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_FREDMAN_TARJAN_H |
---|
20 | #define LEMON_FREDMAN_TARJAN_H |
---|
21 | |
---|
22 | ///\ingroup spantree |
---|
23 | ///\file |
---|
24 | ///\brief FredmanTarjan algorithm to compute minimum spanning forest. |
---|
25 | |
---|
26 | #include <limits> |
---|
27 | #include <vector> |
---|
28 | |
---|
29 | #include <lemon/list_graph.h> |
---|
30 | #include <lemon/smart_graph.h> |
---|
31 | #include <lemon/fib_heap.h> |
---|
32 | #include <lemon/radix_sort.h> |
---|
33 | #include <lemon/bits/invalid.h> |
---|
34 | #include <lemon/error.h> |
---|
35 | #include <lemon/maps.h> |
---|
36 | #include <lemon/bits/traits.h> |
---|
37 | #include <lemon/graph_utils.h> |
---|
38 | |
---|
39 | #include <lemon/concept/ugraph.h> |
---|
40 | |
---|
41 | namespace lemon { |
---|
42 | |
---|
43 | ///Default traits class of FredmanTarjan class. |
---|
44 | |
---|
45 | ///Default traits class of FredmanTarjan class. |
---|
46 | ///\param GR Graph type. |
---|
47 | ///\param CM Type of cost map. |
---|
48 | template<class GR, class CM> |
---|
49 | struct FredmanTarjanDefaultTraits{ |
---|
50 | ///The graph type the algorithm runs on. |
---|
51 | typedef GR UGraph; |
---|
52 | ///The type of the map that stores the edge costs. |
---|
53 | |
---|
54 | ///The type of the map that stores the edge costs. |
---|
55 | ///It must meet the \ref concept::ReadMap "ReadMap" concept. |
---|
56 | typedef CM CostMap; |
---|
57 | //The type of the cost of the edges. |
---|
58 | typedef typename CM::Value Value; |
---|
59 | ///The type of the map that stores whether an edge is in the |
---|
60 | ///spanning tree or not. |
---|
61 | |
---|
62 | ///The type of the map that stores whether an edge is in the |
---|
63 | ///spanning tree or not. |
---|
64 | ///It must meet the \ref concept::ReadWriteMap "ReadWriteMap" concept. |
---|
65 | ///By default it is a BoolEdgeMap. |
---|
66 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
---|
67 | ///Instantiates a TreeMap. |
---|
68 | |
---|
69 | ///This function instantiates a \ref TreeMap. |
---|
70 | ///\param _graph is the graph, to which |
---|
71 | ///we would like to define the \ref TreeMap |
---|
72 | static TreeMap *createTreeMap(const GR &_graph){ |
---|
73 | return new TreeMap(_graph); |
---|
74 | } |
---|
75 | }; |
---|
76 | |
---|
77 | ///%FredmanTarjan algorithm class to find a minimum spanning tree. |
---|
78 | |
---|
79 | /// \ingroup spantree |
---|
80 | /// |
---|
81 | ///This class provides an efficient implementation of %FredmanTarjan |
---|
82 | ///algorithm whitch is sometimes a bit quicker than the Prim |
---|
83 | ///algorithm on larger graphs. Due to the structure of the |
---|
84 | ///algorithm, it has less controll functions than Prim. |
---|
85 | /// |
---|
86 | /// The running time is \f$ O(e\beta(e,n)) \f$ where |
---|
87 | /// \f$ \beta(e,n) = \min\{ i | \log^{i}(n) \le e/n\} \f$ and |
---|
88 | /// \f$ \log^{i+1}(n)=\log(\log^{i}(n)) \f$ |
---|
89 | /// |
---|
90 | ///The edge costs are passed to the algorithm using a \ref |
---|
91 | ///concept::ReadMap "ReadMap", so it is easy to change it to any |
---|
92 | ///kind of cost. |
---|
93 | /// |
---|
94 | ///The type of the cost is determined by the \ref |
---|
95 | ///concept::ReadMap::Value "Value" of the cost map. |
---|
96 | /// |
---|
97 | ///\param GR The graph type the algorithm runs on. The default value |
---|
98 | ///is \ref ListUGraph. The value of GR is not used directly by |
