undirected |
---|
| 1086 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
[1750] | 1087 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
| 1088 | /// connected at least two edge-disjoint paths. |
---|
| 1089 | /// |
---|
[1763] | 1090 | /// \image html edge_biconnected_components.png |
---|
[1767] | 1091 | /// \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth |
---|
[1763] | 1092 | /// |
---|
[1750] | 1093 | /// \param graph The graph. |
---|
[1793] | 1094 | /// \retval compMap A writable node map. The values will be set from 0 to |
---|
[1750] | 1095 | /// the number of the biconnected components minus one. Each values |
---|
| 1096 | /// of the map will be set exactly once, the values of a certain component |
---|
| 1097 | /// will be set continuously. |
---|
| 1098 | /// \return The number of components. |
---|
[1763] | 1099 | /// |
---|
[1909] | 1100 | template <typename UGraph, typename NodeMap> |
---|
| 1101 | int biEdgeConnectedComponents(const UGraph& graph, NodeMap& compMap) { |
---|
| 1102 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 1103 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1104 | typedef typename UGraph::Node Node; |
---|
[1750] | 1105 | checkConcept<concept::WriteMap<Node, int>, NodeMap>(); |
---|
| 1106 | |
---|
| 1107 | using namespace _topology_bits; |
---|
| 1108 | |
---|
[1909] | 1109 | typedef BiEdgeConnectedComponentsVisitor<UGraph, NodeMap> Visitor; |
---|
[1750] | 1110 | |
---|
| 1111 | int compNum = 0; |
---|
| 1112 | Visitor visitor(graph, compMap, compNum); |
---|
| 1113 | |
---|
[1909] | 1114 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 1115 | dfs.init(); |
---|
| 1116 | |
---|
| 1117 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1118 | if (!dfs.reached(it)) { |
---|
| 1119 | dfs.addSource(it); |
---|
| 1120 | dfs.start(); |
---|
| 1121 | } |
---|
| 1122 | } |
---|
| 1123 | return compNum; |
---|
| 1124 | } |
---|
| 1125 | |
---|
| 1126 | /// \ingroup topology |
---|
| 1127 | /// |
---|
[1767] | 1128 | /// \brief Find the bi-edge-connected cut edges. |
---|
[1750] | 1129 | /// |
---|
[1767] | 1130 | /// This function finds the bi-edge-connected components in an undirected |
---|
| 1131 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
[1750] | 1132 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
[1767] | 1133 | /// connected with at least two edge-disjoint paths. The bi-edge-connected |
---|
[1750] | 1134 | /// components are separted by edges which are the cut edges of the |
---|
| 1135 | /// components. |
---|
| 1136 | /// |
---|
| 1137 | /// \param graph The graph. |
---|
[1793] | 1138 | /// \retval cutMap A writable node map. The values will be set true when the |
---|
[1750] | 1139 | /// edge is a cut edge. |
---|
| 1140 | /// \return The number of cut edges. |
---|
[1909] | 1141 | template <typename UGraph, typename UEdgeMap> |
---|
| 1142 | int biEdgeConnectedCutEdges(const UGraph& graph, UEdgeMap& cutMap) { |
---|
| 1143 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 1144 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1145 | typedef typename UGraph::UEdge UEdge; |
---|
| 1146 | checkConcept<concept::WriteMap<UEdge, bool>, UEdgeMap>(); |
---|
[1750] | 1147 | |
---|
| 1148 | using namespace _topology_bits; |
---|
| 1149 | |
---|
[1909] | 1150 | typedef BiEdgeConnectedCutEdgesVisitor<UGraph, UEdgeMap> Visitor; |
---|
[1750] | 1151 | |
---|
| 1152 | int cutNum = 0; |
---|
| 1153 | Visitor visitor(graph, cutMap, cutNum); |
---|
| 1154 | |
---|
[1909] | 1155 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 1156 | dfs.init(); |
---|
| 1157 | |
---|
| 1158 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1159 | if (!dfs.reached(it)) { |
---|
| 1160 | dfs.addSource(it); |
---|
| 1161 | dfs.start(); |
---|
| 1162 | } |
---|
| 1163 | } |
---|
| 1164 | return cutNum; |
---|
| 1165 | } |
---|
| 1166 | |
---|
| 1167 | |
---|
| 1168 | namespace _topology_bits { |
---|
| 1169 | |
---|
| 1170 | template <typename Graph, typename IntNodeMap> |
