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_algorithms[PAGE] Algorithms |
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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 mainly 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 | In addition to the graph structures, the most important parts of LEMON are |
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31 | the various algorithms related to graph theory and combinatorial optimization. |
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32 | The library provides quite flexible and efficient implementations |
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33 | for well-known fundamental algorithms, such as breadth-first |
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34 | search (BFS), depth-first search (DFS), Dijkstra algorithm, Kruskal algorithm |
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35 | and methods for discovering graph properties like connectivity, bipartiteness |
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36 | or Euler property, as well as more complex optimization algorithms for finding |
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37 | maximum flows, minimum cuts, matchings, minimum cost flows and arc-disjoint |
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38 | paths. |
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39 | |
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40 | In this section, we present only some of the most fundamental algorithms. |
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41 | For a complete overview, see the \ref algs module of the reference manual. |
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42 | |
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43 | [SEC]sec_graph_search[SEC] Graph Search |
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44 | |
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45 | See \ref Bfs, \ref Dfs and \ref graph_properties. |
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46 | |
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47 | Both \ref lemon::Bfs "Bfs" and \ref lemon::Dfs "Dfs" are highly adaptable and efficient |
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48 | implementations of the well known algorithms. The algorithms are placed most cases in |
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49 | separated files named after the algorithm itself but lower case as all other header file names. |
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50 | For example the next Bfs class is in the \c lemon/bfs.h. |
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51 | |
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52 | The algorithm is implemented in the \ref lemon::Bfs "Bfs" template class - rather than as function. |
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53 | The class has two template parameters: \b GR and \b TR.<br> |
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54 | GR is the digraph the algorithm runs on. It has \ref lemon::ListDigraph "ListDigraph" as default type. |
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55 | TR is a Traits class commonly used to easy the parameterization of templates. In most cases you |
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56 | wont need to modify the default type \ref lemon::BfsDefaultTraits "BfsDefaultTraits<GR>". |
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57 | |
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58 | To use the class, declare it! |
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59 | \code |
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60 | Bfs<ListGraph> bfs(gr); |
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61 | \endcode |
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62 | Note the lack of second template argument because of the default parameter. |
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63 | |
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64 | It provides a simple but powerful interface to control the execution. |
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65 | \code |
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66 | int dist = bfs.run(s,t); |
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67 | \endcode |
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68 | It finds the shortest path from node \c s to node \c t and returns it, or zero |
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69 | if there is no path from \c s to \c t.<br> |
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70 | If you want the shortest path from a specified node to all other node, just write: |
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71 | \code |
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72 | bfs.run(s); |
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73 | \endcode |
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74 | Now the distances and path information are stored in maps which you can access with |
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75 | member functions like \ref lemon::Bfs::distMap "distMap()" or \ref lemon::Bfs::predMap "predMap()".<br> |
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76 | Or more directly with other member functions like \ref lemon::Bfs::predNode "predNode()". Once the algorithm |
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77 | is finished (or to be precise reached that node) \ref lemon::Bfs::dist "dist()" or \ref lemon::Bfs::predNode |
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78 | "predNode()" can be called. |
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79 | |
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80 | For an example let's say we want to print the shortest path of those nodes which |
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81 | are in a certain distance. |
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82 | \code |
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83 | bfs.run(s); |
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84 | |
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85 | for( ListGraph::NodeIt n(gr); n != INVALID; ++n ) { |
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86 | if( bfs.reached(n) && bfs.dist(n) <= max_dist ) { |
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87 | std::cout << gr.id(n); |
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88 | |
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89 | Node prev = bfs.prevNode(n); |
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90 | while( prev != INVALID ) { |
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91 | std::cout << "<-" << gr.id(prev); |
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92 | prev = bfs.prevNode(n); |
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93 | } |
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94 | |
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95 | std::cout << std::endl; |
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96 | } |
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97 | } |
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98 | \endcode |
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99 | |
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100 | In the previous code we only used \c run(). Now we introduce the way you can directly |
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101 | control the execution of the algorithm. |
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102 | |
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103 | First you have to initialize the variables with \ref lemon::Bfs::init "init()". |
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104 | \code |
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105 | bfs.init(); |
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106 | \endcode |
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107 | |
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108 | Then you add one or more source nodes to the queue. They will be processed, as they would |
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109 | be reached by the algorithm before. And yes - you can add more sources during the execution. |
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110 | \code |
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111 | bfs.addSource(node_1); |
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112 | bfs.addSource(node_2); |
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113 | ... |
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114 | \endcode |
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115 | |
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116 | And finally you can start the process with \ref lemon::Bfs::start "start()", or |
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117 | you can write your own loop to process the nodes one-by-one. |
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118 | |
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119 | |
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120 | Since Dfs is very similar to Bfs with a few tiny differences we only see a bit more complex example |
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121 | to demonstrate Dfs's capabilities. |
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122 | |
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123 | We will see a program, which solves the problem of <b>topological ordering</b>. |
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124 | We need to know in which order we should put on our clothes. The program will do the following: |
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125 | <ol> |
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126 | <li>We run the dfs algorithm to all nodes. |
