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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) 2003-2009 |
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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_graph_structures[PAGE] Graph Structures |
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22 |
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23 The implementation of combinatorial algorithms heavily relies on |
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24 efficient graph structures. Diverse applications require the |
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25 usage of different physical graph storages. |
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26 In \ref sec_basics, we have introduced a general digraph structure, |
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27 \ref ListDigraph. Apart from this class, LEMON provides several |
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28 other classes for handling directed and undirected graphs to meet the |
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29 diverging requirements of the possible users. In order to save on running |
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30 time or on memory usage, some structures may fail to support some graph |
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31 features like node or arc/edge deletion. |
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32 You are free to use the graph structure that fit your requirements the best, |
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33 since most graph algorithms and auxiliary data structures can be used |
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34 with any of them. |
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35 |
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36 |
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37 [SEC]sec_graph_concepts[SEC] Graph Concepts |
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38 |
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39 In LEMON, there are various graph types, which are rather different, but |
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40 they all conform to the corresponding \ref graph_concepts "graph concept", |
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41 which defines the common part of the graph interfaces. |
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42 The \ref concepts::Digraph "Digraph concept" describes the common interface |
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43 of directed graphs (without any sensible implementation), while |
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44 the \ref concepts::Graph "Graph concept" describes the undirected graphs. |
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45 Any generic graph algorithm should only exploit the features of the |
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46 corresponding graph concept. (It should compile with the |
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47 \ref concepts::Digraph "Digraph" or \ref concepts::Graph "Graph" type, |
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48 but it will not run properly, of course.) |
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49 |
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50 The graph %concepts define the member classes for the iterators and maps |
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51 along with some useful basic functions for obtaining the identifiers of |
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52 the items, the end nodes of the arcs (or edges) and their iterators, |
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53 etc. |
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54 An actual graph implementation may have various additional functionalities |
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55 according to its purpose. |
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56 |
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57 |
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58 [SEC]sec_digraph_types[SEC] Digraph Structures |
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59 |
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60 The already used \ref ListDigraph class is the most versatile directed |
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61 graph structure. Apart from the general digraph functionalities, it |
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62 provides operations for adding and removing nodes and arcs, changing |
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63 the source or target node of an arc, and contracting and splitting nodes |
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64 or arcs. |
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65 |
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66 \ref SmartDigraph is another general digraph implementation, which is |
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67 significantly more efficient (both in terms of space and time), but it |
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68 provides less functionality. For example, nodes and arcs cannot be |
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69 removed from it. |
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70 |
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71 \ref FullDigraph is an efficient implementation of a directed full graph. |
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72 This structure is completely static, so you can neither add nor delete |
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73 arcs or nodes, and the class needs constant space in memory. |
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74 |
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75 |
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76 [SEC]sec_undir_graphs[SEC] Undirected Graphs |
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77 |
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78 LEMON also provides undirected graph structures. For example, |
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79 \ref ListGraph and \ref SmartGraph are the undirected versions of |
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80 \ref ListDigraph and \ref SmartDigraph, respectively. |
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81 They provide similar features to the digraph structures. |
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82 |
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83 The \ref concepts::Graph "undirected graphs" also fulfill the concept of |
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84 \ref concepts::Digraph "directed graphs", in such a way that each |
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85 undirected \e edge of a graph can also be regarded as two oppositely |
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86 directed \e arcs. As a result, all directed graph algorithms automatically |
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87 run on undirected graphs, as well. |
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88 |
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89 Undirected graphs provide an \c Edge type for the \e undirected \e edges |
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90 and an \c Arc type for the \e directed \e arcs. The \c Arc type is |
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91 convertible to \c Edge (or inherited from it), thus the corresponding |
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92 edge can always be obtained from an arc. |
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93 |
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94 Only nodes and edges can be added to or removed from an undirected |
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95 graph and the corresponding arcs are added or removed automatically |
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96 (there are twice as many arcs as edges) |
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97 |
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98 For example, |
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99 \code |
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100 ListGraph g; |
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101 |
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102 ListGraph::Node a = g.addNode(); |
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103 ListGraph::Node b = g.addNode(); |
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104 ListGraph::Node c = g.addNode(); |
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105 |
