1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2006 |
---|
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/bits/utility.h> |
---|
26 | #include <lemon/bits/traits.h> |
---|
27 | |
---|
28 | ///\ingroup spantree |
---|
29 | ///\file |
---|
30 | ///\brief Kruskal's algorithm to compute a minimum cost tree |
---|
31 | /// |
---|
32 | ///Kruskal's algorithm to compute a minimum cost tree. |
---|
33 | /// |
---|
34 | ///\todo The file still needs some clean-up. |
---|
35 | |
---|
36 | namespace lemon { |
---|
37 | |
---|
38 | /// \addtogroup spantree |
---|
39 | /// @{ |
---|
40 | |
---|
41 | /// Kruskal's algorithm to find a minimum cost tree of a graph. |
---|
42 | |
---|
43 | /// This function runs Kruskal's algorithm to find a minimum cost tree. |
---|
44 | /// Due to hard C++ hacking, it accepts various input and output types. |
---|
45 | /// |
---|
46 | /// \param g The graph the algorithm runs on. |
---|
47 | /// It can be either \ref concept::StaticGraph "directed" or |
---|
48 | /// \ref concept::UGraph "undirected". |
---|
49 | /// If the graph is directed, the algorithm consider it to be |
---|
50 | /// undirected by disregarding the direction of the edges. |
---|
51 | /// |
---|
52 | /// \param in This object is used to describe the edge costs. It can be one |
---|
53 | /// of the following choices. |
---|
54 | /// - An STL compatible 'Forward Container' |
---|
55 | /// with <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, |
---|
56 | /// where \c X is the type of the costs. The pairs indicates the edges along |
---|
57 | /// with the assigned cost. <em>They must be in a |
---|
58 | /// cost-ascending order.</em> |
---|
59 | /// - Any readable Edge map. The values of the map indicate the edge costs. |
---|
60 | /// |
---|
61 | /// \retval out Here we also have a choise. |
---|
62 | /// - Is can be a writable \c bool edge map. |
---|
63 | /// After running the algorithm |
---|
64 | /// this will contain the found minimum cost spanning tree: the value of an |
---|
65 | /// edge will be set to \c true if it belongs to the tree, otherwise it will |
---|
66 | /// be set to \c false. The value of each edge will be set exactly once. |
---|
67 | /// - It can also be an iteraror of an STL Container with |
---|
68 | /// <tt>GR::Edge</tt> as its <tt>value_type</tt>. |
---|
69 | /// The algorithm copies the elements of the found tree into this sequence. |
---|
70 | /// For example, if we know that the spanning tree of the graph \c g has |
---|
71 | /// say 53 edges, then |
---|
72 | /// we can put its edges into a STL vector \c tree with a code like this. |
---|
73 | ///\code |
---|
74 | /// std::vector<Edge> tree(53); |
---|
75 | /// kruskal(g,cost,tree.begin()); |
---|
76 | ///\endcode |
---|
77 | /// Or if we don't know in advance the size of the tree, we can write this. |
---|
78 | ///\code |
---|
79 | /// std::vector<Edge> tree; |
---|
80 | /// kruskal(g,cost,std::back_inserter(tree)); |
---|
81 | ///\endcode |
---|
82 | /// |
---|
83 | /// \return The cost of the found tree. |
---|
84 | /// |
---|
85 | /// \warning If kruskal is run on an |
---|
86 | /// \ref lemon::concept::UGraph "undirected graph", be sure that the |
---|
87 | /// map storing the tree is also undirected |
---|
88 | /// (e.g. ListUGraph::UEdgeMap<bool>, otherwise the values of the |
---|
89 | /// half of the edges will not be set. |
---|
90 | /// |
---|
91 | /// \todo Discuss the case of undirected graphs: In this case the algorithm |
---|
