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1 // |
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2 //======================================================================= |
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3 // Copyright 1997, 1998, 1999, 2000 University of Notre Dame. |
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4 // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek |
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5 // |
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6 // Distributed under the Boost Software License, Version 1.0. (See |
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7 // accompanying file LICENSE_1_0.txt or copy at |
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8 // http://www.boost.org/LICENSE_1_0.txt) |
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9 //======================================================================= |
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10 // |
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11 #ifndef BOOST_GRAPH_MST_KRUSKAL_HPP |
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12 #define BOOST_GRAPH_MST_KRUSKAL_HPP |
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13 |
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14 /* |
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15 *Minimum Spanning Tree |
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16 * Kruskal Algorithm |
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17 * |
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18 *Requirement: |
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19 * undirected graph |
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20 */ |
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21 |
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22 #include <vector> |
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23 #include <queue> |
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24 #include <functional> |
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25 |
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26 #include <boost/property_map.hpp> |
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27 #include <boost/graph/graph_concepts.hpp> |
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28 #include <boost/graph/named_function_params.hpp> |
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29 #include <boost/pending/disjoint_sets.hpp> |
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30 #include <boost/pending/indirect_cmp.hpp> |
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31 |
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32 |
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33 namespace boost { |
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34 |
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35 // Kruskal's algorithm for Minimum Spanning Tree |
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36 // |
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37 // This is a greedy algorithm to calculate the Minimum Spanning Tree |
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38 // for an undirected graph with weighted edges. The output will be a |
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39 // set of edges. |
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40 // |
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41 |
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42 namespace detail { |
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43 |
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44 template <class Graph, class OutputIterator, |
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45 class Rank, class Parent, class Weight> |
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46 void |
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47 kruskal_mst_impl(const Graph& G, |
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48 OutputIterator spanning_tree_edges, |
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49 Rank rank, Parent parent, Weight weight) |
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50 { |
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51 if (num_vertices(G) == 0) return; // Nothing to do in this case |
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52 typedef typename graph_traits<Graph>::vertex_descriptor Vertex; |
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53 typedef typename graph_traits<Graph>::edge_descriptor Edge; |
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54 function_requires<VertexListGraphConcept<Graph> >(); |
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55 function_requires<EdgeListGraphConcept<Graph> >(); |
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56 function_requires<OutputIteratorConcept<OutputIterator, Edge> >(); |
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57 function_requires<ReadWritePropertyMapConcept<Rank, Vertex> >(); |
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58 function_requires<ReadWritePropertyMapConcept<Parent, Vertex> >(); |
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59 function_requires<ReadablePropertyMapConcept<Weight, Edge> >(); |
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60 typedef typename property_traits<Weight>::value_type W_value; |
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61 typedef typename property_traits<Rank>::value_type R_value; |
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62 typedef typename property_traits<Parent>::value_type P_value; |
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63 function_requires<ComparableConcept<W_value> >(); |
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64 function_requires<ConvertibleConcept<P_value, Vertex> >(); |
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65 function_requires<IntegerConcept<R_value> >(); |
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66 |
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67 disjoint_sets<Rank, Parent> dset(rank, parent); |
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68 |
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69 typename graph_traits<Graph>::vertex_iterator ui, uiend; |
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70 for (boost::tie(ui, uiend) = vertices(G); ui != uiend; ++ui) |
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71 dset.make_set(*ui); |
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72 |
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73 typedef indirect_cmp<Weight, std::greater<W_value> > weight_greater; |
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74 weight_greater wl(weight); |
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75 std::priority_queue<Edge, std::vector<Edge>, weight_greater> Q(wl); |
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76 /*push all edge into Q*/ |
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77 typename graph_traits<Graph>::edge_iterator ei, eiend; |
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78 for (boost::tie(ei, eiend) = edges(G); ei != eiend; ++ei) |
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79 Q.push(*ei); |
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80 |
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81 while (! Q.empty()) { |
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82 Edge e = Q.top(); |
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83 Q.pop(); |
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84 Vertex u = dset.find_set(source(e, G)); |
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85 Vertex v = dset.find_set(target(e, G)); |
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86 if ( u != v ) { |
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87 *spanning_tree_edges++ = e; |
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88 dset.link(u, v); |
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89 } |
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90 } |
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91 } |
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92 |
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93 } // namespace detail |
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94 |
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95 // Named Parameters Variants |
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96 |
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97 template <class Graph, class OutputIterator> |
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98 inline void |
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99 kruskal_minimum_spanning_tree(const Graph& g, |
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100 OutputIterator spanning_tree_edges) |
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101 { |
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102 typedef typename graph_traits<Graph>::vertices_size_type size_type; |
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103 typedef typename graph_traits<Graph>::vertex_descriptor vertex_t; |
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104 typedef typename property_map<Graph, vertex_index_t>::type index_map_t; |
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105 if (num_vertices(g) == 0) return; // Nothing to do in this case |
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106 typename graph_traits<Graph>::vertices_size_type |
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107 n = num_vertices(g); |
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108 std::vector<size_type> rank_map(n); |
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109 std::vector<vertex_t> pred_map(n); |
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110 |
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111 detail::kruskal_mst_impl |
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112 (g, spanning_tree_edges, |
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113 make_iterator_property_map(rank_map.begin(), get(vertex_index, g), rank_map[0]), |
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114 make_iterator_property_map(pred_map.begin(), get(vertex_index, g), pred_map[0]), |
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115 get(edge_weight, g)); |
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116 } |
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117 |
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118 template <class Graph, class OutputIterator, class P, class T, class R> |
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119 inline void |
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120 kruskal_minimum_spanning_tree(const Graph& g, |
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121 OutputIterator spanning_tree_edges, |
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122 const bgl_named_params<P, T, R>& params) |
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123 { |
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124 typedef typename graph_traits<Graph>::vertices_size_type size_type; |
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125 typedef typename graph_traits<Graph>::vertex_descriptor vertex_t; |
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126 if (num_vertices(g) == 0) return; // Nothing to do in this case |
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127 typename graph_traits<Graph>::vertices_size_type n; |
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128 n = is_default_param(get_param(params, vertex_rank)) |
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129 ? num_vertices(g) : 1; |
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130 std::vector<size_type> rank_map(n); |
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131 n = is_default_param(get_param(params, vertex_predecessor)) |
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132 ? num_vertices(g) : 1; |
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133 std::vector<vertex_t> pred_map(n); |
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134 |
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135 detail::kruskal_mst_impl |
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136 (g, spanning_tree_edges, |
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137 choose_param |
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138 (get_param(params, vertex_rank), |
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139 make_iterator_property_map |
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140 (rank_map.begin(), |
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141 choose_pmap(get_param(params, vertex_index), g, vertex_index), rank_map[0])), |
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142 choose_param |
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143 (get_param(params, vertex_predecessor), |
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144 make_iterator_property_map |
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145 (pred_map.begin(), |
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146 choose_const_pmap(get_param(params, vertex_index), g, vertex_index), |
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147 pred_map[0])), |
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148 choose_const_pmap(get_param(params, edge_weight), g, edge_weight)); |
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149 } |
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150 |
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151 } // namespace boost |
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152 |
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153 |
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154 #endif // BOOST_GRAPH_MST_KRUSKAL_HPP |
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155 |