[1698] | 1 | /* -*- C++ -*- |
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| 2 | * lemon/topology.h - Part of LEMON, a generic C++ optimization library |
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| 3 | * |
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[1875] | 4 | * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1698] | 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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| 17 | #ifndef LEMON_TOPOLOGY_H |
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| 18 | #define LEMON_TOPOLOGY_H |
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| 19 | |
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| 20 | #include <lemon/dfs.h> |
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[1740] | 21 | #include <lemon/bfs.h> |
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[1698] | 22 | #include <lemon/graph_utils.h> |
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[1750] | 23 | #include <lemon/graph_adaptor.h> |
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| 24 | #include <lemon/maps.h> |
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[1698] | 25 | |
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| 26 | #include <lemon/concept/graph.h> |
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[1909] | 27 | #include <lemon/concept/ugraph.h> |
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[1698] | 28 | #include <lemon/concept_check.h> |
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| 29 | |
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[1750] | 30 | #include <lemon/bin_heap.h> |
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| 31 | #include <lemon/linear_heap.h> |
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| 32 | |
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| 33 | #include <stack> |
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| 34 | #include <functional> |
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| 35 | |
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| 36 | /// \ingroup topology |
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[1698] | 37 | /// \file |
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| 38 | /// \brief Topology related algorithms |
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| 39 | /// |
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| 40 | /// Topology related algorithms |
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| 41 | |
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| 42 | namespace lemon { |
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| 43 | |
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[1750] | 44 | /// \ingroup topology |
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| 45 | /// |
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| 46 | /// \brief Check that the given undirected graph is connected. |
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| 47 | /// |
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| 48 | /// Check that the given undirected graph connected. |
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| 49 | /// \param graph The undirected graph. |
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| 50 | /// \return %True when there is path between any two nodes in the graph. |
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[1807] | 51 | /// \note By definition, the empty graph is connected. |
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[1909] | 52 | template <typename UGraph> |
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| 53 | bool connected(const UGraph& graph) { |
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| 54 | checkConcept<concept::UGraph, UGraph>(); |
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| 55 | typedef typename UGraph::NodeIt NodeIt; |
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[1807] | 56 | if (NodeIt(graph) == INVALID) return true; |
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[1909] | 57 | Dfs<UGraph> dfs(graph); |
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[1750] | 58 | dfs.run(NodeIt(graph)); |
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| 59 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 60 | if (!dfs.reached(it)) { |
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| 61 | return false; |
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| 62 | } |
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| 63 | } |
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| 64 | return true; |
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| 65 | } |
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| 66 | |
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| 67 | /// \ingroup topology |
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| 68 | /// |
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| 69 | /// \brief Count the number of connected components of an undirected graph |
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| 70 | /// |
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| 71 | /// Count the number of connected components of an undirected graph |
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| 72 | /// |
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[1793] | 73 | /// \param graph The graph. It should be undirected. |
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[1750] | 74 | /// \return The number of components |
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[1807] | 75 | /// \note By definition, the empty graph consists |
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| 76 | /// of zero connected components. |
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[1909] | 77 | template <typename UGraph> |
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| 78 | int countConnectedComponents(const UGraph &graph) { |
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| 79 | checkConcept<concept::UGraph, UGraph>(); |
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| 80 | typedef typename UGraph::Node Node; |
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| 81 | typedef typename UGraph::Edge Edge; |
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[1750] | 82 | |
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| 83 | typedef NullMap<Node, Edge> PredMap; |
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| 84 | typedef NullMap<Node, int> DistMap; |
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| 85 | |
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| 86 | int compNum = 0; |
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[1909] | 87 | typename Bfs<UGraph>:: |
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[1750] | 88 | template DefPredMap<PredMap>:: |
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| 89 | template DefDistMap<DistMap>:: |
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| 90 | Create bfs(graph); |
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| 91 | |
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| 92 | PredMap predMap; |
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| 93 | bfs.predMap(predMap); |
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| 94 | |
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| 95 | DistMap distMap; |
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| 96 | bfs.distMap(distMap); |
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| 97 | |
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| 98 | bfs.init(); |
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[1909] | 99 | for(typename UGraph::NodeIt n(graph); n != INVALID; ++n) { |
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[1750] | 100 | if (!bfs.reached(n)) { |
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| 101 | bfs.addSource(n); |
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| 102 | bfs.start(); |
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| 103 | ++compNum; |
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| 104 | } |
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| 105 | } |
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| 106 | return compNum; |
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| 107 | } |
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| 108 | |
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| 109 | /// \ingroup topology |
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| 110 | /// |
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| 111 | /// \brief Find the connected components of an undirected graph |
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| 112 | /// |
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| 113 | /// Find the connected components of an undirected graph. |
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| 114 | /// |
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[1763] | 115 | /// \image html connected_components.png |
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| 116 | /// \image latex connected_components.eps "Connected components" width=\textwidth |
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| 117 | /// |
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[1793] | 118 | /// \param graph The graph. It should be undirected. |
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| 119 | /// \retval compMap A writable node map. The values will be set from 0 to |
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[1750] | 120 | /// the number of the connected components minus one. Each values of the map |
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| 121 | /// will be set exactly once, the values of a certain component will be |
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| 122 | /// set continuously. |
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| 123 | /// \return The number of components |
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[1763] | 124 | /// |
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[1909] | 125 | template <class UGraph, class NodeMap> |
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| 126 | int connectedComponents(const UGraph &graph, NodeMap &compMap) { |
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| 127 | checkConcept<concept::UGraph, UGraph>(); |
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| 128 | typedef typename UGraph::Node Node; |
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| 129 | typedef typename UGraph::Edge Edge; |
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[1750] | 130 | checkConcept<concept::WriteMap<Node, int>, NodeMap>(); |
