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_basics[PAGE] Basic Concepts |
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22 | |
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23 | Throughout the tutorial we are working with the \ref lemon namespace. |
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24 | To save a lot of typing, we assume that a |
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25 | |
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26 | \code |
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27 | using namespace lemon; |
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28 | \endcode |
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29 | |
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30 | directive is added to the code at the beginning. |
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31 | |
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32 | [SEC]sec_digraphs[SEC] Directed Graphs |
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33 | |
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34 | This section tells you how to work with a directed graph (\e digraph, |
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35 | for short) in LEMON. Here we use \ref ListDigraph, the most versatile |
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36 | digraph structure. (The library also provides other digraph types, |
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37 | see \ref sec_graph_structures "later".) |
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38 | |
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39 | The nodes and the arcs of a graph are identified by two data types called |
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40 | \ref concepts::Digraph::Node "ListDigraph::Node" and \ref concepts::Digraph::Arc |
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41 | "ListDigraph::Arc". You can add new items to the graph using the member |
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42 | functions \ref ListDigraph::addNode() "addNode()" and |
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43 | \ref ListDigraph::addArc() "addArc()", like this: |
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44 | |
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45 | \code |
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46 | ListDigraph g; |
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47 | ListDigraph::Node a = g.addNode(); |
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48 | ListDigraph::Node b = g.addNode(); |
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49 | ListDigraph::Node c = g.addNode(); |
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50 | ListDigraph::Node d = g.addNode(); |
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51 | |
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52 | g.addArc(a,b); |
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53 | g.addArc(b,c); |
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54 | g.addArc(c,d); |
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55 | g.addArc(d,a); |
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56 | \endcode |
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57 | |
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58 | Of course, \ref ListDigraph::addArc() "addArc()" also returns the created arc: |
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59 | |
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60 | \code |
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61 | ListDigraph::Arc arc = g.addArc(a,c); |
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62 | \endcode |
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63 | |
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64 | \note Using ListDigraph, you can also remove nodes or arcs with the |
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65 | \ref ListDigraph::erase() "erase()" function. Moreover, this class provides |
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66 | several other operations, see its \ref ListDigraph "documentation" for more |
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67 | information. |
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68 | However, not all graph structures support the addition and deletion |
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69 | of graph items (see \ref sec_graph_concepts). |
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70 | |
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71 | Two important member functions of the directed graphs are |
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72 | \ref concepts::Digraph::source() "source()" |
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73 | and \ref concepts::Digraph::target() "target()". |
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74 | They give back the two end nodes of an arc. |
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75 | |
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76 | \code |
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77 | if (g.source(arc) == g.target(arc)) |
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78 | std::cout << "This is a loop arc" << std::endl; |
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79 | \endcode |
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80 | |
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81 | Each graph item has a unique integer identifier, which can be obtained using |
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82 | the \ref concepts::Digraph::id() "id()" function of the graph structure. |
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83 | |
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84 | \code |
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85 | std::cout << "Arc " << g.id(arc) << " goes from node " |
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86 | << g.id(g.source(arc)) << " to node " << g.id(g.target(arc)) << std::endl; |
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87 | \endcode |
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88 | |
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89 | \note In fact, the \c Node and \c Arc types are typically simple wrapper |
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90 | classes for a single \c int value, which is the identifier of the item. |
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91 | |
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92 | |
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93 | [SEC]sec_digraph_it[SEC] Iterators |
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94 | |
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95 | Let us assume you want to list the elements of the graph. For this purpose, |
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96 | the graph structures provide several iterators. For example, the following |
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97 | code will count the number of nodes in a graph. |
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98 | |
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99 | \code |
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100 | int cnt = 0; |
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101 | for (ListDigraph::NodeIt n(g); n != INVALID; ++n) |
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102 | cnt++; |
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103 | std::cout << "Number of nodes: " << cnt << std::endl; |
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104 | \endcode |
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105 | |
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106 | Here \ref concepts::Digraph::NodeIt "ListDigraph::NodeIt" |
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107 | is an iterator class that traverses the |
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108 | nodes. You must give the graph to the constructor and the iterator will be set |
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109 | to the first node. The next node is obtained by the prefix ++ |
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110 | operator. If there are no more nodes in the graph, the iterator will |
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111 | be set to \ref INVALID. |
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112 | |
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113 | \note \ref INVALID is a global constant, which converts to |
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114 | and compares with each and every iterator in LEMON. |
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115 | |
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116 | The iterators convert to the corresponding item types. For example, |
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117 | to following code will add a full graph to the existing nodes. |
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118 | |
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119 | \code |
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120 | for (ListDigraph::NodeIt u(g); u != INVALID; ++u) |
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121 | for (ListDigraph::NodeIt v(g); v != INVALID; ++v) |
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122 | if (u != v) g.addArc(u, v); |
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123 | \endcode |
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124 | |
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125 | \note Contrary to the iterators in the C++ Standard Template Library (STL), |
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126 | LEMON iterators are convertible to the corresponding |
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127 | item types without having to use \c %operator*(). This is not confusing, since the |
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128 | program context always indicates whether we refer to the iterator or to the graph |
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129 | item (they do not have conflicting functionalities). |
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130 | |
