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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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5 * Copyright (C) 2003-2010 |
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6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 * |
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9 * Permission to use, modify and distribute this software is granted |
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10 * provided that this copyright notice appears in all copies. For |
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11 * precise terms see the accompanying LICENSE file. |
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12 * |
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13 * This software is provided "AS IS" with no warranty of any kind, |
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14 * express or implied, and with no claim as to its suitability for any |
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15 * purpose. |
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16 * |
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17 */ |
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18 |
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19 namespace lemon { |
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20 /** |
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21 [PAGE]sec_undir_graphs[PAGE] Undirected Graphs |
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22 |
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23 In \ref sec_basics, we have introduced a general digraph structure, |
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24 \ref ListDigraph. LEMON also contains undirected graph classes, |
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25 for example, \ref ListGraph is the undirected versions of \ref ListDigraph. |
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26 |
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27 [SEC]sec_undir_graph_use[SEC] Working with Undirected Graphs |
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28 |
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29 The \ref concepts::Graph "undirected graphs" also fulfill the concept of |
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30 \ref concepts::Digraph "directed graphs", in such a way that each |
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31 undirected \e edge of a graph can also be regarded as two oppositely |
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32 directed \e arcs. As a result, all directed graph algorithms automatically |
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33 run on undirected graphs, as well. |
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34 |
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35 Undirected graphs provide an \c Edge type for the \e undirected \e edges |
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36 and an \c Arc type for the \e directed \e arcs. The \c Arc type is |
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37 convertible to \c Edge (or inherited from it), thus the corresponding |
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38 edge can always be obtained from an arc. |
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39 Of course, only nodes and edges can be added to or removed from an undirected |
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40 graph and the corresponding arcs are added or removed automatically |
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41 (there are twice as many arcs as edges) |
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42 |
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43 For example, |
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44 \code |
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45 ListGraph g; |
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46 |
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47 ListGraph::Node a = g.addNode(); |
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48 ListGraph::Node b = g.addNode(); |
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49 ListGraph::Node c = g.addNode(); |
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50 |
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51 ListGraph::Edge e = g.addEdge(a,b); |
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52 g.addEdge(b,c); |
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53 g.addEdge(c,a); |
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54 \endcode |
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55 |
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56 Each edge has an inherent orientation, thus it can be defined whether |
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57 an arc is forward or backward oriented in an undirected graph with respect |
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58 to this default oriantation of the represented edge. |
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59 The direction of an arc can be obtained and set using the functions |
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60 \ref concepts::Graph::direction() "direction()" and |
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61 \ref concepts::Graph::direct() "direct()", respectively. |
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62 |
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63 For example, |
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64 \code |
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65 ListGraph::Arc a1 = g.direct(e, true); // a1 is the forward arc |
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66 ListGraph::Arc a2 = g.direct(e, false); // a2 is the backward arc |
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67 |
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68 if (a2 == g.oppositeArc(a1)) |
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69 std::cout << "a2 is the opposite of a1" << std::endl; |
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70 \endcode |
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71 |
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72 The end nodes of an edge can be obtained using the functions |
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73 \ref concepts::Graph::source() "u()" and |
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74 \ref concepts::Graph::target() "v()", while the |
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75 \ref concepts::Graph::source() "source()" and |
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76 \ref concepts::Graph::target() "target()" can be used for arcs. |
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77 |
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78 \code |
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79 std::cout << "Edge " << g.id(e) << " connects node " |
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80 << g.id(g.u(e)) << " and node " << g.id(g.v(e)) << std::endl; |
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81 |
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82 std::cout << "Arc " << g.id(a2) << " goes from node " |
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83 << g.id(g.source(a2)) << " to node " << g.id(g.target(a2)) << std::endl; |
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84 \endcode |
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85 |
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86 Similarly to the digraphs, the undirected graphs also provide iterators |
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87 \ref concepts::Graph::NodeIt "NodeIt", \ref concepts::Graph::ArcIt "ArcIt", |
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88 \ref concepts::Graph::OutArcIt "OutArcIt" and \ref concepts::Graph::InArcIt |
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89 "InArcIt", which can be used the same way. |
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90 However, they also have iterator classes for edges. |
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91 \ref concepts::Graph::EdgeIt "EdgeIt" traverses all edges in the graph and |
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92 \ref concepts::Graph::IncEdgeIt "IncEdgeIt" lists the incident edges of a |
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93 certain node. |
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94 |
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95 For example, the degree of each node can be printed out like this: |
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96 |
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97 \code |
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98 for (ListGraph::NodeIt n(g); n != INVALID; ++n) { |
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99 int cnt = 0; |
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100 for (ListGraph::IncEdgeIt e(g, n); e != INVALID; ++e) { |
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101 cnt++; |
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102 } |
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103 std::cout << "deg(" << g.id(n) << ") = " << cnt << std::endl; |
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104 } |
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105 \endcode |
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106 |
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107 In an undirected graph, both \ref concepts::Graph::OutArcIt "OutArcIt" |
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108 and \ref concepts::Graph::InArcIt "InArcIt" iterates on the same \e edges |
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109 but with opposite direction. They are convertible to both \c Arc and |
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110 \c Edge types. \ref concepts::Graph::IncEdgeIt "IncEdgeIt" also iterates |
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111 on these edges, but it is not convertible to \c Arc, only to \c Edge. |
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112 |
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113 Apart from the node and arc maps, an undirected graph also defines |
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114 a member class for constructing edge maps. These maps can be |
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115 used in conjunction with both edges and arcs. |
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116 |
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117 For example, |
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118 \code |
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119 ListGraph::EdgeMap cost(g); |
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120 cost[e] = 10; |
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121 std::cout << cost[e] << std::endl; |
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122 std::cout << cost[a1] << ", " << cost[a2] << std::endl; |
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123 |
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124 ListGraph::ArcMap arc_cost(g); |
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125 arc_cost[a1] = cost[a1]; |
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126 arc_cost[a2] = 2 * cost[a2]; |
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127 // std::cout << arc_cost[e] << std::endl; // this is not valid |
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128 std::cout << arc_cost[a1] << ", " << arc_cost[a2] << std::endl; |
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129 \endcode |
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130 |
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131 |
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132 [SEC]sec_undir_graph_algs[SEC] Undirected Graph Algorihtms |
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133 |
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134 \todo This subsection is under construction. |
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135 |
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136 See \ref spantree for the minimum spanning tree algorithms and |
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137 \ref matching for matching algorithms. |
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138 |
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139 [TRAILER] |
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140 */ |
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141 } |