[417] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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| 4 | * |
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[440] | 5 | * Copyright (C) 2003-2009 |
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[417] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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[419] | 19 | #ifndef LEMON_CONNECTIVITY_H |
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| 20 | #define LEMON_CONNECTIVITY_H |
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[417] | 21 | |
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| 22 | #include <lemon/dfs.h> |
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| 23 | #include <lemon/bfs.h> |
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| 24 | #include <lemon/core.h> |
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| 25 | #include <lemon/maps.h> |
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| 26 | #include <lemon/adaptors.h> |
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| 27 | |
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| 28 | #include <lemon/concepts/digraph.h> |
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| 29 | #include <lemon/concepts/graph.h> |
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| 30 | #include <lemon/concept_check.h> |
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| 31 | |
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| 32 | #include <stack> |
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| 33 | #include <functional> |
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| 34 | |
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[586] | 35 | /// \ingroup graph_properties |
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[417] | 36 | /// \file |
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| 37 | /// \brief Connectivity algorithms |
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| 38 | /// |
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| 39 | /// Connectivity algorithms |
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| 40 | |
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| 41 | namespace lemon { |
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| 42 | |
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[586] | 43 | /// \ingroup graph_properties |
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[417] | 44 | /// |
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[648] | 45 | /// \brief Check whether an undirected graph is connected. |
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[417] | 46 | /// |
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[648] | 47 | /// This function checks whether the given undirected graph is connected, |
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| 48 | /// i.e. there is a path between any two nodes in the graph. |
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| 49 | /// |
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| 50 | /// \return \c true if the graph is connected. |
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[417] | 51 | /// \note By definition, the empty graph is connected. |
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[648] | 52 | /// |
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| 53 | /// \see countConnectedComponents(), connectedComponents() |
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| 54 | /// \see stronglyConnected() |
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[417] | 55 | template <typename Graph> |
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| 56 | bool connected(const Graph& graph) { |
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| 57 | checkConcept<concepts::Graph, Graph>(); |
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| 58 | typedef typename Graph::NodeIt NodeIt; |
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| 59 | if (NodeIt(graph) == INVALID) return true; |
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| 60 | Dfs<Graph> dfs(graph); |
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| 61 | dfs.run(NodeIt(graph)); |
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| 62 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 63 | if (!dfs.reached(it)) { |
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| 64 | return false; |
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| 65 | } |
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| 66 | } |
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| 67 | return true; |
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| 68 | } |
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| 69 | |
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[586] | 70 | /// \ingroup graph_properties |
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[417] | 71 | /// |
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| 72 | /// \brief Count the number of connected components of an undirected graph |
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| 73 | /// |
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[648] | 74 | /// This function counts the number of connected components of the given |
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| 75 | /// undirected graph. |
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[417] | 76 | /// |
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[648] | 77 | /// The connected components are the classes of an equivalence relation |
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| 78 | /// on the nodes of an undirected graph. Two nodes are in the same class |
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| 79 | /// if they are connected with a path. |
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| 80 | /// |
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| 81 | /// \return The number of connected components. |
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[417] | 82 | /// \note By definition, the empty graph consists |
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| 83 | /// of zero connected components. |
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[648] | 84 | /// |
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| 85 | /// \see connected(), connectedComponents() |
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[417] | 86 | template <typename Graph> |
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| 87 | int countConnectedComponents(const Graph &graph) { |
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| 88 | checkConcept<concepts::Graph, Graph>(); |
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| 89 | typedef typename Graph::Node Node; |
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| 90 | typedef typename Graph::Arc Arc; |
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| 91 | |
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| 92 | typedef NullMap<Node, Arc> PredMap; |
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| 93 | typedef NullMap<Node, int> DistMap; |
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| 94 | |
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| 95 | int compNum = 0; |
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| 96 | typename Bfs<Graph>:: |
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| 97 | template SetPredMap<PredMap>:: |
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| 98 | template SetDistMap<DistMap>:: |
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| 99 | Create bfs(graph); |
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| 100 | |
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| 101 | PredMap predMap; |
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| 102 | bfs.predMap(predMap); |
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| 103 | |
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| 104 | DistMap distMap; |
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| 105 | bfs.distMap(distMap); |
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| 106 | |
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| 107 | bfs.init(); |
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| 108 | for(typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
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| 109 | if (!bfs.reached(n)) { |
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| 110 | bfs.addSource(n); |
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| 111 | bfs.start(); |
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| 112 | ++compNum; |
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| 113 | } |
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| 114 | } |
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| 115 | return compNum; |
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| 116 | } |
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| 117 | |
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[586] | 118 | /// \ingroup graph_properties |
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[417] | 119 | /// |
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| 120 | /// \brief Find the connected components of an undirected graph |
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| 121 | /// |
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[648] | 122 | /// This function finds the connected components of the given undirected |
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| 123 | /// graph. |
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| 124 | /// |
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| 125 | /// The connected components are the classes of an equivalence relation |
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| 126 | /// on the nodes of an undirected graph. Two nodes are in the same class |
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| 127 | /// if they are connected with a path. |
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[417] | 128 | /// |
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[586] | 129 | /// \image html connected_components.png |
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| 130 | /// \image latex connected_components.eps "Connected components" width=\textwidth |
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| 131 | /// |
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[648] | 132 | /// \param graph The undirected graph. |
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[417] | 133 | /// \retval compMap A writable node map. The values will be set from 0 to |
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[648] | 134 | /// the number of the connected components minus one. Each value of the map |
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| 135 | /// will be set exactly once, and the values of a certain component will be |
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[417] | 136 | /// set continuously. |
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[648] | 137 | /// \return The number of connected components. |
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| 138 | /// \note By definition, the empty graph consists |
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| 139 | /// of zero connected components. |
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| 140 | /// |
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| 141 | /// \see connected(), countConnectedComponents() |
