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_maps[PAGE] Maps |
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22 | |
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23 | \todo This page is under construction. |
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24 | |
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25 | \todo The following contents are ported from the LEMON 0.x tutorial, |
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26 | thus they have to be thoroughly revised and reworked. |
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27 | |
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28 | \warning Currently, this section may contain old or faulty contents. |
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29 | |
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30 | The LEMON maps are not only just storage classes, but also |
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31 | they are %concepts of any key--value based data access. |
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32 | Beside the standard digraph maps, LEMON contains several "lightweight" |
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33 | \e map \e adaptor \e classes, which perform various operations on the |
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34 | data of the adapted maps when their access operations are called, |
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35 | but without actually copying or modifying the original storage. |
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36 | These classes also conform to the map %concepts, thus they can be used |
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37 | like standard LEMON maps. |
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38 | |
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39 | Let us suppose that we have a traffic network stored in a LEMON digraph |
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40 | structure with two arc maps \c length and \c speed, which |
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41 | denote the physical length of each arc and the maximum (or average) |
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42 | speed that can be achieved on the corresponding road-section, |
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43 | respectively. If we are interested in the best traveling times, |
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44 | the following code can be used. |
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45 | |
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46 | \code |
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47 | dijkstra(g, divMap(length, speed)).distMap(dist).run(s); |
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48 | \endcode |
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49 | |
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50 | |
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51 | Maps play a central role in LEMON. As their name suggests, they map a |
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52 | certain range of \e keys to certain \e values. Each map has two |
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53 | <tt>typedef</tt>'s to determine the types of keys and values, like this: |
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54 | |
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55 | \code |
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56 | typedef Arc Key; |
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57 | typedef double Value; |
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58 | \endcode |
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59 | |
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60 | A map can be |
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61 | \e readable (\ref lemon::concepts::ReadMap "ReadMap", for short), |
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62 | \e writable (\ref lemon::concepts::WriteMap "WriteMap") or both |
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63 | (\ref lemon::concepts::ReadWriteMap "ReadWriteMap"). |
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64 | There also exists a special type of |
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65 | ReadWrite map called \ref lemon::concepts::ReferenceMap "reference map". |
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66 | In addition that you can |
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67 | read and write the values of a key, a reference map |
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68 | can also give you a reference to the |
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69 | value belonging to a key, so you have a direct access to the memory address |
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70 | where it is stored. |
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71 | |
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72 | Each digraph structure in LEMON provides two standard map templates called |
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73 | \c ArcMap and \c NodeMap. Both are reference maps and you can easily |
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74 | assign data to the nodes and to the arcs of the digraph. For example if you |
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75 | have a digraph \c g defined as |
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76 | \code |
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77 | ListDigraph g; |
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78 | \endcode |
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79 | and you want to assign a floating point value to each arc, you can do |
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80 | it like this. |
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81 | \code |
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82 | ListDigraph::ArcMap<double> length(g); |
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83 | \endcode |
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84 | Note that you must give the underlying digraph to the constructor. |
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85 | |
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86 | The value of a readable map can be obtained by <tt>operator[]</tt>. |
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87 | \code |
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88 | d=length[e]; |
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89 | \endcode |
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90 | where \c e is an instance of \c ListDigraph::Arc. |
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91 | (Or anything else |
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92 | that converts to \c ListDigraph::Arc, like \c ListDigraph::ArcIt or |
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93 | \c ListDigraph::OutArcIt etc.) |
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94 | |
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95 | There are two ways to assign a new value to a key |
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96 | |
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97 | - In case of a <em>reference map</em> <tt>operator[]</tt> |
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98 | gives you a reference to the |
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99 | value, thus you can use this. |
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100 | \code |
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101 | length[e]=3.5; |
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102 | \endcode |
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103 | - <em>Writable maps</em> have |
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104 | a member function \c set(Key,const Value &) |
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105 | for this purpose. |
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106 | \code |
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107 | length.set(e,3.5); |
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108 | \endcode |
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109 | |
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110 | The first case is more comfortable and if you store complex structures in your |
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111 | map, it might be more efficient. However, there are writable but |
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112 | not reference maps, so if you want to write a generic algorithm, you should |
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113 | insist on the second way. |
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114 | |
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115 | \section how-to-write-your-own-map How to Write Your Own Maps |
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116 | |
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117 | \subsection read-maps Readable Maps |
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118 | |
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119 | Readable maps are very frequently used as the input of an |