92 | /// also require <tt>Edge</tt>s instead of <tt>UEdge</tt>s, as some |
---|
93 | /// people would expect. So, one should be careful not to add both of the |
---|
94 | /// <tt>Edge</tt>s belonging to a certain <tt>UEdge</tt>. |
---|
95 | /// (\ref kruskal() and \ref KruskalMapInput are kind enough to do so.) |
---|
96 | |
---|
97 | #ifdef DOXYGEN |
---|
98 | template <class GR, class IN, class OUT> |
---|
99 | typename IN::value_type::second_type |
---|
100 | kruskal(GR const& g, IN const& in, |
---|
101 | OUT& out) |
---|
102 | #else |
---|
103 | template <class GR, class IN, class OUT> |
---|
104 | typename IN::value_type::second_type |
---|
105 | kruskal(GR const& g, IN const& in, |
---|
106 | OUT& out, |
---|
107 | // typename IN::value_type::first_type = typename GR::Edge() |
---|
108 | // ,typename OUT::Key = OUT::Key() |
---|
109 | // //,typename OUT::Key = typename GR::Edge() |
---|
110 | const typename IN::value_type::first_type * = |
---|
111 | (const typename IN::value_type::first_type *)(0), |
---|
112 | const typename OUT::Key * = (const typename OUT::Key *)(0) |
---|
113 | ) |
---|
114 | #endif |
---|
115 | { |
---|
116 | typedef typename IN::value_type::second_type EdgeCost; |
---|
117 | typedef typename GR::template NodeMap<int> NodeIntMap; |
---|
118 | typedef typename GR::Node Node; |
---|
119 | |
---|
120 | NodeIntMap comp(g, -1); |
---|
121 | UnionFind<Node,NodeIntMap> uf(comp); |
---|
122 | |
---|
123 | EdgeCost tot_cost = 0; |
---|
124 | for (typename IN::const_iterator p = in.begin(); |
---|
125 | p!=in.end(); ++p ) { |
---|
126 | if ( uf.join(g.target((*p).first), |
---|
127 | g.source((*p).first)) ) { |
---|
128 | out.set((*p).first, true); |
---|
129 | tot_cost += (*p).second; |
---|
130 | } |
---|
131 | else { |
---|
132 | out.set((*p).first, false); |
---|
133 | } |
---|
134 | } |
---|
135 | return tot_cost; |
---|
136 | } |
---|
137 | |
---|
138 | |
---|
139 | /// @} |
---|
140 | |
---|
141 | |
---|
142 | /* A work-around for running Kruskal with const-reference bool maps... */ |
---|
143 | |
---|
144 | /// Helper class for calling kruskal with "constant" output map. |
---|
145 | |
---|
146 | /// Helper class for calling kruskal with output maps constructed |
---|
147 | /// on-the-fly. |
---|
148 | /// |
---|
149 | /// A typical examle is the following call: |
---|
150 | /// <tt>kruskal(g, some_input, makeSequenceOutput(iterator))</tt>. |
---|
151 | /// Here, the third argument is a temporary object (which wraps around an |
---|
152 | /// iterator with a writable bool map interface), and thus by rules of C++ |
---|
153 | /// is a \c const object. To enable call like this exist this class and |
---|
154 | /// the prototype of the \ref kruskal() function with <tt>const& OUT</tt> |
---|
155 | /// third argument. |
---|
156 | template<class Map> |
---|
157 | class NonConstMapWr { |
---|
158 | const Map &m; |
---|
159 | public: |
---|
160 | typedef typename Map::Key Key; |
---|
161 | typedef typename Map::Value Value; |
---|
162 | |
---|
163 | NonConstMapWr(const Map &_m) : m(_m) {} |
---|
164 | |
---|
165 | template<class Key> |
---|
166 | void set(Key const& k, Value const &v) const { m.set(k,v); } |
---|
167 | }; |
---|
168 | |
---|
169 | template <class GR, class IN, class OUT> |
---|
170 | inline |
---|
171 | typename IN::value_type::second_type |
---|
172 | kruskal(GR const& g, IN const& edges, OUT const& out_map, |
---|
173 | // typename IN::value_type::first_type = typename GR::Edge(), |
---|
174 | // typename OUT::Key = GR::Edge() |
---|