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106 ListGraph::Edge e = g.addEdge(a,b); |
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107 g.addEdge(b,c); |
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108 g.addEdge(c,a); |
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109 \endcode |
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110 |
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111 Each edge has an inherent orientation, thus it can be defined whether an |
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112 arc is forward or backward oriented in an undirected graph with respect |
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113 to this default oriantation of the represented edge. |
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114 The direction of an arc can be obtained and set using the functions |
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115 \ref concepts::Graph::direction() "direction()" and |
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116 \ref concepts::Graph::direct() "direct()", respectively. |
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117 |
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118 For example, |
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119 \code |
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120 ListGraph::Arc a1 = g.direct(e, true); // a1 is the forward arc |
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121 ListGraph::Arc a2 = g.direct(e, false); // a2 is the backward arc |
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122 |
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123 if (a2 == g.oppositeArc(a1)) |
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124 std::cout << "a2 is the opposite of a1" << std::endl; |
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125 \endcode |
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126 |
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127 The end nodes of an edge can be obtained using the functions |
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128 \ref concepts::Graph::source() "u()" and |
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129 \ref concepts::Graph::target() "v()", while the |
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130 \ref concepts::Graph::source() "source()" and |
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131 \ref concepts::Graph::target() "target()" can be used for arcs. |
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132 |
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133 \code |
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134 std::cout << "Edge " << g.id(e) << " connects node " |
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135 << g.id(g.u(e)) << " and node " << g.id(g.v(e)) << std::endl; |
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136 |
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137 std::cout << "Arc " << g.id(a2) << " goes from node " |
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138 << g.id(g.source(a2)) << " to node " << g.id(g.target(a2)) << std::endl; |
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139 \endcode |
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140 |
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141 |
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142 Similarly to the digraphs, the undirected graphs also provide iterators |
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143 \ref concepts::Graph::NodeIt "NodeIt", \ref concepts::Graph::ArcIt "ArcIt", |
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144 \ref concepts::Graph::OutArcIt "OutArcIt" and \ref concepts::Graph::InArcIt |
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145 "InArcIt", which can be used the same way. |
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146 However, they also have iterator classes for edges. |
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147 \ref concepts::Graph::EdgeIt "EdgeIt" traverses all edges in the graph and |
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148 \ref concepts::Graph::IncEdgeIt "IncEdgeIt" lists the incident edges of a |
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149 certain node. |
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150 |
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151 For example, the degree of each node can be computed and stored in a node map |
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152 like this: |
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153 |
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154 \code |
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155 ListGraph::NodeMap<int> deg(g, 0); |
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156 for (ListGraph::NodeIt n(g); n != INVALID; ++n) { |
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157 for (ListGraph::IncEdgeIt e(g, n); e != INVALID; ++e) { |
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158 deg[n]++; |
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159 } |
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160 } |
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161 \endcode |
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162 |
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163 In an undirected graph, both \ref concepts::Graph::OutArcIt "OutArcIt" |
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164 and \ref concepts::Graph::InArcIt "InArcIt" iterates on the same \e edges |
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165 but with opposite direction. They are convertible to both \c Arc and |
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166 \c Edge types. \ref concepts::Graph::IncEdgeIt "IncEdgeIt" also iterates |
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167 on these edges, but it is not convertible to \c Arc, only to \c Edge. |
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168 |
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169 Apart from the node and arc maps, an undirected graph also defines |
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170 a template member class for constructing edge maps. These maps can be |
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171 used in conjunction with both edges and arcs. |
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172 |
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173 For example, |
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174 \code |
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175 ListGraph::EdgeMap cost(g); |
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176 cost[e] = 10; |
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177 std::cout << cost[e] << std::endl; |
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178 std::cout << cost[a1] << ", " << cost[a2] << std::endl; |
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179 |
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180 ListGraph::ArcMap arc_cost(g); |
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181 arc_cost[a1] = cost[a1]; |
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182 arc_cost[a2] = 2 * cost[a2]; |
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183 // std::cout << arc_cost[e] << std::endl; // this is not valid |
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184 std::cout << arc_cost[a1] << ", " << arc_cost[a2] << std::endl; |
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185 \endcode |
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186 |
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187 [SEC]sec_special_graphs[SEC] Special Graph Structures |
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188 |
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189 In addition to the general undirected classes \ref ListGraph and |
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190 \ref SmartGraph, LEMON also provides special purpose graph types for |
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191 handling \ref FullGraph "full graphs", \ref GridGraph "grid graphs" and |
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192 \ref HypercubeGraph "hypercube graphs". |
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193 They all static structures, i.e. they do not allow distinct item additions |
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194 or deletions, the graph has to be built at once. |
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195 |
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196 [TRAILER] |
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197 */ |
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198 } |