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120 | algorithm. For this purpose the most straightforward way is the use of the |
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121 | default maps provided by LEMON's digraph structures. |
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122 | Very often however, it is more |
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123 | convenient and/or more efficient to write your own readable map. |
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124 | |
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125 | You can find some examples below. In these examples \c Digraph is the |
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126 | type of the particular digraph structure you use. |
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127 | |
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128 | |
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129 | This simple map assigns \f$\pi\f$ to each arc. |
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130 | |
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131 | \code |
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132 | struct MyMap |
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133 | { |
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134 | typedef double Value; |
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135 | typedef Digraph::Arc Key; |
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136 | double operator[](Key e) const { return PI;} |
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137 | }; |
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138 | \endcode |
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139 | |
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140 | An alternative way to define maps is to use \c MapBase |
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141 | |
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142 | \code |
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143 | struct MyMap : public MapBase<Digraph::Arc,double> |
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144 | { |
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145 | Value operator[](Key e) const { return PI;} |
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146 | }; |
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147 | \endcode |
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148 | |
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149 | Here is a bit more complex example. |
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150 | It provides a length function obtained |
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151 | from a base length function shifted by a potential difference. |
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152 | |
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153 | \code |
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154 | class ReducedLengthMap : public MapBase<Digraph::Arc,double> |
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155 | { |
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156 | const Digraph &g; |
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157 | const Digraph::ArcMap<double> &orig_len; |
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158 | const Digraph::NodeMap<double> &pot; |
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159 | |
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160 | public: |
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161 | Value operator[](Key e) const { |
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162 | return orig_len[e]-(pot[g.target(e)]-pot[g.source(e)]); |
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163 | } |
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164 | |
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165 | ReducedLengthMap(const Digraph &_g, |
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166 | const Digraph::ArcMap &_o, |
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167 | const Digraph::NodeMap &_p) |
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168 | : g(_g), orig_len(_o), pot(_p) {}; |
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169 | }; |
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170 | \endcode |
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171 | |
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172 | Then, you can call e.g. Dijkstra algoritm on this map like this: |
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173 | \code |
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174 | ... |
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175 | ReducedLengthMap rm(g,len,pot); |
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176 | Dijkstra<Digraph,ReducedLengthMap> dij(g,rm); |
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177 | dij.run(s); |
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178 | ... |
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179 | \endcode |
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180 | |
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181 | |
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182 | In the previous section we discussed digraph topology. That is the skeleton a complex |
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183 | digraph represented data-set needs. But how to assign the data itself to that skeleton?<br> |
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184 | Here come the \b maps in. |
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185 | |
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186 | \section maps_intro Introduction to maps |
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187 | Maps play a central role in LEMON. As their name suggests, they map a certain range of <i>keys</i> to certain <i>values</i>. |
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188 | In LEMON there is many types of maps. Each map has two typedef's to determine the types of keys and values, like this: |
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189 | \code |
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190 | typedef Arc Key; |
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191 | typedef double Value; |
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192 | \endcode |
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193 | (Except matrix maps, they have two key types.) |
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194 | |
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195 | To make easy to use them - especially as template parameters - there are <i>map concepts</i> like by digraph classes. |
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196 | <ul> |
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197 | <li>\ref concepts::ReadMap "ReadMap" - values can be read out with the \c operator[]. |
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198 | \code value_typed_variable = map_instance[key_value]; \endcode |
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199 | </li> |
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200 | <li>\ref concepts::WriteMap "WriteMap" - values can be set with the \c set() member function. |
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201 | \code map_instance.set(key_value, value_typed_expression); \endcode |
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202 | </li> |
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203 | <li>\ref concepts::ReadWriteMap "ReadWriteMap" - it's just a shortcut to indicate that the map is both |
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204 | readable and writable. It is delivered from them. |
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205 | </li> |
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206 | <li>\ref concepts::ReferenceMap "ReferenceMap" - a subclass of ReadWriteMap. It has two additional typedefs |
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207 | <i>Reference</i> and <i>ConstReference</i> and two overloads of \c operator[] to |
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208 | providing you constant or non-constant reference to the value belonging to a key, |
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209 | so you have a direct access to the memory address where it is stored. |
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210 | </li> |
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211 | <li>And there are the Matrix version of these maps, where the values are assigned to a pair of keys. |
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212 | The keys can be different types. (\ref concepts::ReadMatrixMap "ReadMatrixMap", |
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213 | \ref concepts::WriteMatrixMap "WriteMatrixMap", \ref concepts::ReadWriteMatrixMap "ReadWriteMatrixMap", |
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214 | \ref concepts::ReferenceMatrixMap "ReferenceMatrixMap") |
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215 | </li> |
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216 | </ul> |
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217 | |
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218 | \section maps_graph Digraphs' maps |
