1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_KRUSKAL_H |
---|
20 | #define LEMON_KRUSKAL_H |
---|
21 | |
---|
22 | #include <algorithm> |
---|
23 | #include <vector> |
---|
24 | #include <lemon/unionfind.h> |
---|
25 | // #include <lemon/graph_utils.h> |
---|
26 | #include <lemon/maps.h> |
---|
27 | |
---|
28 | // #include <lemon/radix_sort.h> |
---|
29 | |
---|
30 | #include <lemon/bits/utility.h> |
---|
31 | #include <lemon/bits/traits.h> |
---|
32 | |
---|
33 | ///\ingroup spantree |
---|
34 | ///\file |
---|
35 | ///\brief Kruskal's algorithm to compute a minimum cost tree |
---|
36 | /// |
---|
37 | ///Kruskal's algorithm to compute a minimum cost tree. |
---|
38 | /// |
---|
39 | |
---|
40 | namespace lemon { |
---|
41 | |
---|
42 | namespace _kruskal_bits { |
---|
43 | |
---|
44 | // Kruskal for directed graphs. |
---|
45 | |
---|
46 | template <typename Digraph, typename In, typename Out> |
---|
47 | typename disable_if<lemon::UndirectedTagIndicator<Digraph>, |
---|
48 | typename In::value_type::second_type >::type |
---|
49 | kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) { |
---|
50 | typedef typename In::value_type::second_type Value; |
---|
51 | typedef typename Digraph::template NodeMap<int> IndexMap; |
---|
52 | typedef typename Digraph::Node Node; |
---|
53 | |
---|
54 | IndexMap index(digraph); |
---|
55 | UnionFind<IndexMap> uf(index); |
---|
56 | for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) { |
---|
57 | uf.insert(it); |
---|
58 | } |
---|
59 | |
---|
60 | Value tree_value = 0; |
---|
61 | for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) { |
---|
62 | if (uf.join(digraph.target(it->first),digraph.source(it->first))) { |
---|
63 | out.set(it->first, true); |
---|
64 | tree_value += it->second; |
---|
65 | } |
---|
66 | else { |
---|
67 | out.set(it->first, false); |
---|
68 | } |
---|
69 | } |
---|
70 | return tree_value; |
---|
71 | } |
---|
72 | |
---|
73 | // Kruskal for undirected graphs. |
---|
74 | |
---|
75 | template <typename Graph, typename In, typename Out> |
---|
76 | typename enable_if<lemon::UndirectedTagIndicator<Graph>, |
---|
77 | typename In::value_type::second_type >::type |
---|
78 | kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) { |
---|
79 | typedef typename In::value_type::second_type Value; |
---|
80 | typedef typename Graph::template NodeMap<int> IndexMap; |
---|
81 | typedef typename Graph::Node Node; |
---|
82 | |
---|
83 | IndexMap index(graph); |
---|
84 | UnionFind<IndexMap> uf(index); |
---|
85 | for (typename Graph::NodeIt it(graph); it != INVALID; ++it) { |
---|
86 | uf.insert(it); |
---|
87 | } |
---|
88 | |
---|
89 | Value tree_value = 0; |
---|
90 | for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) { |
---|
91 | if (uf.join(graph.u(it->first),graph.v(it->first))) { |
---|
92 | out.set(it->first, true); |
---|
93 | tree_value += it->second; |
---|
94 | } |
---|
95 | else { |
---|
96 | out.set(it->first, false); |
---|
97 | } |
---|
98 | } |
---|
99 | return tree_value; |
---|
100 | } |
---|
101 | |
---|
102 | |
---|
103 | template <typename Sequence> |
---|
104 | struct PairComp { |
---|
105 | typedef typename Sequence::value_type Value; |
---|
106 | bool operator()(const Value& left, const Value& right) { |
---|
107 | return left.second < right.second; |
---|
108 | } |
---|
109 | }; |
---|
110 | |
---|
111 | template <typename In, typename Enable = void> |
---|
112 | struct SequenceInputIndicator { |
---|
113 | static const bool value = false; |
---|
114 | }; |
---|
115 | |
---|
116 | template <typename In> |
---|
117 | struct SequenceInputIndicator<In, |
---|
118 | typename exists<typename In::value_type::first_type>::type> { |
---|
119 | static const bool value = true; |
---|
120 | }; |
---|
121 | |
---|
122 | template <typename In, typename Enable = void> |
---|
123 | struct MapInputIndicator { |
---|
124 | static const bool value = false; |
---|
125 | }; |
---|
126 | |
---|
127 | template <typename In> |
---|
128 | struct MapInputIndicator<In, |
---|
129 | typename exists<typename In::Value>::type> { |
---|
130 | static const bool value = true; |
---|
131 | }; |
---|
132 | |
---|