175 | const typename IN::value_type::first_type * = |
---|
176 | (const typename IN::value_type::first_type *)(0), |
---|
177 | const typename OUT::Key * = (const typename OUT::Key *)(0) |
---|
178 | ) |
---|
179 | { |
---|
180 | NonConstMapWr<OUT> map_wr(out_map); |
---|
181 | return kruskal(g, edges, map_wr); |
---|
182 | } |
---|
183 | |
---|
184 | /* ** ** Input-objects ** ** */ |
---|
185 | |
---|
186 | /// Kruskal's input source. |
---|
187 | |
---|
188 | /// Kruskal's input source. |
---|
189 | /// |
---|
190 | /// In most cases you possibly want to use the \ref kruskal() instead. |
---|
191 | /// |
---|
192 | /// \sa makeKruskalMapInput() |
---|
193 | /// |
---|
194 | ///\param GR The type of the graph the algorithm runs on. |
---|
195 | ///\param Map An edge map containing the cost of the edges. |
---|
196 | ///\par |
---|
197 | ///The cost type can be any type satisfying |
---|
198 | ///the STL 'LessThan comparable' |
---|
199 | ///concept if it also has an operator+() implemented. (It is necessary for |
---|
200 | ///computing the total cost of the tree). |
---|
201 | /// |
---|
202 | template<class GR, class Map> |
---|
203 | class KruskalMapInput |
---|
204 | : public std::vector< std::pair<typename GR::Edge, |
---|
205 | typename Map::Value> > { |
---|
206 | |
---|
207 | public: |
---|
208 | typedef std::vector< std::pair<typename GR::Edge, |
---|
209 | typename Map::Value> > Parent; |
---|
210 | typedef typename Parent::value_type value_type; |
---|
211 | |
---|
212 | private: |
---|
213 | class comparePair { |
---|
214 | public: |
---|
215 | bool operator()(const value_type& a, |
---|
216 | const value_type& b) { |
---|
217 | return a.second < b.second; |
---|
218 | } |
---|
219 | }; |
---|
220 | |
---|
221 | template<class _GR> |
---|
222 | typename enable_if<UndirectedTagIndicator<_GR>,void>::type |
---|
223 | fillWithEdges(const _GR& g, const Map& m,dummy<0> = 0) |
---|
224 | { |
---|
225 | for(typename GR::UEdgeIt e(g);e!=INVALID;++e) |
---|
226 | push_back(value_type(g.direct(e, true), m[e])); |
---|
227 | } |
---|
228 | |
---|
229 | template<class _GR> |
---|
230 | typename disable_if<UndirectedTagIndicator<_GR>,void>::type |
---|
231 | fillWithEdges(const _GR& g, const Map& m,dummy<1> = 1) |
---|
232 | { |
---|
233 | for(typename GR::EdgeIt e(g);e!=INVALID;++e) |
---|
234 | push_back(value_type(e, m[e])); |
---|
235 | } |
---|
236 | |
---|
237 | |
---|
238 | public: |
---|
239 | |
---|
240 | void sort() { |
---|
241 | std::sort(this->begin(), this->end(), comparePair()); |
---|
242 | } |
---|
243 | |
---|
244 | KruskalMapInput(GR const& g, Map const& m) { |
---|
245 | fillWithEdges(g,m); |
---|
246 | sort(); |
---|
247 | } |
---|
248 | }; |
---|
249 | |
---|
250 | /// Creates a KruskalMapInput object for \ref kruskal() |
---|
251 | |
---|
252 | /// It makes easier to use |
---|
253 | /// \ref KruskalMapInput by making it unnecessary |
---|
254 | /// to explicitly give the type of the parameters. |
---|
255 | /// |
---|
256 | /// In most cases you possibly |
---|
257 | /// want to use \ref kruskal() instead. |
---|
258 | /// |
---|
259 | ///\param g The type of the graph the algorithm runs on. |
---|
260 | ///\param m An edge map containing the cost of the edges. |
---|
261 | ///\par |
---|
262 | ///The cost type can be any type satisfying the |
---|
263 | ///STL 'LessThan Comparable' |
---|
264 | ///concept if it also has an operator+() implemented. (It is necessary for |
---|
265 | ///computing the total cost of the tree). |