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| 131 | |
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| 132 | typedef NullMap<Node, Edge> PredMap; |
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| 133 | typedef NullMap<Node, int> DistMap; |
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| 134 | |
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| 135 | int compNum = 0; |
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[1909] | 136 | typename Bfs<UGraph>:: |
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[1750] | 137 | template DefPredMap<PredMap>:: |
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| 138 | template DefDistMap<DistMap>:: |
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| 139 | Create bfs(graph); |
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| 140 | |
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| 141 | PredMap predMap; |
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| 142 | bfs.predMap(predMap); |
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| 143 | |
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| 144 | DistMap distMap; |
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| 145 | bfs.distMap(distMap); |
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| 146 | |
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| 147 | bfs.init(); |
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[1909] | 148 | for(typename UGraph::NodeIt n(graph); n != INVALID; ++n) { |
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[1750] | 149 | if(!bfs.reached(n)) { |
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| 150 | bfs.addSource(n); |
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| 151 | while (!bfs.emptyQueue()) { |
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| 152 | compMap.set(bfs.nextNode(), compNum); |
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| 153 | bfs.processNextNode(); |
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| 154 | } |
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| 155 | ++compNum; |
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| 156 | } |
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| 157 | } |
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| 158 | return compNum; |
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| 159 | } |
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| 160 | |
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| 161 | namespace _topology_bits { |
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| 162 | |
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| 163 | template <typename Graph, typename Iterator > |
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| 164 | struct LeaveOrderVisitor : public DfsVisitor<Graph> { |
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| 165 | public: |
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| 166 | typedef typename Graph::Node Node; |
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| 167 | LeaveOrderVisitor(Iterator it) : _it(it) {} |
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| 168 | |
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| 169 | void leave(const Node& node) { |
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| 170 | *(_it++) = node; |
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| 171 | } |
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| 172 | |
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| 173 | private: |
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| 174 | Iterator _it; |
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| 175 | }; |
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| 176 | |
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| 177 | template <typename Graph, typename Map> |
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| 178 | struct FillMapVisitor : public DfsVisitor<Graph> { |
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| 179 | public: |
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| 180 | typedef typename Graph::Node Node; |
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| 181 | typedef typename Map::Value Value; |
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| 182 | |
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| 183 | FillMapVisitor(Map& map, Value& value) |
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| 184 | : _map(map), _value(value) {} |
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| 185 | |
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| 186 | void reach(const Node& node) { |
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| 187 | _map.set(node, _value); |
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| 188 | } |
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| 189 | private: |
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| 190 | Map& _map; |
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| 191 | Value& _value; |
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| 192 | }; |
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| 193 | |
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| 194 | template <typename Graph, typename EdgeMap> |
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| 195 | struct StronglyConnectedCutEdgesVisitor : public DfsVisitor<Graph> { |
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| 196 | public: |
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| 197 | typedef typename Graph::Node Node; |
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| 198 | typedef typename Graph::Edge Edge; |
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| 199 | |
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| 200 | StronglyConnectedCutEdgesVisitor(const Graph& graph, EdgeMap& cutMap, |
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| 201 | int& cutNum) |
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| 202 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
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| 203 | _compMap(graph), _num(0) { |
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| 204 | } |
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| 205 | |
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| 206 | void stop(const Node&) { |
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| 207 | ++_num; |
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| 208 | } |
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| 209 | |
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| 210 | void reach(const Node& node) { |
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| 211 | _compMap.set(node, _num); |
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| 212 | } |
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| 213 | |
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| 214 | void examine(const Edge& edge) { |
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| 215 | if (_compMap[_graph.source(edge)] != _compMap[_graph.target(edge)]) { |
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| 216 | _cutMap.set(edge, true); |
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| 217 | ++_cutNum; |
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| 218 | } |
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| 219 | } |
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| 220 | private: |
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| 221 | const Graph& _graph; |
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| 222 | EdgeMap& _cutMap; |
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| 223 | int& _cutNum; |
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| 224 | |
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| 225 | typename Graph::template NodeMap<int> _compMap; |
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| 226 | int _num; |
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| 227 | }; |
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| 228 | |
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| 229 | } |
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| 230 | |
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| 231 | |
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| 232 | /// \ingroup topology |
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| 233 | /// |
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| 234 | /// \brief Check that the given directed graph is strongly connected. |
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| 235 | /// |
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| 236 | /// Check that the given directed graph is strongly connected. The |
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| 237 | /// graph is strongly connected when any two nodes of the graph are |
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[1817] | 238 | /// connected with directed paths in both direction. |
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[1750] | 239 | /// \return %False when the graph is not strongly connected. |
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| 240 | /// \see connected |
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| 241 | /// |
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[1807] | 242 | /// \note By definition, the empty graph is strongly connected. |
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[1750] | 243 | template <typename Graph> |
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| 244 | bool stronglyConnected(const Graph& graph) { |
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| 245 | checkConcept<concept::StaticGraph, Graph>(); |
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[1807] | 246 | if (NodeIt(graph) == INVALID) return true; |
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[1750] | 247 | |
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| 248 | typedef typename Graph::Node Node; |
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| 249 | typedef typename Graph::NodeIt NodeIt; |
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| 250 | |
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| 251 | using namespace _topology_bits; |
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| 252 | |
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| 253 | typedef DfsVisitor<Graph> Visitor; |
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| 254 | Visitor visitor; |
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| 255 | |
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| 256 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 257 | dfs.init(); |