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[417] | 142 | template <class Graph, class NodeMap> |
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| 143 | int connectedComponents(const Graph &graph, NodeMap &compMap) { |
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| 144 | checkConcept<concepts::Graph, Graph>(); |
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| 145 | typedef typename Graph::Node Node; |
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| 146 | typedef typename Graph::Arc Arc; |
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| 147 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
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| 148 | |
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| 149 | typedef NullMap<Node, Arc> PredMap; |
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| 150 | typedef NullMap<Node, int> DistMap; |
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| 151 | |
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| 152 | int compNum = 0; |
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| 153 | typename Bfs<Graph>:: |
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| 154 | template SetPredMap<PredMap>:: |
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| 155 | template SetDistMap<DistMap>:: |
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| 156 | Create bfs(graph); |
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| 157 | |
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| 158 | PredMap predMap; |
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| 159 | bfs.predMap(predMap); |
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| 160 | |
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| 161 | DistMap distMap; |
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| 162 | bfs.distMap(distMap); |
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| 163 | |
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| 164 | bfs.init(); |
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| 165 | for(typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
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| 166 | if(!bfs.reached(n)) { |
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| 167 | bfs.addSource(n); |
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| 168 | while (!bfs.emptyQueue()) { |
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| 169 | compMap.set(bfs.nextNode(), compNum); |
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| 170 | bfs.processNextNode(); |
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| 171 | } |
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| 172 | ++compNum; |
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| 173 | } |
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| 174 | } |
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| 175 | return compNum; |
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| 176 | } |
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| 177 | |
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[419] | 178 | namespace _connectivity_bits { |
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[417] | 179 | |
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| 180 | template <typename Digraph, typename Iterator > |
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| 181 | struct LeaveOrderVisitor : public DfsVisitor<Digraph> { |
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| 182 | public: |
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| 183 | typedef typename Digraph::Node Node; |
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| 184 | LeaveOrderVisitor(Iterator it) : _it(it) {} |
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| 185 | |
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| 186 | void leave(const Node& node) { |
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| 187 | *(_it++) = node; |
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| 188 | } |
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| 189 | |
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| 190 | private: |
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| 191 | Iterator _it; |
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| 192 | }; |
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| 193 | |
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| 194 | template <typename Digraph, typename Map> |
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| 195 | struct FillMapVisitor : public DfsVisitor<Digraph> { |
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| 196 | public: |
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| 197 | typedef typename Digraph::Node Node; |
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| 198 | typedef typename Map::Value Value; |
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| 199 | |
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| 200 | FillMapVisitor(Map& map, Value& value) |
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| 201 | : _map(map), _value(value) {} |
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| 202 | |
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| 203 | void reach(const Node& node) { |
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| 204 | _map.set(node, _value); |
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| 205 | } |
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| 206 | private: |
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| 207 | Map& _map; |
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| 208 | Value& _value; |
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| 209 | }; |
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| 210 | |
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| 211 | template <typename Digraph, typename ArcMap> |
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[419] | 212 | struct StronglyConnectedCutArcsVisitor : public DfsVisitor<Digraph> { |
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[417] | 213 | public: |
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| 214 | typedef typename Digraph::Node Node; |
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| 215 | typedef typename Digraph::Arc Arc; |
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| 216 | |
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[419] | 217 | StronglyConnectedCutArcsVisitor(const Digraph& digraph, |
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| 218 | ArcMap& cutMap, |
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| 219 | int& cutNum) |
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[417] | 220 | : _digraph(digraph), _cutMap(cutMap), _cutNum(cutNum), |
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[419] | 221 | _compMap(digraph, -1), _num(-1) { |
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[417] | 222 | } |
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| 223 | |
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[419] | 224 | void start(const Node&) { |
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[417] | 225 | ++_num; |
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| 226 | } |
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| 227 | |
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| 228 | void reach(const Node& node) { |
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| 229 | _compMap.set(node, _num); |
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| 230 | } |
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| 231 | |
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| 232 | void examine(const Arc& arc) { |
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| 233 | if (_compMap[_digraph.source(arc)] != |
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| 234 | _compMap[_digraph.target(arc)]) { |
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| 235 | _cutMap.set(arc, true); |
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| 236 | ++_cutNum; |
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| 237 | } |
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| 238 | } |
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| 239 | private: |
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| 240 | const Digraph& _digraph; |
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| 241 | ArcMap& _cutMap; |
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| 242 | int& _cutNum; |
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| 243 | |
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| 244 | typename Digraph::template NodeMap<int> _compMap; |
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| 245 | int _num; |
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| 246 | }; |
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| 247 | |
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| 248 | } |
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| 249 | |
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| 250 | |
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[586] | 251 | /// \ingroup graph_properties |
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[417] | 252 | /// |
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[648] | 253 | /// \brief Check whether a directed graph is strongly connected. |
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[417] | 254 | /// |
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[648] | 255 | /// This function checks whether the given directed graph is strongly |
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| 256 | /// connected, i.e. any two nodes of the digraph are |
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[417] | 257 | /// connected with directed paths in both direction. |
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| 258 | /// |
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[648] | 259 | /// \return \c true if the digraph is strongly connected. |
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| 260 | /// \note By definition, the empty digraph is strongly connected. |
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| 261 | /// |
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| 262 | /// \see countStronglyConnectedComponents(), stronglyConnectedComponents() |
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| 263 | /// \see connected() |
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[417] | 264 | template <typename Digraph> |
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| 265 | bool stronglyConnected(const Digraph& digraph) { |
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| 266 | checkConcept<concepts::Digraph, Digraph>(); |
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| 267 | |
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| 268 | typedef typename Digraph::Node Node; |
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| 269 | typedef typename Digraph::NodeIt NodeIt; |
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| 270 | |
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| 271 | typename Digraph::Node source = NodeIt(digraph); |
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| 272 | if (source == INVALID) return true; |
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| 273 | |
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[419] | 274 | using namespace _connectivity_bits; |
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[417] | 275 | |
