[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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[2553] | 5 | * Copyright (C) 2003-2008 |
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[1956] | 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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[2260] | 28 | #include <lemon/concepts/graph.h> |
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| 29 | #include <lemon/concepts/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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[2038] | 33 | #include <lemon/bucket_heap.h> |
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[1750] | 34 | |
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| 35 | #include <stack> |
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| 36 | #include <functional> |
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| 37 | |
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[2429] | 38 | /// \ingroup graph_prop |
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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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[2429] | 46 | /// \ingroup graph_prop |
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[1750] | 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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[2260] | 56 | checkConcept<concepts::UGraph, UGraph>(); |
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[1909] | 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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[2429] | 69 | /// \ingroup graph_prop |
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[1750] | 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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[2260] | 81 | checkConcept<concepts::UGraph, UGraph>(); |
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[1909] | 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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[2429] | 111 | /// \ingroup graph_prop |
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[1750] | 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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[2260] | 129 | checkConcept<concepts::UGraph, UGraph>(); |
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[1909] | 130 | typedef typename UGraph::Node Node; |
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| 131 | typedef typename UGraph::Edge Edge; |
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[2260] | 132 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
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[1750] | 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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[2429] | 234 | /// \ingroup graph_prop |
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[1750] | 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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[2260] | 247 | checkConcept<concepts::Graph, Graph>(); |
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[1750] | 248 | |
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| 249 | typedef typename Graph::Node Node; |
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| 250 | typedef typename Graph::NodeIt NodeIt; |
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| 251 | |
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[2082] | 252 | if (NodeIt(graph) == INVALID) return true; |
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| 253 | |
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[1750] | 254 | using namespace _topology_bits; |
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| 255 | |
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| 256 | typedef DfsVisitor<Graph> Visitor; |
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| 257 | Visitor visitor; |
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| 258 | |
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| 259 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 260 | dfs.init(); |
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| 261 | dfs.addSource(NodeIt(graph)); |
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| 262 | dfs.start(); |
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| 263 | |
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| 264 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 265 | if (!dfs.reached(it)) { |
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| 266 | return false; |
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| 267 | } |
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| 268 | } |
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| 269 | |
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| 270 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 271 | RGraph rgraph(graph); |
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| 272 | |
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| 273 | typedef DfsVisitor<Graph> RVisitor; |
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| 274 | RVisitor rvisitor; |
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| 275 | |
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| 276 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 277 | rdfs.init(); |
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| 278 | rdfs.addSource(NodeIt(graph)); |
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| 279 | rdfs.start(); |
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| 280 | |
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| 281 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 282 | if (!rdfs.reached(it)) { |
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| 283 | return false; |
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| 284 | } |
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| 285 | } |
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| 286 | |
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| 287 | return true; |
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| 288 | } |
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| 289 | |
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[2429] | 290 | /// \ingroup graph_prop |
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[1750] | 291 | /// |
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| 292 | /// \brief Count the strongly connected components of a directed graph |
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| 293 | /// |
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| 294 | /// Count the strongly connected components of a directed graph. |
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[2421] | 295 | /// The strongly connected components are the classes of an |
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| 296 | /// equivalence relation on the nodes of the graph. Two nodes are in |
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| 297 | /// the same class if they are connected with directed paths in both |
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| 298 | /// direction. |
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[1750] | 299 | /// |
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[1793] | 300 | /// \param graph The graph. |
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[1750] | 301 | /// \return The number of components |
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[1807] | 302 | /// \note By definition, the empty graph has zero |
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| 303 | /// strongly connected components. |
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[1750] | 304 | template <typename Graph> |
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| 305 | int countStronglyConnectedComponents(const Graph& graph) { |
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[2260] | 306 | checkConcept<concepts::Graph, Graph>(); |
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[1750] | 307 | |
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| 308 | using namespace _topology_bits; |
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| 309 | |
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| 310 | typedef typename Graph::Node Node; |
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| 311 | typedef typename Graph::Edge Edge; |
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| 312 | typedef typename Graph::NodeIt NodeIt; |
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| 313 | typedef typename Graph::EdgeIt EdgeIt; |
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| 314 | |
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| 315 | typedef std::vector<Node> Container; |