---|
| 1171 | class TopologicalSortVisitor : public DfsVisitor<Graph> { |
---|
| 1172 | public: |
---|
| 1173 | typedef typename Graph::Node Node; |
---|
| 1174 | typedef typename Graph::Edge edge; |
---|
| 1175 | |
---|
| 1176 | TopologicalSortVisitor(IntNodeMap& order, int num) |
---|
| 1177 | : _order(order), _num(num) {} |
---|
| 1178 | |
---|
| 1179 | void leave(const Node& node) { |
---|
| 1180 | _order.set(node, --_num); |
---|
[1698] | 1181 | } |
---|
| 1182 | |
---|
| 1183 | private: |
---|
[1750] | 1184 | IntNodeMap& _order; |
---|
| 1185 | int _num; |
---|
[1698] | 1186 | }; |
---|
[1750] | 1187 | |
---|
[1698] | 1188 | } |
---|
| 1189 | |
---|
[1750] | 1190 | /// \ingroup topology |
---|
| 1191 | /// |
---|
| 1192 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
| 1193 | /// |
---|
| 1194 | /// Sort the nodes of a DAG into topolgical order. |
---|
| 1195 | /// |
---|
[1793] | 1196 | /// \param graph The graph. It should be directed and acyclic. |
---|
| 1197 | /// \retval order A writable node map. The values will be set from 0 to |
---|
[1750] | 1198 | /// the number of the nodes in the graph minus one. Each values of the map |
---|
| 1199 | /// will be set exactly once, the values will be set descending order. |
---|
| 1200 | /// |
---|
| 1201 | /// \see checkedTopologicalSort |
---|
| 1202 | /// \see dag |
---|
[1698] | 1203 | template <typename Graph, typename NodeMap> |
---|
[1750] | 1204 | void topologicalSort(const Graph& graph, NodeMap& order) { |
---|
| 1205 | using namespace _topology_bits; |
---|
| 1206 | |
---|
| 1207 | checkConcept<concept::StaticGraph, Graph>(); |
---|
| 1208 | checkConcept<concept::WriteMap<typename Graph::Node, int>, NodeMap>(); |
---|
| 1209 | |
---|
| 1210 | typedef typename Graph::Node Node; |
---|
| 1211 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1212 | typedef typename Graph::Edge Edge; |
---|
| 1213 | |
---|
| 1214 | TopologicalSortVisitor<Graph, NodeMap> |
---|
| 1215 | visitor(order, countNodes(graph)); |
---|
| 1216 | |
---|
| 1217 | DfsVisit<Graph, TopologicalSortVisitor<Graph, NodeMap> > |
---|
| 1218 | dfs(graph, visitor); |
---|
| 1219 | |
---|
| 1220 | dfs.init(); |
---|
| 1221 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1222 | if (!dfs.reached(it)) { |
---|
| 1223 | dfs.addSource(it); |
---|
| 1224 | dfs.start(); |
---|
| 1225 | } |
---|
| 1226 | } |
---|
| 1227 | } |
---|
| 1228 | |
---|
| 1229 | /// \ingroup topology |
---|
| 1230 | /// |
---|
| 1231 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
| 1232 | /// |
---|
| 1233 | /// Sort the nodes of a DAG into topolgical order. It also checks |
---|
| 1234 | /// that the given graph is DAG. |
---|
| 1235 | /// |
---|
[1793] | 1236 | /// \param graph The graph. It should be directed and acyclic. |
---|
[1750] | 1237 | /// \retval order A readable - writable node map. The values will be set |
---|
| 1238 | /// from 0 to the number of the nodes in the graph minus one. Each values |
---|
| 1239 | /// of the map will be set exactly once, the values will be set descending |
---|
| 1240 | /// order. |
---|
| 1241 | /// \return %False when the graph is not DAG. |
---|
| 1242 | /// |
---|
| 1243 | /// \see topologicalSort |
---|
| 1244 | /// \see dag |
---|
| 1245 | template <typename Graph, typename NodeMap> |
---|
| 1246 | bool checkedTopologicalSort(const Graph& graph, NodeMap& order) { |
---|
[1698] | 1247 | using namespace _topology_bits; |
---|
| 1248 | |
---|
| 1249 | checkConcept<concept::StaticGraph, Graph>(); |
---|
| 1250 | checkConcept<concept::ReadWriteMap<typename Graph::Node, int>, NodeMap>(); |
---|
| 1251 | |
---|
| 1252 | typedef typename Graph::Node Node; |
---|
| 1253 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1254 | typedef typename Graph::Edge Edge; |
---|
| 1255 | |
---|
[1750] | 1256 | order = constMap<Node, int, -1>(); |
---|
[1698] | 1257 | |
---|
[1750] | 1258 | TopologicalSortVisitor<Graph, NodeMap> |
---|
| 1259 | visitor(order, countNodes(graph)); |