---|
266 | /// |
---|
267 | ///\return An appropriate input source for \ref kruskal(). |
---|
268 | /// |
---|
269 | template<class GR, class Map> |
---|
270 | inline |
---|
271 | KruskalMapInput<GR,Map> makeKruskalMapInput(const GR &g,const Map &m) |
---|
272 | { |
---|
273 | return KruskalMapInput<GR,Map>(g,m); |
---|
274 | } |
---|
275 | |
---|
276 | |
---|
277 | |
---|
278 | /* ** ** Output-objects: simple writable bool maps ** ** */ |
---|
279 | |
---|
280 | |
---|
281 | |
---|
282 | /// A writable bool-map that makes a sequence of "true" keys |
---|
283 | |
---|
284 | /// A writable bool-map that creates a sequence out of keys that receives |
---|
285 | /// the value "true". |
---|
286 | /// |
---|
287 | /// \sa makeKruskalSequenceOutput() |
---|
288 | /// |
---|
289 | /// Very often, when looking for a min cost spanning tree, we want as |
---|
290 | /// output a container containing the edges of the found tree. For this |
---|
291 | /// purpose exist this class that wraps around an STL iterator with a |
---|
292 | /// writable bool map interface. When a key gets value "true" this key |
---|
293 | /// is added to sequence pointed by the iterator. |
---|
294 | /// |
---|
295 | /// A typical usage: |
---|
296 | ///\code |
---|
297 | /// std::vector<Graph::Edge> v; |
---|
298 | /// kruskal(g, input, makeKruskalSequenceOutput(back_inserter(v))); |
---|
299 | ///\endcode |
---|
300 | /// |
---|
301 | /// For the most common case, when the input is given by a simple edge |
---|
302 | /// map and the output is a sequence of the tree edges, a special |
---|
303 | /// wrapper function exists: \ref kruskalEdgeMap_IteratorOut(). |
---|
304 | /// |
---|
305 | /// \warning Not a regular property map, as it doesn't know its Key |
---|
306 | |
---|
307 | template<class Iterator> |
---|
308 | class KruskalSequenceOutput { |
---|
309 | mutable Iterator it; |
---|
310 | |
---|
311 | public: |
---|
312 | typedef typename std::iterator_traits<Iterator>::value_type Key; |
---|
313 | typedef bool Value; |
---|
314 | |
---|
315 | KruskalSequenceOutput(Iterator const &_it) : it(_it) {} |
---|
316 | |
---|
317 | template<typename Key> |
---|
318 | void set(Key const& k, bool v) const { if(v) {*it=k; ++it;} } |
---|
319 | }; |
---|
320 | |
---|
321 | template<class Iterator> |
---|
322 | inline |
---|
323 | KruskalSequenceOutput<Iterator> |
---|
324 | makeKruskalSequenceOutput(Iterator it) { |
---|
325 | return KruskalSequenceOutput<Iterator>(it); |
---|
326 | } |
---|
327 | |
---|
328 | |
---|
329 | |
---|
330 | /* ** ** Wrapper funtions ** ** */ |
---|
331 | |
---|
332 | // \brief Wrapper function to kruskal(). |
---|
333 | // Input is from an edge map, output is a plain bool map. |
---|
334 | // |
---|
335 | // Wrapper function to kruskal(). |
---|
336 | // Input is from an edge map, output is a plain bool map. |
---|
337 | // |
---|
338 | // \param g The type of the graph the algorithm runs on. |
---|
339 | // \param in An edge map containing the cost of the edges. |
---|
340 | // \par |
---|
341 | // The cost type can be any type satisfying the |
---|
342 | // STL 'LessThan Comparable' |
---|
343 | // concept if it also has an operator+() implemented. (It is necessary for |
---|
344 | // computing the total cost of the tree). |
---|
345 | // |
---|
346 | // \retval out This must be a writable \c bool edge map. |
---|
347 | // After running the algorithm |
---|
348 | // this will contain the found minimum cost spanning tree: the value of an |
---|