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219 | Every \ref MappableDigraphComponent "mappable" digraph class has two public templates: NodeMap<VALUE> and ArcMap<VALUE> |
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220 | satisfying the \ref DigraphMap concept. |
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221 | If you want to assign data to nodes, just declare a NodeMap with the corresponding |
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222 | type. As an example, think of a arc-weighted digraph. |
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223 | \code ListDigraph::ArcMap<int> weight(digraph); \endcode |
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224 | You can see that the map needs the digraph whose arcs will mapped, but nothing more. |
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225 | |
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226 | If the digraph class is extendable or erasable the map will automatically follow |
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227 | the changes you make. If a new node is added a default value is mapped to it. |
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228 | You can define the default value by passing a second argument to the map's constructor. |
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229 | \code ListDigraph::ArcMap<int> weight(digraph, 13); \endcode |
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230 | But keep in mind that \c VALUE has to have copy constructor. |
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231 | |
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232 | Of course \c VALUE can be a rather complex type. |
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233 | |
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234 | For practice let's see the following template function (from \ref maps_summary "maps-summary.cc" in the \ref demo directory)! |
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235 | \dontinclude maps_summary.cc |
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236 | \skip template |
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237 | \until } |
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238 | The task is simple. We need the summary of some kind of data assigned to a digraph's nodes. |
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239 | (Whit a little trick the summary can be calculated only to a sub-digraph without changing |
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240 | this code. See \ref SubDigraph techniques - that's LEMON's true potential.) |
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241 | |
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242 | And the usage is simpler than the declaration suggests. The compiler deduces the |
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243 | template specialization, so the usage is like a simple function call. |
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244 | \skip std |
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245 | \until ; |
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246 | |
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247 | Most of the time you will probably use digraph maps, but keep in mind, that in LEMON maps are more general and can be used widely. |
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248 | |
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249 | If you want some 'real-life' examples see the next page, where we discuss \ref algorithms |
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250 | (coming soon) and will use maps hardly. |
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251 | Or if you want to know more about maps read these \ref maps2 "advanced map techniques". |
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252 | |
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253 | Here we discuss some advanced map techniques. Like writing your own maps or how to |
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254 | extend/modify a maps functionality with adaptors. |
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255 | |
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256 | \section custom_maps Writing Custom ReadMap |
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257 | \subsection custom_read_maps Readable Maps |
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258 | |
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259 | Readable maps are very frequently used as the input of an |
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260 | algorithm. For this purpose the most straightforward way is the use of the |
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261 | default maps provided by LEMON's digraph structures. |
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262 | Very often however, it is more |
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263 | convenient and/or more efficient to write your own readable map. |
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264 | |
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265 | You can find some examples below. In these examples \c Digraph is the |
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266 | type of the particular digraph structure you use. |
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267 | |
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268 | |
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269 | This simple map assigns \f$\pi\f$ to each arc. |
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270 | |
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271 | \code |
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272 | struct MyMap |
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273 | { |
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274 | typedef double Value; |
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275 | typedef Digraph::Arc Key; |
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276 | double operator[](const Key &e) const { return PI;} |
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277 | }; |
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278 | \endcode |
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279 | |
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280 | An alternative way to define maps is to use MapBase |
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281 | |
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282 | \code |
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283 | struct MyMap : public MapBase<Digraph::Arc,double> |
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284 | { |
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285 | Value operator[](const Key& e) const { return PI;} |
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286 | }; |
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287 | \endcode |
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288 | |
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289 | Here is a bit more complex example. |
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290 | It provides a length function obtained |
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291 | from a base length function shifted by a potential difference. |
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292 | |
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293 | \code |
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294 | class ReducedLengthMap : public MapBase<Digraph::Arc,double> |
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295 | { |
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296 | const Digraph &g; |
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297 | const Digraph::ArcMap<double> &orig_len; |
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298 | const Digraph::NodeMap<double> &pot; |
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299 | |
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300 | public: |
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301 | Value operator[](Key e) const { |
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302 | return orig_len[e]-(pot[g.target(e)]-pot[g.source(e)]); |
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303 | } |
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304 | |
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305 | ReducedLengthMap(const Digraph &_g, |
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306 | const Digraph::ArcMap &_o, |
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307 | const Digraph::NodeMap &_p) |
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308 | : g(_g), orig_len(_o), pot(_p) {}; |
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309 | }; |
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310 | \endcode |
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311 | |
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312 | Then, you can call e.g. Dijkstra algoritm on this map like this: |
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313 | \code |
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314 | ... |
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315 | ReducedLengthMap rm(g,len,pot); |
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316 | Dijkstra<Digraph,ReducedLengthMap> dij(g,rm); |