---|
[1698] | 1260 | |
---|
[1750] | 1261 | DfsVisit<Graph, TopologicalSortVisitor<Graph, NodeMap> > |
---|
| 1262 | dfs(graph, visitor); |
---|
[1698] | 1263 | |
---|
| 1264 | dfs.init(); |
---|
| 1265 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1266 | if (!dfs.reached(it)) { |
---|
| 1267 | dfs.addSource(it); |
---|
| 1268 | while (!dfs.emptyQueue()) { |
---|
[1750] | 1269 | Edge edge = dfs.nextEdge(); |
---|
| 1270 | Node target = graph.target(edge); |
---|
| 1271 | if (dfs.reached(target) && order[target] == -1) { |
---|
| 1272 | return false; |
---|
| 1273 | } |
---|
| 1274 | dfs.processNextEdge(); |
---|
| 1275 | } |
---|
[1698] | 1276 | } |
---|
[1750] | 1277 | } |
---|
[1698] | 1278 | return true; |
---|
| 1279 | } |
---|
| 1280 | |
---|
[1750] | 1281 | /// \ingroup topology |
---|
[1698] | 1282 | /// |
---|
[1750] | 1283 | /// \brief Check that the given directed graph is a DAG. |
---|
| 1284 | /// |
---|
| 1285 | /// Check that the given directed graph is a DAG. The DAG is |
---|
[1698] | 1286 | /// an Directed Acyclic Graph. |
---|
[1750] | 1287 | /// \return %False when the graph is not DAG. |
---|
| 1288 | /// \see acyclic |
---|
[1698] | 1289 | template <typename Graph> |
---|
| 1290 | bool dag(const Graph& graph) { |
---|
| 1291 | |
---|
| 1292 | checkConcept<concept::StaticGraph, Graph>(); |
---|
| 1293 | |
---|
| 1294 | typedef typename Graph::Node Node; |
---|
| 1295 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1296 | typedef typename Graph::Edge Edge; |
---|
| 1297 | |
---|
| 1298 | typedef typename Graph::template NodeMap<bool> ProcessedMap; |
---|
| 1299 | |
---|
| 1300 | typename Dfs<Graph>::template DefProcessedMap<ProcessedMap>:: |
---|
[1709] | 1301 | Create dfs(graph); |
---|
[1698] | 1302 | |
---|
| 1303 | ProcessedMap processed(graph); |
---|
| 1304 | dfs.processedMap(processed); |
---|
| 1305 | |
---|
| 1306 | dfs.init(); |
---|
| 1307 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1308 | if (!dfs.reached(it)) { |
---|
| 1309 | dfs.addSource(it); |
---|
| 1310 | while (!dfs.emptyQueue()) { |
---|
| 1311 | Edge edge = dfs.nextEdge(); |
---|
| 1312 | Node target = graph.target(edge); |
---|
| 1313 | if (dfs.reached(target) && !processed[target]) { |
---|
| 1314 | return false; |
---|
| 1315 | } |
---|
| 1316 | dfs.processNextEdge(); |
---|
| 1317 | } |
---|
| 1318 | } |
---|
| 1319 | } |
---|
| 1320 | return true; |
---|
| 1321 | } |
---|
| 1322 | |
---|
[1750] | 1323 | /// \ingroup topology |
---|
[1698] | 1324 | /// |
---|
| 1325 | /// \brief Check that the given undirected graph is acyclic. |
---|
| 1326 | /// |
---|
| 1327 | /// Check that the given undirected graph acyclic. |
---|
[1750] | 1328 | /// \param graph The undirected graph. |
---|
| 1329 | /// \return %True when there is no circle in the graph. |
---|
| 1330 | /// \see dag |
---|
[1909] | 1331 | template <typename UGraph> |
---|
| 1332 | bool acyclic(const UGraph& graph) { |
---|
| 1333 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 1334 | typedef typename UGraph::Node Node; |
---|
| 1335 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1336 | typedef typename UGraph::Edge Edge; |
---|
| 1337 | Dfs<UGraph> dfs(graph); |
---|
[1698] | 1338 | dfs.init(); |
---|
| 1339 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1340 | if (!dfs.reached(it)) { |
---|
| 1341 | dfs.addSource(it); |
---|
| 1342 | while (!dfs.emptyQueue()) { |
---|
| 1343 | Edge edge = dfs.nextEdge(); |
---|
| 1344 | Node source = graph.source(edge); |
---|
| 1345 | Node target = graph.target(edge); |
---|
| 1346 | if (dfs.reached(target) && |
---|
[1763] | 1347 | dfs.predEdge(source) != graph.oppositeEdge(edge)) { |
---|
[1698] | 1348 | return false; |
---|
| 1349 | } |
---|
| 1350 | dfs.processNextEdge(); |
---|
| 1351 | } |
---|
| 1352 | } |
---|
| 1353 | } |
---|
| 1354 | return true; |
---|
| 1355 | } |
---|
| 1356 | |
---|
[1750] | 1357 | /// \ingroup topology |
---|
| 1358 | /// |
---|
[1698] | 1359 | /// \brief Check that the given undirected graph is tree. |