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| 276 | typedef DfsVisitor<Digraph> Visitor; |
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| 277 | Visitor visitor; |
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| 278 | |
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| 279 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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| 280 | dfs.init(); |
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| 281 | dfs.addSource(source); |
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| 282 | dfs.start(); |
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| 283 | |
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| 284 | for (NodeIt it(digraph); it != INVALID; ++it) { |
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| 285 | if (!dfs.reached(it)) { |
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| 286 | return false; |
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| 287 | } |
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| 288 | } |
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| 289 | |
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| 290 | typedef ReverseDigraph<const Digraph> RDigraph; |
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[419] | 291 | typedef typename RDigraph::NodeIt RNodeIt; |
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[417] | 292 | RDigraph rdigraph(digraph); |
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| 293 | |
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[648] | 294 | typedef DfsVisitor<RDigraph> RVisitor; |
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[417] | 295 | RVisitor rvisitor; |
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| 296 | |
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| 297 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
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| 298 | rdfs.init(); |
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| 299 | rdfs.addSource(source); |
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| 300 | rdfs.start(); |
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| 301 | |
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[419] | 302 | for (RNodeIt it(rdigraph); it != INVALID; ++it) { |
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[417] | 303 | if (!rdfs.reached(it)) { |
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| 304 | return false; |
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| 305 | } |
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| 306 | } |
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| 307 | |
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| 308 | return true; |
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| 309 | } |
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| 310 | |
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[586] | 311 | /// \ingroup graph_properties |
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[417] | 312 | /// |
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[648] | 313 | /// \brief Count the number of strongly connected components of a |
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| 314 | /// directed graph |
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[417] | 315 | /// |
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[648] | 316 | /// This function counts the number of strongly connected components of |
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| 317 | /// the given directed graph. |
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| 318 | /// |
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[417] | 319 | /// The strongly connected components are the classes of an |
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[648] | 320 | /// equivalence relation on the nodes of a digraph. Two nodes are in |
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[417] | 321 | /// the same class if they are connected with directed paths in both |
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| 322 | /// direction. |
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| 323 | /// |
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[648] | 324 | /// \return The number of strongly connected components. |
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| 325 | /// \note By definition, the empty digraph has zero |
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[417] | 326 | /// strongly connected components. |
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[648] | 327 | /// |
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| 328 | /// \see stronglyConnected(), stronglyConnectedComponents() |
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[417] | 329 | template <typename Digraph> |
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| 330 | int countStronglyConnectedComponents(const Digraph& digraph) { |
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| 331 | checkConcept<concepts::Digraph, Digraph>(); |
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| 332 | |
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[419] | 333 | using namespace _connectivity_bits; |
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[417] | 334 | |
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| 335 | typedef typename Digraph::Node Node; |
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| 336 | typedef typename Digraph::Arc Arc; |
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| 337 | typedef typename Digraph::NodeIt NodeIt; |
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| 338 | typedef typename Digraph::ArcIt ArcIt; |
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| 339 | |
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| 340 | typedef std::vector<Node> Container; |
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| 341 | typedef typename Container::iterator Iterator; |
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| 342 | |
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| 343 | Container nodes(countNodes(digraph)); |
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| 344 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
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| 345 | Visitor visitor(nodes.begin()); |
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| 346 | |
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| 347 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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| 348 | dfs.init(); |
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| 349 | for (NodeIt it(digraph); it != INVALID; ++it) { |
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| 350 | if (!dfs.reached(it)) { |
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| 351 | dfs.addSource(it); |
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| 352 | dfs.start(); |
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| 353 | } |
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| 354 | } |
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| 355 | |
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| 356 | typedef typename Container::reverse_iterator RIterator; |
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| 357 | typedef ReverseDigraph<const Digraph> RDigraph; |
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| 358 | |
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| 359 | RDigraph rdigraph(digraph); |
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| 360 | |
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| 361 | typedef DfsVisitor<Digraph> RVisitor; |
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| 362 | RVisitor rvisitor; |
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| 363 | |
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| 364 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
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| 365 | |
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| 366 | int compNum = 0; |
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| 367 | |
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| 368 | rdfs.init(); |
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| 369 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 370 | if (!rdfs.reached(*it)) { |
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| 371 | rdfs.addSource(*it); |
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| 372 | rdfs.start(); |
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| 373 | ++compNum; |
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| 374 | } |
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| 375 | } |
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| 376 | return compNum; |
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| 377 | } |
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| 378 | |
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[586] | 379 | /// \ingroup graph_properties |
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[417] | 380 | /// |
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| 381 | /// \brief Find the strongly connected components of a directed graph |
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| 382 | /// |
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[648] | 383 | /// This function finds the strongly connected components of the given |
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| 384 | /// directed graph. In addition, the numbering of the components will |
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| 385 | /// satisfy that there is no arc going from a higher numbered component |
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| 386 | /// to a lower one (i.e. it provides a topological order of the components). |
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| 387 | /// |
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| 388 | /// The strongly connected components are the classes of an |
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| 389 | /// equivalence relation on the nodes of a digraph. Two nodes are in |
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| 390 | /// the same class if they are connected with directed paths in both |
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| 391 | /// direction. |
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[417] | 392 | /// |
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[586] | 393 | /// \image html strongly_connected_components.png |
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| 394 | /// \image latex strongly_connected_components.eps "Strongly connected components" width=\textwidth |
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| 395 | /// |
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[417] | 396 | /// \param digraph The digraph. |
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| 397 | /// \retval compMap A writable node map. The values will be set from 0 to |
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| 398 | /// the number of the strongly connected components minus one. Each value |
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[648] | 399 | /// of the map will be set exactly once, and the values of a certain |
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| 400 | /// component will be set continuously. |
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| 401 | /// \return The number of strongly connected components. |