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| 316 | typedef typename Container::iterator Iterator; |
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| 317 | |
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| 318 | Container nodes(countNodes(graph)); |
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| 319 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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| 320 | Visitor visitor(nodes.begin()); |
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| 321 | |
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| 322 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 323 | dfs.init(); |
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| 324 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 325 | if (!dfs.reached(it)) { |
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| 326 | dfs.addSource(it); |
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| 327 | dfs.start(); |
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| 328 | } |
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| 329 | } |
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| 330 | |
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| 331 | typedef typename Container::reverse_iterator RIterator; |
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| 332 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 333 | |
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| 334 | RGraph rgraph(graph); |
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| 335 | |
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| 336 | typedef DfsVisitor<Graph> RVisitor; |
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| 337 | RVisitor rvisitor; |
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| 338 | |
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| 339 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 340 | |
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| 341 | int compNum = 0; |
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| 342 | |
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| 343 | rdfs.init(); |
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| 344 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 345 | if (!rdfs.reached(*it)) { |
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| 346 | rdfs.addSource(*it); |
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| 347 | rdfs.start(); |
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| 348 | ++compNum; |
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| 349 | } |
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| 350 | } |
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| 351 | return compNum; |
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| 352 | } |
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| 353 | |
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[2429] | 354 | /// \ingroup graph_prop |
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[1750] | 355 | /// |
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| 356 | /// \brief Find the strongly connected components of a directed graph |
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| 357 | /// |
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[2421] | 358 | /// Find the strongly connected components of a directed graph. The |
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| 359 | /// strongly connected components are the classes of an equivalence |
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| 360 | /// relation on the nodes of the graph. Two nodes are in |
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| 361 | /// relationship when there are directed paths between them in both |
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| 362 | /// direction. In addition, the numbering of components will satisfy |
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| 363 | /// that there is no edge going from a higher numbered component to |
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| 364 | /// a lower. |
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[1750] | 365 | /// |
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[1763] | 366 | /// \image html strongly_connected_components.png |
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| 367 | /// \image latex strongly_connected_components.eps "Strongly connected components" width=\textwidth |
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| 368 | /// |
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[1793] | 369 | /// \param graph The graph. |
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| 370 | /// \retval compMap A writable node map. The values will be set from 0 to |
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[2421] | 371 | /// the number of the strongly connected components minus one. Each value |
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[1750] | 372 | /// of the map will be set exactly once, the values of a certain component |
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| 373 | /// will be set continuously. |
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| 374 | /// \return The number of components |
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[1763] | 375 | /// |
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[1750] | 376 | template <typename Graph, typename NodeMap> |
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| 377 | int stronglyConnectedComponents(const Graph& graph, NodeMap& compMap) { |
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[2260] | 378 | checkConcept<concepts::Graph, Graph>(); |
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[1750] | 379 | typedef typename Graph::Node Node; |
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| 380 | typedef typename Graph::NodeIt NodeIt; |
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[2260] | 381 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
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[1750] | 382 | |
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| 383 | using namespace _topology_bits; |
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| 384 | |
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| 385 | typedef std::vector<Node> Container; |
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| 386 | typedef typename Container::iterator Iterator; |
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| 387 | |
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| 388 | Container nodes(countNodes(graph)); |
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| 389 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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| 390 | Visitor visitor(nodes.begin()); |
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| 391 | |
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| 392 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 393 | dfs.init(); |
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| 394 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 395 | if (!dfs.reached(it)) { |
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| 396 | dfs.addSource(it); |
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| 397 | dfs.start(); |
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| 398 | } |
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| 399 | } |
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| 400 | |
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| 401 | typedef typename Container::reverse_iterator RIterator; |
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| 402 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 403 | |
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| 404 | RGraph rgraph(graph); |
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| 405 | |
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| 406 | int compNum = 0; |
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| 407 | |
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| 408 | typedef FillMapVisitor<RGraph, NodeMap> RVisitor; |
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| 409 | RVisitor rvisitor(compMap, compNum); |
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| 410 | |
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| 411 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 412 | |
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| 413 | rdfs.init(); |
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| 414 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 415 | if (!rdfs.reached(*it)) { |
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| 416 | rdfs.addSource(*it); |
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| 417 | rdfs.start(); |
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| 418 | ++compNum; |
