Fixed the mailinglist link and removed the gui section.
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2006
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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.
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
19 #ifndef LEMON_KRUSKAL_H
20 #define LEMON_KRUSKAL_H
24 #include <lemon/unionfind.h>
25 #include <lemon/bits/utility.h>
26 #include <lemon/bits/traits.h>
30 ///\brief Kruskal's algorithm to compute a minimum cost tree
32 ///Kruskal's algorithm to compute a minimum cost tree.
34 ///\todo The file still needs some clean-up.
38 /// \addtogroup spantree
41 /// Kruskal's algorithm to find a minimum cost tree of a graph.
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.
46 /// \param g The graph the algorithm runs on.
47 /// It can be either \ref concept::Graph "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.
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.
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.
74 /// std::vector<Edge> tree(53);
75 /// kruskal(g,cost,tree.begin());
77 /// Or if we don't know in advance the size of the tree, we can write this.
79 /// std::vector<Edge> tree;
80 /// kruskal(g,cost,std::back_inserter(tree));
83 /// \return The cost of the found tree.
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.
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.)
98 template <class GR, class IN, class OUT>
99 typename IN::value_type::second_type
100 kruskal(GR const& g, IN const& in,
103 template <class GR, class IN, class OUT>
104 typename IN::value_type::second_type
105 kruskal(GR const& g, IN const& in,
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)
116 typedef typename IN::value_type::second_type EdgeCost;
117 typedef typename GR::template NodeMap<int> NodeIntMap;
118 typedef typename GR::Node Node;
120 NodeIntMap comp(g, -1);
121 UnionFind<Node,NodeIntMap> uf(comp);
123 EdgeCost tot_cost = 0;
124 for (typename IN::const_iterator p = in.begin();
126 if ( uf.join(g.target((*p).first),
127 g.source((*p).first)) ) {
128 out.set((*p).first, true);
129 tot_cost += (*p).second;
132 out.set((*p).first, false);
142 /* A work-around for running Kruskal with const-reference bool maps... */
144 /// Helper class for calling kruskal with "constant" output map.
146 /// Helper class for calling kruskal with output maps constructed
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>
157 class NonConstMapWr {
160 typedef typename Map::Key Key;
161 typedef typename Map::Value Value;
163 NonConstMapWr(const Map &_m) : m(_m) {}
166 void set(Key const& k, Value const &v) const { m.set(k,v); }
169 template <class GR, class IN, class OUT>
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)
180 NonConstMapWr<OUT> map_wr(out_map);
181 return kruskal(g, edges, map_wr);
184 /* ** ** Input-objects ** ** */
186 /// Kruskal's input source.
188 /// Kruskal's input source.
190 /// In most cases you possibly want to use the \ref kruskal() instead.
192 /// \sa makeKruskalMapInput()
194 ///\param GR The type of the graph the algorithm runs on.
195 ///\param Map An edge map containing the cost of the edges.
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).
202 template<class GR, class Map>
203 class KruskalMapInput
204 : public std::vector< std::pair<typename GR::Edge,
205 typename Map::Value> > {
208 typedef std::vector< std::pair<typename GR::Edge,
209 typename Map::Value> > Parent;
210 typedef typename Parent::value_type value_type;
215 bool operator()(const value_type& a,
216 const value_type& b) {
217 return a.second < b.second;
222 typename enable_if<UndirectedTagIndicator<_GR>,void>::type
223 fillWithEdges(const _GR& g, const Map& m,dummy<0> = 0)
225 for(typename GR::UEdgeIt e(g);e!=INVALID;++e)
226 push_back(value_type(g.direct(e, true), m[e]));
230 typename disable_if<UndirectedTagIndicator<_GR>,void>::type
231 fillWithEdges(const _GR& g, const Map& m,dummy<1> = 1)
233 for(typename GR::EdgeIt e(g);e!=INVALID;++e)
234 push_back(value_type(e, m[e]));
241 std::sort(this->begin(), this->end(), comparePair());
244 KruskalMapInput(GR const& g, Map const& m) {
250 /// Creates a KruskalMapInput object for \ref kruskal()
252 /// It makes easier to use
253 /// \ref KruskalMapInput by making it unnecessary
254 /// to explicitly give the type of the parameters.
256 /// In most cases you possibly
257 /// want to use \ref kruskal() instead.
259 ///\param g The type of the graph the algorithm runs on.
260 ///\param m An edge map containing the cost of the edges.
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).
267 ///\return An appropriate input source for \ref kruskal().
269 template<class GR, class Map>
271 KruskalMapInput<GR,Map> makeKruskalMapInput(const GR &g,const Map &m)
273 return KruskalMapInput<GR,Map>(g,m);
278 /* ** ** Output-objects: simple writable bool maps ** ** */
282 /// A writable bool-map that makes a sequence of "true" keys
284 /// A writable bool-map that creates a sequence out of keys that receives
285 /// the value "true".
287 /// \sa makeKruskalSequenceOutput()
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.
297 /// std::vector<Graph::Edge> v;
298 /// kruskal(g, input, makeKruskalSequenceOutput(back_inserter(v)));
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().
305 /// \warning Not a regular property map, as it doesn't know its Key
307 template<class Iterator>
308 class KruskalSequenceOutput {
312 typedef typename std::iterator_traits<Iterator>::value_type Key;
315 KruskalSequenceOutput(Iterator const &_it) : it(_it) {}
317 template<typename Key>
318 void set(Key const& k, bool v) const { if(v) {*it=k; ++it;} }
321 template<class Iterator>
323 KruskalSequenceOutput<Iterator>
324 makeKruskalSequenceOutput(Iterator it) {
325 return KruskalSequenceOutput<Iterator>(it);
330 /* ** ** Wrapper funtions ** ** */
332 // \brief Wrapper function to kruskal().
333 // Input is from an edge map, output is a plain bool map.
335 // Wrapper function to kruskal().
336 // Input is from an edge map, output is a plain bool map.
338 // \param g The type of the graph the algorithm runs on.
339 // \param in An edge map containing the cost of the edges.
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).
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.
352 // \return The cost of the found tree.
354 template <class GR, class IN, class RET>
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)
368 KruskalMapInput<GR,IN>(g,in),
372 // \brief Wrapper function to kruskal().
373 // Input is from an edge map, output is an STL Sequence.
375 // Wrapper function to kruskal().
376 // Input is from an edge map, output is an STL Sequence.
378 // \param g The type of the graph the algorithm runs on.
379 // \param in An edge map containing the cost of the edges.
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).
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.
393 // std::vector<Edge> tree(53);
394 // kruskal(g,cost,tree.begin());
396 // Or if we don't know in advance the size of the tree, we can write this.
398 // std::vector<Edge> tree;
399 // kruskal(g,cost,std::back_inserter(tree));
402 // \return The cost of the found tree.
404 // \bug its name does not follow the coding style.
406 template <class GR, class IN, class RET>
412 const typename RET::value_type * =
413 (const typename RET::value_type *)(0)
416 KruskalSequenceOutput<RET> _out(out);
417 return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out);
420 template <class GR, class IN, class RET>
428 KruskalSequenceOutput<RET*> _out(out);
429 return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out);
436 #endif //LEMON_KRUSKAL_H