349 | // edge will be set to \c true if it belongs to the tree, otherwise it will |
---|
350 | // be set to \c false. The value of each edge will be set exactly once. |
---|
351 | // |
---|
352 | // \return The cost of the found tree. |
---|
353 | |
---|
354 | template <class GR, class IN, class RET> |
---|
355 | inline |
---|
356 | typename IN::Value |
---|
357 | kruskal(GR const& g, |
---|
358 | IN const& in, |
---|
359 | RET &out, |
---|
360 | // typename IN::Key = typename GR::Edge(), |
---|
361 | //typename IN::Key = typename IN::Key (), |
---|
362 | // typename RET::Key = typename GR::Edge() |
---|
363 | const typename IN::Key * = (const typename IN::Key *)(0), |
---|
364 | const typename RET::Key * = (const typename RET::Key *)(0) |
---|
365 | ) |
---|
366 | { |
---|
367 | return kruskal(g, |
---|
368 | KruskalMapInput<GR,IN>(g,in), |
---|
369 | out); |
---|
370 | } |
---|
371 | |
---|
372 | // \brief Wrapper function to kruskal(). |
---|
373 | // Input is from an edge map, output is an STL Sequence. |
---|
374 | // |
---|
375 | // Wrapper function to kruskal(). |
---|
376 | // Input is from an edge map, output is an STL Sequence. |
---|
377 | // |
---|
378 | // \param g The type of the graph the algorithm runs on. |
---|
379 | // \param in An edge map containing the cost of the edges. |
---|
380 | // \par |
---|
381 | // The cost type can be any type satisfying the |
---|
382 | // STL 'LessThan Comparable' |
---|
383 | // concept if it also has an operator+() implemented. (It is necessary for |
---|
384 | // computing the total cost of the tree). |
---|
385 | // |
---|
386 | // \retval out This must be an iteraror of an STL Container with |
---|
387 | // <tt>GR::Edge</tt> as its <tt>value_type</tt>. |
---|
388 | // The algorithm copies the elements of the found tree into this sequence. |
---|
389 | // For example, if we know that the spanning tree of the graph \c g has |
---|
390 | // say 53 edges, then |
---|
391 | // we can put its edges into a STL vector \c tree with a code like this. |
---|
392 | //\code |
---|
393 | // std::vector<Edge> tree(53); |
---|
394 | // kruskal(g,cost,tree.begin()); |
---|
395 | //\endcode |
---|
396 | // Or if we don't know in advance the size of the tree, we can write this. |
---|
397 | //\code |
---|
398 | // std::vector<Edge> tree; |
---|
399 | // kruskal(g,cost,std::back_inserter(tree)); |
---|
400 | //\endcode |
---|
401 | // |
---|
402 | // \return The cost of the found tree. |
---|
403 | // |
---|
404 | // \bug its name does not follow the coding style. |
---|
405 | |
---|
406 | template <class GR, class IN, class RET> |
---|
407 | inline |
---|
408 | typename IN::Value |
---|
409 | kruskal(const GR& g, |
---|
410 | const IN& in, |
---|
411 | RET out, |
---|
412 | const typename RET::value_type * = |
---|
413 | (const typename RET::value_type *)(0) |
---|
414 | ) |
---|
415 | { |
---|
416 | KruskalSequenceOutput<RET> _out(out); |
---|
417 | return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out); |
---|
418 | } |
---|
419 | |
---|
420 | template <class GR, class IN, class RET> |
---|
421 | inline |
---|
422 | typename IN::Value |
---|
423 | kruskal(const GR& g, |
---|
424 | const IN& in, |
---|
425 | RET *out |
---|
426 | ) |
---|
427 | { |
---|
428 | KruskalSequenceOutput<RET*> _out(out); |
---|
429 | return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out); |
---|
430 | } |
---|
431 | |
---|
432 | /// @} |
---|
433 | |
---|
434 | } //namespace lemon |
---|
435 | |
---|
436 | #endif //LEMON_KRUSKAL_H |
---|