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| 258 | dfs.addSource(NodeIt(graph)); |
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| 259 | dfs.start(); |
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| 260 | |
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| 261 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 262 | if (!dfs.reached(it)) { |
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| 263 | return false; |
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| 264 | } |
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| 265 | } |
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| 266 | |
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| 267 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 268 | RGraph rgraph(graph); |
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| 269 | |
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| 270 | typedef DfsVisitor<Graph> RVisitor; |
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| 271 | RVisitor rvisitor; |
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| 272 | |
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| 273 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 274 | rdfs.init(); |
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| 275 | rdfs.addSource(NodeIt(graph)); |
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| 276 | rdfs.start(); |
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| 277 | |
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| 278 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 279 | if (!rdfs.reached(it)) { |
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| 280 | return false; |
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| 281 | } |
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| 282 | } |
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| 283 | |
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| 284 | return true; |
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| 285 | } |
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| 286 | |
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| 287 | /// \ingroup topology |
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| 288 | /// |
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| 289 | /// \brief Count the strongly connected components of a directed graph |
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| 290 | /// |
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| 291 | /// Count the strongly connected components of a directed graph. |
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| 292 | /// The strongly connected components are the classes of an equivalence |
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| 293 | /// relation on the nodes of the graph. Two nodes are connected with |
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| 294 | /// directed paths in both direction. |
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| 295 | /// |
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[1793] | 296 | /// \param graph The graph. |
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[1750] | 297 | /// \return The number of components |
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[1807] | 298 | /// \note By definition, the empty graph has zero |
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| 299 | /// strongly connected components. |
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[1750] | 300 | template <typename Graph> |
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| 301 | int countStronglyConnectedComponents(const Graph& graph) { |
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| 302 | checkConcept<concept::StaticGraph, Graph>(); |
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| 303 | |
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| 304 | using namespace _topology_bits; |
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| 305 | |
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| 306 | typedef typename Graph::Node Node; |
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| 307 | typedef typename Graph::Edge Edge; |
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| 308 | typedef typename Graph::NodeIt NodeIt; |
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| 309 | typedef typename Graph::EdgeIt EdgeIt; |
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| 310 | |
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| 311 | typedef std::vector<Node> Container; |
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| 312 | typedef typename Container::iterator Iterator; |
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| 313 | |
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| 314 | Container nodes(countNodes(graph)); |
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| 315 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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| 316 | Visitor visitor(nodes.begin()); |
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| 317 | |
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| 318 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 319 | dfs.init(); |
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| 320 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 321 | if (!dfs.reached(it)) { |
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| 322 | dfs.addSource(it); |
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| 323 | dfs.start(); |
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| 324 | } |
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| 325 | } |
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| 326 | |
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| 327 | typedef typename Container::reverse_iterator RIterator; |
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| 328 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 329 | |
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| 330 | RGraph rgraph(graph); |
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| 331 | |
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| 332 | typedef DfsVisitor<Graph> RVisitor; |
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| 333 | RVisitor rvisitor; |
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| 334 | |
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| 335 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 336 | |
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| 337 | int compNum = 0; |
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| 338 | |
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| 339 | rdfs.init(); |
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| 340 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 341 | if (!rdfs.reached(*it)) { |
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| 342 | rdfs.addSource(*it); |
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| 343 | rdfs.start(); |
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| 344 | ++compNum; |
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| 345 | } |
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| 346 | } |
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| 347 | return compNum; |
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| 348 | } |
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| 349 | |
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| 350 | /// \ingroup topology |
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| 351 | /// |
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| 352 | /// \brief Find the strongly connected components of a directed graph |
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| 353 | /// |
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| 354 | /// Find the strongly connected components of a directed graph. |
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| 355 | /// The strongly connected components are the classes of an equivalence |
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| 356 | /// relation on the nodes of the graph. Two nodes are in relationship |
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| 357 | /// when there are directed paths between them in both direction. |
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| 358 | /// |
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[1763] | 359 | /// \image html strongly_connected_components.png |
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| 360 | /// \image latex strongly_connected_components.eps "Strongly connected components" width=\textwidth |
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| 361 | /// |
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[1793] | 362 | /// \param graph The graph. |
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| 363 | /// \retval compMap A writable node map. The values will be set from 0 to |
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[1750] | 364 | /// the number of the strongly connected components minus one. Each values |
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| 365 | /// of the map will be set exactly once, the values of a certain component |
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| 366 | /// will be set continuously. |
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| 367 | /// \return The number of components |
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[1763] | 368 | /// |
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[1750] | 369 | template <typename Graph, typename NodeMap> |
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| 370 | int stronglyConnectedComponents(const Graph& graph, NodeMap& compMap) { |
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| 371 | checkConcept<concept::StaticGraph, Graph>(); |
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| 372 | typedef typename Graph::Node Node; |
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| 373 | typedef typename Graph::NodeIt NodeIt; |
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| 374 | checkConcept<concept::WriteMap<Node, int>, NodeMap>(); |
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| 375 | |
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| 376 | using namespace _topology_bits; |
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| 377 | |
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| 378 | typedef std::vector<Node> Container; |
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| 379 | typedef typename Container::iterator Iterator; |
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| 380 | |
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| 381 | Container nodes(countNodes(graph)); |
