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 HugoLib 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 \ref ConstGraph concept. This concept does |
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12 | makes it possible to change the graph (i.e. it is not possible to add |
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13 | or delete edges or nodes). Most of the graph algorithms will run on |
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14 | these graphs. |
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15 | |
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16 | The graphs meeting the \ref ExtendableGraph concept allow node and |
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17 | edge addition. You can also "clear" (i.e. erase all edges and nodes) |
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18 | such a graph. |
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19 | |
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20 | In case of graphs meeting the full feature \ref ErasableGraph concept |
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21 | you can also erase individual edges and node in arbitrary order. |
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22 | |
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23 | The implemented graph structures are the following. |
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24 | \li \ref hugo::ListGraph "ListGraph" is the most versatile graph class. It meets |
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25 | the ErasableGraph concept and it also have some convenience features. |
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26 | \li \ref hugo::SmartGraph "SmartGraph" is a more memory |
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27 | efficient version of \ref hugo::ListGraph "ListGraph". The |
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28 | price of it is that it only meets the \ref ExtendableGraph concept, |
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29 | so you cannot delete individual edges or nodes. |
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30 | \li \ref hugo::SymListGraph "SymListGraph" and |
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31 | \ref hugo::SymSmartGraph "SymSmartGraph" classes are very similar to |
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32 | \ref hugo::ListGraph "ListGraph" and \ref hugo::SmartGraph "SmartGraph". |
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33 | The difference is that whenever you add a |
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34 | new edge to the graph, it actually adds a pair of oppositely directed edges. |
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35 | They are linked together so it is possible to access the counterpart of an |
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36 | edge. An even more important feature is that using these classes you can also |
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37 | attach data to the edges in such a way that the stored data |
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38 | are shared by the edge pairs. |
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39 | \li \ref hugo::FullGraph "FullGraph" |
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40 | implements a full graph. It is a \ref ConstGraph, so you cannot |
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41 | change the number of nodes once it is constructed. It is extremely memory |
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42 | efficient: it uses constant amount of memory independently from the number of |
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43 | the nodes of the graph. Of course, the size of the \ref maps "NodeMap"'s and |
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44 | \ref maps "EdgeMap"'s will depend on the number of nodes. |
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45 | |
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46 | \li \ref hugo::NodeSet "NodeSet" implements a graph with no edges. This class |
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47 | can be used as a base class of \ref hugo::EdgeSet "EdgeSet". |
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48 | \li \ref hugo::EdgeSet "EdgeSet" can be used to create a new graph on |
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49 | the edge set of another graph. The base graph can be an arbitrary graph and it |
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50 | is possible to attach several \ref hugo::EdgeSet "EdgeSet"'s to a base graph. |
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51 | |
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52 | \todo Don't we need SmartNodeSet and SmartEdgeSet? |
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53 | \todo Some cross-refs are wrong. |
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54 | |
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55 | |
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56 | The graph structures itself can not store data attached |
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57 | to the edges and nodes. However they all provide |
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58 | \ref maps "map classes" |
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59 | to dynamically attach data the to graph components. |
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60 | |
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61 | |
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62 | |
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63 | |
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64 | The following program demonstrates the basic features of HugoLib's graph |
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65 | structures. |
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66 | |
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67 | \code |
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68 | #include <iostream> |
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69 | #include <hugo/list_graph.h> |
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70 | |
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71 | using namespace hugo; |
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72 | |
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73 | int main() |
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74 | { |
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75 | typedef ListGraph Graph; |
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76 | \endcode |
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77 | |
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78 | ListGraph is one of HugoLib's graph classes. It is based on linked lists, |
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79 | therefore iterating throuh its edges and nodes is fast. |
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80 | |
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81 | \code |
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82 | typedef Graph::Edge Edge; |
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83 | typedef Graph::InEdgeIt InEdgeIt; |
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84 | typedef Graph::OutEdgeIt OutEdgeIt; |
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85 | typedef Graph::EdgeIt EdgeIt; |
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86 | typedef Graph::Node Node; |
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87 | typedef Graph::NodeIt NodeIt; |
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88 | |
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89 | Graph g; |
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90 | |
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91 | for (int i = 0; i < 3; i++) |
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92 | g.addNode(); |
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93 | |
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94 | for (NodeIt i(g); g.valid(i); g.next(i)) |
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95 | for (NodeIt j(g); g.valid(j); g.next(j)) |
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96 | if (i != j) g.addEdge(i, j); |
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97 | \endcode |
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98 | |
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99 | After some convenience typedefs we create a graph and add three nodes to it. |
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100 | Then we add edges to it to form a full graph. |
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101 | |
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102 | \code |
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103 | std::cout << "Nodes:"; |
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104 | for (NodeIt i(g); g.valid(i); g.next(i)) |
