1 | /* -*- C++ -*- |
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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) 2003-2007 |
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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 algorithms Algorithms |
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22 | |
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23 | \section algo_bfs_dfs Bfs/Dfs |
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24 | Both \ref lemon::Bfs "Bfs" and \ref lemon::Dfs "Dfs" are highly adaptable and efficient |
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25 | implementations of the well known algorithms. The algorithms are placed most cases in |
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26 | separated files named after the algorithm itself but lower case as all other header file names. |
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27 | For example the next Bfs class is in the \c lemon/bfs.h. |
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28 | |
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29 | \subsection Bfs |
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30 | The algorithm is implemented in the \ref lemon::Bfs "Bfs" template class - rather than as function. |
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31 | The class has two template parameters: \b GR and \TR.<br> |
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32 | GR is the graph the algorithm runs on. It has \ref lemon::ListGraph "ListGraph" as default type. |
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33 | TR is a Traits class commonly used to easy the parametrization of templates. In most cases you |
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34 | wont need to modify the default type \ref lemon::BfsDefaultTraits "BfsDefaultTraits<GR>". |
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35 | |
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36 | To use the class, declare it! |
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37 | \code |
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38 | Bfs<ListUGraph> bfs(gr); |
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39 | \endcode |
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40 | Note the lack of second template argument because of the default parameter. |
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41 | |
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42 | It provides a simple but powerful interface to control the execution. |
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43 | \code |
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44 | int dist = bfs.run(s,t); |
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45 | \endcode |
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46 | It finds the shortest path from node \c s to node \c t and returns it, or zero |
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47 | if there is no path from \c s to \c t.<br> |
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48 | If you want the shortest path from a specified node to all other node, just write: |
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49 | \code |
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50 | bfs.run(s); |
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51 | \endcode |
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52 | Now the distances and path information are stored in maps which you can access with |
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53 | member functions like \ref lemon::Bfs::distMap "distMap()" or \ref lemon::Bfs::predMap "predMap()".<br> |
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54 | Or more directly whit other member functions like \c predNode(). Once the algorithm |
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55 | is finished (or to be precise reached that node) \ref lemon::Bfs::dist "dist()" or \ref lemon::Bfs::predNode |
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56 | "predNode()" can be called. |
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57 | |
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58 | For an example let's say we want to print the shortest path of those nodes which |
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59 | are in a certain distance. |
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60 | \code |
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61 | bfs.run(s); |
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62 | |
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63 | for( ListUGraph::NodeIt n(gr); n != INVALID; ++n ) { |
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64 | if( bfs.reached(n) && bfs.dist(n) <= max_dist ) { |
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65 | std::cout << gr.id(n); |
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66 | |
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67 | Node prev = bfs.prevNode(n); |
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68 | while( prev != INVALID ) { |
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69 | std::cout << "<-" << gr.id(prev); |
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70 | prev = bfs.prevNode(n); |
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71 | } |
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72 | |
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73 | std::cout << std::endl; |
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74 | } |
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75 | } |
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76 | \endcode |
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77 | |
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78 | \subsubsection bfs_adv_control Advanced control |
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79 | In the previous code we only used \c run(). Now we introduce the way you can directly |
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80 | control the execution of the algorithm. |
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81 | |
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82 | First you have to initialize the variables with \ref lemon::Bfs::init "init()". |
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83 | \code |
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84 | bfs.init(); |
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85 | \endcode |
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86 | |
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87 | Then you add one or more source nodes to the queue. They will be processed, as they would |
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88 | be reached by the algorithm before. And yes - you can add more sources during the execution. |
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89 | \code |
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90 | bfs.addSource(node_1); |
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91 | bfs.addSource(node_2); |
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92 | ... |
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93 | \endcode |
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94 | |
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95 | And finally you can start the process with \ref lemon::Bfs::start "start()", or |
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96 | you can write your own loop to process the nodes one-by-one. |
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97 | |
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98 | \todo demo for bfs advanced control |
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99 | |
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100 | \subsection Dfs |
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101 | Since Dfs is very similar to Bfs with a few tiny differences we only see a bit more complex example |
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102 | to demonstrate Dfs's capabilities. |
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103 | |
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104 | We will see a program, which solves the problem of <b>topological ordering</b>. |
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105 | We need to know in which order we should put on our clothes. The program will do the following: |
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106 | <ol> |
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107 | <li>We run the dfs algorithm to all nodes. |
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108 | <li>Put every node into a list when processed completely. |
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109 | <li>Write out the list in reverse order. |
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110 | </ol> |
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111 | |
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112 | \dontinclude topological_ordering.cc |
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113 | First of all we will need an own \ref lemon::Dfs::ProcessedMap "ProcessedMap". The ordering |
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114 | will be done through it. |
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115 | \skip MyOrdererMap |
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116 | \until }; |
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117 | The class meets the \ref lemon::WriteMap "WriteMap" concept. In it's \c set() method the only thing |
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118 | we need to do is insert the key - that is the node who's processing just finished - into the beginning |
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119 | of the list.<br> |
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120 | Although we implemented this needed helper class ourselves it was not necessary. |
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121 | The \ref lemon::FrontInserterBoolMap "FrontInserterBoolMap" class does exactly |
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122 | what we needed. To be correct it's more general - and it's all in \c LEMON. But |
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123 | we wanted to show you, how easy is to add additional functionality. |
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124 | |
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125 | First we declare the needed data structures: the graph and a map to store the nodes' label. |
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126 | \skip ListGraph |
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127 | \until label |
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128 | |
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129 | Now we build a graph. But keep in mind that it must be DAG because cyclic graphs has no topological |
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130 | ordering. |
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131 | \skip belt |
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132 | \until trousers |
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133 | We label them... |
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134 | \skip label |
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135 | \until trousers |
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136 | Then add directed edges which represent the precedences between those items. |
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137 | \skip trousers, belt |
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138 | \until ); |
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139 | |
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140 | See how easy is to access the internal information of this algorithm trough maps. |
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141 | We only need to set our own map as the class's \ref lemon::Dfs::ProcessedMap "ProcessedMap". |
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142 | \skip Dfs |
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143 | \until run |
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144 | |
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145 | And now comes the third part. Write out the list in reverse order. But the list was |
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146 | composed in reverse way (with \c push_front() instead of \c push_back() so we just iterate it. |
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147 | \skip std |
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148 | \until endl |
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149 | |
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150 | The program is to be found in the \ref demo directory: \ref topological_ordering.cc |
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151 | |
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152 | More algorithms are described in the \ref algorithms2 "second part". |
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153 | */ |
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154 | } |
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