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| 382 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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| 383 | Visitor visitor(nodes.begin()); |
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| 384 | |
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| 385 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 386 | dfs.init(); |
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| 387 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 388 | if (!dfs.reached(it)) { |
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| 389 | dfs.addSource(it); |
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| 390 | dfs.start(); |
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| 391 | } |
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| 392 | } |
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| 393 | |
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| 394 | typedef typename Container::reverse_iterator RIterator; |
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| 395 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 396 | |
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| 397 | RGraph rgraph(graph); |
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| 398 | |
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| 399 | int compNum = 0; |
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| 400 | |
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| 401 | typedef FillMapVisitor<RGraph, NodeMap> RVisitor; |
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| 402 | RVisitor rvisitor(compMap, compNum); |
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| 403 | |
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| 404 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 405 | |
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| 406 | rdfs.init(); |
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| 407 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 408 | if (!rdfs.reached(*it)) { |
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| 409 | rdfs.addSource(*it); |
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| 410 | rdfs.start(); |
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| 411 | ++compNum; |
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| 412 | } |
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| 413 | } |
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| 414 | return compNum; |
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| 415 | } |
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| 416 | |
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| 417 | /// \ingroup topology |
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| 418 | /// |
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| 419 | /// \brief Find the cut edges of the strongly connected components. |
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| 420 | /// |
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| 421 | /// Find the cut edges of the strongly connected components. |
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| 422 | /// The strongly connected components are the classes of an equivalence |
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| 423 | /// relation on the nodes of the graph. Two nodes are in relationship |
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| 424 | /// when there are directed paths between them in both direction. |
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| 425 | /// The strongly connected components are separated by the cut edges. |
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| 426 | /// |
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[1793] | 427 | /// \param graph The graph. |
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| 428 | /// \retval cutMap A writable node map. The values will be set true when the |
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| 429 | /// edge is a cut edge. |
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[1750] | 430 | /// |
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| 431 | /// \return The number of cut edges |
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| 432 | template <typename Graph, typename EdgeMap> |
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| 433 | int stronglyConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) { |
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| 434 | checkConcept<concept::StaticGraph, Graph>(); |
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| 435 | typedef typename Graph::Node Node; |
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| 436 | typedef typename Graph::Edge Edge; |
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| 437 | typedef typename Graph::NodeIt NodeIt; |
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| 438 | checkConcept<concept::WriteMap<Edge, bool>, EdgeMap>(); |
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| 439 | |
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| 440 | using namespace _topology_bits; |
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| 441 | |
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| 442 | typedef std::vector<Node> Container; |
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| 443 | typedef typename Container::iterator Iterator; |
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| 444 | |
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| 445 | Container nodes(countNodes(graph)); |
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| 446 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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| 447 | Visitor visitor(nodes.begin()); |
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| 448 | |
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| 449 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 450 | dfs.init(); |
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| 451 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 452 | if (!dfs.reached(it)) { |
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| 453 | dfs.addSource(it); |
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| 454 | dfs.start(); |
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| 455 | } |
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| 456 | } |
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| 457 | |
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| 458 | typedef typename Container::reverse_iterator RIterator; |
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| 459 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 460 | |
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| 461 | RGraph rgraph(graph); |
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| 462 | |
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| 463 | int cutNum = 0; |
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| 464 | |
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| 465 | typedef StronglyConnectedCutEdgesVisitor<RGraph, EdgeMap> RVisitor; |
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| 466 | RVisitor rvisitor(rgraph, cutMap, cutNum); |
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| 467 | |
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| 468 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 469 | |
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| 470 | rdfs.init(); |
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| 471 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 472 | if (!rdfs.reached(*it)) { |
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| 473 | rdfs.addSource(*it); |
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| 474 | rdfs.start(); |
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| 475 | } |
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| 476 | } |
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| 477 | return cutNum; |
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| 478 | } |
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| 479 | |
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[1698] | 480 | namespace _topology_bits { |
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| 481 | |
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[1750] | 482 | template <typename Graph> |
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[1800] | 483 | class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
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[1698] | 484 | public: |
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[1750] | 485 | typedef typename Graph::Node Node; |
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| 486 | typedef typename Graph::Edge Edge; |
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[1909] | 487 | typedef typename Graph::UEdge UEdge; |
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[1698] | 488 | |
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[1800] | 489 | CountBiNodeConnectedComponentsVisitor(const Graph& graph, int &compNum) |
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[1750] | 490 | : _graph(graph), _compNum(compNum), |
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| 491 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
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| 492 | |
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| 493 | void start(const Node& node) { |
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| 494 | _predMap.set(node, INVALID); |
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| 495 | } |
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| 496 | |
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| 497 | void reach(const Node& node) { |
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| 498 | _numMap.set(node, _num); |
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| 499 | _retMap.set(node, _num); |
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| 500 | ++_num; |
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| 501 | } |
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| 502 | |
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| 503 | void discover(const Edge& edge) { |
---|
| 504 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
| 505 | } |
---|
| 506 | |
---|
| 507 | void examine(const Edge& edge) { |
---|
| 508 | if (_graph.source(edge) == _graph.target(edge) && |
---|
| 509 | _graph.direction(edge)) { |
---|
| 510 | ++_compNum; |
---|
| 511 | return; |
---|
| 512 | } |
---|
| 513 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) { |
---|
| 514 | return; |
---|
| 515 | } |
---|