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| 402 | /// \note By definition, the empty digraph has zero |
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| 403 | /// strongly connected components. |
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| 404 | /// |
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| 405 | /// \see stronglyConnected(), countStronglyConnectedComponents() |
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[417] | 406 | template <typename Digraph, typename NodeMap> |
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| 407 | int stronglyConnectedComponents(const Digraph& digraph, NodeMap& compMap) { |
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| 408 | checkConcept<concepts::Digraph, Digraph>(); |
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| 409 | typedef typename Digraph::Node Node; |
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| 410 | typedef typename Digraph::NodeIt NodeIt; |
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| 411 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
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| 412 | |
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[419] | 413 | using namespace _connectivity_bits; |
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[417] | 414 | |
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| 415 | typedef std::vector<Node> Container; |
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| 416 | typedef typename Container::iterator Iterator; |
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| 417 | |
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| 418 | Container nodes(countNodes(digraph)); |
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| 419 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
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| 420 | Visitor visitor(nodes.begin()); |
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| 421 | |
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| 422 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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| 423 | dfs.init(); |
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| 424 | for (NodeIt it(digraph); it != INVALID; ++it) { |
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| 425 | if (!dfs.reached(it)) { |
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| 426 | dfs.addSource(it); |
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| 427 | dfs.start(); |
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| 428 | } |
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| 429 | } |
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| 430 | |
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| 431 | typedef typename Container::reverse_iterator RIterator; |
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| 432 | typedef ReverseDigraph<const Digraph> RDigraph; |
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| 433 | |
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| 434 | RDigraph rdigraph(digraph); |
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| 435 | |
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| 436 | int compNum = 0; |
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| 437 | |
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| 438 | typedef FillMapVisitor<RDigraph, NodeMap> RVisitor; |
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| 439 | RVisitor rvisitor(compMap, compNum); |
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| 440 | |
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| 441 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
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| 442 | |
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| 443 | rdfs.init(); |
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| 444 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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| 445 | if (!rdfs.reached(*it)) { |
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| 446 | rdfs.addSource(*it); |
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| 447 | rdfs.start(); |
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| 448 | ++compNum; |
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| 449 | } |
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| 450 | } |
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| 451 | return compNum; |
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| 452 | } |
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| 453 | |
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[586] | 454 | /// \ingroup graph_properties |
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[417] | 455 | /// |
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| 456 | /// \brief Find the cut arcs of the strongly connected components. |
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| 457 | /// |
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[648] | 458 | /// This function finds the cut arcs of the strongly connected components |
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| 459 | /// of the given digraph. |
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| 460 | /// |
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| 461 | /// The strongly connected components are the classes of an |
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| 462 | /// equivalence relation on the nodes of a digraph. Two nodes are in |
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| 463 | /// the same class if they are connected with directed paths in both |
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| 464 | /// direction. |
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[417] | 465 | /// The strongly connected components are separated by the cut arcs. |
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| 466 | /// |
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[648] | 467 | /// \param digraph The digraph. |
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| 468 | /// \retval cutMap A writable arc map. The values will be set to \c true |
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| 469 | /// for the cut arcs (exactly once for each cut arc), and will not be |
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| 470 | /// changed for other arcs. |
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| 471 | /// \return The number of cut arcs. |
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[417] | 472 | /// |
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[648] | 473 | /// \see stronglyConnected(), stronglyConnectedComponents() |
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[417] | 474 | template <typename Digraph, typename ArcMap> |
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[648] | 475 | int stronglyConnectedCutArcs(const Digraph& digraph, ArcMap& cutMap) { |
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[417] | 476 | checkConcept<concepts::Digraph, Digraph>(); |
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| 477 | typedef typename Digraph::Node Node; |
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| 478 | typedef typename Digraph::Arc Arc; |
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| 479 | typedef typename Digraph::NodeIt NodeIt; |
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| 480 | checkConcept<concepts::WriteMap<Arc, bool>, ArcMap>(); |
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| 481 | |
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[419] | 482 | using namespace _connectivity_bits; |
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[417] | 483 | |
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| 484 | typedef std::vector<Node> Container; |
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| 485 | typedef typename Container::iterator Iterator; |
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| 486 | |
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[648] | 487 | Container nodes(countNodes(digraph)); |
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[417] | 488 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
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| 489 | Visitor visitor(nodes.begin()); |
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| 490 | |
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[648] | 491 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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[417] | 492 | dfs.init(); |
---|
[648] | 493 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
[417] | 494 | if (!dfs.reached(it)) { |
---|
| 495 | dfs.addSource(it); |
---|
| 496 | dfs.start(); |
---|
| 497 | } |
---|
| 498 | } |
---|
| 499 | |
---|
| 500 | typedef typename Container::reverse_iterator RIterator; |
---|
| 501 | typedef ReverseDigraph<const Digraph> RDigraph; |
---|
| 502 | |
---|
[648] | 503 | RDigraph rdigraph(digraph); |
---|
[417] | 504 | |
---|
| 505 | int cutNum = 0; |
---|
| 506 | |
---|
[419] | 507 | typedef StronglyConnectedCutArcsVisitor<RDigraph, ArcMap> RVisitor; |
---|
[648] | 508 | RVisitor rvisitor(rdigraph, cutMap, cutNum); |
---|
[417] | 509 | |
---|
[648] | 510 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
---|
[417] | 511 | |
---|
| 512 | rdfs.init(); |
---|
| 513 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
---|
| 514 | if (!rdfs.reached(*it)) { |
---|
| 515 | rdfs.addSource(*it); |
---|
| 516 | rdfs.start(); |
---|
| 517 | } |
---|
| 518 | } |
---|
| 519 | return cutNum; |
---|
| 520 | } |
---|
| 521 | |
---|
[419] | 522 | namespace _connectivity_bits { |
---|
[417] | 523 | |
---|
| 524 | template <typename Digraph> |
---|
| 525 | class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
| 526 | public: |
---|
| 527 | typedef typename Digraph::Node Node; |
---|
| 528 | typedef typename Digraph::Arc Arc; |
---|
| 529 | typedef typename Digraph::Edge Edge; |
---|
| 530 | |
---|
| 531 | CountBiNodeConnectedComponentsVisitor(const Digraph& graph, int &compNum) |
---|
| 532 | : _graph(graph), _compNum(compNum), |
---|
| 533 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 534 | |
---|
| 535 | void start(const Node& node) { |
---|
| 536 | _predMap.set(node, INVALID); |
---|
| 537 | } |
---|
| 538 | |
---|
| 539 | void reach(const Node& node) { |
---|
| 540 | _numMap.set(node, _num); |
---|
| 541 | _retMap.set(node, _num); |
---|
| 542 | ++_num; |
---|
| 543 | } |
---|
| 544 | |
---|
| 545 | void discover(const Arc& edge) { |
---|
| 546 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
| 547 | } |
---|
| 548 | |
---|
| 549 | void examine(const Arc& edge) { |
---|
| 550 | if (_graph.source(edge) == _graph.target(edge) && |
---|
| 551 | _graph.direction(edge)) { |
---|
| 552 | ++_compNum; |
---|
| 553 | return; |
---|
| 554 | } |
---|
| 555 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) { |
---|
| 556 | return; |
---|
| 557 | } |
---|
| 558 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
| 559 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
| 560 | } |
---|
| 561 | } |
---|
| 562 | |
---|
| 563 | void backtrack(const Arc& edge) { |
---|
| 564 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 565 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 566 | } |
---|
| 567 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
| 568 | ++_compNum; |
---|
| 569 | } |
---|
| 570 | } |
---|
| 571 | |
---|
| 572 | private: |
---|