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105 | std::cout << " " << g.id(i); |
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106 | std::cout << std::endl; |
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107 | \endcode |
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108 | |
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109 | Here we iterate through all nodes of the graph. We use a constructor of the |
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110 | node iterator to initialize it to the first node. The next member function is |
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111 | used to step to the next node, and valid is used to check if we have passed the |
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112 | last one. |
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113 | |
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114 | \code |
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115 | std::cout << "Nodes:"; |
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116 | NodeIt n; |
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117 | for (g.first(n); n != INVALID; g.next(n)) |
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118 | std::cout << " " << g.id(n); |
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119 | std::cout << std::endl; |
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120 | \endcode |
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121 | |
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122 | Here you can see an alternative way to iterate through all nodes. Here we use a |
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123 | member function of the graph to initialize the node iterator to the first node |
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124 | of the graph. Using next on the iterator pointing to the last node invalidates |
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125 | the iterator i.e. sets its value to INVALID. Checking for this value is |
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126 | equivalent to using the valid member function. |
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127 | |
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128 | Both of the previous code fragments print out the same: |
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129 | |
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130 | \code |
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131 | Nodes: 2 1 0 |
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132 | \endcode |
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133 | |
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134 | \code |
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135 | std::cout << "Edges:"; |
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136 | for (EdgeIt i(g); g.valid(i); g.next(i)) |
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137 | std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; |
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138 | std::cout << std::endl; |
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139 | \endcode |
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140 | |
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141 | \code |
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142 | Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0) |
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143 | \endcode |
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144 | |
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145 | We can also iterate through all edges of the graph very similarly. The head and |
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146 | tail member functions can be used to access the endpoints of an edge. |
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147 | |
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148 | \code |
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149 | NodeIt first_node(g); |
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150 | |
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151 | std::cout << "Out-edges of node " << g.id(first_node) << ":"; |
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152 | for (OutEdgeIt i(g, first_node); g.valid(i); g.next(i)) |
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153 | std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; |
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154 | std::cout << std::endl; |
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155 | |
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156 | std::cout << "In-edges of node " << g.id(first_node) << ":"; |
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157 | for (InEdgeIt i(g, first_node); g.valid(i); g.next(i)) |
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158 | std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; |
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159 | std::cout << std::endl; |
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160 | \endcode |
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161 | |
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162 | \code |
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163 | Out-edges of node 2: (2,0) (2,1) |
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164 | In-edges of node 2: (0,2) (1,2) |
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165 | \endcode |
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166 | |
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167 | We can also iterate through the in and out-edges of a node. In the above |
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168 | example we print out the in and out-edges of the first node of the graph. |
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169 | |
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170 | \code |
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171 | Graph::EdgeMap<int> m(g); |
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172 | |
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173 | for (EdgeIt e(g); g.valid(e); g.next(e)) |
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174 | m.set(e, 10 - g.id(e)); |
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175 | |
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176 | std::cout << "Id Edge Value" << std::endl; |
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177 | for (EdgeIt e(g); g.valid(e); g.next(e)) |
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178 | std::cout << g.id(e) << " (" << g.id(g.tail(e)) << "," << g.id(g.head(e)) |
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179 | << ") " << m[e] << std::endl; |
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180 | \endcode |
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181 | |
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182 | \code |
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183 | Id Edge Value |
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184 | 4 (0,2) 6 |
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185 | 2 (1,2) 8 |
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186 | 5 (0,1) 5 |
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187 | 0 (2,1) 10 |
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188 | 3 (1,0) 7 |
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189 | 1 (2,0) 9 |
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190 | \endcode |
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191 | |
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192 | In generic graph optimization programming graphs are not containers rather |
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193 | incidence structures which are iterable in many ways. HugoLib introduces |
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194 | concepts that allow us to attach containers to graphs. These containers are |
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195 | called maps. |
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196 | |
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197 | In the example above we create an EdgeMap which assigns an int value to all |
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198 | edges of the graph. We use the set member function of the map to write values |
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199 | into the map and the operator[] to retrieve them. |
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200 | |
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201 | Here we used the maps provided by the ListGraph class, but you can also write |
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202 | your own maps. You can read more about using maps \ref maps "here". |
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203 | |
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204 | */ |
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