1 | /*! |
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2 | |
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3 | \page graphs How to use graphs |
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4 | |
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5 | The primary data structures of LEMON are the graph classes. They all |
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6 | provide a node list - edge list interface, i.e. they have |
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7 | functionalities to list the nodes and the edges of the graph as well |
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8 | as in incoming and outgoing edges of a given node. |
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9 | |
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10 | |
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11 | Each graph should meet the |
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12 | \ref lemon::skeleton::StaticGraph "StaticGraph" concept. |
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13 | This concept does not |
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14 | makes it possible to change the graph (i.e. it is not possible to add |
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15 | or delete edges or nodes). Most of the graph algorithms will run on |
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16 | these graphs. |
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17 | |
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18 | The graphs meeting the |
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19 | \ref lemon::skeleton::ExtendableGraph "ExtendableGraph" |
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20 | concept allow node and |
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21 | edge addition. You can also "clear" (i.e. erase all edges and nodes) |
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22 | such a graph. |
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23 | |
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24 | In case of graphs meeting the full feature |
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25 | \ref lemon::skeleton::ErasableGraph "ErasableGraph" |
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26 | concept |
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27 | you can also erase individual edges and node in arbitrary order. |
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28 | |
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29 | The implemented graph structures are the following. |
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30 | \li \ref lemon::ListGraph "ListGraph" is the most versatile graph class. It meets |
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31 | the \ref lemon::skeleton::ErasableGraph "ErasableGraph" concept |
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32 | and it also have some convenience features. |
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33 | \li \ref lemon::SmartGraph "SmartGraph" is a more memory |
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34 | efficient version of \ref lemon::ListGraph "ListGraph". The |
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35 | price of it is that it only meets the |
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36 | \ref lemon::skeleton::ExtendableGraph "ExtendableGraph" concept, |
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37 | so you cannot delete individual edges or nodes. |
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38 | \li \ref lemon::SymListGraph "SymListGraph" and |
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39 | \ref lemon::SymSmartGraph "SymSmartGraph" classes are very similar to |
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40 | \ref lemon::ListGraph "ListGraph" and \ref lemon::SmartGraph "SmartGraph". |
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41 | The difference is that whenever you add a |
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42 | new edge to the graph, it actually adds a pair of oppositely directed edges. |
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43 | They are linked together so it is possible to access the counterpart of an |
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44 | edge. An even more important feature is that using these classes you can also |
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45 | attach data to the edges in such a way that the stored data |
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46 | are shared by the edge pairs. |
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47 | \li \ref lemon::FullGraph "FullGraph" |
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48 | implements a full graph. It is a \ref lemon::skeleton::StaticGraph, so you cannot |
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49 | change the number of nodes once it is constructed. It is extremely memory |
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50 | efficient: it uses constant amount of memory independently from the number of |
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51 | the nodes of the graph. Of course, the size of the \ref maps "NodeMap"'s and |
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52 | \ref maps "EdgeMap"'s will depend on the number of nodes. |
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53 | |
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54 | \li \ref lemon::NodeSet "NodeSet" implements a graph with no edges. This class |
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55 | can be used as a base class of \ref lemon::EdgeSet "EdgeSet". |
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56 | \li \ref lemon::EdgeSet "EdgeSet" can be used to create a new graph on |
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57 | the node set of another graph. The base graph can be an arbitrary graph and it |
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58 | is possible to attach several \ref lemon::EdgeSet "EdgeSet"'s to a base graph. |
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59 | |
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60 | \todo Don't we need SmartNodeSet and SmartEdgeSet? |
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61 | \todo Some cross-refs are wrong. |
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62 | |
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63 | The graph structures itself can not store data attached |
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64 | to the edges and nodes. However they all provide |
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65 | \ref maps "map classes" |
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66 | to dynamically attach data the to graph components. |
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67 | |
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68 | The following program demonstrates the basic features of LEMON's graph |
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69 | structures. |
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70 | |
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71 | \code |
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72 | #include <iostream> |
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73 | #include <lemon/list_graph.h> |
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74 | |
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75 | using namespace lemon; |
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76 | |
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77 | int main() |
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78 | { |
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79 | typedef ListGraph Graph; |
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80 | \endcode |
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81 | |
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82 | ListGraph is one of LEMON's graph classes. It is based on linked lists, |
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83 | therefore iterating throuh its edges and nodes is fast. |
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84 | |
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85 | \code |
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86 | typedef Graph::Edge Edge; |
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87 | typedef Graph::InEdgeIt InEdgeIt; |
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88 | typedef Graph::OutEdgeIt OutEdgeIt; |
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89 | typedef Graph::EdgeIt EdgeIt; |
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90 | typedef Graph::Node Node; |
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91 | typedef Graph::NodeIt NodeIt; |
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92 | |
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93 | Graph g; |