| 573 | const Digraph& _graph; |
---|
| 574 | int& _compNum; |
---|
| 575 | |
---|
| 576 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 577 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 578 | typename Digraph::template NodeMap<Node> _predMap; |
---|
| 579 | int _num; |
---|
| 580 | }; |
---|
| 581 | |
---|
| 582 | template <typename Digraph, typename ArcMap> |
---|
| 583 | class BiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
| 584 | public: |
---|
| 585 | typedef typename Digraph::Node Node; |
---|
| 586 | typedef typename Digraph::Arc Arc; |
---|
| 587 | typedef typename Digraph::Edge Edge; |
---|
| 588 | |
---|
| 589 | BiNodeConnectedComponentsVisitor(const Digraph& graph, |
---|
| 590 | ArcMap& compMap, int &compNum) |
---|
| 591 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
| 592 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 593 | |
---|
| 594 | void start(const Node& node) { |
---|
| 595 | _predMap.set(node, INVALID); |
---|
| 596 | } |
---|
| 597 | |
---|
| 598 | void reach(const Node& node) { |
---|
| 599 | _numMap.set(node, _num); |
---|
| 600 | _retMap.set(node, _num); |
---|
| 601 | ++_num; |
---|
| 602 | } |
---|
| 603 | |
---|
| 604 | void discover(const Arc& edge) { |
---|
| 605 | Node target = _graph.target(edge); |
---|
| 606 | _predMap.set(target, edge); |
---|
| 607 | _edgeStack.push(edge); |
---|
| 608 | } |
---|
| 609 | |
---|
| 610 | void examine(const Arc& edge) { |
---|
| 611 | Node source = _graph.source(edge); |
---|
| 612 | Node target = _graph.target(edge); |
---|
| 613 | if (source == target && _graph.direction(edge)) { |
---|
| 614 | _compMap.set(edge, _compNum); |
---|
| 615 | ++_compNum; |
---|
| 616 | return; |
---|
| 617 | } |
---|
| 618 | if (_numMap[target] < _numMap[source]) { |
---|
| 619 | if (_predMap[source] != _graph.oppositeArc(edge)) { |
---|
| 620 | _edgeStack.push(edge); |
---|
| 621 | } |
---|
| 622 | } |
---|
| 623 | if (_predMap[source] != INVALID && |
---|
| 624 | target == _graph.source(_predMap[source])) { |
---|
| 625 | return; |
---|
| 626 | } |
---|
| 627 | if (_retMap[source] > _numMap[target]) { |
---|
| 628 | _retMap.set(source, _numMap[target]); |
---|
| 629 | } |
---|
| 630 | } |
---|
| 631 | |
---|
| 632 | void backtrack(const Arc& edge) { |
---|
| 633 | Node source = _graph.source(edge); |
---|
| 634 | Node target = _graph.target(edge); |
---|
| 635 | if (_retMap[source] > _retMap[target]) { |
---|
| 636 | _retMap.set(source, _retMap[target]); |
---|
| 637 | } |
---|
| 638 | if (_numMap[source] <= _retMap[target]) { |
---|
| 639 | while (_edgeStack.top() != edge) { |
---|
| 640 | _compMap.set(_edgeStack.top(), _compNum); |
---|
| 641 | _edgeStack.pop(); |
---|
| 642 | } |
---|
| 643 | _compMap.set(edge, _compNum); |
---|
| 644 | _edgeStack.pop(); |
---|
| 645 | ++_compNum; |
---|
| 646 | } |
---|
| 647 | } |
---|
| 648 | |
---|
| 649 | private: |
---|
| 650 | const Digraph& _graph; |
---|
| 651 | ArcMap& _compMap; |
---|
| 652 | int& _compNum; |
---|
| 653 | |
---|
| 654 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 655 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 656 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
| 657 | std::stack<Edge> _edgeStack; |
---|
| 658 | int _num; |
---|
| 659 | }; |
---|
| 660 | |
---|
| 661 | |
---|
| 662 | template <typename Digraph, typename NodeMap> |
---|
| 663 | class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Digraph> { |
---|
| 664 | public: |
---|
| 665 | typedef typename Digraph::Node Node; |
---|
| 666 | typedef typename Digraph::Arc Arc; |
---|
| 667 | typedef typename Digraph::Edge Edge; |
---|
| 668 | |
---|
| 669 | BiNodeConnectedCutNodesVisitor(const Digraph& graph, NodeMap& cutMap, |
---|
| 670 | int& cutNum) |
---|
| 671 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
| 672 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 673 | |
---|
| 674 | void start(const Node& node) { |
---|
| 675 | _predMap.set(node, INVALID); |
---|
| 676 | rootCut = false; |
---|
| 677 | } |
---|
| 678 | |
---|
| 679 | void reach(const Node& node) { |
---|
| 680 | _numMap.set(node, _num); |
---|
| 681 | _retMap.set(node, _num); |
---|
| 682 | ++_num; |
---|
| 683 | } |
---|
| 684 | |
---|
| 685 | void discover(const Arc& edge) { |
---|
| 686 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
| 687 | } |
---|
| 688 | |
---|
| 689 | void examine(const Arc& edge) { |
---|
| 690 | if (_graph.source(edge) == _graph.target(edge) && |
---|
| 691 | _graph.direction(edge)) { |
---|
| 692 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 693 | _cutMap.set(_graph.source(edge), true); |
---|
| 694 | ++_cutNum; |
---|
| 695 | } |
---|
| 696 | return; |
---|
| 697 | } |
---|
| 698 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) return; |
---|
| 699 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
| 700 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
| 701 | } |
---|
| 702 | } |
---|
| 703 | |
---|
| 704 | void backtrack(const Arc& edge) { |
---|
| 705 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 706 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 707 | } |
---|
| 708 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
| 709 | if (_predMap[_graph.source(edge)] != INVALID) { |
---|
| 710 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 711 | _cutMap.set(_graph.source(edge), true); |
---|
| 712 | ++_cutNum; |
---|
| 713 | } |
---|
| 714 | } else if (rootCut) { |
---|
| 715 | if (!_cutMap[_graph.source(edge)]) { |
---|
| 716 | _cutMap.set(_graph.source(edge), true); |
---|
| 717 | ++_cutNum; |
---|
| 718 | } |
---|
| 719 | } else { |
---|
| 720 | rootCut = true; |
---|
| 721 | } |
---|
| 722 | } |
---|
| 723 | } |
---|
| 724 | |
---|
| 725 | private: |
---|
| 726 | const Digraph& _graph; |
---|
| 727 | NodeMap& _cutMap; |
---|
| 728 | int& _cutNum; |
---|
| 729 | |
---|
| 730 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 731 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 732 | typename Digraph::template NodeMap<Node> _predMap; |
---|
| 733 | std::stack<Edge> _edgeStack; |
---|
| 734 | int _num; |
---|
| 735 | bool rootCut; |
---|
| 736 | }; |
---|
| 737 | |
---|
| 738 | } |
---|
| 739 | |
---|
| 740 | template <typename Graph> |
---|
| 741 | int countBiNodeConnectedComponents(const Graph& graph); |
---|
| 742 | |
---|
[586] | 743 | /// \ingroup graph_properties |
---|
[417] | 744 | /// |
---|
[648] | 745 | /// \brief Check whether an undirected graph is bi-node-connected. |
---|
[417] | 746 | /// |
---|
[648] | 747 | /// This function checks whether the given undirected graph is |
---|
| 748 | /// bi-node-connected, i.e. any two edges are on same circle. |
---|
[417] | 749 | /// |
---|
[648] | 750 | /// \return \c true if the graph bi-node-connected. |
---|
| 751 | /// \note By definition, the empty graph is bi-node-connected. |
---|
| 752 | /// |
---|
| 753 | /// \see countBiNodeConnectedComponents(), biNodeConnectedComponents() |
---|
[417] | 754 | template <typename Graph> |
---|
| 755 | bool biNodeConnected(const Graph& graph) { |
---|
| 756 | return countBiNodeConnectedComponents(graph) <= 1; |
---|
| 757 | } |
---|
| 758 | |
---|
[586] | 759 | /// \ingroup graph_properties |
---|
[417] | 760 | /// |
---|
[648] | 761 | /// \brief Count the number of bi-node-connected components of an |
---|
| 762 | /// undirected graph. |
---|
[417] | 763 | /// |
---|
[648] | 764 | /// This function counts the number of bi-node-connected components of |
---|
| 765 | /// the given undirected graph. |
---|
[417] | 766 | /// |
---|
[648] | 767 | /// The bi-node-connected components are the classes of an equivalence |
---|
| 768 | /// relation on the edges of a undirected graph. Two edges are in the |
---|
| 769 | /// same class if they are on same circle. |
---|
| 770 | /// |
---|
| 771 | /// \return The number of bi-node-connected components. |
---|
| 772 | /// |
---|
| 773 | /// \see biNodeConnected(), biNodeConnectedComponents() |
---|
[417] | 774 | template <typename Graph> |
---|
| 775 | int countBiNodeConnectedComponents(const Graph& graph) { |
---|
| 776 | checkConcept<concepts::Graph, Graph>(); |
---|
| 777 | typedef typename Graph::NodeIt NodeIt; |
---|
| 778 | |
---|
[419] | 779 | using namespace _connectivity_bits; |
---|
[417] | 780 | |
---|
| 781 | typedef CountBiNodeConnectedComponentsVisitor<Graph> Visitor; |
---|
| 782 | |
---|
| 783 | int compNum = 0; |
---|
| 784 | Visitor visitor(graph, compNum); |
---|
| 785 | |
---|
| 786 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 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 | |
---|
[586] | 798 | /// \ingroup graph_properties |
---|
[417] | 799 | /// |
---|
[648] | 800 | /// \brief Find the bi-node-connected components of an undirected graph. |
---|
[417] | 801 | /// |
---|
[648] | 802 | /// This function finds the bi-node-connected components of the given |
---|
| 803 | /// undirected graph. |
---|
| 804 | /// |
---|
| 805 | /// The bi-node-connected components are the classes of an equivalence |
---|
| 806 | /// relation on the edges of a undirected graph. Two edges are in the |
---|
| 807 | /// same class if they are on same circle. |
---|
[417] | 808 | /// |
---|
[586] | 809 | /// \image html node_biconnected_components.png |
---|
| 810 | /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth |
---|
| 811 | /// |
---|
[648] | 812 | /// \param graph The undirected graph. |
---|
| 813 | /// \retval compMap A writable edge map. The values will be set from 0 |
---|
| 814 | /// to the number of the bi-node-connected components minus one. Each |
---|
| 815 | /// value of the map will be set exactly once, and the values of a |
---|
| 816 | /// certain component will be set continuously. |
---|
| 817 | /// \return The number of bi-node-connected components. |
---|
| 818 | /// |
---|
| 819 | /// \see biNodeConnected(), countBiNodeConnectedComponents() |
---|
[417] | 820 | template <typename Graph, typename EdgeMap> |
---|
| 821 | int biNodeConnectedComponents(const Graph& graph, |
---|
| 822 | EdgeMap& compMap) { |
---|
| 823 | checkConcept<concepts::Graph, Graph>(); |
---|
| 824 | typedef typename Graph::NodeIt NodeIt; |
---|
| 825 | typedef typename Graph::Edge Edge; |
---|
| 826 | checkConcept<concepts::WriteMap<Edge, int>, EdgeMap>(); |
---|
| 827 | |
---|
[419] | 828 | using namespace _connectivity_bits; |
---|
[417] | 829 | |
---|
| 830 | typedef BiNodeConnectedComponentsVisitor<Graph, EdgeMap> Visitor; |
---|
| 831 | |
---|
| 832 | int compNum = 0; |
---|
| 833 | Visitor visitor(graph, compMap, compNum); |
---|
| 834 | |
---|
| 835 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 836 | dfs.init(); |
---|
| 837 | |
---|
| 838 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 839 | if (!dfs.reached(it)) { |
---|
| 840 | dfs.addSource(it); |
---|
| 841 | dfs.start(); |
---|
| 842 | } |
---|
| 843 | } |
---|
| 844 | return compNum; |
---|
| 845 | } |
---|
| 846 | |
---|
[586] | 847 | /// \ingroup graph_properties |
---|
[417] | 848 | /// |
---|
[648] | 849 | /// \brief Find the bi-node-connected cut nodes in an undirected graph. |
---|
[417] | 850 | /// |
---|
[648] | 851 | /// This function finds the bi-node-connected cut nodes in the given |
---|
| 852 | /// undirected graph. |
---|
[417] | 853 | /// |
---|
[648] | 854 | /// The bi-node-connected components are the classes of an equivalence |
---|
| 855 | /// relation on the edges of a undirected graph. Two edges are in the |
---|
| 856 | /// same class if they are on same circle. |