---|
| 1360 | /// |
---|
| 1361 | /// Check that the given undirected graph is tree. |
---|
[1750] | 1362 | /// \param graph The undirected graph. |
---|
| 1363 | /// \return %True when the graph is acyclic and connected. |
---|
[1909] | 1364 | template <typename UGraph> |
---|
| 1365 | bool tree(const UGraph& graph) { |
---|
| 1366 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 1367 | typedef typename UGraph::Node Node; |
---|
| 1368 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1369 | typedef typename UGraph::Edge Edge; |
---|
| 1370 | Dfs<UGraph> dfs(graph); |
---|
[1698] | 1371 | dfs.init(); |
---|
| 1372 | dfs.addSource(NodeIt(graph)); |
---|
| 1373 | while (!dfs.emptyQueue()) { |
---|
| 1374 | Edge edge = dfs.nextEdge(); |
---|
| 1375 | Node source = graph.source(edge); |
---|
| 1376 | Node target = graph.target(edge); |
---|
| 1377 | if (dfs.reached(target) && |
---|
[1763] | 1378 | dfs.predEdge(source) != graph.oppositeEdge(edge)) { |
---|
[1698] | 1379 | return false; |
---|
| 1380 | } |
---|
| 1381 | dfs.processNextEdge(); |
---|
| 1382 | } |
---|
| 1383 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1384 | if (!dfs.reached(it)) { |
---|
| 1385 | return false; |
---|
| 1386 | } |
---|
| 1387 | } |
---|
| 1388 | return true; |
---|
| 1389 | } |
---|
[1739] | 1390 | |
---|
[1750] | 1391 | /// \ingroup topology |
---|
[1739] | 1392 | /// |
---|
[1800] | 1393 | /// \brief Check if the given undirected graph is bipartite or not |
---|
[1750] | 1394 | /// |
---|
[1800] | 1395 | /// The function checks if the given undirected \c graph graph is bipartite |
---|
| 1396 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
---|
[1750] | 1397 | /// \param graph The undirected graph. |
---|
[1800] | 1398 | /// \return %True if \c graph is bipartite, %false otherwise. |
---|
| 1399 | /// \sa bipartitePartitions |
---|
| 1400 | /// |
---|
| 1401 | /// \author Balazs Attila Mihaly |
---|
[1909] | 1402 | template<typename UGraph> |
---|
| 1403 | inline bool bipartite(const UGraph &graph){ |
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| 1404 | checkConcept<concept::UGraph, UGraph>(); |
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[1800] | 1405 | |
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[1909] | 1406 | typedef typename UGraph::NodeIt NodeIt; |
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| 1407 | typedef typename UGraph::EdgeIt EdgeIt; |
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[1800] | 1408 | |
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[1909] | 1409 | Bfs<UGraph> bfs(graph); |
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[1800] | 1410 | bfs.init(); |
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| 1411 | for(NodeIt i(graph);i!=INVALID;++i){ |
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| 1412 | if(!bfs.reached(i)){ |
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| 1413 | bfs.run(i); |
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| 1414 | } |
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| 1415 | } |
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| 1416 | for(EdgeIt i(graph);i!=INVALID;++i){ |
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| 1417 | if(bfs.dist(graph.source(i))==bfs.dist(graph.target(i)))return false; |
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| 1418 | } |
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| 1419 | return true; |
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[1979] | 1420 | } |
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[1800] | 1421 | |
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| 1422 | /// \ingroup topology |
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| 1423 | /// |
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| 1424 | /// \brief Check if the given undirected graph is bipartite or not |
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| 1425 | /// |