---|
99 | ///FredmanTarjan, it is only passed to \ref |
---|
100 | ///FredmanTarjanDefaultTraits. |
---|
101 | /// |
---|
102 | ///\param CM This read-only UEdgeMap determines the costs of the |
---|
103 | ///edges. It is read once for each edge, so the map may involve in |
---|
104 | ///relatively time consuming process to compute the edge cost if it |
---|
105 | ///is necessary. The default map type is \ref |
---|
106 | ///concept::UGraph::UEdgeMap "UGraph::UEdgeMap<int>". The value of |
---|
107 | ///CM is not used directly by FredmanTarjan, it is only passed to |
---|
108 | ///\ref FredmanTarjanDefaultTraits. |
---|
109 | /// |
---|
110 | ///\param TR Traits class to set various data types used by the |
---|
111 | ///algorithm. The default traits class is \ref |
---|
112 | ///FredmanTarjanDefaultTraits "FredmanTarjanDefaultTraits<GR,CM>". |
---|
113 | ///See \ref FredmanTarjanDefaultTraits for the documentation of a |
---|
114 | ///FredmanTarjan traits class. |
---|
115 | /// |
---|
116 | ///\author Balazs Attila Mihaly |
---|
117 | |
---|
118 | #ifdef DOXYGEN |
---|
119 | template <typename GR, |
---|
120 | typename CM, |
---|
121 | typename TR> |
---|
122 | #else |
---|
123 | template <typename GR=ListUGraph, |
---|
124 | typename CM=typename GR::template UEdgeMap<int>, |
---|
125 | typename TR=FredmanTarjanDefaultTraits<GR,CM> > |
---|
126 | #endif |
---|
127 | class FredmanTarjan { |
---|
128 | public: |
---|
129 | ///\brief \ref Exception for uninitialized parameters. |
---|
130 | /// |
---|
131 | ///This error represents problems in the initialization |
---|
132 | ///of the parameters of the algorithms. |
---|
133 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
134 | public: |
---|
135 | virtual const char* what() const throw() { |
---|
136 | return "lemon::FredmanTarjan::UninitializedParameter"; |
---|
137 | } |
---|
138 | }; |
---|
139 | |
---|
140 | typedef GR Graph; |
---|
141 | typedef TR Traits; |
---|
142 | ///The type of the underlying graph. |
---|
143 | typedef typename TR::UGraph UGraph; |
---|
144 | ///\e |
---|
145 | typedef typename UGraph::Node Node; |
---|
146 | ///\e |
---|
147 | typedef typename UGraph::NodeIt NodeIt; |
---|
148 | ///\e |
---|
149 | typedef typename UGraph::UEdge UEdge; |
---|
150 | ///\e |
---|
151 | typedef typename UGraph::UEdgeIt UEdgeIt; |
---|
152 | ///\e |
---|
153 | typedef typename UGraph::IncEdgeIt IncEdgeIt; |
---|
154 | |
---|
155 | ///The type of the cost of the edges. |
---|
156 | typedef typename TR::CostMap::Value Value; |
---|
157 | ///The type of the map that stores the edge costs. |
---|
158 | typedef typename TR::CostMap CostMap; |
---|
159 | ///Edges of the spanning tree. |
---|
160 | typedef typename TR::TreeMap TreeMap; |
---|
161 | private: |
---|
162 | ///Pointer to the underlying graph. |
---|
163 | const UGraph *graph; |
---|
164 | ///Pointer to the cost map |
---|
165 | const CostMap *cost; |
---|
166 | ///Pointer to the map of tree edges. |
---|
167 | TreeMap *_tree; |
---|
168 | ///Indicates if \ref _tree is locally allocated (\c true) or not. |
---|
169 | bool local_tree; |
---|
170 | |
---|
171 | ///Creates the maps if necessary. |
---|
172 | |
---|
173 | void create_maps(){ |
---|
174 | if(!_tree){ |
---|
175 | local_tree=true; |
---|
176 | _tree=Traits::createTreeMap(*graph); |
---|
177 | } |
---|
178 | } |
---|
179 | |
---|
180 | public : |
---|
181 | |
---|
182 | typedef FredmanTarjan Create; |
---|
183 | |
---|