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| 419 | } |
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| 420 | } |
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| 421 | return compNum; |
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| 422 | } |
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| 423 | |
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[2429] | 424 | /// \ingroup graph_prop |
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[1750] | 425 | /// |
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| 426 | /// \brief Find the cut edges of the strongly connected components. |
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| 427 | /// |
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| 428 | /// Find the cut edges of the strongly connected components. |
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| 429 | /// The strongly connected components are the classes of an equivalence |
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| 430 | /// relation on the nodes of the graph. Two nodes are in relationship |
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| 431 | /// when there are directed paths between them in both direction. |
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| 432 | /// The strongly connected components are separated by the cut edges. |
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| 433 | /// |
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[1793] | 434 | /// \param graph The graph. |
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| 435 | /// \retval cutMap A writable node map. The values will be set true when the |
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| 436 | /// edge is a cut edge. |
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[1750] | 437 | /// |
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| 438 | /// \return The number of cut edges |
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| 439 | template <typename Graph, typename EdgeMap> |
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| 440 | int stronglyConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) { |
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[2260] | 441 | checkConcept<concepts::Graph, Graph>(); |
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[1750] | 442 | typedef typename Graph::Node Node; |
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| 443 | typedef typename Graph::Edge Edge; |
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| 444 | typedef typename Graph::NodeIt NodeIt; |
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[2260] | 445 | checkConcept<concepts::WriteMap<Edge, bool>, EdgeMap>(); |
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[1750] | 446 | |
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| 447 | using namespace _topology_bits; |
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| 448 | |
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| 449 | typedef std::vector<Node> Container; |
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| 450 | typedef typename Container::iterator Iterator; |
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| 451 | |
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| 452 | Container nodes(countNodes(graph)); |
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| 453 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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| 454 | Visitor visitor(nodes.begin()); |
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| 455 | |
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| 456 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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| 457 | dfs.init(); |
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| 458 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 459 | if (!dfs.reached(it)) { |
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| 460 | dfs.addSource(it); |
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| 461 | dfs.start(); |
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| 462 | } |
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| 463 | } |
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| 464 | |
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| 465 | typedef typename Container::reverse_iterator RIterator; |
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| 466 | typedef RevGraphAdaptor<const Graph> RGraph; |
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| 467 | |
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| 468 | RGraph rgraph(graph); |
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| 469 | |
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| 470 | int cutNum = 0; |
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| 471 | |
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| 472 | typedef StronglyConnectedCutEdgesVisitor<RGraph, EdgeMap> RVisitor; |
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| 473 | RVisitor rvisitor(rgraph, cutMap, cutNum); |
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| 474 | |
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| 475 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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| 476 | |
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| 477 | rdfs.init(); |
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| 478 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 479 | if (!rdfs.reached(*it)) { |
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| 480 | rdfs.addSource(*it); |
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| 481 | rdfs.start(); |
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| 482 | } |
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| 483 | } |
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| 484 | return cutNum; |
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| 485 | } |
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| 486 | |
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[1698] | 487 | namespace _topology_bits { |
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| 488 | |
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[1750] | 489 | template <typename Graph> |
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[1800] | 490 | class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
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[1698] | 491 | public: |
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[1750] | 492 | typedef typename Graph::Node Node; |
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| 493 | typedef typename Graph::Edge Edge; |
---|
[1909] | 494 | typedef typename Graph::UEdge UEdge; |
---|
[1698] | 495 | |
---|
[1800] | 496 | CountBiNodeConnectedComponentsVisitor(const Graph& graph, int &compNum) |
---|
[1750] | 497 | : _graph(graph), _compNum(compNum), |
---|
| 498 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 499 | |
---|
| 500 | void start(const Node& node) { |
---|
| 501 | _predMap.set(node, INVALID); |
---|
| 502 | } |
---|
| 503 | |
---|
| 504 | void reach(const Node& node) { |
---|
| 505 | _numMap.set(node, _num); |
---|
| 506 | _retMap.set(node, _num); |
---|
| 507 | ++_num; |
---|
| 508 | } |
---|
| 509 | |
---|
| 510 | void discover(const Edge& edge) { |
---|
| 511 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
| 512 | } |
---|
| 513 | |
---|
| 514 | void examine(const Edge& edge) { |
---|
| 515 | if (_graph.source(edge) == _graph.target(edge) && |
---|
| 516 | _graph.direction(edge)) { |
---|
| 517 | ++_compNum; |
---|
| 518 | return; |
---|
| 519 | } |
---|
| 520 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) { |
---|
| 521 | return; |
---|
| 522 | } |
---|
| 523 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
| 524 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
[1698] | 525 | } |
---|
| 526 | } |
---|
| 527 | |
---|
[1750] | 528 | void backtrack(const Edge& edge) { |
---|
| 529 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 530 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 531 | } |
---|
| 532 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
| 533 | ++_compNum; |
---|
| 534 | } |
---|
| 535 | } |
---|
| 536 | |
---|
| 537 | private: |
---|
| 538 | const Graph& _graph; |
---|
| 539 | int& _compNum; |
---|
| 540 | |
---|
| 541 | typename Graph::template NodeMap<int> _numMap; |
---|
| 542 | typename Graph::template NodeMap<int> _retMap; |
---|
| 543 | typename Graph::template NodeMap<Node> _predMap; |
---|
| 544 | int _num; |
---|
| 545 | }; |
---|
| 546 | |
---|
| 547 | template <typename Graph, typename EdgeMap> |
---|
[1800] | 548 | class BiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 549 | public: |
---|