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| 1426 | /// The function checks if the given undirected graph is bipartite |
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| 1427 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
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| 1428 | /// During the execution, the \c partMap will be set as the two |
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| 1429 | /// partitions of the graph. |
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| 1430 | /// \param graph The undirected graph. |
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[1808] | 1431 | /// \retval partMap A writable bool map of nodes. It will be set as the |
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[1800] | 1432 | /// two partitions of the graph. |
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| 1433 | /// \return %True if \c graph is bipartite, %false otherwise. |
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| 1434 | /// |
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| 1435 | /// \author Balazs Attila Mihaly |
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| 1436 | /// |
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| 1437 | /// \image html bipartite_partitions.png |
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| 1438 | /// \image latex bipartite_partitions.eps "Bipartite partititions" width=\textwidth |
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[1909] | 1439 | template<typename UGraph, typename NodeMap> |
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| 1440 | inline bool bipartitePartitions(const UGraph &graph, NodeMap &partMap){ |
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| 1441 | checkConcept<concept::UGraph, UGraph>(); |
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[1800] | 1442 | |
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[1909] | 1443 | typedef typename UGraph::Node Node; |
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| 1444 | typedef typename UGraph::NodeIt NodeIt; |
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| 1445 | typedef typename UGraph::EdgeIt EdgeIt; |
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[1800] | 1446 | |
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[1909] | 1447 | Bfs<UGraph> bfs(graph); |
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[1800] | 1448 | bfs.init(); |
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| 1449 | for(NodeIt i(graph);i!=INVALID;++i){ |
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| 1450 | if(!bfs.reached(i)){ |
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| 1451 | bfs.addSource(i); |
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| 1452 | for(Node j=bfs.processNextNode();!bfs.emptyQueue(); |
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| 1453 | j=bfs.processNextNode()){ |
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| 1454 | partMap.set(j,bfs.dist(j)%2==0); |
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[1750] | 1455 | } |
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[1740] | 1456 | } |
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| 1457 | } |
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[1800] | 1458 | for(EdgeIt i(graph);i!=INVALID;++i){ |
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| 1459 | if(bfs.dist(graph.source(i)) == bfs.dist(graph.target(i)))return false; |
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| 1460 | } |
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[1750] | 1461 | return true; |
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[1979] | 1462 | } |
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[1750] | 1463 | |
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[1698] | 1464 | } //namespace lemon |
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| 1465 | |
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| 1466 | #endif //LEMON_TOPOLOGY_H |
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