---|
| 857 | /// The bi-node-connected components are separted by the cut nodes of |
---|
| 858 | /// the components. |
---|
| 859 | /// |
---|
| 860 | /// \param graph The undirected graph. |
---|
| 861 | /// \retval cutMap A writable node map. The values will be set to |
---|
| 862 | /// \c true for the nodes that separate two or more components |
---|
| 863 | /// (exactly once for each cut node), and will not be changed for |
---|
| 864 | /// other nodes. |
---|
[417] | 865 | /// \return The number of the cut nodes. |
---|
[648] | 866 | /// |
---|
| 867 | /// \see biNodeConnected(), biNodeConnectedComponents() |
---|
[417] | 868 | template <typename Graph, typename NodeMap> |
---|
| 869 | int biNodeConnectedCutNodes(const Graph& graph, NodeMap& cutMap) { |
---|
| 870 | checkConcept<concepts::Graph, Graph>(); |
---|
| 871 | typedef typename Graph::Node Node; |
---|
| 872 | typedef typename Graph::NodeIt NodeIt; |
---|
| 873 | checkConcept<concepts::WriteMap<Node, bool>, NodeMap>(); |
---|
| 874 | |
---|
[419] | 875 | using namespace _connectivity_bits; |
---|
[417] | 876 | |
---|
| 877 | typedef BiNodeConnectedCutNodesVisitor<Graph, NodeMap> Visitor; |
---|
| 878 | |
---|
| 879 | int cutNum = 0; |
---|
| 880 | Visitor visitor(graph, cutMap, cutNum); |
---|
| 881 | |
---|
| 882 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 883 | dfs.init(); |
---|
| 884 | |
---|
| 885 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 886 | if (!dfs.reached(it)) { |
---|
| 887 | dfs.addSource(it); |
---|
| 888 | dfs.start(); |
---|
| 889 | } |
---|
| 890 | } |
---|
| 891 | return cutNum; |
---|
| 892 | } |
---|
| 893 | |
---|
[419] | 894 | namespace _connectivity_bits { |
---|
[417] | 895 | |
---|
| 896 | template <typename Digraph> |
---|
| 897 | class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
| 898 | public: |
---|
| 899 | typedef typename Digraph::Node Node; |
---|
| 900 | typedef typename Digraph::Arc Arc; |
---|
| 901 | typedef typename Digraph::Edge Edge; |
---|
| 902 | |
---|
| 903 | CountBiEdgeConnectedComponentsVisitor(const Digraph& graph, int &compNum) |
---|
| 904 | : _graph(graph), _compNum(compNum), |
---|
| 905 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 906 | |
---|
| 907 | void start(const Node& node) { |
---|
| 908 | _predMap.set(node, INVALID); |
---|
| 909 | } |
---|
| 910 | |
---|
| 911 | void reach(const Node& node) { |
---|
| 912 | _numMap.set(node, _num); |
---|
| 913 | _retMap.set(node, _num); |
---|
| 914 | ++_num; |
---|
| 915 | } |
---|
| 916 | |
---|
| 917 | void leave(const Node& node) { |
---|
| 918 | if (_numMap[node] <= _retMap[node]) { |
---|
| 919 | ++_compNum; |
---|
| 920 | } |
---|
| 921 | } |
---|
| 922 | |
---|
| 923 | void discover(const Arc& edge) { |
---|
| 924 | _predMap.set(_graph.target(edge), edge); |
---|
| 925 | } |
---|
| 926 | |
---|
| 927 | void examine(const Arc& edge) { |
---|
| 928 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
| 929 | return; |
---|
| 930 | } |
---|
| 931 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 932 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 933 | } |
---|
| 934 | } |
---|
| 935 | |
---|
| 936 | void backtrack(const Arc& edge) { |
---|
| 937 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 938 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 939 | } |
---|
| 940 | } |
---|
| 941 | |
---|
| 942 | private: |
---|
| 943 | const Digraph& _graph; |
---|
| 944 | int& _compNum; |
---|
| 945 | |
---|
| 946 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 947 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 948 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
| 949 | int _num; |
---|
| 950 | }; |
---|
| 951 | |
---|
| 952 | template <typename Digraph, typename NodeMap> |
---|
| 953 | class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
| 954 | public: |
---|
| 955 | typedef typename Digraph::Node Node; |
---|
| 956 | typedef typename Digraph::Arc Arc; |
---|
| 957 | typedef typename Digraph::Edge Edge; |
---|
| 958 | |
---|
| 959 | BiEdgeConnectedComponentsVisitor(const Digraph& graph, |
---|
| 960 | NodeMap& compMap, int &compNum) |
---|
| 961 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
| 962 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 963 | |
---|
| 964 | void start(const Node& node) { |
---|
| 965 | _predMap.set(node, INVALID); |
---|
| 966 | } |
---|
| 967 | |
---|
| 968 | void reach(const Node& node) { |
---|
| 969 | _numMap.set(node, _num); |
---|
| 970 | _retMap.set(node, _num); |
---|
| 971 | _nodeStack.push(node); |
---|
| 972 | ++_num; |
---|
| 973 | } |
---|
| 974 | |
---|
| 975 | void leave(const Node& node) { |
---|
| 976 | if (_numMap[node] <= _retMap[node]) { |
---|
| 977 | while (_nodeStack.top() != node) { |
---|
| 978 | _compMap.set(_nodeStack.top(), _compNum); |
---|
| 979 | _nodeStack.pop(); |
---|
| 980 | } |
---|
| 981 | _compMap.set(node, _compNum); |
---|
| 982 | _nodeStack.pop(); |
---|
| 983 | ++_compNum; |
---|
| 984 | } |
---|
| 985 | } |
---|
| 986 | |
---|
| 987 | void discover(const Arc& edge) { |
---|
| 988 | _predMap.set(_graph.target(edge), edge); |
---|
| 989 | } |
---|
| 990 | |
---|
| 991 | void examine(const Arc& edge) { |
---|
| 992 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
| 993 | return; |
---|
| 994 | } |
---|
| 995 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 996 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 997 | } |
---|
| 998 | } |
---|
| 999 | |
---|
| 1000 | void backtrack(const Arc& edge) { |
---|
| 1001 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1002 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1003 | } |
---|
| 1004 | } |
---|
| 1005 | |
---|
| 1006 | private: |
---|
| 1007 | const Digraph& _graph; |
---|
| 1008 | NodeMap& _compMap; |
---|
| 1009 | int& _compNum; |
---|
| 1010 | |
---|
| 1011 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 1012 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 1013 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
| 1014 | std::stack<Node> _nodeStack; |
---|
| 1015 | int _num; |
---|
| 1016 | }; |
---|
| 1017 | |
---|
| 1018 | |
---|
| 1019 | template <typename Digraph, typename ArcMap> |
---|
| 1020 | class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Digraph> { |
---|
| 1021 | public: |
---|
| 1022 | typedef typename Digraph::Node Node; |
---|
| 1023 | typedef typename Digraph::Arc Arc; |
---|
| 1024 | typedef typename Digraph::Edge Edge; |
---|
| 1025 | |
---|
| 1026 | BiEdgeConnectedCutEdgesVisitor(const Digraph& graph, |
---|
| 1027 | ArcMap& cutMap, int &cutNum) |
---|
| 1028 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
| 1029 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
| 1030 | |
---|
| 1031 | void start(const Node& node) { |
---|
| 1032 | _predMap[node] = INVALID; |
---|
| 1033 | } |
---|
| 1034 | |
---|
| 1035 | void reach(const Node& node) { |
---|
| 1036 | _numMap.set(node, _num); |
---|
| 1037 | _retMap.set(node, _num); |
---|
| 1038 | ++_num; |
---|
| 1039 | } |
---|
| 1040 | |
---|
| 1041 | void leave(const Node& node) { |
---|
| 1042 | if (_numMap[node] <= _retMap[node]) { |
---|
| 1043 | if (_predMap[node] != INVALID) { |
---|
| 1044 | _cutMap.set(_predMap[node], true); |
---|
| 1045 | ++_cutNum; |
---|
| 1046 | } |
---|
| 1047 | } |
---|
| 1048 | } |
---|
| 1049 | |
---|
| 1050 | void discover(const Arc& edge) { |
---|
| 1051 | _predMap.set(_graph.target(edge), edge); |
---|
| 1052 | } |
---|
| 1053 | |
---|
| 1054 | void examine(const Arc& edge) { |
---|
| 1055 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
| 1056 | return; |
---|
| 1057 | } |
---|
| 1058 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1059 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1060 | } |
---|
| 1061 | } |
---|
| 1062 | |
---|
| 1063 | void backtrack(const Arc& edge) { |
---|
| 1064 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
| 1065 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
| 1066 | } |
---|
| 1067 | } |
---|
| 1068 | |
---|
| 1069 | private: |
---|
| 1070 | const Digraph& _graph; |
---|
| 1071 | ArcMap& _cutMap; |
---|
| 1072 | int& _cutNum; |
---|
| 1073 | |
---|
| 1074 | typename Digraph::template NodeMap<int> _numMap; |
---|
| 1075 | typename Digraph::template NodeMap<int> _retMap; |
---|
| 1076 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
| 1077 | int _num; |
---|
| 1078 | }; |
---|
| 1079 | } |
---|
| 1080 | |
---|
| 1081 | template <typename Graph> |
---|
| 1082 | int countBiEdgeConnectedComponents(const Graph& graph); |
---|
| 1083 | |
---|
[586] | 1084 | /// \ingroup graph_properties |
---|
[417] | 1085 | /// |
---|
[648] | 1086 | /// \brief Check whether an undirected graph is bi-edge-connected. |
---|
[417] | 1087 | /// |
---|
[648] | 1088 | /// This function checks whether the given undirected graph is |
---|
| 1089 | /// bi-edge-connected, i.e. any two nodes are connected with at least |
---|
| 1090 | /// two edge-disjoint paths. |
---|
[417] | 1091 | /// |
---|
[648] | 1092 | /// \return \c true if the graph is bi-edge-connected. |
---|
| 1093 | /// \note By definition, the empty graph is bi-edge-connected. |
---|
| 1094 | /// |
---|
| 1095 | /// \see countBiEdgeConnectedComponents(), biEdgeConnectedComponents() |
---|
[417] | 1096 | template <typename Graph> |
---|
| 1097 | bool biEdgeConnected(const Graph& graph) { |
---|
| 1098 | return countBiEdgeConnectedComponents(graph) <= 1; |
---|
| 1099 | } |
---|
| 1100 | |
---|
[586] | 1101 | /// \ingroup graph_properties |
---|
[417] | 1102 | /// |
---|
[648] | 1103 | /// \brief Count the number of bi-edge-connected components of an |
---|
| 1104 | /// undirected graph. |
---|
[417] | 1105 | /// |
---|
[648] | 1106 | /// This function counts the number of bi-edge-connected components of |
---|
| 1107 | /// the given undirected graph. |
---|
[417] | 1108 | /// |
---|
[648] | 1109 | /// The bi-edge-connected components are the classes of an equivalence |
---|
| 1110 | /// relation on the nodes of an undirected graph. Two nodes are in the |
---|
| 1111 | /// same class if they are connected with at least two edge-disjoint |
---|
| 1112 | /// paths. |
---|
| 1113 | /// |
---|
| 1114 | /// \return The number of bi-edge-connected components. |
---|
| 1115 | /// |
---|
| 1116 | /// \see biEdgeConnected(), biEdgeConnectedComponents() |
---|
[417] | 1117 | template <typename Graph> |
---|
| 1118 | int countBiEdgeConnectedComponents(const Graph& graph) { |
---|
| 1119 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1120 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1121 | |
---|
[419] | 1122 | using namespace _connectivity_bits; |
---|
[417] | 1123 | |
---|
| 1124 | typedef CountBiEdgeConnectedComponentsVisitor<Graph> Visitor; |
---|
| 1125 | |
---|
| 1126 | int compNum = 0; |
---|
| 1127 | Visitor visitor(graph, compNum); |
---|
| 1128 | |
---|
| 1129 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 1130 | dfs.init(); |
---|
| 1131 | |
---|
| 1132 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1133 | if (!dfs.reached(it)) { |
---|
| 1134 | dfs.addSource(it); |
---|
| 1135 | dfs.start(); |
---|
| 1136 | } |
---|
| 1137 | } |
---|
| 1138 | return compNum; |
---|
| 1139 | } |
---|
| 1140 | |
---|
[586] | 1141 | /// \ingroup graph_properties |
---|
[417] | 1142 | /// |
---|
[648] | 1143 | /// \brief Find the bi-edge-connected components of an undirected graph. |
---|
[417] | 1144 | /// |
---|
[648] | 1145 | /// This function finds the bi-edge-connected components of the given |