| 550 | typedef typename Graph::Node Node; |
---|
| 551 | typedef typename Graph::Edge Edge; |
---|
[1909] | 552 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 553 | |
---|
[1800] | 554 | BiNodeConnectedComponentsVisitor(const Graph& graph, |
---|
[1750] | 555 | EdgeMap& compMap, int &compNum) |
---|
| 556 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
| 557 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 558 | |
---|
| 559 | void start(const Node& node) { |
---|
| 560 | _predMap.set(node, INVALID); |
---|
| 561 | } |
---|
| 562 | |
---|
| 563 | void reach(const Node& node) { |
---|
| 564 | _numMap.set(node, _num); |
---|
| 565 | _retMap.set(node, _num); |
---|
| 566 | ++_num; |
---|
| 567 | } |
---|
| 568 | |
---|
| 569 | void discover(const Edge& edge) { |
---|
| 570 | Node target = _graph.target(edge); |
---|
| 571 | _predMap.set(target, edge); |
---|
| 572 | _edgeStack.push(edge); |
---|
| 573 | } |
---|
| 574 | |
---|
| 575 | void examine(const Edge& edge) { |
---|
| 576 | Node source = _graph.source(edge); |
---|
| 577 | Node target = _graph.target(edge); |
---|
| 578 | if (source == target && _graph.direction(edge)) { |
---|
| 579 | _compMap.set(edge, _compNum); |
---|
| 580 | ++_compNum; |
---|
| 581 | return; |
---|
| 582 | } |
---|
| 583 | if (_numMap[target] < _numMap[source]) { |
---|
| 584 | if (_predMap[source] != _graph.oppositeEdge(edge)) { |
---|
| 585 | _edgeStack.push(edge); |
---|
| 586 | } |
---|
| 587 | } |
---|
| 588 | if (_predMap[source] != INVALID && |
---|
| 589 | target == _graph.source(_predMap[source])) { |
---|
| 590 | return; |
---|
| 591 | } |
---|
| 592 | if (_retMap[source] > _numMap[target]) { |
---|
| 593 | _retMap.set(source, _numMap[target]); |
---|
| 594 | } |
---|
| 595 | } |
---|
| 596 | |
---|
| 597 | void backtrack(const Edge& edge) { |
---|
| 598 | Node source = _graph.source(edge); |
---|
| 599 | Node target = _graph.target(edge); |
---|
| 600 | if (_retMap[source] > _retMap[target]) { |
---|
| 601 | _retMap.set(source, _retMap[target]); |
---|
| 602 | } |
---|
| 603 | if (_numMap[source] <= _retMap[target]) { |
---|
| 604 | while (_edgeStack.top() != edge) { |
---|
| 605 | _compMap.set(_edgeStack.top(), _compNum); |
---|
| 606 | _edgeStack.pop(); |
---|
| 607 | } |
---|
| 608 | _compMap.set(edge, _compNum); |
---|
| 609 | _edgeStack.pop(); |
---|
| 610 | ++_compNum; |
---|
| 611 | } |
---|
| 612 | } |
---|
| 613 | |
---|
| 614 | private: |
---|
| 615 | const Graph& _graph; |
---|
| 616 | EdgeMap& _compMap; |
---|
| 617 | int& _compNum; |
---|
| 618 | |
---|
| 619 | typename Graph::template NodeMap<int> _numMap; |
---|
| 620 | typename Graph::template NodeMap<int> _retMap; |
---|
| 621 | typename Graph::template NodeMap<Edge> _predMap; |
---|
[1909] | 622 | std::stack<UEdge> _edgeStack; |
---|
[1750] | 623 | int _num; |
---|
| 624 | }; |
---|
| 625 | |
---|
| 626 | |
---|
| 627 | template <typename Graph, typename NodeMap> |
---|
[1800] | 628 | class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 629 | public: |
---|
| 630 | typedef typename Graph::Node Node; |
---|
| 631 | typedef typename Graph::Edge Edge; |
---|
[1909] | 632 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 633 | |
---|
[1800] | 634 | BiNodeConnectedCutNodesVisitor(const Graph& graph, NodeMap& cutMap, |
---|
[1750] | 635 | int& cutNum) |
---|
| 636 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
| 637 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 638 | |
---|
| 639 | void start(const Node& node) { |
---|
| 640 | _predMap.set(node, INVALID); |
---|
| 641 | rootCut = false; |
---|
| 642 | } |
---|
| 643 | |
---|
| 644 | void reach(const Node& node) { |
---|
| 645 | _numMap.set(node, _num); |
---|
| 646 | _retMap.set(node, _num); |
---|
| 647 | ++_num; |
---|
| 648 | } |
---|
| 649 | |
---|
| 650 | void discover(const Edge& edge) { |
---|
| 651 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
| 652 | } |
---|
| 653 | |
---|
| 654 | void examine(const Edge& edge) { |
---|
| 655 | if (_graph.source(edge) == _graph.target(edge) && |
---|
| 656 | _graph.direction(edge)) { |
---|
| 657 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 658 | _cutMap.set(_graph.source(edge), true); |
---|
| 659 | ++_cutNum; |
---|
| 660 | } |
---|
| 661 | return; |
---|
| 662 | } |
---|
| 663 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) return; |
---|
| 664 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
| 665 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
| 666 | } |
---|
| 667 | } |
---|
| 668 | |
---|
| 669 | void backtrack(const Edge& edge) { |
---|
| 670 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 671 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 672 | } |
---|
| 673 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
| 674 | if (_predMap[_graph.source(edge)] != INVALID) { |
---|
| 675 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 676 | _cutMap.set(_graph.source(edge), true); |
---|
| 677 | ++_cutNum; |
---|
| 678 | } |
---|
| 679 | } else if (rootCut) { |
---|
| 680 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 681 | _cutMap.set(_graph.source(edge), true); |
---|
| 682 | ++_cutNum; |
---|
| 683 | } |
---|
| 684 | } else { |
---|
| 685 | rootCut = true; |
---|
| 686 | } |
---|
| 687 | } |
---|
| 688 | } |
---|
| 689 | |
---|
| 690 | private: |
---|
| 691 | const Graph& _graph; |
---|
| 692 | NodeMap& _cutMap; |
---|
| 693 | int& _cutNum; |
---|
| 694 | |
---|
| 695 | typename Graph::template NodeMap<int> _numMap; |
---|
| 696 | typename Graph::template NodeMap<int> _retMap; |
---|
| 697 | typename Graph::template NodeMap<Node> _predMap; |
---|
[1909] | 698 | std::stack<UEdge> _edgeStack; |
---|
[1750] | 699 | int _num; |
---|
| 700 | bool rootCut; |
---|
| 701 | }; |
---|
| 702 | |
---|
| 703 | } |
---|
| 704 | |
---|
[1909] | 705 | template <typename UGraph> |
---|
| 706 | int countBiNodeConnectedComponents(const UGraph& graph); |
---|
[1750] | 707 | |
---|
[2429] | 708 | /// \ingroup graph_prop |
---|
[1750] | 709 | /// |
---|
[1767] | 710 | /// \brief Checks the graph is bi-node-connected. |
---|
[1750] | 711 | /// |
---|
[1767] | 712 | /// This function checks that the undirected graph is bi-node-connected |
---|
| 713 | /// graph. The graph is bi-node-connected if any two undirected edge is |
---|
[1750] | 714 | /// on same circle. |
---|
| 715 | /// |
---|
| 716 | /// \param graph The graph. |
---|
[1767] | 717 | /// \return %True when the graph bi-node-connected. |
---|
[1909] | 718 | template <typename UGraph> |
---|
| 719 | bool biNodeConnected(const UGraph& graph) { |
---|
[1800] | 720 | return countBiNodeConnectedComponents(graph) == 1; |
---|
[1750] | 721 | } |
---|
| 722 | |
---|
[2429] | 723 | /// \ingroup graph_prop |
---|
[1750] | 724 | /// |
---|
| 725 | /// \brief Count the biconnected components. |
---|
| 726 | /// |
---|
[1767] | 727 | /// This function finds the bi-node-connected components in an undirected |
---|
[1750] | 728 | /// graph. The biconnected components are the classes of an equivalence |
---|
| 729 | /// relation on the undirected edges. Two undirected edge is in relationship |
---|
| 730 | /// when they are on same circle. |
---|
| 731 | /// |
---|
| 732 | /// \param graph The graph. |
---|
| 733 | /// \return The number of components. |
---|
[1909] | 734 | template <typename UGraph> |
---|
| 735 | int countBiNodeConnectedComponents(const UGraph& graph) { |
---|
[2260] | 736 | checkConcept<concepts::UGraph, UGraph>(); |
---|
[1909] | 737 | typedef typename UGraph::NodeIt NodeIt; |
---|
[1750] | 738 | |
---|
| 739 | using namespace _topology_bits; |
---|
| 740 | |
---|
[1909] | 741 | typedef CountBiNodeConnectedComponentsVisitor<UGraph> Visitor; |
---|
[1750] | 742 | |
---|
| 743 | int compNum = 0; |
---|
| 744 | Visitor visitor(graph, compNum); |
---|
| 745 | |
---|
[1909] | 746 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 747 | dfs.init(); |
---|
| 748 | |
---|
| 749 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 750 | if (!dfs.reached(it)) { |
---|
| 751 | dfs.addSource(it); |
---|
| 752 | dfs.start(); |
---|
| 753 | } |
---|
| 754 | } |
---|
| 755 | return compNum; |
---|
| 756 | } |
---|
| 757 | |
---|
[2429] | 758 | /// \ingroup graph_prop |
---|
[1750] | 759 | /// |
---|
[1767] | 760 | /// \brief Find the bi-node-connected components. |
---|
[1750] | 761 | /// |
---|
[1767] | 762 | /// This function finds the bi-node-connected components in an undirected |
---|
| 763 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
[1750] | 764 | /// relation on the undirected edges. Two undirected edge are in relationship |
---|
| 765 | /// when they are on same circle. |
---|
| 766 | /// |
---|
[1763] | 767 | /// \image html node_biconnected_components.png |
---|