| 516 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
| 517 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
[1698] | 518 | } |
---|
| 519 | } |
---|
| 520 | |
---|
[1750] | 521 | void backtrack(const Edge& edge) { |
---|
| 522 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 523 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 524 | } |
---|
| 525 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
| 526 | ++_compNum; |
---|
| 527 | } |
---|
| 528 | } |
---|
| 529 | |
---|
| 530 | private: |
---|
| 531 | const Graph& _graph; |
---|
| 532 | int& _compNum; |
---|
| 533 | |
---|
| 534 | typename Graph::template NodeMap<int> _numMap; |
---|
| 535 | typename Graph::template NodeMap<int> _retMap; |
---|
| 536 | typename Graph::template NodeMap<Node> _predMap; |
---|
| 537 | int _num; |
---|
| 538 | }; |
---|
| 539 | |
---|
| 540 | template <typename Graph, typename EdgeMap> |
---|
[1800] | 541 | class BiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 542 | public: |
---|
| 543 | typedef typename Graph::Node Node; |
---|
| 544 | typedef typename Graph::Edge Edge; |
---|
[1909] | 545 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 546 | |
---|
[1800] | 547 | BiNodeConnectedComponentsVisitor(const Graph& graph, |
---|
[1750] | 548 | EdgeMap& compMap, int &compNum) |
---|
| 549 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
| 550 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 551 | |
---|
| 552 | void start(const Node& node) { |
---|
| 553 | _predMap.set(node, INVALID); |
---|
| 554 | } |
---|
| 555 | |
---|
| 556 | void reach(const Node& node) { |
---|
| 557 | _numMap.set(node, _num); |
---|
| 558 | _retMap.set(node, _num); |
---|
| 559 | ++_num; |
---|
| 560 | } |
---|
| 561 | |
---|
| 562 | void discover(const Edge& edge) { |
---|
| 563 | Node target = _graph.target(edge); |
---|
| 564 | _predMap.set(target, edge); |
---|
| 565 | _edgeStack.push(edge); |
---|
| 566 | } |
---|
| 567 | |
---|
| 568 | void examine(const Edge& edge) { |
---|
| 569 | Node source = _graph.source(edge); |
---|
| 570 | Node target = _graph.target(edge); |
---|
| 571 | if (source == target && _graph.direction(edge)) { |
---|
| 572 | _compMap.set(edge, _compNum); |
---|
| 573 | ++_compNum; |
---|
| 574 | return; |
---|
| 575 | } |
---|
| 576 | if (_numMap[target] < _numMap[source]) { |
---|
| 577 | if (_predMap[source] != _graph.oppositeEdge(edge)) { |
---|
| 578 | _edgeStack.push(edge); |
---|
| 579 | } |
---|
| 580 | } |
---|
| 581 | if (_predMap[source] != INVALID && |
---|
| 582 | target == _graph.source(_predMap[source])) { |
---|
| 583 | return; |
---|
| 584 | } |
---|
| 585 | if (_retMap[source] > _numMap[target]) { |
---|
| 586 | _retMap.set(source, _numMap[target]); |
---|
| 587 | } |
---|
| 588 | } |
---|
| 589 | |
---|
| 590 | void backtrack(const Edge& edge) { |
---|
| 591 | Node source = _graph.source(edge); |
---|
| 592 | Node target = _graph.target(edge); |
---|
| 593 | if (_retMap[source] > _retMap[target]) { |
---|
| 594 | _retMap.set(source, _retMap[target]); |
---|
| 595 | } |
---|
| 596 | if (_numMap[source] <= _retMap[target]) { |
---|
| 597 | while (_edgeStack.top() != edge) { |
---|
| 598 | _compMap.set(_edgeStack.top(), _compNum); |
---|
| 599 | _edgeStack.pop(); |
---|
| 600 | } |
---|
| 601 | _compMap.set(edge, _compNum); |
---|
| 602 | _edgeStack.pop(); |
---|
| 603 | ++_compNum; |
---|
| 604 | } |
---|
| 605 | } |
---|
| 606 | |
---|
| 607 | private: |
---|
| 608 | const Graph& _graph; |
---|
| 609 | EdgeMap& _compMap; |
---|
| 610 | int& _compNum; |
---|
| 611 | |
---|
| 612 | typename Graph::template NodeMap<int> _numMap; |
---|
| 613 | typename Graph::template NodeMap<int> _retMap; |
---|
| 614 | typename Graph::template NodeMap<Edge> _predMap; |
---|
[1909] | 615 | std::stack<UEdge> _edgeStack; |
---|
[1750] | 616 | int _num; |
---|
| 617 | }; |
---|
| 618 | |
---|
| 619 | |
---|
| 620 | template <typename Graph, typename NodeMap> |
---|
[1800] | 621 | class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 622 | public: |
---|
| 623 | typedef typename Graph::Node Node; |
---|
| 624 | typedef typename Graph::Edge Edge; |
---|
[1909] | 625 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 626 | |
---|
[1800] | 627 | BiNodeConnectedCutNodesVisitor(const Graph& graph, NodeMap& cutMap, |
---|
[1750] | 628 | int& cutNum) |
---|
| 629 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
| 630 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 631 | |
---|
| 632 | void start(const Node& node) { |
---|
| 633 | _predMap.set(node, INVALID); |
---|
| 634 | rootCut = false; |
---|
| 635 | } |
---|
| 636 | |
---|
| 637 | void reach(const Node& node) { |
---|
| 638 | _numMap.set(node, _num); |
---|
| 639 | _retMap.set(node, _num); |
---|
| 640 | ++_num; |
---|
| 641 | } |
---|
| 642 | |
---|
| 643 | void discover(const Edge& edge) { |
---|
| 644 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
| 645 | } |
---|
| 646 | |
---|
| 647 | void examine(const Edge& edge) { |
---|
| 648 | if (_graph.source(edge) == _graph.target(edge) && |
---|
| 649 | _graph.direction(edge)) { |
---|
| 650 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 651 | _cutMap.set(_graph.source(edge), true); |
---|
| 652 | ++_cutNum; |
---|
| 653 | } |
---|
| 654 | return; |
---|
| 655 | } |
---|
| 656 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) return; |
---|
| 657 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
| 658 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
| 659 | } |
---|
| 660 | } |
---|
| 661 | |
---|
| 662 | void backtrack(const Edge& edge) { |
---|
| 663 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 664 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 665 | } |
---|
| 666 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
| 667 | if (_predMap[_graph.source(edge)] != INVALID) { |
---|
| 668 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 669 | _cutMap.set(_graph.source(edge), true); |
---|
| 670 | ++_cutNum; |
---|
| 671 | } |
---|
| 672 | } else if (rootCut) { |
---|
| 673 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 674 | _cutMap.set(_graph.source(edge), true); |
---|
| 675 | ++_cutNum; |
---|
| 676 | } |
---|
| 677 | } else { |
---|
| 678 | rootCut = true; |
---|
| 679 | } |
---|
| 680 | } |
---|
| 681 | } |
---|
| 682 | |
---|
| 683 | private: |
---|
| 684 | const Graph& _graph; |
---|
| 685 | NodeMap& _cutMap; |
---|
| 686 | int& _cutNum; |
---|
| 687 | |
---|
| 688 | typename Graph::template NodeMap<int> _numMap; |
---|
| 689 | typename Graph::template NodeMap<int> _retMap; |
---|
| 690 | typename Graph::template NodeMap<Node> _predMap; |
---|
[1909] | 691 | std::stack<UEdge> _edgeStack; |
---|
[1750] | 692 | int _num; |
---|
| 693 | bool rootCut; |
---|
| 694 | }; |
---|
| 695 | |
---|
| 696 | } |
---|
| 697 | |
---|
[1909] | 698 | template <typename UGraph> |
---|
| 699 | int countBiNodeConnectedComponents(const UGraph& graph); |
---|
[1750] | 700 | |
---|
| 701 | /// \ingroup topology |
---|
| 702 | /// |
---|
[1767] | 703 | /// \brief Checks the graph is bi-node-connected. |
---|
[1750] | 704 | /// |
---|
[1767] | 705 | /// This function checks that the undirected graph is bi-node-connected |
---|
| 706 | /// graph. The graph is bi-node-connected if any two undirected edge is |
---|
[1750] | 707 | /// on same circle. |
---|
| 708 | /// |
---|
| 709 | /// \param graph The graph. |
---|
[1767] | 710 | /// \return %True when the graph bi-node-connected. |
---|
[1750] | 711 | /// \todo Make it faster. |
---|
[1909] | 712 | template <typename UGraph> |
---|
| 713 | bool biNodeConnected(const UGraph& graph) { |
---|
[1800] | 714 | return countBiNodeConnectedComponents(graph) == 1; |
---|
[1750] | 715 | } |
---|
| 716 | |
---|
| 717 | /// \ingroup topology |
---|
| 718 | /// |
---|
| 719 | /// \brief Count the biconnected components. |
---|
| 720 | /// |
---|
[1767] | 721 | /// This function finds the bi-node-connected components in an undirected |
---|
[1750] | 722 | /// graph. The biconnected components are the classes of an equivalence |
---|
| 723 | /// relation on the undirected edges. Two undirected edge is in relationship |
---|
| 724 | /// when they are on same circle. |
---|
| 725 | /// |
---|
| 726 | /// \param graph The graph. |
---|
| 727 | /// \return The number of components. |
---|
[1909] | 728 | template <typename UGraph> |
---|
| 729 | int countBiNodeConnectedComponents(const UGraph& graph) { |
---|
| 730 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 731 | typedef typename UGraph::NodeIt NodeIt; |
---|
[1750] | 732 | |
---|
| 733 | using namespace _topology_bits; |
---|
| 734 | |
---|
[1909] | 735 | typedef CountBiNodeConnectedComponentsVisitor<UGraph> Visitor; |
---|
[1750] | 736 | |
---|
| 737 | int compNum = 0; |
---|
| 738 | Visitor visitor(graph, compNum); |
---|
| 739 | |
---|
[1909] | 740 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 741 | dfs.init(); |
---|
| 742 | |
---|
| 743 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 744 | if (!dfs.reached(it)) { |
---|
| 745 | dfs.addSource(it); |
---|
| 746 | dfs.start(); |
---|
| 747 | } |
---|
| 748 | } |
---|
| 749 | return compNum; |
---|
| 750 | } |
---|
| 751 | |
---|
| 752 | /// \ingroup topology |
---|
| 753 | /// |
---|
[1767] | 754 | /// \brief Find the bi-node-connected components. |
---|
[1750] | 755 | /// |
---|
[1767] | 756 | /// This function finds the bi-node-connected components in an undirected |
---|
| 757 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
[1750] | 758 | /// relation on the undirected edges. Two undirected edge are in relationship |
---|
| 759 | /// when they are on same circle. |
---|
| 760 | /// |
---|
[1763] | 761 | /// \image html node_biconnected_components.png |
---|
[1767] | 762 | /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth |
---|
[1763] | 763 | /// |
---|
[1750] | 764 | /// \param graph The graph. |
---|
[1909] | 765 | /// \retval compMap A writable uedge map. The values will be set from 0 |
---|
[1793] | 766 | /// to the number of the biconnected components minus one. Each values |
---|
[1750] | 767 | /// of the map will be set exactly once, the values of a certain component |
---|
| 768 | /// will be set continuously. |
---|
| 769 | /// \return The number of components. |
---|
[1763] | 770 | /// |
---|
[1909] | 771 | template <typename UGraph, typename UEdgeMap> |
---|
| 772 | int biNodeConnectedComponents(const UGraph& graph, |
---|
| 773 | UEdgeMap& compMap) { |
---|
| 774 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 775 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 776 | typedef typename UGraph::UEdge UEdge; |
---|