133 | template <typename In, typename Enable = void> |
---|
134 | struct SequenceOutputIndicator { |
---|
135 | static const bool value = false; |
---|
136 | }; |
---|
137 | |
---|
138 | template <typename Out> |
---|
139 | struct SequenceOutputIndicator<Out, |
---|
140 | typename exists<typename Out::value_type>::type> { |
---|
141 | static const bool value = true; |
---|
142 | }; |
---|
143 | |
---|
144 | template <typename Out, typename Enable = void> |
---|
145 | struct MapOutputIndicator { |
---|
146 | static const bool value = false; |
---|
147 | }; |
---|
148 | |
---|
149 | template <typename Out> |
---|
150 | struct MapOutputIndicator<Out, |
---|
151 | typename exists<typename Out::Value>::type> { |
---|
152 | static const bool value = true; |
---|
153 | }; |
---|
154 | |
---|
155 | template <typename In, typename InEnable = void> |
---|
156 | struct KruskalValueSelector {}; |
---|
157 | |
---|
158 | template <typename In> |
---|
159 | struct KruskalValueSelector<In, |
---|
160 | typename enable_if<SequenceInputIndicator<In>, void>::type> |
---|
161 | { |
---|
162 | typedef typename In::value_type::second_type Value; |
---|
163 | }; |
---|
164 | |
---|
165 | template <typename In> |
---|
166 | struct KruskalValueSelector<In, |
---|
167 | typename enable_if<MapInputIndicator<In>, void>::type> |
---|
168 | { |
---|
169 | typedef typename In::Value Value; |
---|
170 | }; |
---|
171 | |
---|
172 | template <typename Graph, typename In, typename Out, |
---|
173 | typename InEnable = void> |
---|
174 | struct KruskalInputSelector {}; |
---|
175 | |
---|
176 | template <typename Graph, typename In, typename Out, |
---|
177 | typename InEnable = void> |
---|
178 | struct KruskalOutputSelector {}; |
---|
179 | |
---|
180 | template <typename Graph, typename In, typename Out> |
---|
181 | struct KruskalInputSelector<Graph, In, Out, |
---|
182 | typename enable_if<SequenceInputIndicator<In>, void>::type > |
---|
183 | { |
---|
184 | typedef typename In::value_type::second_type Value; |
---|
185 | |
---|
186 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
---|
187 | return KruskalOutputSelector<Graph, In, Out>:: |
---|
188 | kruskal(graph, in, out); |
---|
189 | } |
---|
190 | |
---|
191 | }; |
---|
192 | |
---|
193 | template <typename Graph, typename In, typename Out> |
---|
194 | struct KruskalInputSelector<Graph, In, Out, |
---|
195 | typename enable_if<MapInputIndicator<In>, void>::type > |
---|
196 | { |
---|
197 | typedef typename In::Value Value; |
---|
198 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
---|
199 | typedef typename In::Key MapArc; |
---|
200 | typedef typename In::Value Value; |
---|
201 | typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt; |
---|
202 | typedef std::vector<std::pair<MapArc, Value> > Sequence; |
---|
203 | Sequence seq; |
---|
204 | |
---|
205 | for (MapArcIt it(graph); it != INVALID; ++it) { |
---|
206 | seq.push_back(std::make_pair(it, in[it])); |
---|
207 | } |
---|
208 | |
---|
209 | std::sort(seq.begin(), seq.end(), PairComp<Sequence>()); |
---|
210 | return KruskalOutputSelector<Graph, Sequence, Out>:: |
---|
211 | kruskal(graph, seq, out); |
---|
212 | } |
---|
213 | }; |
---|
214 | |
---|
215 | template <typename T> |
---|
216 | struct RemoveConst { |
---|
217 | typedef T type; |
---|
218 | }; |
---|
219 | |
---|
220 | template <typename T> |
---|
221 | struct RemoveConst<const T> { |
---|
222 | typedef T type; |
---|
223 | }; |
---|
224 | |
---|
225 | template <typename Graph, typename In, typename Out> |
---|
226 | struct KruskalOutputSelector<Graph, In, Out, |
---|
227 | typename enable_if<SequenceOutputIndicator<Out>, void>::type > |
---|
228 | { |
---|
229 | typedef typename In::value_type::second_type Value; |
---|
230 | |
---|
231 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
---|
232 | typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map; |
---|
233 | Map map(out); |
---|
234 | return _kruskal_bits::kruskal(graph, in, map); |
---|
235 | } |
---|
236 | |
---|
237 | }; |
---|
238 | |
---|
239 | template <typename Graph, typename In, typename Out> |
---|
240 | struct KruskalOutputSelector<Graph, In, Out, |
---|