[1767] | 768 | /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth |
---|
[1763] | 769 | /// |
---|
[1750] | 770 | /// \param graph The graph. |
---|
[1909] | 771 | /// \retval compMap A writable uedge map. The values will be set from 0 |
---|
[1793] | 772 | /// to the number of the biconnected components minus one. Each values |
---|
[1750] | 773 | /// of the map will be set exactly once, the values of a certain component |
---|
| 774 | /// will be set continuously. |
---|
| 775 | /// \return The number of components. |
---|
[1763] | 776 | /// |
---|
[1909] | 777 | template <typename UGraph, typename UEdgeMap> |
---|
| 778 | int biNodeConnectedComponents(const UGraph& graph, |
---|
| 779 | UEdgeMap& compMap) { |
---|
[2260] | 780 | checkConcept<concepts::UGraph, UGraph>(); |
---|
[1909] | 781 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 782 | typedef typename UGraph::UEdge UEdge; |
---|
[2260] | 783 | checkConcept<concepts::WriteMap<UEdge, int>, UEdgeMap>(); |
---|
[1750] | 784 | |
---|
| 785 | using namespace _topology_bits; |
---|
| 786 | |
---|
[1909] | 787 | typedef BiNodeConnectedComponentsVisitor<UGraph, UEdgeMap> Visitor; |
---|
[1750] | 788 | |
---|
| 789 | int compNum = 0; |
---|
| 790 | Visitor visitor(graph, compMap, compNum); |
---|
| 791 | |
---|
[1909] | 792 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 793 | dfs.init(); |
---|
| 794 | |
---|
| 795 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 796 | if (!dfs.reached(it)) { |
---|
| 797 | dfs.addSource(it); |
---|
| 798 | dfs.start(); |
---|
| 799 | } |
---|
| 800 | } |
---|
| 801 | return compNum; |
---|
| 802 | } |
---|
| 803 | |
---|
[2429] | 804 | /// \ingroup graph_prop |
---|
[1750] | 805 | /// |
---|
[1767] | 806 | /// \brief Find the bi-node-connected cut nodes. |
---|
[1750] | 807 | /// |
---|
[1767] | 808 | /// This function finds the bi-node-connected cut nodes in an undirected |
---|
| 809 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
[1750] | 810 | /// relation on the undirected edges. Two undirected edges are in |
---|
| 811 | /// relationship when they are on same circle. The biconnected components |
---|
| 812 | /// are separted by nodes which are the cut nodes of the components. |
---|
| 813 | /// |
---|
| 814 | /// \param graph The graph. |
---|
[1793] | 815 | /// \retval cutMap A writable edge map. The values will be set true when |
---|
[1750] | 816 | /// the node separate two or more components. |
---|
| 817 | /// \return The number of the cut nodes. |
---|
[1909] | 818 | template <typename UGraph, typename NodeMap> |
---|
| 819 | int biNodeConnectedCutNodes(const UGraph& graph, NodeMap& cutMap) { |
---|
[2260] | 820 | checkConcept<concepts::UGraph, UGraph>(); |
---|
[1909] | 821 | typedef typename UGraph::Node Node; |
---|
| 822 | typedef typename UGraph::NodeIt NodeIt; |
---|
[2260] | 823 | checkConcept<concepts::WriteMap<Node, bool>, NodeMap>(); |
---|
[1750] | 824 | |
---|
| 825 | using namespace _topology_bits; |
---|
| 826 | |
---|
[1909] | 827 | typedef BiNodeConnectedCutNodesVisitor<UGraph, NodeMap> Visitor; |
---|
[1750] | 828 | |
---|
| 829 | int cutNum = 0; |
---|
| 830 | Visitor visitor(graph, cutMap, cutNum); |
---|
| 831 | |
---|
[1909] | 832 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 833 | dfs.init(); |
---|
| 834 | |
---|
| 835 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 836 | if (!dfs.reached(it)) { |
---|
| 837 | dfs.addSource(it); |
---|
| 838 | dfs.start(); |
---|
| 839 | } |
---|
| 840 | } |
---|
| 841 | return cutNum; |
---|
| 842 | } |
---|
| 843 | |
---|
| 844 | namespace _topology_bits { |
---|
| 845 | |
---|
| 846 | template <typename Graph> |
---|
[1800] | 847 | class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 848 | public: |
---|
| 849 | typedef typename Graph::Node Node; |
---|
| 850 | typedef typename Graph::Edge Edge; |
---|
[1909] | 851 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 852 | |
---|
[1800] | 853 | CountBiEdgeConnectedComponentsVisitor(const Graph& graph, int &compNum) |
---|
[1750] | 854 | : _graph(graph), _compNum(compNum), |
---|
| 855 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 856 | |
---|
| 857 | void start(const Node& node) { |
---|
| 858 | _predMap.set(node, INVALID); |
---|
| 859 | } |
---|
| 860 | |
---|
| 861 | void reach(const Node& node) { |
---|
| 862 | _numMap.set(node, _num); |
---|
| 863 | _retMap.set(node, _num); |
---|
| 864 | ++_num; |
---|
| 865 | } |
---|
| 866 | |
---|
| 867 | void leave(const Node& node) { |
---|
| 868 | if (_numMap[node] <= _retMap[node]) { |
---|
| 869 | ++_compNum; |
---|
| 870 | } |
---|
| 871 | } |
---|
| 872 | |
---|
| 873 | void discover(const Edge& edge) { |
---|
| 874 | _predMap.set(_graph.target(edge), edge); |
---|
| 875 | } |
---|
| 876 | |
---|
| 877 | void examine(const Edge& edge) { |
---|
| 878 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
| 879 | return; |
---|
| 880 | } |
---|
| 881 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 882 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 883 | } |
---|
| 884 | } |
---|
| 885 | |
---|
| 886 | void backtrack(const Edge& edge) { |
---|
| 887 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 888 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 889 | } |
---|
| 890 | } |
---|
| 891 | |
---|
| 892 | private: |
---|
| 893 | const Graph& _graph; |
---|
| 894 | int& _compNum; |
---|
| 895 | |
---|
| 896 | typename Graph::template NodeMap<int> _numMap; |
---|
| 897 | typename Graph::template NodeMap<int> _retMap; |
---|
| 898 | typename Graph::template NodeMap<Edge> _predMap; |
---|
| 899 | int _num; |
---|
| 900 | }; |
---|
| 901 | |
---|
| 902 | template <typename Graph, typename NodeMap> |
---|
[1800] | 903 | class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 904 | public: |
---|
| 905 | typedef typename Graph::Node Node; |
---|
| 906 | typedef typename Graph::Edge Edge; |
---|
[1909] | 907 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 908 | |
---|
[1800] | 909 | BiEdgeConnectedComponentsVisitor(const Graph& graph, |
---|
[1750] | 910 | NodeMap& compMap, int &compNum) |
---|
| 911 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
| 912 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 913 | |
---|
| 914 | void start(const Node& node) { |
---|
| 915 | _predMap.set(node, INVALID); |
---|
| 916 | } |
---|
| 917 | |
---|
| 918 | void reach(const Node& node) { |
---|
| 919 | _numMap.set(node, _num); |
---|
| 920 | _retMap.set(node, _num); |
---|
| 921 | _nodeStack.push(node); |
---|
| 922 | ++_num; |
---|
| 923 | } |
---|
| 924 | |
---|
| 925 | void leave(const Node& node) { |
---|
| 926 | if (_numMap[node] <= _retMap[node]) { |
---|
| 927 | while (_nodeStack.top() != node) { |
---|
| 928 | _compMap.set(_nodeStack.top(), _compNum); |
---|
| 929 | _nodeStack.pop(); |
---|
| 930 | } |
---|
| 931 | _compMap.set(node, _compNum); |
---|
| 932 | _nodeStack.pop(); |
---|
| 933 | ++_compNum; |
---|
| 934 | } |
---|
| 935 | } |
---|
| 936 | |
---|
| 937 | void discover(const Edge& edge) { |
---|
| 938 | _predMap.set(_graph.target(edge), edge); |
---|
| 939 | } |
---|
| 940 | |
---|
| 941 | void examine(const Edge& edge) { |
---|
| 942 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
| 943 | return; |
---|
| 944 | } |
---|
| 945 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 946 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 947 | } |
---|
| 948 | } |
---|
| 949 | |
---|
| 950 | void backtrack(const Edge& edge) { |
---|
| 951 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 952 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 953 | } |
---|
| 954 | } |
---|
| 955 | |
---|
| 956 | private: |
---|
| 957 | const Graph& _graph; |
---|
| 958 | NodeMap& _compMap; |
---|
| 959 | int& _compNum; |
---|
| 960 | |
---|
| 961 | typename Graph::template NodeMap<int> _numMap; |
---|
| 962 | typename Graph::template NodeMap<int> _retMap; |
---|
| 963 | typename Graph::template NodeMap<Edge> _predMap; |
---|
| 964 | std::stack<Node> _nodeStack; |
---|
| 965 | int _num; |
---|
| 966 | }; |
---|
| 967 | |
---|
| 968 | |
---|
| 969 | template <typename Graph, typename EdgeMap> |
---|
[1800] | 970 | class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Graph> { |
---|
[1750] | 971 | public: |
---|
| 972 | typedef typename Graph::Node Node; |
---|
| 973 | typedef typename Graph::Edge Edge; |
---|
[1909] | 974 | typedef typename Graph::UEdge UEdge; |
---|
[1750] | 975 | |
---|
[1800] | 976 | BiEdgeConnectedCutEdgesVisitor(const Graph& graph, |
---|
[1750] | 977 | EdgeMap& cutMap, int &cutNum) |
---|
| 978 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
| 979 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 980 | |
---|
| 981 | void start(const Node& node) { |
---|
| 982 | _predMap[node] = INVALID; |
---|
| 983 | } |