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317 | dij.run(s); |
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318 | ... |
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319 | \endcode |
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320 | |
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321 | |
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322 | [SEC]sec_map_concepts[SEC] Map Concepts |
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323 | |
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324 | ... |
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325 | |
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326 | |
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327 | [SEC]sec_own_maps[SEC] Creating Own Maps |
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328 | |
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329 | ... |
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330 | |
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331 | [SEC]sec_map_adaptors[SEC] Map Adaptors |
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332 | |
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333 | See \ref map_adaptors in the reference manual. |
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334 | |
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335 | |
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336 | [SEC]sec_algs_with_maps[SEC] Using Algorithms with Special Maps |
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337 | |
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338 | The basic functionality of the algorithms can be highly extended using |
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339 | special purpose map types for their internal data structures. |
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340 | For example, the \ref Dijkstra class stores a |
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341 | ef ProcessedMap, |
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342 | which has to be a writable node map of \ref bool value type. |
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343 | The assigned value of each node is set to \ref true when the node is |
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344 | processed, i.e., its actual distance is found. |
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345 | Applying a special map, \ref LoggerBoolMap, the processed order of |
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346 | the nodes can easily be stored in a standard container. |
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347 | |
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348 | Such specific map types can be passed to the algorithms using the technique of |
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349 | named template parameters. Similarly to the named function parameters, |
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350 | they allow specifying any subset of the parameters and in arbitrary order. |
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351 | |
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352 | \code |
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353 | typedef vector<ListDigraph::Node> Container; |
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354 | typedef back_insert_iterator<Container> InsertIterator; |
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355 | typedef LoggerBoolMap<InsertIterator> ProcessedMap; |
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356 | Dijkstra<ListDigraph> |
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357 | ::SetProcessedMap<ProcessedMap> |
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358 | ::Create dijktra(g, length); |
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359 | |
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360 | Container container; |
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361 | InsertIterator iterator(container); |
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362 | ProcessedMap processed(iterator); |
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363 | |
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364 | dijkstra.processedMap(processed).run(s); |
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365 | \endcode |
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366 | |
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367 | The function-type interfaces are considerably simpler, but they can be |
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368 | used in almost all practical cases. Surprisingly, even the above example |
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369 | can also be implemented using the \ref dijkstra() function and |
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370 | named parameters, as follows. |
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371 | Note that the function-type interface has the major advantage |
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372 | that temporary objects can be passed as parameters. |
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373 | |
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374 | \code |
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375 | vector<ListDigraph::Node> process_order; |
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376 | dijkstra(g, length) |
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377 | .processedMap(loggerBoolMap(back_inserter(process_order))) |
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378 | .run(s); |
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379 | \endcode |
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380 | |
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381 | LEMON also contains visitor based algorithm classes for |
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382 | BFS and DFS. |
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383 | |
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384 | Skeleton visitor classes are defined for both BFS and DFS, the concrete |
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385 | implementations can be inherited from them. |
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386 | \code |
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387 | template <typename GR> |
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388 | struct DfsVisitor { |
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389 | void start(const typename GR::Node& node) {} |
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390 | void stop(const typename GR::Node& node) {} |
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391 | void reach(const typename GR::Node& node) {} |
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392 | void leave(const typename GR::Node& node) {} |
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393 | void discover(const typename GR::Arc& arc) {} |
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394 | void examine(const typename GR::Arc& arc) {} |
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395 | void backtrack(const typename GR::Arc& arc) {} |
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396 | }; |
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397 | \endcode |
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398 | |
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399 | In the following example, the \ref discover()} and \code{examine() |
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400 | events are processed and the DFS tree is stored in an arc map. |
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401 | The values of this map indicate whether the corresponding arc |
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402 | reaches a new node or its target node is already reached. |
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403 | \code |
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404 | template <typename GR> |
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405 | struct TreeVisitor : public DfsVisitor<GR> { |
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406 | TreeVisitor(typename GR::ArcMap<bool>& tree) |
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407 | : _tree(tree) {} |
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408 | void discover(const typename GR::Arc& arc) |
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409 | { _tree[arc] = true; } |
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410 | void examine(const typename GR::Arc& arc) |
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411 | { _tree[arc] = false; } |
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412 | typename GR::ArcMap<bool>& _tree; |
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413 | }; |
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414 | \endcode |
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415 | |
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416 | |
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417 | [TRAILER] |
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418 | */ |
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419 | } |
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