---|
| 1146 | /// undirected graph. |
---|
| 1147 | /// |
---|
| 1148 | /// The bi-edge-connected components are the classes of an equivalence |
---|
| 1149 | /// relation on the nodes of an undirected graph. Two nodes are in the |
---|
| 1150 | /// same class if they are connected with at least two edge-disjoint |
---|
| 1151 | /// paths. |
---|
[417] | 1152 | /// |
---|
[586] | 1153 | /// \image html edge_biconnected_components.png |
---|
| 1154 | /// \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth |
---|
| 1155 | /// |
---|
[648] | 1156 | /// \param graph The undirected graph. |
---|
[417] | 1157 | /// \retval compMap A writable node map. The values will be set from 0 to |
---|
[648] | 1158 | /// the number of the bi-edge-connected components minus one. Each value |
---|
| 1159 | /// of the map will be set exactly once, and the values of a certain |
---|
| 1160 | /// component will be set continuously. |
---|
| 1161 | /// \return The number of bi-edge-connected components. |
---|
| 1162 | /// |
---|
| 1163 | /// \see biEdgeConnected(), countBiEdgeConnectedComponents() |
---|
[417] | 1164 | template <typename Graph, typename NodeMap> |
---|
| 1165 | int biEdgeConnectedComponents(const Graph& graph, NodeMap& compMap) { |
---|
| 1166 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1167 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1168 | typedef typename Graph::Node Node; |
---|
| 1169 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
---|
| 1170 | |
---|
[419] | 1171 | using namespace _connectivity_bits; |
---|
[417] | 1172 | |
---|
| 1173 | typedef BiEdgeConnectedComponentsVisitor<Graph, NodeMap> Visitor; |
---|
| 1174 | |
---|
| 1175 | int compNum = 0; |
---|
| 1176 | Visitor visitor(graph, compMap, compNum); |
---|
| 1177 | |
---|
| 1178 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 1179 | dfs.init(); |
---|
| 1180 | |
---|
| 1181 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1182 | if (!dfs.reached(it)) { |
---|
| 1183 | dfs.addSource(it); |
---|
| 1184 | dfs.start(); |
---|
| 1185 | } |
---|
| 1186 | } |
---|
| 1187 | return compNum; |
---|
| 1188 | } |
---|
| 1189 | |
---|
[586] | 1190 | /// \ingroup graph_properties |
---|
[417] | 1191 | /// |
---|
[648] | 1192 | /// \brief Find the bi-edge-connected cut edges in an undirected graph. |
---|
[417] | 1193 | /// |
---|
[648] | 1194 | /// This function finds the bi-edge-connected cut edges in the given |
---|
| 1195 | /// undirected graph. |
---|
[417] | 1196 | /// |
---|
[648] | 1197 | /// The bi-edge-connected components are the classes of an equivalence |
---|
| 1198 | /// relation on the nodes of an undirected graph. Two nodes are in the |
---|
| 1199 | /// same class if they are connected with at least two edge-disjoint |
---|
| 1200 | /// paths. |
---|
| 1201 | /// The bi-edge-connected components are separted by the cut edges of |
---|
| 1202 | /// the components. |
---|
| 1203 | /// |
---|
| 1204 | /// \param graph The undirected graph. |
---|
| 1205 | /// \retval cutMap A writable edge map. The values will be set to \c true |
---|
| 1206 | /// for the cut edges (exactly once for each cut edge), and will not be |
---|
| 1207 | /// changed for other edges. |
---|
[417] | 1208 | /// \return The number of cut edges. |
---|
[648] | 1209 | /// |
---|
| 1210 | /// \see biEdgeConnected(), biEdgeConnectedComponents() |
---|
[417] | 1211 | template <typename Graph, typename EdgeMap> |
---|
| 1212 | int biEdgeConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) { |
---|
| 1213 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1214 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1215 | typedef typename Graph::Edge Edge; |
---|
| 1216 | checkConcept<concepts::WriteMap<Edge, bool>, EdgeMap>(); |
---|
| 1217 | |
---|
[419] | 1218 | using namespace _connectivity_bits; |
---|
[417] | 1219 | |
---|
| 1220 | typedef BiEdgeConnectedCutEdgesVisitor<Graph, EdgeMap> Visitor; |
---|
| 1221 | |
---|
| 1222 | int cutNum = 0; |
---|
| 1223 | Visitor visitor(graph, cutMap, cutNum); |
---|
| 1224 | |
---|
| 1225 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
| 1226 | dfs.init(); |
---|
| 1227 | |
---|
| 1228 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1229 | if (!dfs.reached(it)) { |
---|
| 1230 | dfs.addSource(it); |
---|
| 1231 | dfs.start(); |
---|
| 1232 | } |
---|
| 1233 | } |
---|
| 1234 | return cutNum; |
---|
| 1235 | } |
---|
| 1236 | |
---|
| 1237 | |
---|
[419] | 1238 | namespace _connectivity_bits { |
---|
[417] | 1239 | |
---|
| 1240 | template <typename Digraph, typename IntNodeMap> |
---|
| 1241 | class TopologicalSortVisitor : public DfsVisitor<Digraph> { |
---|
| 1242 | public: |
---|
| 1243 | typedef typename Digraph::Node Node; |
---|
| 1244 | typedef typename Digraph::Arc edge; |
---|
| 1245 | |
---|
| 1246 | TopologicalSortVisitor(IntNodeMap& order, int num) |
---|
| 1247 | : _order(order), _num(num) {} |
---|
| 1248 | |
---|
| 1249 | void leave(const Node& node) { |
---|
| 1250 | _order.set(node, --_num); |
---|
| 1251 | } |
---|
| 1252 | |
---|
| 1253 | private: |
---|
| 1254 | IntNodeMap& _order; |
---|
| 1255 | int _num; |
---|
| 1256 | }; |
---|
| 1257 | |
---|
| 1258 | } |
---|
| 1259 | |
---|
[586] | 1260 | /// \ingroup graph_properties |
---|
[417] | 1261 | /// |
---|
[648] | 1262 | /// \brief Check whether a digraph is DAG. |
---|
| 1263 | /// |
---|
| 1264 | /// This function checks whether the given digraph is DAG, i.e. |
---|
| 1265 | /// \e Directed \e Acyclic \e Graph. |
---|
| 1266 | /// \return \c true if there is no directed cycle in the digraph. |
---|
| 1267 | /// \see acyclic() |
---|
| 1268 | template <typename Digraph> |
---|
| 1269 | bool dag(const Digraph& digraph) { |
---|
| 1270 | |
---|
| 1271 | checkConcept<concepts::Digraph, Digraph>(); |
---|
| 1272 | |
---|
| 1273 | typedef typename Digraph::Node Node; |
---|
| 1274 | typedef typename Digraph::NodeIt NodeIt; |
---|
| 1275 | typedef typename Digraph::Arc Arc; |
---|
| 1276 | |
---|
| 1277 | typedef typename Digraph::template NodeMap<bool> ProcessedMap; |
---|
| 1278 | |
---|
| 1279 | typename Dfs<Digraph>::template SetProcessedMap<ProcessedMap>:: |
---|
| 1280 | Create dfs(digraph); |
---|
| 1281 | |
---|
| 1282 | ProcessedMap processed(digraph); |
---|
| 1283 | dfs.processedMap(processed); |
---|
| 1284 | |
---|
| 1285 | dfs.init(); |
---|
| 1286 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
| 1287 | if (!dfs.reached(it)) { |
---|
| 1288 | dfs.addSource(it); |
---|
| 1289 | while (!dfs.emptyQueue()) { |
---|
| 1290 | Arc arc = dfs.nextArc(); |
---|
| 1291 | Node target = digraph.target(arc); |
---|
| 1292 | if (dfs.reached(target) && !processed[target]) { |
---|
| 1293 | return false; |
---|
| 1294 | } |
---|
| 1295 | dfs.processNextArc(); |
---|
| 1296 | } |
---|
| 1297 | } |
---|
| 1298 | } |
---|
| 1299 | return true; |
---|
| 1300 | } |
---|
| 1301 | |
---|
| 1302 | /// \ingroup graph_properties |
---|
| 1303 | /// |
---|
[417] | 1304 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
| 1305 | /// |
---|
[648] | 1306 | /// This function sorts the nodes of the given acyclic digraph (DAG) |
---|
| 1307 | /// into topolgical order. |
---|
[417] | 1308 | /// |
---|
[648] | 1309 | /// \param digraph The digraph, which must be DAG. |
---|
[417] | 1310 | /// \retval order A writable node map. The values will be set from 0 to |
---|
[648] | 1311 | /// the number of the nodes in the digraph minus one. Each value of the |
---|
| 1312 | /// map will be set exactly once, and the values will be set descending |
---|
| 1313 | /// order. |
---|
[417] | 1314 | /// |
---|
[648] | 1315 | /// \see dag(), checkedTopologicalSort() |
---|
[417] | 1316 | template <typename Digraph, typename NodeMap> |
---|
[648] | 1317 | void topologicalSort(const Digraph& digraph, NodeMap& order) { |
---|
[419] | 1318 | using namespace _connectivity_bits; |
---|
[417] | 1319 | |
---|
| 1320 | checkConcept<concepts::Digraph, Digraph>(); |
---|
| 1321 | checkConcept<concepts::WriteMap<typename Digraph::Node, int>, NodeMap>(); |
---|
| 1322 | |
---|
| 1323 | typedef typename Digraph::Node Node; |
---|
| 1324 | typedef typename Digraph::NodeIt NodeIt; |
---|
| 1325 | typedef typename Digraph::Arc Arc; |
---|
| 1326 | |
---|
| 1327 | TopologicalSortVisitor<Digraph, NodeMap> |
---|
[648] | 1328 | visitor(order, countNodes(digraph)); |
---|
[417] | 1329 | |
---|
| 1330 | DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> > |
---|
[648] | 1331 | dfs(digraph, visitor); |
---|
[417] | 1332 | |
---|
| 1333 | dfs.init(); |
---|
[648] | 1334 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
[417] | 1335 | if (!dfs.reached(it)) { |
---|
| 1336 | dfs.addSource(it); |
---|
| 1337 | dfs.start(); |
---|
| 1338 | } |
---|
| 1339 | } |
---|
| 1340 | } |
---|
| 1341 | |
---|
[586] | 1342 | /// \ingroup graph_properties |
---|
[417] | 1343 | /// |
---|
| 1344 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
| 1345 | /// |
---|
[648] | 1346 | /// This function sorts the nodes of the given acyclic digraph (DAG) |
---|
| 1347 | /// into topolgical order and also checks whether the given digraph |
---|
| 1348 | /// is DAG. |
---|
[417] | 1349 | /// |
---|
[648] | 1350 | /// \param digraph The digraph. |
---|
| 1351 | /// \retval order A readable and writable node map. The values will be |
---|
| 1352 | /// set from 0 to the number of the nodes in the digraph minus one. |
---|
| 1353 | /// Each value of the map will be set exactly once, and the values will |
---|
| 1354 | /// be set descending order. |
---|
| 1355 | /// \return \c false if the digraph is not DAG. |
---|
[417] | 1356 | /// |
---|
[648] | 1357 | /// \see dag(), topologicalSort() |
---|
[417] | 1358 | template <typename Digraph, typename NodeMap> |
---|
[419] | 1359 | bool checkedTopologicalSort(const Digraph& digraph, NodeMap& order) { |
---|
| 1360 | using namespace _connectivity_bits; |
---|
[417] | 1361 | |
---|
| 1362 | checkConcept<concepts::Digraph, Digraph>(); |
---|
| 1363 | checkConcept<concepts::ReadWriteMap<typename Digraph::Node, int>, |
---|
| 1364 | NodeMap>(); |
---|
| 1365 | |
---|
| 1366 | typedef typename Digraph::Node Node; |
---|
| 1367 | typedef typename Digraph::NodeIt NodeIt; |
---|
| 1368 | typedef typename Digraph::Arc Arc; |
---|
| 1369 | |
---|
[419] | 1370 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
| 1371 | order.set(it, -1); |
---|
| 1372 | } |
---|
[417] | 1373 | |
---|
| 1374 | TopologicalSortVisitor<Digraph, NodeMap> |
---|
[419] | 1375 | visitor(order, countNodes(digraph)); |
---|
[417] | 1376 | |
---|
| 1377 | DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> > |
---|
[419] | 1378 | dfs(digraph, visitor); |
---|
[417] | 1379 | |
---|
| 1380 | dfs.init(); |
---|
[419] | 1381 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
[417] | 1382 | if (!dfs.reached(it)) { |
---|
| 1383 | dfs.addSource(it); |
---|
| 1384 | while (!dfs.emptyQueue()) { |
---|
[419] | 1385 | Arc arc = dfs.nextArc(); |
---|
| 1386 | Node target = digraph.target(arc); |
---|
[417] | 1387 | if (dfs.reached(target) && order[target] == -1) { |
---|
| 1388 | return false; |
---|
| 1389 | } |
---|
| 1390 | dfs.processNextArc(); |
---|
| 1391 | } |
---|
| 1392 | } |
---|
| 1393 | } |
---|
| 1394 | return true; |
---|
| 1395 | } |
---|
| 1396 | |
---|
[586] | 1397 | /// \ingroup graph_properties |
---|
[417] | 1398 | /// |
---|
[648] | 1399 | /// \brief Check whether an undirected graph is acyclic. |
---|
[417] | 1400 | /// |
---|