---|
| 984 | |
---|
| 985 | void reach(const Node& node) { |
---|
| 986 | _numMap.set(node, _num); |
---|
| 987 | _retMap.set(node, _num); |
---|
| 988 | ++_num; |
---|
| 989 | } |
---|
| 990 | |
---|
| 991 | void leave(const Node& node) { |
---|
| 992 | if (_numMap[node] <= _retMap[node]) { |
---|
| 993 | if (_predMap[node] != INVALID) { |
---|
| 994 | _cutMap.set(_predMap[node], true); |
---|
| 995 | ++_cutNum; |
---|
| 996 | } |
---|
| 997 | } |
---|
| 998 | } |
---|
| 999 | |
---|
| 1000 | void discover(const Edge& edge) { |
---|
| 1001 | _predMap.set(_graph.target(edge), edge); |
---|
| 1002 | } |
---|
| 1003 | |
---|
| 1004 | void examine(const Edge& edge) { |
---|
| 1005 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
| 1006 | return; |
---|
| 1007 | } |
---|
| 1008 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1009 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1010 | } |
---|
| 1011 | } |
---|
| 1012 | |
---|
| 1013 | void backtrack(const Edge& edge) { |
---|
| 1014 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1015 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1016 | } |
---|
| 1017 | } |
---|
| 1018 | |
---|
| 1019 | private: |
---|
| 1020 | const Graph& _graph; |
---|
| 1021 | EdgeMap& _cutMap; |
---|
| 1022 | int& _cutNum; |
---|
| 1023 | |
---|
| 1024 | typename Graph::template NodeMap<int> _numMap; |
---|
| 1025 | typename Graph::template NodeMap<int> _retMap; |
---|
| 1026 | typename Graph::template NodeMap<Edge> _predMap; |
---|
| 1027 | int _num; |
---|
| 1028 | }; |
---|
| 1029 | } |
---|
| 1030 | |
---|
[1909] | 1031 | template <typename UGraph> |
---|
[2421] | 1032 | int countBiEdgeConnectedComponents(const UGraph& graph); |
---|
[1750] | 1033 | |
---|
[2429] | 1034 | /// \ingroup graph_prop |
---|
[1750] | 1035 | /// |
---|
[1767] | 1036 | /// \brief Checks that the graph is bi-edge-connected. |
---|
[1750] | 1037 | /// |
---|
[1767] | 1038 | /// This function checks that the graph is bi-edge-connected. The undirected |
---|
| 1039 | /// graph is bi-edge-connected when any two nodes are connected with two |
---|
[1750] | 1040 | /// edge-disjoint paths. |
---|
| 1041 | /// |
---|
| 1042 | /// \param graph The undirected graph. |
---|
| 1043 | /// \return The number of components. |
---|
[1909] | 1044 | template <typename UGraph> |
---|
| 1045 | bool biEdgeConnected(const UGraph& graph) { |
---|
[1800] | 1046 | return countBiEdgeConnectedComponents(graph) == 1; |
---|
[1750] | 1047 | } |
---|
| 1048 | |
---|
[2429] | 1049 | /// \ingroup graph_prop |
---|
[1750] | 1050 | /// |
---|
[1767] | 1051 | /// \brief Count the bi-edge-connected components. |
---|
[1750] | 1052 | /// |
---|
[1767] | 1053 | /// This function count the bi-edge-connected components in an undirected |
---|
| 1054 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
[1750] | 1055 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
| 1056 | /// connected with at least two edge-disjoint paths. |
---|
| 1057 | /// |
---|
| 1058 | /// \param graph The undirected graph. |
---|
| 1059 | /// \return The number of components. |
---|
[1909] | 1060 | template <typename UGraph> |
---|
| 1061 | int countBiEdgeConnectedComponents(const UGraph& graph) { |
---|
[2260] | 1062 | checkConcept<concepts::UGraph, UGraph>(); |
---|
[1909] | 1063 | typedef typename UGraph::NodeIt NodeIt; |
---|
[1750] | 1064 | |
---|
| 1065 | using namespace _topology_bits; |
---|
| 1066 | |
---|
[1909] | 1067 | typedef CountBiEdgeConnectedComponentsVisitor<UGraph> Visitor; |
---|
[1750] | 1068 | |
---|
| 1069 | int compNum = 0; |
---|
| 1070 | Visitor visitor(graph, compNum); |
---|
| 1071 | |
---|
[1909] | 1072 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 1073 | dfs.init(); |
---|
| 1074 | |
---|
| 1075 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1076 | if (!dfs.reached(it)) { |
---|
| 1077 | dfs.addSource(it); |
---|
| 1078 | dfs.start(); |
---|
| 1079 | } |
---|
| 1080 | } |
---|
| 1081 | return compNum; |
---|
| 1082 | } |
---|
| 1083 | |
---|
[2429] | 1084 | /// \ingroup graph_prop |
---|
[1750] | 1085 | /// |
---|
[1767] | 1086 | /// \brief Find the bi-edge-connected components. |
---|
[1750] | 1087 | /// |
---|
[1767] | 1088 | /// This function finds the bi-edge-connected components in an undirected |
---|
| 1089 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
[1750] | 1090 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
| 1091 | /// connected at least two edge-disjoint paths. |
---|
| 1092 | /// |
---|
[1763] | 1093 | /// \image html edge_biconnected_components.png |
---|
[1767] | 1094 | /// \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth |
---|
[1763] | 1095 | /// |
---|
[1750] | 1096 | /// \param graph The graph. |
---|
[1793] | 1097 | /// \retval compMap A writable node map. The values will be set from 0 to |
---|
[1750] | 1098 | /// the number of the biconnected components minus one. Each values |
---|
| 1099 | /// of the map will be set exactly once, the values of a certain component |
---|
| 1100 | /// will be set continuously. |
---|
| 1101 | /// \return The number of components. |
---|
[1763] | 1102 | /// |
---|
[1909] | 1103 | template <typename UGraph, typename NodeMap> |
---|
| 1104 | int biEdgeConnectedComponents(const UGraph& graph, NodeMap& compMap) { |
---|
[2260] | 1105 | checkConcept<concepts::UGraph, UGraph>(); |
---|
[1909] | 1106 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1107 | typedef typename UGraph::Node Node; |
---|
[2260] | 1108 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
---|
[1750] | 1109 | |
---|
| 1110 | using namespace _topology_bits; |
---|
| 1111 | |
---|
[1909] | 1112 | typedef BiEdgeConnectedComponentsVisitor<UGraph, NodeMap> Visitor; |
---|
[1750] | 1113 | |
---|
| 1114 | int compNum = 0; |
---|
| 1115 | Visitor visitor(graph, compMap, compNum); |
---|
| 1116 | |
---|
[1909] | 1117 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 1118 | dfs.init(); |
---|
| 1119 | |
---|
| 1120 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1121 | if (!dfs.reached(it)) { |
---|
| 1122 | dfs.addSource(it); |
---|
| 1123 | dfs.start(); |
---|
| 1124 | } |
---|
| 1125 | } |
---|
| 1126 | return compNum; |
---|
| 1127 | } |
---|
| 1128 | |
---|
[2429] | 1129 | /// \ingroup graph_prop |
---|
[1750] | 1130 | /// |
---|
[1767] | 1131 | /// \brief Find the bi-edge-connected cut edges. |
---|
[1750] | 1132 | /// |
---|
[1767] | 1133 | /// This function finds the bi-edge-connected components in an undirected |
---|
| 1134 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
[1750] | 1135 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
[1767] | 1136 | /// connected with at least two edge-disjoint paths. The bi-edge-connected |
---|
[1750] | 1137 | /// components are separted by edges which are the cut edges of the |
---|
| 1138 | /// components. |
---|
| 1139 | /// |
---|
| 1140 | /// \param graph The graph. |
---|
[1793] | 1141 | /// \retval cutMap A writable node map. The values will be set true when the |
---|
[1750] | 1142 | /// edge is a cut edge. |
---|
| 1143 | /// \return The number of cut edges. |
---|
[1909] | 1144 | template <typename UGraph, typename UEdgeMap> |
---|
| 1145 | int biEdgeConnectedCutEdges(const UGraph& graph, UEdgeMap& cutMap) { |
---|
[2260] | 1146 | checkConcept<concepts::UGraph, UGraph>(); |
---|
[1909] | 1147 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1148 | typedef typename UGraph::UEdge UEdge; |
---|
[2260] | 1149 | checkConcept<concepts::WriteMap<UEdge, bool>, UEdgeMap>(); |
---|
[1750] | 1150 | |
---|
| 1151 | using namespace _topology_bits; |
---|
| 1152 | |
---|
[1909] | 1153 | typedef BiEdgeConnectedCutEdgesVisitor<UGraph, UEdgeMap> Visitor; |
---|
[1750] | 1154 | |
---|
| 1155 | int cutNum = 0; |
---|
| 1156 | Visitor visitor(graph, cutMap, cutNum); |
---|
| 1157 | |
---|
[1909] | 1158 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
[1750] | 1159 | dfs.init(); |
---|
| 1160 | |
---|
| 1161 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1162 | if (!dfs.reached(it)) { |
---|
| 1163 | dfs.addSource(it); |
---|
| 1164 | dfs.start(); |
---|
| 1165 | } |
---|
| 1166 | } |
---|
| 1167 | return cutNum; |
---|
| 1168 | } |
---|
| 1169 | |
---|
| 1170 | |
---|
| 1171 | namespace _topology_bits { |
---|
| 1172 | |
---|
| 1173 | template <typename Graph, typename IntNodeMap> |
---|
| 1174 | class TopologicalSortVisitor : public DfsVisitor<Graph> { |
---|
| 1175 | public: |
---|
| 1176 | typedef typename Graph::Node Node; |
---|
| 1177 | typedef typename Graph::Edge edge; |
---|
| 1178 | |
---|
| 1179 | TopologicalSortVisitor(IntNodeMap& order, int num) |
---|
| 1180 | : _order(order), _num(num) {} |
---|
| 1181 | |
---|
| 1182 | void leave(const Node& node) { |
---|
| 1183 | _order.set(node, --_num); |
---|