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127 | <li>Put every node into a list when processed completely. |
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128 | <li>Write out the list in reverse order. |
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129 | </ol> |
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130 | |
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131 | \dontinclude topological_ordering.cc |
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132 | First of all we will need an own \ref lemon::Dfs::ProcessedMap "ProcessedMap". The ordering |
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133 | will be done through it. |
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134 | \skip MyOrdererMap |
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135 | \until }; |
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136 | The class meets the \ref concepts::WriteMap "WriteMap" concept. In it's \c set() method the only thing |
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137 | we need to do is insert the key - that is the node whose processing just finished - into the beginning |
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138 | of the list.<br> |
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139 | Although we implemented this needed helper class ourselves it was not necessary. |
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140 | The \ref lemon::FrontInserterBoolMap "FrontInserterBoolMap" class does exactly |
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141 | what we needed. To be correct it's more general - and it's all in \c LEMON. But |
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142 | we wanted to show you, how easy is to add additional functionality. |
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143 | |
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144 | First we declare the needed data structures: the digraph and a map to store the nodes' label. |
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145 | \skip ListDigraph |
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146 | \until label |
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147 | |
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148 | Now we build a digraph. But keep in mind that it must be DAG because cyclic digraphs has no topological |
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149 | ordering. |
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150 | \skip belt |
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151 | \until trousers |
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152 | We label them... |
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153 | \skip label |
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154 | \until trousers |
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155 | Then add arcs which represent the precedences between those items. |
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156 | \skip trousers, belt |
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157 | \until ); |
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158 | |
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159 | See how easy is to access the internal information of this algorithm trough maps. |
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160 | We only need to set our own map as the class's \ref lemon::Dfs::ProcessedMap "ProcessedMap". |
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161 | \skip Dfs |
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162 | \until run |
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163 | |
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164 | And now comes the third part. Write out the list in reverse order. But the list was |
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165 | composed in reverse way (with \c push_front() instead of \c push_back() so we just iterate it. |
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166 | \skip std |
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167 | \until endl |
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168 | |
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169 | The program is to be found in the \ref demo directory: \ref topological_ordering.cc |
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170 | |
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171 | \todo Check the linking of the demo file, the code samples are missing. |
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172 | |
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173 | More algorithms are described in the \ref algorithms2 "second part". |
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174 | |
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175 | |
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176 | [SEC]sec_shortest_paths[SEC] Shortest Paths |
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177 | |
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178 | See \ref Dijkstra and \ref BellmanFord. |
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179 | |
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180 | |
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181 | If you want to solve some transportation problems in a network then you |
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182 | will want to find shortest paths between nodes of a graph. This is |
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183 | usually solved using Dijkstra's algorithm. A utility that solves this is |
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184 | the LEMON Dijkstra class. The following code is a simple program using |
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185 | the LEMON Dijkstra class: it calculates the shortest path between node s |
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186 | and t in a graph g. We omit the part reading the graph g and the length |
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187 | map len. |
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188 | |
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189 | <hr> |
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190 | |
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191 | In LEMON, the algorithms are implemented basically as classes, but |
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192 | for some of them, function-type interfaces are also available |
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193 | for the sake of convenience. |
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194 | For instance, the Dijkstra algorithm is implemented in the \ref Dijkstra |
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195 | template class, but the \ref dijkstra() function is also defined, |
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196 | which can still be used quite flexibly due to named parameters. |
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197 | |
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198 | The original sample code could also use the class interface as follows. |
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199 | |
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200 | \code |
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201 | Dijkstra<ListDigraph> dijkstra(g, length); |
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202 | dijkstra.distMap(dist); |
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203 | dijsktra.init(); |
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204 | dijkstra.addSource(u); |
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205 | dijkstra.start(); |
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206 | \endcode |
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207 | |
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208 | The previous code is obviously longer than the original, but the |
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209 | execution can be controlled to a higher extent. While using the function-type |
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210 | interface, only one source can be added to the algorithm, the class |
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211 | interface makes it possible to specify several root nodes. |
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212 | Moreover, the algorithm can also be executed step-by-step. For instance, |
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213 | the following code can be used instead of \ref dijkstra.start(). |
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214 | |
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215 | \code |
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216 | while (!dijkstra.emptyQueue()) { |
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217 | ListDigraph::Node n = dijkstra.processNextNode(); |
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218 | cout << g.id(n) << ' ' << dijkstra.dist(g) << endl; |
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219 | } |
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220 | \endcode |
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221 | |
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222 | |
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223 | [SEC]sec_max_flow[SEC] Maximum Flows |
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224 | |
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225 | See \ref Preflow. |
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226 | |
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227 | [TRAILER] |
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228 | */ |
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229 | } |
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