| 777 | checkConcept<concept::WriteMap<UEdge, int>, UEdgeMap>(); |
---|
[1750] | 778 | |
---|
| 779 | using namespace _topology_bits; |
---|
| 780 | |
---|
[1909] | 781 | typedef BiNodeConnectedComponentsVisitor<UGraph, UEdgeMap> Visitor; |
---|
[1750] | 782 | |
---|
| 783 | int compNum = 0; |
---|
| 784 | Visitor visitor(graph, compMap, compNum); |
---|
| 785 | |
---|
[1909] | 786 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 787 | dfs.init(); |
---|
| 788 | |
---|
| 789 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 790 | if (!dfs.reached(it)) { |
---|
| 791 | dfs.addSource(it); |
---|
| 792 | dfs.start(); |
---|
| 793 | } |
---|
| 794 | } |
---|
| 795 | return compNum; |
---|
| 796 | } |
---|
| 797 | |
---|
| 798 | /// \ingroup topology |
---|
| 799 | /// |
---|
[1767] | 800 | /// \brief Find the bi-node-connected cut nodes. |
---|
[1750] | 801 | /// |
---|
[1767] | 802 | /// This function finds the bi-node-connected cut nodes in an undirected |
---|
| 803 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
[1750] | 804 | /// relation on the undirected edges. Two undirected edges are in |
---|
| 805 | /// relationship when they are on same circle. The biconnected components |
---|
| 806 | /// are separted by nodes which are the cut nodes of the components. |
---|
| 807 | /// |
---|
| 808 | /// \param graph The graph. |
---|
[1793] | 809 | /// \retval cutMap A writable edge map. The values will be set true when |
---|
[1750] | 810 | /// the node separate two or more components. |
---|
| 811 | /// \return The number of the cut nodes. |
---|
[1909] | 812 | template <typename UGraph, typename NodeMap> |
---|
| 813 | int biNodeConnectedCutNodes(const UGraph& graph, NodeMap& cutMap) { |
---|
| 814 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 815 | typedef typename UGraph::Node Node; |
---|
| 816 | typedef typename UGraph::NodeIt NodeIt; |
---|
[1750] | 817 | checkConcept<concept::WriteMap<Node, bool>, NodeMap>(); |
---|
| 818 | |
---|
| 819 | using namespace _topology_bits; |
---|
| 820 | |
---|
[1909] | 821 | typedef BiNodeConnectedCutNodesVisitor<UGraph, NodeMap> Visitor; |
---|
[1750] | 822 | |
---|
| 823 | int cutNum = 0; |
---|
| 824 | Visitor visitor(graph, cutMap, cutNum); |
---|
| 825 | |
---|
[1909] | 826 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 827 | dfs.init(); |
---|
| 828 | |
---|
| 829 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 830 | if (!dfs.reached(it)) { |
---|
| 831 | dfs.addSource(it); |
---|
| 832 | dfs.start(); |
---|
| 833 | } |
---|
| 834 | } |
---|
| 835 | return cutNum; |
---|
| 836 | } |
---|
| 837 | |
---|
| 838 | namespace _topology_bits { |
---|
| 839 | |
---|
| 840 | template <typename Graph> |
---|
[1800] | 841 | class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 842 | public: |
---|
| 843 | typedef typename Graph::Node Node; |
---|
| 844 | typedef typename Graph::Edge Edge; |
---|
[1909] | 845 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 846 | |
---|
[1800] | 847 | CountBiEdgeConnectedComponentsVisitor(const Graph& graph, int &compNum) |
---|
[1750] | 848 | : _graph(graph), _compNum(compNum), |
---|
| 849 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 850 | |
---|
| 851 | void start(const Node& node) { |
---|
| 852 | _predMap.set(node, INVALID); |
---|
| 853 | } |
---|
| 854 | |
---|
| 855 | void reach(const Node& node) { |
---|
| 856 | _numMap.set(node, _num); |
---|
| 857 | _retMap.set(node, _num); |
---|
| 858 | ++_num; |
---|
| 859 | } |
---|
| 860 | |
---|
| 861 | void leave(const Node& node) { |
---|
| 862 | if (_numMap[node] <= _retMap[node]) { |
---|
| 863 | ++_compNum; |
---|
| 864 | } |
---|
| 865 | } |
---|
| 866 | |
---|
| 867 | void discover(const Edge& edge) { |
---|
| 868 | _predMap.set(_graph.target(edge), edge); |
---|
| 869 | } |
---|
| 870 | |
---|
| 871 | void examine(const Edge& edge) { |
---|
| 872 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
| 873 | return; |
---|
| 874 | } |
---|
| 875 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 876 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 877 | } |
---|
| 878 | } |
---|
| 879 | |
---|
| 880 | void backtrack(const Edge& edge) { |
---|
| 881 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 882 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 883 | } |
---|
| 884 | } |
---|
| 885 | |
---|
| 886 | private: |
---|
| 887 | const Graph& _graph; |
---|
| 888 | int& _compNum; |
---|
| 889 | |
---|
| 890 | typename Graph::template NodeMap<int> _numMap; |
---|
| 891 | typename Graph::template NodeMap<int> _retMap; |
---|
| 892 | typename Graph::template NodeMap<Edge> _predMap; |
---|
| 893 | int _num; |
---|
| 894 | }; |
---|
| 895 | |
---|
| 896 | template <typename Graph, typename NodeMap> |
---|
[1800] | 897 | class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 898 | public: |
---|
| 899 | typedef typename Graph::Node Node; |
---|
| 900 | typedef typename Graph::Edge Edge; |
---|
[1909] | 901 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 902 | |
---|
[1800] | 903 | BiEdgeConnectedComponentsVisitor(const Graph& graph, |
---|
[1750] | 904 | NodeMap& compMap, int &compNum) |
---|
| 905 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
| 906 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 907 | |
---|
| 908 | void start(const Node& node) { |
---|
| 909 | _predMap.set(node, INVALID); |
---|
| 910 | } |
---|
| 911 | |
---|
| 912 | void reach(const Node& node) { |
---|
| 913 | _numMap.set(node, _num); |
---|
| 914 | _retMap.set(node, _num); |
---|
| 915 | _nodeStack.push(node); |
---|
| 916 | ++_num; |
---|
| 917 | } |
---|
| 918 | |
---|
| 919 | void leave(const Node& node) { |
---|
| 920 | if (_numMap[node] <= _retMap[node]) { |
---|
| 921 | while (_nodeStack.top() != node) { |
---|
| 922 | _compMap.set(_nodeStack.top(), _compNum); |
---|
| 923 | _nodeStack.pop(); |
---|
| 924 | } |
---|
| 925 | _compMap.set(node, _compNum); |
---|
| 926 | _nodeStack.pop(); |
---|
| 927 | ++_compNum; |
---|
| 928 | } |
---|
| 929 | } |
---|
| 930 | |
---|
| 931 | void discover(const Edge& edge) { |
---|
| 932 | _predMap.set(_graph.target(edge), edge); |
---|
| 933 | } |
---|
| 934 | |
---|
| 935 | void examine(const Edge& edge) { |
---|
| 936 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
| 937 | return; |
---|
| 938 | } |
---|
| 939 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 940 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 941 | } |
---|
| 942 | } |
---|
| 943 | |
---|
| 944 | void backtrack(const Edge& edge) { |
---|
| 945 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 946 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 947 | } |
---|
| 948 | } |
---|
| 949 | |
---|
| 950 | private: |
---|
| 951 | const Graph& _graph; |
---|
| 952 | NodeMap& _compMap; |
---|
| 953 | int& _compNum; |
---|
| 954 | |
---|
| 955 | typename Graph::template NodeMap<int> _numMap; |
---|
| 956 | typename Graph::template NodeMap<int> _retMap; |
---|
| 957 | typename Graph::template NodeMap<Edge> _predMap; |
---|
| 958 | std::stack<Node> _nodeStack; |
---|
| 959 | int _num; |
---|
| 960 | }; |
---|
| 961 | |
---|
| 962 | |
---|
| 963 | template <typename Graph, typename EdgeMap> |
---|
[1800] | 964 | class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 965 | public: |
---|
| 966 | typedef typename Graph::Node Node; |
---|
| 967 | typedef typename Graph::Edge Edge; |
---|
[1909] | 968 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 969 | |
---|
[1800] | 970 | BiEdgeConnectedCutEdgesVisitor(const Graph& graph, |
---|
[1750] | 971 | EdgeMap& cutMap, int &cutNum) |
---|
| 972 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
| 973 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 974 | |
---|
| 975 | void start(const Node& node) { |
---|
| 976 | _predMap[node] = INVALID; |
---|
| 977 | } |
---|
| 978 | |
---|
| 979 | void reach(const Node& node) { |
---|
| 980 | _numMap.set(node, _num); |
---|
| 981 | _retMap.set(node, _num); |
---|
| 982 | ++_num; |
---|
| 983 | } |
---|
| 984 | |
---|
| 985 | void leave(const Node& node) { |
---|
| 986 | if (_numMap[node] <= _retMap[node]) { |
---|
| 987 | if (_predMap[node] != INVALID) { |
---|
| 988 | _cutMap.set(_predMap[node], true); |
---|
| 989 | ++_cutNum; |
---|
| 990 | } |
---|
| 991 | } |
---|
| 992 | } |
---|
| 993 | |
---|
| 994 | void discover(const Edge& edge) { |
---|
| 995 | _predMap.set(_graph.target(edge), edge); |
---|
| 996 | } |
---|
| 997 | |
---|
| 998 | void examine(const Edge& edge) { |
---|
| 999 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
| 1000 | return; |
---|
| 1001 | } |
---|
| 1002 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1003 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1004 | } |
---|
| 1005 | } |
---|
| 1006 | |
---|
| 1007 | void backtrack(const Edge& edge) { |
---|
| 1008 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1009 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1010 | } |
---|
| 1011 | } |
---|
| 1012 | |
---|
| 1013 | private: |
---|
| 1014 | const Graph& _graph; |
---|
| 1015 | EdgeMap& _cutMap; |
---|
| 1016 | int& _cutNum; |
---|
| 1017 | |
---|
| 1018 | typename Graph::template NodeMap<int> _numMap; |
---|
| 1019 | typename Graph::template NodeMap<int> _retMap; |
---|
| 1020 | typename Graph::template NodeMap<Edge> _predMap; |
---|
| 1021 | int _num; |
---|
| 1022 | }; |
---|
| 1023 | } |
---|
| 1024 | |
---|
[1909] | 1025 | template <typename UGraph> |
---|
| 1026 | int countbiEdgeConnectedComponents(const UGraph& graph); |
---|
[1750] | 1027 | |
---|
| 1028 | /// \ingroup topology |
---|
| 1029 | /// |
---|
[1767] | 1030 | /// \brief Checks that the graph is bi-edge-connected. |
---|
[1750] | 1031 | /// |
---|
[1767] | 1032 | /// This function checks that the graph is bi-edge-connected. The undirected |
---|
| 1033 | /// graph is bi-edge-connected when any two nodes are connected with two |
---|
[1750] | 1034 | /// edge-disjoint paths. |
---|
| 1035 | /// |
---|
| 1036 | /// \param graph The undirected graph. |
---|
| 1037 | /// \return The number of components. |
---|
| 1038 | /// \todo Make it faster. |
---|
[1909] | 1039 | template <typename UGraph> |
---|
| 1040 | bool biEdgeConnected(const UGraph& graph) { |
---|
[1800] | 1041 | return countBiEdgeConnectedComponents(graph) == 1; |
---|
[1750] | 1042 | } |
---|
| 1043 | |
---|
| 1044 | /// \ingroup topology |
---|
| 1045 | /// |
---|
[1767] | 1046 | /// \brief Count the bi-edge-connected components. |
---|
[1750] | 1047 | /// |
---|
[1767] | 1048 | /// This function count the bi-edge-connected components in an undirected |
---|
| 1049 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