[1698] | 1184 | } |
---|
| 1185 | |
---|
| 1186 | private: |
---|
[1750] | 1187 | IntNodeMap& _order; |
---|
| 1188 | int _num; |
---|
[1698] | 1189 | }; |
---|
[1750] | 1190 | |
---|
[1698] | 1191 | } |
---|
| 1192 | |
---|
[2429] | 1193 | /// \ingroup graph_prop |
---|
[1750] | 1194 | /// |
---|
| 1195 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
| 1196 | /// |
---|
| 1197 | /// Sort the nodes of a DAG into topolgical order. |
---|
| 1198 | /// |
---|
[1793] | 1199 | /// \param graph The graph. It should be directed and acyclic. |
---|
| 1200 | /// \retval order A writable node map. The values will be set from 0 to |
---|
[1750] | 1201 | /// the number of the nodes in the graph minus one. Each values of the map |
---|
| 1202 | /// will be set exactly once, the values will be set descending order. |
---|
| 1203 | /// |
---|
| 1204 | /// \see checkedTopologicalSort |
---|
| 1205 | /// \see dag |
---|
[1698] | 1206 | template <typename Graph, typename NodeMap> |
---|
[1750] | 1207 | void topologicalSort(const Graph& graph, NodeMap& order) { |
---|
| 1208 | using namespace _topology_bits; |
---|
| 1209 | |
---|
[2260] | 1210 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1211 | checkConcept<concepts::WriteMap<typename Graph::Node, int>, NodeMap>(); |
---|
[1750] | 1212 | |
---|
| 1213 | typedef typename Graph::Node Node; |
---|
| 1214 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1215 | typedef typename Graph::Edge Edge; |
---|
| 1216 | |
---|
| 1217 | TopologicalSortVisitor<Graph, NodeMap> |
---|
| 1218 | visitor(order, countNodes(graph)); |
---|
| 1219 | |
---|
| 1220 | DfsVisit<Graph, TopologicalSortVisitor<Graph, NodeMap> > |
---|
| 1221 | dfs(graph, visitor); |
---|
| 1222 | |
---|
| 1223 | dfs.init(); |
---|
| 1224 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1225 | if (!dfs.reached(it)) { |
---|
| 1226 | dfs.addSource(it); |
---|
| 1227 | dfs.start(); |
---|
| 1228 | } |
---|
| 1229 | } |
---|
| 1230 | } |
---|
| 1231 | |
---|
[2429] | 1232 | /// \ingroup graph_prop |
---|
[1750] | 1233 | /// |
---|
| 1234 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
| 1235 | /// |
---|
| 1236 | /// Sort the nodes of a DAG into topolgical order. It also checks |
---|
| 1237 | /// that the given graph is DAG. |
---|
| 1238 | /// |
---|
[1793] | 1239 | /// \param graph The graph. It should be directed and acyclic. |
---|
[1750] | 1240 | /// \retval order A readable - writable node map. The values will be set |
---|
| 1241 | /// from 0 to the number of the nodes in the graph minus one. Each values |
---|
| 1242 | /// of the map will be set exactly once, the values will be set descending |
---|
| 1243 | /// order. |
---|
| 1244 | /// \return %False when the graph is not DAG. |
---|
| 1245 | /// |
---|
| 1246 | /// \see topologicalSort |
---|
| 1247 | /// \see dag |
---|
| 1248 | template <typename Graph, typename NodeMap> |
---|
| 1249 | bool checkedTopologicalSort(const Graph& graph, NodeMap& order) { |
---|
[1698] | 1250 | using namespace _topology_bits; |
---|
| 1251 | |
---|
[2260] | 1252 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1253 | checkConcept<concepts::ReadWriteMap<typename Graph::Node, int>, NodeMap>(); |
---|
[1698] | 1254 | |
---|
| 1255 | typedef typename Graph::Node Node; |
---|
| 1256 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1257 | typedef typename Graph::Edge Edge; |
---|
| 1258 | |
---|
[1750] | 1259 | order = constMap<Node, int, -1>(); |
---|
[1698] | 1260 | |
---|
[1750] | 1261 | TopologicalSortVisitor<Graph, NodeMap> |
---|
| 1262 | visitor(order, countNodes(graph)); |
---|
[1698] | 1263 | |
---|
[1750] | 1264 | DfsVisit<Graph, TopologicalSortVisitor<Graph, NodeMap> > |
---|
| 1265 | dfs(graph, visitor); |
---|
[1698] | 1266 | |
---|
| 1267 | dfs.init(); |
---|
| 1268 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1269 | if (!dfs.reached(it)) { |
---|
| 1270 | dfs.addSource(it); |
---|
| 1271 | while (!dfs.emptyQueue()) { |
---|
[1750] | 1272 | Edge edge = dfs.nextEdge(); |
---|
| 1273 | Node target = graph.target(edge); |
---|
| 1274 | if (dfs.reached(target) && order[target] == -1) { |
---|
| 1275 | return false; |
---|
| 1276 | } |
---|
| 1277 | dfs.processNextEdge(); |
---|
| 1278 | } |
---|
[1698] | 1279 | } |
---|
[1750] | 1280 | } |
---|
[1698] | 1281 | return true; |
---|
| 1282 | } |
---|
| 1283 | |
---|
[2429] | 1284 | /// \ingroup graph_prop |
---|
[1698] | 1285 | /// |
---|
[1750] | 1286 | /// \brief Check that the given directed graph is a DAG. |
---|
| 1287 | /// |
---|
| 1288 | /// Check that the given directed graph is a DAG. The DAG is |
---|
[1698] | 1289 | /// an Directed Acyclic Graph. |
---|
[1750] | 1290 | /// \return %False when the graph is not DAG. |
---|
| 1291 | /// \see acyclic |
---|
[1698] | 1292 | template <typename Graph> |
---|
| 1293 | bool dag(const Graph& graph) { |
---|
| 1294 | |
---|
[2260] | 1295 | checkConcept<concepts::Graph, Graph>(); |
---|
[1698] | 1296 | |
---|
| 1297 | typedef typename Graph::Node Node; |
---|
| 1298 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1299 | typedef typename Graph::Edge Edge; |
---|
| 1300 | |
---|
| 1301 | typedef typename Graph::template NodeMap<bool> ProcessedMap; |
---|
| 1302 | |
---|
| 1303 | typename Dfs<Graph>::template DefProcessedMap<ProcessedMap>:: |
---|
[1709] | 1304 | Create dfs(graph); |
---|
[1698] | 1305 | |
---|
| 1306 | ProcessedMap processed(graph); |
---|
| 1307 | dfs.processedMap(processed); |
---|
| 1308 | |
---|
| 1309 | dfs.init(); |
---|
| 1310 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1311 | if (!dfs.reached(it)) { |
---|
| 1312 | dfs.addSource(it); |
---|
| 1313 | while (!dfs.emptyQueue()) { |
---|
| 1314 | Edge edge = dfs.nextEdge(); |
---|
| 1315 | Node target = graph.target(edge); |
---|
| 1316 | if (dfs.reached(target) && !processed[target]) { |
---|
| 1317 | return false; |
---|
| 1318 | } |
---|
| 1319 | dfs.processNextEdge(); |
---|
| 1320 | } |
---|
| 1321 | } |
---|
| 1322 | } |
---|
| 1323 | return true; |
---|
| 1324 | } |
---|
| 1325 | |
---|
[2429] | 1326 | /// \ingroup graph_prop |
---|
[1698] | 1327 | /// |
---|
| 1328 | /// \brief Check that the given undirected graph is acyclic. |
---|
| 1329 | /// |
---|
| 1330 | /// Check that the given undirected graph acyclic. |
---|
[1750] | 1331 | /// \param graph The undirected graph. |
---|
| 1332 | /// \return %True when there is no circle in the graph. |
---|
| 1333 | /// \see dag |
---|
[1909] | 1334 | template <typename UGraph> |
---|
| 1335 | bool acyclic(const UGraph& graph) { |
---|
[2260] | 1336 | checkConcept<concepts::UGraph, UGraph>(); |
---|
[1909] | 1337 | typedef typename UGraph::Node Node; |
---|
| 1338 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1339 | typedef typename UGraph::Edge Edge; |
---|
| 1340 | Dfs<UGraph> dfs(graph); |
---|
[1698] | 1341 | dfs.init(); |
---|
| 1342 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1343 | if (!dfs.reached(it)) { |
---|
| 1344 | dfs.addSource(it); |
---|
| 1345 | while (!dfs.emptyQueue()) { |
---|
| 1346 | Edge edge = dfs.nextEdge(); |
---|
| 1347 | Node source = graph.source(edge); |
---|
| 1348 | Node target = graph.target(edge); |
---|
| 1349 | if (dfs.reached(target) && |
---|
[1763] | 1350 | dfs.predEdge(source) != graph.oppositeEdge(edge)) { |
---|
[1698] | 1351 | return false; |
---|
| 1352 | } |
---|
| 1353 | dfs.processNextEdge(); |
---|
| 1354 | } |
---|
| 1355 | } |
---|
| 1356 | } |
---|
| 1357 | return true; |
---|
| 1358 | } |
---|
| 1359 | |
---|
[2429] | 1360 | /// \ingroup graph_prop |
---|
[1750] | 1361 | /// |
---|
[1698] | 1362 | /// \brief Check that the given undirected graph is tree. |
---|
| 1363 | /// |
---|
| 1364 | /// Check that the given undirected graph is tree. |
---|
[1750] | 1365 | /// \param graph The undirected graph. |
---|
| 1366 | /// \return %True when the graph is acyclic and connected. |
---|
[1909] | 1367 | template <typename UGraph> |
---|
| 1368 | bool tree(const UGraph& graph) { |
---|
[2260] | 1369 | checkConcept<concepts::UGraph, UGraph>(); |
---|
[1909] | 1370 | typedef typename UGraph::Node Node; |
---|
| 1371 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1372 | typedef typename UGraph::Edge Edge; |
---|
| 1373 | Dfs<UGraph> dfs(graph); |
---|
[1698] | 1374 | dfs.init(); |
---|
| 1375 | dfs.addSource(NodeIt(graph)); |
---|
| 1376 | while (!dfs.emptyQueue()) { |
---|
| 1377 | Edge edge = dfs.nextEdge(); |
---|
| 1378 | Node source = graph.source(edge); |
---|
| 1379 | Node target = graph.target(edge); |
---|
| 1380 | if (dfs.reached(target) && |
---|
[1763] | 1381 | dfs.predEdge(source) != graph.oppositeEdge(edge)) { |
---|
[1698] | 1382 | return false; |
---|
| 1383 | } |
---|
| 1384 | dfs.processNextEdge(); |
---|
| 1385 | } |
---|