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94 | |
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95 | for (int i = 0; i < 3; i++) |
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96 | g.addNode(); |
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97 | |
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98 | for (NodeIt i(g); i!=INVALID; ++i) |
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99 | for (NodeIt j(g); j!=INVALID; ++j) |
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100 | if (i != j) g.addEdge(i, j); |
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101 | \endcode |
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102 | |
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103 | After some convenience typedefs we create a graph and add three nodes to it. |
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104 | Then we add edges to it to form a full graph. |
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105 | |
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106 | \code |
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107 | std::cout << "Nodes:"; |
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108 | for (NodeIt i(g); i!=INVALID; ++i) |
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109 | std::cout << " " << g.id(i); |
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110 | std::cout << std::endl; |
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111 | \endcode |
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112 | |
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113 | Here we iterate through all nodes of the graph. We use a constructor of the |
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114 | node iterator to initialize it to the first node. The operator++ is used to |
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115 | step to the next node. Using operator++ on the iterator pointing to the last |
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116 | node invalidates the iterator i.e. sets its value to |
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117 | \ref lemon::INVALID "INVALID". This is what we exploit in the stop condition. |
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118 | |
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119 | The previous code fragment prints out the following: |
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120 | |
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121 | \code |
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122 | Nodes: 2 1 0 |
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123 | \endcode |
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124 | |
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125 | \code |
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126 | std::cout << "Edges:"; |
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127 | for (EdgeIt i(g); i!=INVALID; ++i) |
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128 | std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; |
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129 | std::cout << std::endl; |
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130 | \endcode |
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131 | |
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132 | \code |
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133 | Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0) |
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134 | \endcode |
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135 | |
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136 | We can also iterate through all edges of the graph very similarly. The head and |
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137 | tail member functions can be used to access the endpoints of an edge. |
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138 | |
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139 | \code |
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140 | NodeIt first_node(g); |
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141 | |
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142 | std::cout << "Out-edges of node " << g.id(first_node) << ":"; |
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143 | for (OutEdgeIt i(g, first_node); i!=INVALID; ++i) |
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144 | std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; |
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145 | std::cout << std::endl; |
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146 | |
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147 | std::cout << "In-edges of node " << g.id(first_node) << ":"; |
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148 | for (InEdgeIt i(g, first_node); i!=INVALID; ++i) |
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149 | std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; |
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150 | std::cout << std::endl; |
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151 | \endcode |
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152 | |
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153 | \code |
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154 | Out-edges of node 2: (2,0) (2,1) |
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155 | In-edges of node 2: (0,2) (1,2) |
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156 | \endcode |
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157 | |
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158 | We can also iterate through the in and out-edges of a node. In the above |
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159 | example we print out the in and out-edges of the first node of the graph. |
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160 | |
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161 | \code |
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162 | Graph::EdgeMap<int> m(g); |
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163 | |
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164 | for (EdgeIt e(g); e!=INVALID; ++e) |
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165 | m.set(e, 10 - g.id(e)); |
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166 | |
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167 | std::cout << "Id Edge Value" << std::endl; |
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168 | for (EdgeIt e(g); e!=INVALID; ++e) |
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169 | std::cout << g.id(e) << " (" << g.id(g.tail(e)) << "," << g.id(g.head(e)) |
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170 | << ") " << m[e] << std::endl; |
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171 | \endcode |
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172 | |
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173 | \code |
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174 | Id Edge Value |
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175 | 4 (0,2) 6 |
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176 | 2 (1,2) 8 |
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177 | 5 (0,1) 5 |
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178 | 0 (2,1) 10 |
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179 | 3 (1,0) 7 |
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180 | 1 (2,0) 9 |
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181 | \endcode |
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182 | |
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183 | As we mentioned above, graphs are not containers rather |
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184 | incidence structures which are iterable in many ways. LEMON introduces |
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185 | concepts that allow us to attach containers to graphs. These containers are |
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186 | called maps. |
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187 | |
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188 | In the example above we create an EdgeMap which assigns an int value to all |
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189 | edges of the graph. We use the set member function of the map to write values |
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190 | into the map and the operator[] to retrieve them. |
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191 | |
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192 | Here we used the maps provided by the ListGraph class, but you can also write |
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193 | your own maps. You can read more about using maps \ref maps "here". |
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194 | |
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195 | */ |
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