[1750] | 1050 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
| 1051 | /// connected with at least two edge-disjoint paths. |
---|
| 1052 | /// |
---|
| 1053 | /// \param graph The undirected graph. |
---|
| 1054 | /// \return The number of components. |
---|
[1909] | 1055 | template <typename UGraph> |
---|
| 1056 | int countBiEdgeConnectedComponents(const UGraph& graph) { |
---|
| 1057 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 1058 | typedef typename UGraph::NodeIt NodeIt; |
---|
[1750] | 1059 | |
---|
| 1060 | using namespace _topology_bits; |
---|
| 1061 | |
---|
[1909] | 1062 | typedef CountBiEdgeConnectedComponentsVisitor<UGraph> Visitor; |
---|
[1750] | 1063 | |
---|
| 1064 | int compNum = 0; |
---|
| 1065 | Visitor visitor(graph, compNum); |
---|
| 1066 | |
---|
[1909] | 1067 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 1068 | dfs.init(); |
---|
| 1069 | |
---|
| 1070 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1071 | if (!dfs.reached(it)) { |
---|
| 1072 | dfs.addSource(it); |
---|
| 1073 | dfs.start(); |
---|
| 1074 | } |
---|
| 1075 | } |
---|
| 1076 | return compNum; |
---|
| 1077 | } |
---|
| 1078 | |
---|
| 1079 | /// \ingroup topology |
---|
| 1080 | /// |
---|
[1767] | 1081 | /// \brief Find the bi-edge-connected components. |
---|
[1750] | 1082 | /// |
---|
[1767] | 1083 | /// This function finds the bi-edge-connected components in an undirected |
---|
| 1084 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
[1750] | 1085 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
| 1086 | /// connected at least two edge-disjoint paths. |
---|
| 1087 | /// |
---|
[1763] | 1088 | /// \image html edge_biconnected_components.png |
---|
[1767] | 1089 | /// \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth |
---|
[1763] | 1090 | /// |
---|
[1750] | 1091 | /// \param graph The graph. |
---|
[1793] | 1092 | /// \retval compMap A writable node map. The values will be set from 0 to |
---|
[1750] | 1093 | /// the number of the biconnected components minus one. Each values |
---|
| 1094 | /// of the map will be set exactly once, the values of a certain component |
---|
| 1095 | /// will be set continuously. |
---|
| 1096 | /// \return The number of components. |
---|
[1763] | 1097 | /// |
---|
[1909] | 1098 | template <typename UGraph, typename NodeMap> |
---|
| 1099 | int biEdgeConnectedComponents(const UGraph& graph, NodeMap& compMap) { |
---|
| 1100 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 1101 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1102 | typedef typename UGraph::Node Node; |
---|
[1750] | 1103 | checkConcept<concept::WriteMap<Node, int>, NodeMap>(); |
---|
| 1104 | |
---|
| 1105 | using namespace _topology_bits; |
---|
| 1106 | |
---|
[1909] | 1107 | typedef BiEdgeConnectedComponentsVisitor<UGraph, NodeMap> Visitor; |
---|
[1750] | 1108 | |
---|
| 1109 | int compNum = 0; |
---|
| 1110 | Visitor visitor(graph, compMap, compNum); |
---|
| 1111 | |
---|
[1909] | 1112 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 1113 | dfs.init(); |
---|
| 1114 | |
---|
| 1115 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1116 | if (!dfs.reached(it)) { |
---|
| 1117 | dfs.addSource(it); |
---|
| 1118 | dfs.start(); |
---|
| 1119 | } |
---|
| 1120 | } |
---|
| 1121 | return compNum; |
---|
| 1122 | } |
---|
| 1123 | |
---|
| 1124 | /// \ingroup topology |
---|
| 1125 | /// |
---|
[1767] | 1126 | /// \brief Find the bi-edge-connected cut edges. |
---|
[1750] | 1127 | /// |
---|
[1767] | 1128 | /// This function finds the bi-edge-connected components in an undirected |
---|
| 1129 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
[1750] | 1130 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
[1767] | 1131 | /// connected with at least two edge-disjoint paths. The bi-edge-connected |
---|
[1750] | 1132 | /// components are separted by edges which are the cut edges of the |
---|
| 1133 | /// components. |
---|
| 1134 | /// |
---|
| 1135 | /// \param graph The graph. |
---|
[1793] | 1136 | /// \retval cutMap A writable node map. The values will be set true when the |
---|
[1750] | 1137 | /// edge is a cut edge. |
---|
| 1138 | /// \return The number of cut edges. |
---|
[1909] | 1139 | template <typename UGraph, typename UEdgeMap> |
---|
| 1140 | int biEdgeConnectedCutEdges(const UGraph& graph, UEdgeMap& cutMap) { |
---|
| 1141 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 1142 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1143 | typedef typename UGraph::UEdge UEdge; |
---|
| 1144 | checkConcept<concept::WriteMap<UEdge, bool>, UEdgeMap>(); |
---|
[1750] | 1145 | |
---|
| 1146 | using namespace _topology_bits; |
---|
| 1147 | |
---|
[1909] | 1148 | typedef BiEdgeConnectedCutEdgesVisitor<UGraph, UEdgeMap> Visitor; |
---|
[1750] | 1149 | |
---|
| 1150 | int cutNum = 0; |
---|
| 1151 | Visitor visitor(graph, cutMap, cutNum); |
---|
| 1152 | |
---|
[1909] | 1153 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 1154 | dfs.init(); |
---|
| 1155 | |
---|
| 1156 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1157 | if (!dfs.reached(it)) { |
---|
| 1158 | dfs.addSource(it); |
---|
| 1159 | dfs.start(); |
---|
| 1160 | } |
---|
| 1161 | } |
---|
| 1162 | return cutNum; |
---|
| 1163 | } |
---|
| 1164 | |
---|
| 1165 | |
---|
| 1166 | namespace _topology_bits { |
---|
| 1167 | |
---|
| 1168 | template <typename Graph, typename IntNodeMap> |
---|
| 1169 | class TopologicalSortVisitor : public DfsVisitor<Graph> { |
---|
| 1170 | public: |
---|
| 1171 | typedef typename Graph::Node Node; |
---|
| 1172 | typedef typename Graph::Edge edge; |
---|
| 1173 | |
---|
| 1174 | TopologicalSortVisitor(IntNodeMap& order, int num) |
---|
| 1175 | : _order(order), _num(num) {} |
---|
| 1176 | |
---|
| 1177 | void leave(const Node& node) { |
---|
| 1178 | _order.set(node, --_num); |
---|
[1698] | 1179 | } |
---|
| 1180 | |
---|
| 1181 | private: |
---|
[1750] | 1182 | IntNodeMap& _order; |
---|
| 1183 | int _num; |
---|
[1698] | 1184 | }; |
---|
[1750] | 1185 | |
---|
[1698] | 1186 | } |
---|
| 1187 | |
---|
[1750] | 1188 | /// \ingroup topology |
---|
| 1189 | /// |
---|
| 1190 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
| 1191 | /// |
---|
| 1192 | /// Sort the nodes of a DAG into topolgical order. |
---|
| 1193 | /// |
---|
[1793] | 1194 | /// \param graph The graph. It should be directed and acyclic. |
---|
| 1195 | /// \retval order A writable node map. The values will be set from 0 to |
---|
[1750] | 1196 | /// the number of the nodes in the graph minus one. Each values of the map |
---|
| 1197 | /// will be set exactly once, the values will be set descending order. |
---|
| 1198 | /// |
---|
| 1199 | /// \see checkedTopologicalSort |
---|
| 1200 | /// \see dag |
---|
[1698] | 1201 | template <typename Graph, typename NodeMap> |
---|
[1750] | 1202 | void topologicalSort(const Graph& graph, NodeMap& order) { |
---|
| 1203 | using namespace _topology_bits; |
---|
| 1204 | |
---|
| 1205 | checkConcept<concept::StaticGraph, Graph>(); |
---|
| 1206 | checkConcept<concept::WriteMap<typename Graph::Node, int>, NodeMap>(); |
---|
| 1207 | |
---|
| 1208 | typedef typename Graph::Node Node; |
---|
| 1209 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1210 | typedef typename Graph::Edge Edge; |
---|
| 1211 | |
---|
| 1212 | TopologicalSortVisitor<Graph, NodeMap> |
---|
| 1213 | visitor(order, countNodes(graph)); |
---|
| 1214 | |
---|
| 1215 | DfsVisit<Graph, TopologicalSortVisitor<Graph, NodeMap> > |
---|
| 1216 | dfs(graph, visitor); |
---|
| 1217 | |
---|
| 1218 | dfs.init(); |
---|
| 1219 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1220 | if (!dfs.reached(it)) { |
---|
| 1221 | dfs.addSource(it); |
---|
| 1222 | dfs.start(); |
---|
| 1223 | } |
---|
| 1224 | } |
---|
| 1225 | } |
---|
| 1226 | |
---|
| 1227 | /// \ingroup topology |
---|
| 1228 | /// |
---|
| 1229 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
| 1230 | /// |
---|
| 1231 | /// Sort the nodes of a DAG into topolgical order. It also checks |
---|
| 1232 | /// that the given graph is DAG. |
---|
| 1233 | /// |
---|
[1793] | 1234 | /// \param graph The graph. It should be directed and acyclic. |
---|
[1750] | 1235 | /// \retval order A readable - writable node map. The values will be set |
---|
| 1236 | /// from 0 to the number of the nodes in the graph minus one. Each values |
---|
| 1237 | /// of the map will be set exactly once, the values will be set descending |
---|
| 1238 | /// order. |
---|
| 1239 | /// \return %False when the graph is not DAG. |
---|
| 1240 | /// |
---|
| 1241 | /// \see topologicalSort |
---|
| 1242 | /// \see dag |
---|
| 1243 | template <typename Graph, typename NodeMap> |
---|
| 1244 | bool checkedTopologicalSort(const Graph& graph, NodeMap& order) { |
---|
[1698] | 1245 | using namespace _topology_bits; |
---|
| 1246 | |
---|
| 1247 | checkConcept<concept::StaticGraph, Graph>(); |
---|
| 1248 | checkConcept<concept::ReadWriteMap<typename Graph::Node, int>, NodeMap>(); |
---|
| 1249 | |
---|
| 1250 | typedef typename Graph::Node Node; |
---|
| 1251 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1252 | typedef typename Graph::Edge Edge; |
---|
| 1253 | |
---|
[1750] | 1254 | order = constMap<Node, int, -1>(); |
---|
[1698] | 1255 | |
---|
[1750] | 1256 | TopologicalSortVisitor<Graph, NodeMap> |
---|
| 1257 | visitor(order, countNodes(graph)); |
---|
[1698] | 1258 | |
---|
[1750] | 1259 | DfsVisit<Graph, TopologicalSortVisitor<Graph, NodeMap> > |
---|
| 1260 | dfs(graph, visitor); |
---|
[1698] | 1261 | |
---|
| 1262 | dfs.init(); |
---|
| 1263 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1264 | if (!dfs.reached(it)) { |
---|
| 1265 | dfs.addSource(it); |
---|
| 1266 | while (!dfs.emptyQueue()) { |
---|
[1750] | 1267 | Edge edge = dfs.nextEdge(); |
---|
| 1268 | Node target = graph.target(edge); |
---|
| 1269 | if (dfs.reached(target) && order[target] == -1) { |
---|
| 1270 | return false; |
---|
| 1271 | } |
---|
| 1272 | dfs.processNextEdge(); |
---|
| 1273 | } |
---|
[1698] | 1274 | } |
---|
[1750] | 1275 | } |
---|
[1698] | 1276 | return true; |
---|
| 1277 | } |
---|
| 1278 | |
---|
[1750] | 1279 | /// \ingroup topology |
---|
[1698] | 1280 | /// |
---|
[1750] | 1281 | /// \brief Check that the given directed graph is a DAG. |
---|
| 1282 | /// |
---|
| 1283 | /// Check that the given directed graph is a DAG. The DAG is |
---|
[1698] | 1284 | /// an Directed Acyclic Graph. |
---|
[1750] | 1285 | /// \return %False when the graph is not DAG. |
---|
| 1286 | /// \see acyclic |
---|
[1698] | 1287 | template <typename Graph> |
---|
| 1288 | bool dag(const Graph& graph) { |
---|
| 1289 | |
---|
