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