241 | typename enable_if<MapOutputIndicator<Out>, void>::type > |
---|
242 | { |
---|
243 | typedef typename In::value_type::second_type Value; |
---|
244 | |
---|
245 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
---|
246 | return _kruskal_bits::kruskal(graph, in, out); |
---|
247 | } |
---|
248 | }; |
---|
249 | |
---|
250 | } |
---|
251 | |
---|
252 | /// \ingroup spantree |
---|
253 | /// |
---|
254 | /// \brief Kruskal's algorithm to find a minimum cost tree of a graph. |
---|
255 | /// |
---|
256 | /// This function runs Kruskal's algorithm to find a minimum cost tree. |
---|
257 | /// Due to some C++ hacking, it accepts various input and output types. |
---|
258 | /// |
---|
259 | /// \param g The graph the algorithm runs on. |
---|
260 | /// It can be either \ref concepts::Digraph "directed" or |
---|
261 | /// \ref concepts::Graph "undirected". |
---|
262 | /// If the graph is directed, the algorithm consider it to be |
---|
263 | /// undirected by disregarding the direction of the arcs. |
---|
264 | /// |
---|
265 | /// \param in This object is used to describe the arc costs. It can be one |
---|
266 | /// of the following choices. |
---|
267 | /// - An STL compatible 'Forward Container' with |
---|
268 | /// <tt>std::pair<GR::Edge,X></tt> or |
---|
269 | /// <tt>std::pair<GR::Arc,X></tt> as its <tt>value_type</tt>, where |
---|
270 | /// \c X is the type of the costs. The pairs indicates the arcs |
---|
271 | /// along with the assigned cost. <em>They must be in a |
---|
272 | /// cost-ascending order.</em> |
---|
273 | /// - Any readable Arc map. The values of the map indicate the arc costs. |
---|
274 | /// |
---|
275 | /// \retval out Here we also have a choise. |
---|
276 | /// - It can be a writable \c bool arc map. After running the |
---|
277 | /// algorithm this will contain the found minimum cost spanning |
---|
278 | /// tree: the value of an arc will be set to \c true if it belongs |
---|
279 | /// to the tree, otherwise it will be set to \c false. The value of |
---|
280 | /// each arc will be set exactly once. |
---|
281 | /// - It can also be an iteraror of an STL Container with |
---|
282 | /// <tt>GR::Edge</tt> or <tt>GR::Arc</tt> as its |
---|
283 | /// <tt>value_type</tt>. The algorithm copies the elements of the |
---|
284 | /// found tree into this sequence. For example, if we know that the |
---|
285 | /// spanning tree of the graph \c g has say 53 arcs, then we can |
---|
286 | /// put its arcs into an STL vector \c tree with a code like this. |
---|
287 | ///\code |
---|
288 | /// std::vector<Arc> tree(53); |
---|
289 | /// kruskal(g,cost,tree.begin()); |
---|
290 | ///\endcode |
---|
291 | /// Or if we don't know in advance the size of the tree, we can |
---|
292 | /// write this. |
---|
293 | ///\code std::vector<Arc> tree; |
---|
294 | /// kruskal(g,cost,std::back_inserter(tree)); |
---|
295 | ///\endcode |
---|
296 | /// |
---|
297 | /// \return The total cost of the found tree. |
---|
298 | /// |
---|
299 | /// \warning If kruskal runs on an be consistent of using the same |
---|
300 | /// Arc type for input and output. |
---|
301 | /// |
---|
302 | |
---|
303 | #ifdef DOXYGEN |
---|
304 | template <class Graph, class In, class Out> |
---|
305 | Value kruskal(GR const& g, const In& in, Out& out) |
---|
306 | #else |
---|
307 | template <class Graph, class In, class Out> |
---|
308 | inline typename _kruskal_bits::KruskalValueSelector<In>::Value |
---|
309 | kruskal(const Graph& graph, const In& in, Out& out) |
---|
310 | #endif |
---|
311 | { |
---|
312 | return _kruskal_bits::KruskalInputSelector<Graph, In, Out>:: |
---|
313 | kruskal(graph, in, out); |
---|
314 | } |
---|
315 | |
---|
316 | |
---|
317 | |
---|
318 | |
---|
319 | template <class Graph, class In, class Out> |
---|
320 | inline typename _kruskal_bits::KruskalValueSelector<In>::Value |
---|
321 | kruskal(const Graph& graph, const In& in, const Out& out) |
---|
322 | { |
---|
323 | return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>:: |
---|
324 | kruskal(graph, in, out); |
---|
325 | } |
---|
326 | |
---|
327 | } //namespace lemon |
---|
328 | |
---|
329 | #endif //LEMON_KRUSKAL_H |
---|