[648] | 1401 | /// This function checks whether the given undirected graph is acyclic. |
---|
| 1402 | /// \return \c true if there is no cycle in the graph. |
---|
| 1403 | /// \see dag() |
---|
[417] | 1404 | template <typename Graph> |
---|
| 1405 | bool acyclic(const Graph& graph) { |
---|
| 1406 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1407 | typedef typename Graph::Node Node; |
---|
| 1408 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1409 | typedef typename Graph::Arc Arc; |
---|
| 1410 | Dfs<Graph> dfs(graph); |
---|
| 1411 | dfs.init(); |
---|
| 1412 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1413 | if (!dfs.reached(it)) { |
---|
| 1414 | dfs.addSource(it); |
---|
| 1415 | while (!dfs.emptyQueue()) { |
---|
[648] | 1416 | Arc arc = dfs.nextArc(); |
---|
| 1417 | Node source = graph.source(arc); |
---|
| 1418 | Node target = graph.target(arc); |
---|
[417] | 1419 | if (dfs.reached(target) && |
---|
[648] | 1420 | dfs.predArc(source) != graph.oppositeArc(arc)) { |
---|
[417] | 1421 | return false; |
---|
| 1422 | } |
---|
| 1423 | dfs.processNextArc(); |
---|
| 1424 | } |
---|
| 1425 | } |
---|
| 1426 | } |
---|
| 1427 | return true; |
---|
| 1428 | } |
---|
| 1429 | |
---|
[586] | 1430 | /// \ingroup graph_properties |
---|
[417] | 1431 | /// |
---|
[648] | 1432 | /// \brief Check whether an undirected graph is tree. |
---|
[417] | 1433 | /// |
---|
[648] | 1434 | /// This function checks whether the given undirected graph is tree. |
---|
| 1435 | /// \return \c true if the graph is acyclic and connected. |
---|
| 1436 | /// \see acyclic(), connected() |
---|
[417] | 1437 | template <typename Graph> |
---|
| 1438 | bool tree(const Graph& graph) { |
---|
| 1439 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1440 | typedef typename Graph::Node Node; |
---|
| 1441 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1442 | typedef typename Graph::Arc Arc; |
---|
[647] | 1443 | if (NodeIt(graph) == INVALID) return true; |
---|
[417] | 1444 | Dfs<Graph> dfs(graph); |
---|
| 1445 | dfs.init(); |
---|
| 1446 | dfs.addSource(NodeIt(graph)); |
---|
| 1447 | while (!dfs.emptyQueue()) { |
---|
[648] | 1448 | Arc arc = dfs.nextArc(); |
---|
| 1449 | Node source = graph.source(arc); |
---|
| 1450 | Node target = graph.target(arc); |
---|
[417] | 1451 | if (dfs.reached(target) && |
---|
[648] | 1452 | dfs.predArc(source) != graph.oppositeArc(arc)) { |
---|
[417] | 1453 | return false; |
---|
| 1454 | } |
---|
| 1455 | dfs.processNextArc(); |
---|
| 1456 | } |
---|
| 1457 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1458 | if (!dfs.reached(it)) { |
---|
| 1459 | return false; |
---|
| 1460 | } |
---|
| 1461 | } |
---|
| 1462 | return true; |
---|
| 1463 | } |
---|
| 1464 | |
---|
[419] | 1465 | namespace _connectivity_bits { |
---|
[417] | 1466 | |
---|
| 1467 | template <typename Digraph> |
---|
| 1468 | class BipartiteVisitor : public BfsVisitor<Digraph> { |
---|
| 1469 | public: |
---|
| 1470 | typedef typename Digraph::Arc Arc; |
---|
| 1471 | typedef typename Digraph::Node Node; |
---|
| 1472 | |
---|
| 1473 | BipartiteVisitor(const Digraph& graph, bool& bipartite) |
---|
| 1474 | : _graph(graph), _part(graph), _bipartite(bipartite) {} |
---|
| 1475 | |
---|
| 1476 | void start(const Node& node) { |
---|
| 1477 | _part[node] = true; |
---|
| 1478 | } |
---|
| 1479 | void discover(const Arc& edge) { |
---|
| 1480 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
| 1481 | } |
---|
| 1482 | void examine(const Arc& edge) { |
---|
| 1483 | _bipartite = _bipartite && |
---|
| 1484 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
| 1485 | } |
---|
| 1486 | |
---|
| 1487 | private: |
---|
| 1488 | |
---|
| 1489 | const Digraph& _graph; |
---|
| 1490 | typename Digraph::template NodeMap<bool> _part; |
---|
| 1491 | bool& _bipartite; |
---|
| 1492 | }; |
---|
| 1493 | |
---|
| 1494 | template <typename Digraph, typename PartMap> |
---|
| 1495 | class BipartitePartitionsVisitor : public BfsVisitor<Digraph> { |
---|
| 1496 | public: |
---|
| 1497 | typedef typename Digraph::Arc Arc; |
---|
| 1498 | typedef typename Digraph::Node Node; |
---|
| 1499 | |
---|
| 1500 | BipartitePartitionsVisitor(const Digraph& graph, |
---|
| 1501 | PartMap& part, bool& bipartite) |
---|
| 1502 | : _graph(graph), _part(part), _bipartite(bipartite) {} |
---|
| 1503 | |
---|
| 1504 | void start(const Node& node) { |
---|
| 1505 | _part.set(node, true); |
---|
| 1506 | } |
---|
| 1507 | void discover(const Arc& edge) { |
---|
| 1508 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
| 1509 | } |
---|
| 1510 | void examine(const Arc& edge) { |
---|
| 1511 | _bipartite = _bipartite && |
---|
| 1512 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
| 1513 | } |
---|
| 1514 | |
---|
| 1515 | private: |
---|
| 1516 | |
---|
| 1517 | const Digraph& _graph; |
---|
| 1518 | PartMap& _part; |
---|
| 1519 | bool& _bipartite; |
---|
| 1520 | }; |
---|
| 1521 | } |
---|
| 1522 | |
---|
[586] | 1523 | /// \ingroup graph_properties |
---|
[417] | 1524 | /// |
---|
[648] | 1525 | /// \brief Check whether an undirected graph is bipartite. |
---|
[417] | 1526 | /// |
---|
[648] | 1527 | /// The function checks whether the given undirected graph is bipartite. |
---|
| 1528 | /// \return \c true if the graph is bipartite. |
---|
| 1529 | /// |
---|
| 1530 | /// \see bipartitePartitions() |
---|
[417] | 1531 | template<typename Graph> |
---|
[648] | 1532 | bool bipartite(const Graph &graph){ |
---|
[419] | 1533 | using namespace _connectivity_bits; |
---|
[417] | 1534 | |
---|
| 1535 | checkConcept<concepts::Graph, Graph>(); |
---|
| 1536 | |
---|
| 1537 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1538 | typedef typename Graph::ArcIt ArcIt; |
---|
| 1539 | |
---|
| 1540 | bool bipartite = true; |
---|
| 1541 | |
---|
| 1542 | BipartiteVisitor<Graph> |
---|
| 1543 | visitor(graph, bipartite); |
---|
| 1544 | BfsVisit<Graph, BipartiteVisitor<Graph> > |
---|
| 1545 | bfs(graph, visitor); |
---|
| 1546 | bfs.init(); |
---|
| 1547 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1548 | if(!bfs.reached(it)){ |
---|
| 1549 | bfs.addSource(it); |
---|
| 1550 | while (!bfs.emptyQueue()) { |
---|
| 1551 | bfs.processNextNode(); |
---|
| 1552 | if (!bipartite) return false; |
---|
| 1553 | } |
---|
| 1554 | } |
---|
| 1555 | } |
---|
| 1556 | return true; |
---|
| 1557 | } |
---|
| 1558 | |
---|
[586] | 1559 | /// \ingroup graph_properties |
---|
[417] | 1560 | /// |
---|
[648] | 1561 | /// \brief Find the bipartite partitions of an undirected graph. |
---|
[417] | 1562 | /// |
---|
[648] | 1563 | /// This function checks whether the given undirected graph is bipartite |
---|
| 1564 | /// and gives back the bipartite partitions. |
---|
[586] | 1565 | /// |
---|
| 1566 | /// \image html bipartite_partitions.png |
---|
| 1567 | /// \image latex bipartite_partitions.eps "Bipartite partititions" width=\textwidth |
---|
| 1568 | /// |
---|
[417] | 1569 | /// \param graph The undirected graph. |
---|
[648] | 1570 | /// \retval partMap A writable node map of \c bool (or convertible) value |
---|
| 1571 | /// type. The values will be set to \c true for one component and |
---|
| 1572 | /// \c false for the other one. |
---|
| 1573 | /// \return \c true if the graph is bipartite, \c false otherwise. |
---|
| 1574 | /// |
---|
| 1575 | /// \see bipartite() |
---|
[417] | 1576 | template<typename Graph, typename NodeMap> |
---|
[648] | 1577 | bool bipartitePartitions(const Graph &graph, NodeMap &partMap){ |
---|
[419] | 1578 | using namespace _connectivity_bits; |
---|
[417] | 1579 | |
---|
| 1580 | checkConcept<concepts::Graph, Graph>(); |
---|
[648] | 1581 | checkConcept<concepts::WriteMap<typename Graph::Node, bool>, NodeMap>(); |
---|
[417] | 1582 | |
---|
| 1583 | typedef typename Graph::Node Node; |
---|
| 1584 | typedef typename Graph::NodeIt NodeIt; |
---|
| 1585 | typedef typename Graph::ArcIt ArcIt; |
---|
| 1586 | |
---|
| 1587 | bool bipartite = true; |
---|
| 1588 | |
---|
| 1589 | BipartitePartitionsVisitor<Graph, NodeMap> |
---|
| 1590 | visitor(graph, partMap, bipartite); |
---|
| 1591 | BfsVisit<Graph, BipartitePartitionsVisitor<Graph, NodeMap> > |
---|
| 1592 | bfs(graph, visitor); |
---|
| 1593 | bfs.init(); |
---|
| 1594 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
| 1595 | if(!bfs.reached(it)){ |
---|
| 1596 | bfs.addSource(it); |
---|
| 1597 | while (!bfs.emptyQueue()) { |
---|
| 1598 | bfs.processNextNode(); |
---|
| 1599 | if (!bipartite) return false; |
---|
| 1600 | } |
---|
| 1601 | } |
---|
| 1602 | } |
---|
| 1603 | return true; |
---|
| 1604 | } |
---|
| 1605 | |
---|
[648] | 1606 | /// \ingroup graph_properties |
---|
[417] | 1607 | /// |
---|
[648] | 1608 | /// \brief Check whether the given graph contains no loop arcs/edges. |
---|
| 1609 | /// |
---|
| 1610 | /// This function returns \c true if there are no loop arcs/edges in |
---|
| 1611 | /// the given graph. It works for both directed and undirected graphs. |
---|
| 1612 | template <typename Graph> |
---|
| 1613 | bool loopFree(const Graph& graph) { |
---|
| 1614 | for (typename Graph::ArcIt it(graph); it != INVALID; ++it) { |
---|
| 1615 | if (graph.source(it) == graph.target(it)) return false; |
---|
[417] | 1616 | } |
---|
| 1617 | return true; |
---|
| 1618 | } |
---|
| 1619 | |
---|
[648] | 1620 | /// \ingroup graph_properties |
---|
[417] | 1621 | /// |
---|
[648] | 1622 | /// \brief Check whether the given graph contains no parallel arcs/edges. |
---|
| 1623 | /// |
---|
| 1624 | /// This function returns \c true if there are no parallel arcs/edges in |
---|
| 1625 | /// the given graph. It works for both directed and undirected graphs. |
---|
[647] | 1626 | template <typename Graph> |
---|
| 1627 | bool parallelFree(const Graph& graph) { |
---|
| 1628 | typename Graph::template NodeMap<int> reached(graph, 0); |
---|
| 1629 | int cnt = 1; |
---|
| 1630 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
| 1631 | for (typename Graph::OutArcIt a(graph, n); a != INVALID; ++a) { |
---|
| 1632 | if (reached[graph.target(a)] == cnt) return false; |
---|
| 1633 | reached[graph.target(a)] = cnt; |
---|
[417] | 1634 | } |
---|
[647] | 1635 | ++cnt; |
---|
[417] | 1636 | } |
---|
| 1637 | return true; |
---|
| 1638 | } |
---|
| 1639 | |
---|
[648] | 1640 | /// \ingroup graph_properties |
---|
[417] | 1641 | /// |
---|
[648] | 1642 | /// \brief Check whether the given graph is simple. |
---|
| 1643 | /// |
---|
| 1644 | /// This function returns \c true if the given graph is simple, i.e. |
---|
| 1645 | /// it contains no loop arcs/edges and no parallel arcs/edges. |
---|
| 1646 | /// The function works for both directed and undirected graphs. |
---|
| 1647 | /// \see loopFree(), parallelFree() |
---|
[647] | 1648 | template <typename Graph> |
---|
| 1649 | bool simpleGraph(const Graph& graph) { |
---|
| 1650 | typename Graph::template NodeMap<int> reached(graph, 0); |
---|
| 1651 | int cnt = 1; |
---|
| 1652 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
| 1653 | reached[n] = cnt; |
---|
| 1654 | for (typename Graph::OutArcIt a(graph, n); a != INVALID; ++a) { |
---|
| 1655 | if (reached[graph.target(a)] == cnt) return false; |
---|
| 1656 | reached[graph.target(a)] = cnt; |
---|
[417] | 1657 | } |
---|
[647] | 1658 | ++cnt; |
---|
[417] | 1659 | } |
---|
| 1660 | return true; |
---|
| 1661 | } |
---|
| 1662 | |
---|
| 1663 | } //namespace lemon |
---|
| 1664 | |
---|
[419] | 1665 | #endif //LEMON_CONNECTIVITY_H |
---|