| 1386 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1387 | if (!dfs.reached(it)) { |
---|
| 1388 | return false; |
---|
| 1389 | } |
---|
| 1390 | } |
---|
| 1391 | return true; |
---|
| 1392 | } |
---|
[1739] | 1393 | |
---|
[2306] | 1394 | namespace _topology_bits { |
---|
| 1395 | |
---|
| 1396 | template <typename Graph> |
---|
| 1397 | class BipartiteVisitor : public BfsVisitor<Graph> { |
---|
| 1398 | public: |
---|
| 1399 | typedef typename Graph::Edge Edge; |
---|
| 1400 | typedef typename Graph::Node Node; |
---|
| 1401 | |
---|
| 1402 | BipartiteVisitor(const Graph& graph, bool& bipartite) |
---|
| 1403 | : _graph(graph), _part(graph), _bipartite(bipartite) {} |
---|
| 1404 | |
---|
| 1405 | void start(const Node& node) { |
---|
| 1406 | _part[node] = true; |
---|
| 1407 | } |
---|
| 1408 | void discover(const Edge& edge) { |
---|
| 1409 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
| 1410 | } |
---|
| 1411 | void examine(const Edge& edge) { |
---|
| 1412 | _bipartite = _bipartite && |
---|
| 1413 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
| 1414 | } |
---|
| 1415 | |
---|
| 1416 | private: |
---|
| 1417 | |
---|
| 1418 | const Graph& _graph; |
---|
| 1419 | typename Graph::template NodeMap<bool> _part; |
---|
| 1420 | bool& _bipartite; |
---|
| 1421 | }; |
---|
| 1422 | |
---|
| 1423 | template <typename Graph, typename PartMap> |
---|
| 1424 | class BipartitePartitionsVisitor : public BfsVisitor<Graph> { |
---|
| 1425 | public: |
---|
| 1426 | typedef typename Graph::Edge Edge; |
---|
| 1427 | typedef typename Graph::Node Node; |
---|
| 1428 | |
---|
| 1429 | BipartitePartitionsVisitor(const Graph& graph, |
---|
| 1430 | PartMap& part, bool& bipartite) |
---|
| 1431 | : _graph(graph), _part(part), _bipartite(bipartite) {} |
---|
| 1432 | |
---|
| 1433 | void start(const Node& node) { |
---|
| 1434 | _part.set(node, true); |
---|
| 1435 | } |
---|
| 1436 | void discover(const Edge& edge) { |
---|
| 1437 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
| 1438 | } |
---|
| 1439 | void examine(const Edge& edge) { |
---|
| 1440 | _bipartite = _bipartite && |
---|
| 1441 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
| 1442 | } |
---|
| 1443 | |
---|
| 1444 | private: |
---|
| 1445 | |
---|
| 1446 | const Graph& _graph; |
---|
| 1447 | PartMap& _part; |
---|
| 1448 | bool& _bipartite; |
---|
| 1449 | }; |
---|
| 1450 | } |
---|
| 1451 | |
---|
[2429] | 1452 | /// \ingroup graph_prop |
---|
[1739] | 1453 | /// |
---|
[1800] | 1454 | /// \brief Check if the given undirected graph is bipartite or not |
---|
[1750] | 1455 | /// |
---|
[1800] | 1456 | /// The function checks if the given undirected \c graph graph is bipartite |
---|
| 1457 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
---|
[1750] | 1458 | /// \param graph The undirected graph. |
---|
[1800] | 1459 | /// \return %True if \c graph is bipartite, %false otherwise. |
---|
| 1460 | /// \sa bipartitePartitions |
---|
| 1461 | /// |
---|
| 1462 | /// \author Balazs Attila Mihaly |
---|
[1909] | 1463 | template<typename UGraph> |
---|
| 1464 | inline bool bipartite(const UGraph &graph){ |
---|
[2306] | 1465 | using namespace _topology_bits; |
---|
| 1466 | |
---|
[2260] | 1467 | checkConcept<concepts::UGraph, UGraph>(); |
---|
[1800] | 1468 | |
---|
[1909] | 1469 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1470 | typedef typename UGraph::EdgeIt EdgeIt; |
---|
[1800] | 1471 | |
---|
[2306] | 1472 | bool bipartite = true; |
---|
| 1473 | |
---|
| 1474 | BipartiteVisitor<UGraph> |
---|
| 1475 | visitor(graph, bipartite); |
---|
| 1476 | BfsVisit<UGraph, BipartiteVisitor<UGraph> > |
---|
| 1477 | bfs(graph, visitor); |
---|
[1800] | 1478 | bfs.init(); |
---|
[2306] | 1479 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1480 | if(!bfs.reached(it)){ |
---|
| 1481 | bfs.addSource(it); |
---|
| 1482 | while (!bfs.emptyQueue()) { |
---|
| 1483 | bfs.processNextNode(); |
---|
| 1484 | if (!bipartite) return false; |
---|
| 1485 | } |
---|
[1800] | 1486 | } |
---|
| 1487 | } |
---|
| 1488 | return true; |
---|
[1979] | 1489 | } |
---|
[1800] | 1490 | |
---|
[2429] | 1491 | /// \ingroup graph_prop |
---|
[1800] | 1492 | /// |
---|
| 1493 | /// \brief Check if the given undirected graph is bipartite or not |
---|
| 1494 | /// |
---|
| 1495 | /// The function checks if the given undirected graph is bipartite |
---|
| 1496 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
---|
| 1497 | /// During the execution, the \c partMap will be set as the two |
---|
| 1498 | /// partitions of the graph. |
---|
| 1499 | /// \param graph The undirected graph. |
---|
[1808] | 1500 | /// \retval partMap A writable bool map of nodes. It will be set as the |
---|
[1800] | 1501 | /// two partitions of the graph. |
---|
| 1502 | /// \return %True if \c graph is bipartite, %false otherwise. |
---|
| 1503 | /// |
---|
| 1504 | /// \author Balazs Attila Mihaly |
---|
| 1505 | /// |
---|
| 1506 | /// \image html bipartite_partitions.png |
---|
| 1507 | /// \image latex bipartite_partitions.eps "Bipartite partititions" width=\textwidth |
---|
[1909] | 1508 | template<typename UGraph, typename NodeMap> |
---|
| 1509 | inline bool bipartitePartitions(const UGraph &graph, NodeMap &partMap){ |
---|
[2306] | 1510 | using namespace _topology_bits; |
---|
| 1511 | |
---|
[2260] | 1512 | checkConcept<concepts::UGraph, UGraph>(); |
---|
[1800] | 1513 | |
---|
[1909] | 1514 | typedef typename UGraph::Node Node; |
---|
| 1515 | typedef typename UGraph::NodeIt NodeIt; |
---|
| 1516 | typedef typename UGraph::EdgeIt EdgeIt; |
---|
[2306] | 1517 | |
---|
| 1518 | bool bipartite = true; |
---|
| 1519 | |
---|
| 1520 | BipartitePartitionsVisitor<UGraph, NodeMap> |
---|
| 1521 | visitor(graph, partMap, bipartite); |
---|
| 1522 | BfsVisit<UGraph, BipartitePartitionsVisitor<UGraph, NodeMap> > |
---|
| 1523 | bfs(graph, visitor); |
---|
[1800] | 1524 | bfs.init(); |
---|
[2306] | 1525 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1526 | if(!bfs.reached(it)){ |
---|
| 1527 | bfs.addSource(it); |
---|
| 1528 | while (!bfs.emptyQueue()) { |
---|
| 1529 | bfs.processNextNode(); |
---|
| 1530 | if (!bipartite) return false; |
---|
| 1531 | } |
---|
[1740] | 1532 | } |
---|
| 1533 | } |
---|
[2306] | 1534 | return true; |
---|
| 1535 | } |
---|
| 1536 | |
---|
| 1537 | /// \brief Returns true when there is not loop edge in the graph. |
---|
| 1538 | /// |
---|
| 1539 | /// Returns true when there is not loop edge in the graph. |
---|
| 1540 | template <typename Graph> |
---|
| 1541 | bool loopFree(const Graph& graph) { |
---|
| 1542 | for (typename Graph::EdgeIt it(graph); it != INVALID; ++it) { |
---|
| 1543 | if (graph.source(it) == graph.target(it)) return false; |
---|
| 1544 | } |
---|
| 1545 | return true; |
---|
| 1546 | } |
---|
| 1547 | |
---|
| 1548 | /// \brief Returns true when there is not parallel edges in the graph. |
---|
| 1549 | /// |
---|
| 1550 | /// Returns true when there is not parallel edges in the graph. |
---|
| 1551 | template <typename Graph> |
---|
| 1552 | bool parallelFree(const Graph& graph) { |
---|
| 1553 | typename Graph::template NodeMap<bool> reached(graph, false); |
---|
| 1554 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
| 1555 | for (typename Graph::OutEdgeIt e(graph, n); e != INVALID; ++e) { |
---|
| 1556 | if (reached[graph.target(e)]) return false; |
---|
| 1557 | reached.set(graph.target(e), true); |
---|
| 1558 | } |
---|
| 1559 | for (typename Graph::OutEdgeIt e(graph, n); e != INVALID; ++e) { |
---|
| 1560 | reached.set(graph.target(e), false); |
---|
| 1561 | } |
---|
| 1562 | } |
---|
| 1563 | return true; |
---|
| 1564 | } |
---|
| 1565 | |
---|
| 1566 | /// \brief Returns true when there is not loop edge and parallel |
---|
| 1567 | /// edges in the graph. |
---|
| 1568 | /// |
---|
| 1569 | /// Returns true when there is not loop edge and parallel edges in |
---|
| 1570 | /// the graph. |
---|
| 1571 | template <typename Graph> |
---|
| 1572 | bool simpleGraph(const Graph& graph) { |
---|
| 1573 | typename Graph::template NodeMap<bool> reached(graph, false); |
---|
| 1574 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
| 1575 | reached.set(n, true); |
---|
| 1576 | for (typename Graph::OutEdgeIt e(graph, n); e != INVALID; ++e) { |
---|
| 1577 | if (reached[graph.target(e)]) return false; |
---|
| 1578 | reached.set(graph.target(e), true); |
---|
| 1579 | } |
---|
| 1580 | for (typename Graph::OutEdgeIt e(graph, n); e != INVALID; ++e) { |
---|
| 1581 | reached.set(graph.target(e), false); |
---|
| 1582 | } |
---|
| 1583 | reached.set(n, false); |
---|
[1800] | 1584 | } |
---|
[1750] | 1585 | return true; |
---|
[1979] | 1586 | } |
---|
[1750] | 1587 | |
---|
[1698] | 1588 | } //namespace lemon |
---|
| 1589 | |
---|
| 1590 | #endif //LEMON_TOPOLOGY_H |
---|