| 1290 | checkConcept<concept::StaticGraph, Graph>(); |
---|
| 1291 | |
---|
| 1292 | typedef typename Graph::Node Node; |
---|
| 1293 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1294 | typedef typename Graph::Edge Edge; |
---|
| 1295 | |
---|
| 1296 | typedef typename Graph::template NodeMap<bool> ProcessedMap; |
---|
| 1297 | |
---|
| 1298 | typename Dfs<Graph>::template DefProcessedMap<ProcessedMap>:: |
---|
[1709] | 1299 | Create dfs(graph); |
---|
[1698] | 1300 | |
---|
| 1301 | ProcessedMap processed(graph); |
---|
| 1302 | dfs.processedMap(processed); |
---|
| 1303 | |
---|
| 1304 | dfs.init(); |
---|
| 1305 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1306 | if (!dfs.reached(it)) { |
---|
| 1307 | dfs.addSource(it); |
---|
| 1308 | while (!dfs.emptyQueue()) { |
---|
| 1309 | Edge edge = dfs.nextEdge(); |
---|
| 1310 | Node target = graph.target(edge); |
---|
| 1311 | if (dfs.reached(target) && !processed[target]) { |
---|
| 1312 | return false; |
---|
| 1313 | } |
---|
| 1314 | dfs.processNextEdge(); |
---|
| 1315 | } |
---|
| 1316 | } |
---|
| 1317 | } |
---|
| 1318 | return true; |
---|
| 1319 | } |
---|
| 1320 | |
---|
[1750] | 1321 | /// \ingroup topology |
---|
[1698] | 1322 | /// |
---|
| 1323 | /// \brief Check that the given undirected graph is acyclic. |
---|
| 1324 | /// |
---|
| 1325 | /// Check that the given undirected graph acyclic. |
---|
[1750] | 1326 | /// \param graph The undirected graph. |
---|
| 1327 | /// \return %True when there is no circle in the graph. |
---|
| 1328 | /// \see dag |
---|
[1909] | 1329 | template <typename UGraph> |
---|
| 1330 | bool acyclic(const UGraph& graph) { |
---|
| 1331 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 1332 | typedef typename UGraph::Node Node; |
---|
| 1333 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1334 | typedef typename UGraph::Edge Edge; |
---|
| 1335 | Dfs<UGraph> dfs(graph); |
---|
[1698] | 1336 | dfs.init(); |
---|
| 1337 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1338 | if (!dfs.reached(it)) { |
---|
| 1339 | dfs.addSource(it); |
---|
| 1340 | while (!dfs.emptyQueue()) { |
---|
| 1341 | Edge edge = dfs.nextEdge(); |
---|
| 1342 | Node source = graph.source(edge); |
---|
| 1343 | Node target = graph.target(edge); |
---|
| 1344 | if (dfs.reached(target) && |
---|
[1763] | 1345 | dfs.predEdge(source) != graph.oppositeEdge(edge)) { |
---|
[1698] | 1346 | return false; |
---|
| 1347 | } |
---|
| 1348 | dfs.processNextEdge(); |
---|
| 1349 | } |
---|
| 1350 | } |
---|
| 1351 | } |
---|
| 1352 | return true; |
---|
| 1353 | } |
---|
| 1354 | |
---|
[1750] | 1355 | /// \ingroup topology |
---|
| 1356 | /// |
---|
[1698] | 1357 | /// \brief Check that the given undirected graph is tree. |
---|
| 1358 | /// |
---|
| 1359 | /// Check that the given undirected graph is tree. |
---|
[1750] | 1360 | /// \param graph The undirected graph. |
---|
| 1361 | /// \return %True when the graph is acyclic and connected. |
---|
[1909] | 1362 | template <typename UGraph> |
---|
| 1363 | bool tree(const UGraph& graph) { |
---|
| 1364 | checkConcept<concept::UGraph, UGraph>(); |
---|
| 1365 | typedef typename UGraph::Node Node; |
---|
| 1366 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1367 | typedef typename UGraph::Edge Edge; |
---|
| 1368 | Dfs<UGraph> dfs(graph); |
---|
[1698] | 1369 | dfs.init(); |
---|
| 1370 | dfs.addSource(NodeIt(graph)); |
---|
| 1371 | while (!dfs.emptyQueue()) { |
---|
| 1372 | Edge edge = dfs.nextEdge(); |
---|
| 1373 | Node source = graph.source(edge); |
---|
| 1374 | Node target = graph.target(edge); |
---|
| 1375 | if (dfs.reached(target) && |
---|
[1763] | 1376 | dfs.predEdge(source) != graph.oppositeEdge(edge)) { |
---|
[1698] | 1377 | return false; |
---|
| 1378 | } |
---|
| 1379 | dfs.processNextEdge(); |
---|
| 1380 | } |
---|
| 1381 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1382 | if (!dfs.reached(it)) { |
---|
| 1383 | return false; |
---|
| 1384 | } |
---|
| 1385 | } |
---|
| 1386 | return true; |
---|
| 1387 | } |
---|
[1739] | 1388 | |
---|
[1750] | 1389 | /// \ingroup topology |
---|
[1739] | 1390 | /// |
---|
[1800] | 1391 | /// \brief Check if the given undirected graph is bipartite or not |
---|
[1750] | 1392 | /// |
---|
[1800] | 1393 | /// The function checks if the given undirected \c graph graph is bipartite |
---|
| 1394 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
---|
[1750] | 1395 | /// \param graph The undirected graph. |
---|
[1800] | 1396 | /// \return %True if \c graph is bipartite, %false otherwise. |
---|
| 1397 | /// \sa bipartitePartitions |
---|
| 1398 | /// |
---|
| 1399 | /// \author Balazs Attila Mihaly |
---|
[1909] | 1400 | template<typename UGraph> |
---|
| 1401 | inline bool bipartite(const UGraph &graph){ |
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| 1402 | checkConcept<concept::UGraph, UGraph>(); |
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[1800] | 1403 | |
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[1909] | 1404 | typedef typename UGraph::NodeIt NodeIt; |
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| 1405 | typedef typename UGraph::EdgeIt EdgeIt; |
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[1800] | 1406 | |
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[1909] | 1407 | Bfs<UGraph> bfs(graph); |
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[1800] | 1408 | bfs.init(); |
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| 1409 | for(NodeIt i(graph);i!=INVALID;++i){ |
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| 1410 | if(!bfs.reached(i)){ |
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| 1411 | bfs.run(i); |
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| 1412 | } |
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| 1413 | } |
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| 1414 | for(EdgeIt i(graph);i!=INVALID;++i){ |
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| 1415 | if(bfs.dist(graph.source(i))==bfs.dist(graph.target(i)))return false; |
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| 1416 | } |
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| 1417 | return true; |
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| 1418 | }; |
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| 1419 | |
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| 1420 | /// \ingroup topology |
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| 1421 | /// |
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| 1422 | /// \brief Check if the given undirected graph is bipartite or not |
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| 1423 | /// |
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| 1424 | /// The function checks if the given undirected graph is bipartite |
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| 1425 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
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| 1426 | /// During the execution, the \c partMap will be set as the two |
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| 1427 | /// partitions of the graph. |
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| 1428 | /// \param graph The undirected graph. |
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[1808] | 1429 | /// \retval partMap A writable bool map of nodes. It will be set as the |
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[1800] | 1430 | /// two partitions of the graph. |
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| 1431 | /// \return %True if \c graph is bipartite, %false otherwise. |
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| 1432 | /// |
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| 1433 | /// \author Balazs Attila Mihaly |
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| 1434 | /// |
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| 1435 | /// \image html bipartite_partitions.png |
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| 1436 | /// \image latex bipartite_partitions.eps "Bipartite partititions" width=\textwidth |
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[1909] | 1437 | template<typename UGraph, typename NodeMap> |
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| 1438 | inline bool bipartitePartitions(const UGraph &graph, NodeMap &partMap){ |
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| 1439 | checkConcept<concept::UGraph, UGraph>(); |
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[1800] | 1440 | |
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[1909] | 1441 | typedef typename UGraph::Node Node; |
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| 1442 | typedef typename UGraph::NodeIt NodeIt; |
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| 1443 | typedef typename UGraph::EdgeIt EdgeIt; |
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[1800] | 1444 | |
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[1909] | 1445 | Bfs<UGraph> bfs(graph); |
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[1800] | 1446 | bfs.init(); |
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| 1447 | for(NodeIt i(graph);i!=INVALID;++i){ |
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| 1448 | if(!bfs.reached(i)){ |
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| 1449 | bfs.addSource(i); |
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| 1450 | for(Node j=bfs.processNextNode();!bfs.emptyQueue(); |
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| 1451 | j=bfs.processNextNode()){ |
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| 1452 | partMap.set(j,bfs.dist(j)%2==0); |
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[1750] | 1453 | } |
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[1740] | 1454 | } |
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| 1455 | } |
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[1800] | 1456 | for(EdgeIt i(graph);i!=INVALID;++i){ |
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| 1457 | if(bfs.dist(graph.source(i)) == bfs.dist(graph.target(i)))return false; |
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| 1458 | } |
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[1750] | 1459 | return true; |
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[1800] | 1460 | }; |
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[1750] | 1461 | |
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[1698] | 1462 | } //namespace lemon |
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| 1463 | |
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| 1464 | #endif //LEMON_TOPOLOGY_H |
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