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131 | The graph items are also ordered by the 'less than' operator (with respect to |
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132 | their integer identifiers). For example, this code will add only one of the |
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133 | opposite arcs. |
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134 | |
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135 | \code |
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136 | for (ListDigraph::NodeIt u(g); u != INVALID; ++u) |
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137 | for (ListDigraph::NodeIt v(g); v != INVALID; ++v) |
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138 | if (u < v) g.addArc(u, v); |
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139 | \endcode |
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140 | |
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141 | \warning The order in which the iterators visit the items is |
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142 | undefined. The only thing you may assume that they will list the items |
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143 | in the same order until the graph is not changed. |
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144 | |
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145 | Similarly, \ref concepts::Digraph::ArcIt "ListDigraph::ArcIt" |
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146 | lists the arcs. Its usage is the same as of |
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147 | \ref concepts::Digraph::NodeIt "ListDigraph::NodeIt". |
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148 | |
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149 | \code |
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150 | int cnt = 0; |
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151 | for (ListDigraph::ArcIt a(g); a != INVALID; ++a) |
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152 | cnt++; |
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153 | std::cout << "Number of arcs: " << cnt << std::endl; |
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154 | \endcode |
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155 | |
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156 | Finally, you can also list the arcs starting from or arriving at a |
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157 | certain node with |
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158 | \ref concepts::Digraph::OutArcIt "ListDigraph::OutArcIt" |
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159 | and |
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160 | \ref concepts::Digraph::InArcIt "ListDigraph::InArcIt". |
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161 | Their usage is the same, but you must also give the node to the constructor. |
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162 | |
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163 | \code |
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164 | int cnt = 0; |
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165 | for (ListDigraph::OutArcIt a(g, start); a != INVALID; ++a) |
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166 | cnt++; |
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167 | std::cout << "Number of arcs leaving the node 'start': " << cnt << std::endl; |
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168 | \endcode |
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169 | |
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170 | |
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171 | [SEC]sec_digraph_maps[SEC] Maps |
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172 | |
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173 | The concept of "maps" is another fundamental part of LEMON. They allow assigning |
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174 | values of any type to the nodes or arcs of a graph. The standard maps |
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175 | provided by the graph structures have a couple of nice properties. |
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176 | |
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177 | - \e Fast. Accessing (reading/writing) the values is as fast as a |
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178 | simple vector reading/writing. |
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179 | - \e Dynamic. Whenever you need, you |
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180 | can allocate new maps in your code, just as a local variable. So when you |
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181 | leave its scope, it will be de-allocated automatically. |
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182 | - \e Automatic. If you add new nodes or arcs to the graph, the storage of the |
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183 | existing maps will automatically expanded and the new slots will be |
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184 | initialized. On the removal of an item, the corresponding values in the maps |
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185 | are properly destructed. |
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186 | |
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187 | \note These maps must not be confused with \c std::map, since they provide |
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188 | O(1) time acces to the elements instead of O(log n). |
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189 | |
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190 | So, if you want to assign \c int values to each node, you have to allocate a |
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191 | \ref concepts::Digraph::NodeMap "NodeMap<int>". |
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192 | |
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193 | \code |
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194 | ListDigraph::NodeMap<int> map(g); |
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195 | \endcode |
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196 | |
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197 | As you see, the graph you want to assign a map is given to the |
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198 | constructor. Then you can access its element as if it were a vector. |
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199 | |
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200 | \code |
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201 | map[a] = 2; |
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202 | map[b] = 3; |
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203 | map[c] = map[a] + map[b]; |
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204 | \endcode |
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205 | |
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206 | Any kind of data can be assigned to the graph items. |
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207 | |
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208 | \code |
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209 | ListDigraph::NodeMap<std::string> label(g); |
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210 | label[a] = "Node A"; |
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211 | label[b] = "Node B"; |
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212 | \endcode |
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213 | |
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214 | For a more complex example, let us create a map that assigns a unique |
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215 | integer number to each node. |
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216 | |
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217 | \code |
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218 | ListDigraph::NodeMap<int> id(g); |
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219 | int cnt = 0; |
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220 | for (ListDigraph::NodeIt n(g); n != INVALID; ++n) |
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221 | id[n] = cnt++; |
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222 | \endcode |
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223 | |
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224 | When you create a map, you can also give an initial value of the elements |
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225 | as a second parameter. For example, the following code puts the number |
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226 | of outgoing arcs for each node in a map. |
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227 | |
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228 | \code |
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229 | ListDigraph::NodeMap<int> out_deg(g, 0); |
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230 | |
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231 | for (ListDigraph::ArcIt a(g); a != INVALID; ++a) |
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232 | out_deg[g.source(a)]++; |
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233 | \endcode |
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234 | |
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235 | \warning The initial value will apply to the currently existing items only. If |
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236 | you add new nodes/arcs to the graph, then the corresponding values in the |
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237 | map will be initialized with the default constructor of the |
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238 | type. |
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239 | |
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240 | [TRAILER] |
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241 | */ |
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242 | } |
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