184 | ///\name Named template parameters |
---|
185 | |
---|
186 | ///@{ |
---|
187 | |
---|
188 | template <class TM> |
---|
189 | struct DefTreeMapTraits : public Traits { |
---|
190 | typedef TM TreeMap; |
---|
191 | static TreeMap *createTreeMap(const UGraph &) { |
---|
192 | throw UninitializedParameter(); |
---|
193 | } |
---|
194 | }; |
---|
195 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
---|
196 | |
---|
197 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
---|
198 | /// |
---|
199 | template <class TM> |
---|
200 | struct DefTreeMap |
---|
201 | : public FredmanTarjan< UGraph, CostMap, DefTreeMapTraits<TM> > { |
---|
202 | typedef FredmanTarjan< UGraph, CostMap, DefTreeMapTraits<TM> > Create; |
---|
203 | }; |
---|
204 | |
---|
205 | ///@} |
---|
206 | |
---|
207 | |
---|
208 | protected: |
---|
209 | |
---|
210 | FredmanTarjan() {} |
---|
211 | |
---|
212 | private: |
---|
213 | |
---|
214 | template<class SrcGraph,class OrigMap,class Heap,class HeapCrossRef, |
---|
215 | class ProcessedMap,class PredMap> |
---|
216 | void processNextTree(const SrcGraph& graph,const OrigMap& orig, |
---|
217 | Heap &heap, HeapCrossRef& crossref, |
---|
218 | ProcessedMap& processed,PredMap& pred, |
---|
219 | int& tree_counter,const int limit){ |
---|
220 | std::vector<typename SrcGraph::Node> tree_nodes; |
---|
221 | int tree_index=tree_counter; |
---|
222 | bool stop=false; |
---|
223 | while(!heap.empty() && !stop){ |
---|
224 | typename SrcGraph::Node v=heap.top(); |
---|
225 | heap.pop(); |
---|
226 | if(processed[v]!=-1){ |
---|
227 | heap.state(v,Heap::PRE_HEAP); |
---|
228 | tree_index=processed[v]; |
---|
229 | _tree->set(orig[pred[v]],true); |
---|
230 | stop=true; |
---|
231 | break; |
---|
232 | } |
---|
233 | tree_nodes.push_back(v); |
---|
234 | for(typename SrcGraph::IncEdgeIt e(graph,v);e!=INVALID;++e){ |
---|
235 | typename SrcGraph::Node w=graph.oppositeNode(v,e); |
---|
236 | switch(heap.state(w)){ |
---|
237 | case Heap::PRE_HEAP: |
---|
238 | if(heap.size()>=limit){ |
---|
239 | stop=true; |
---|
240 | } |
---|
241 | else{ |
---|
242 | heap.push(w,(*cost)[orig[e]]); |
---|
243 | pred.set(w,e); |
---|
244 | } |
---|
245 | break; |
---|
246 | case Heap::IN_HEAP: |
---|
247 | if ((*cost)[orig[e]]<heap[w]){ |
---|
248 | heap.decrease(w,(*cost)[orig[e]]); |
---|
249 | pred.set(w,e); |
---|
250 | } |
---|
251 | break; |
---|
252 | case Heap::POST_HEAP: |
---|
253 | break; |
---|
254 | } |
---|
255 | } |
---|
256 | } |
---|
257 | for(int i=1;i<(int)tree_nodes.size();++i){ |
---|
258 | _tree->set(orig[pred[tree_nodes[i]]],true); |
---|
259 | processed.set(tree_nodes[i],tree_index); |
---|
260 | crossref[tree_nodes[i]] = Heap::PRE_HEAP; |
---|
261 | } |
---|
262 | processed.set(tree_nodes[0],tree_index); |
---|
263 | crossref[tree_nodes[0]] = Heap::PRE_HEAP; |
---|
264 | while (!heap.empty()) { |
---|
265 | typename SrcGraph::Node v=heap.top(); |
---|
266 | heap.pop(); |
---|
267 | crossref[v] = Heap::PRE_HEAP; |
---|
268 | } |
---|
269 | heap.clear(); |
---|
270 | if(!stop)++tree_counter; |
---|
271 | } |
---|
272 | |
---|
273 | template<class SrcGraph,class OrigMap,class ProcessedMap> |
---|
274 | void createTrees(const SrcGraph& graph, const OrigMap& orig, |
---|
275 | ProcessedMap& processed, |
---|
276 | int edgenum,int& tree_counter){ |
---|
277 | typedef typename SrcGraph::Node Node; |
---|
278 | typedef typename SrcGraph::UEdge UEdge; |
---|
279 | typedef typename SrcGraph::NodeIt NodeIt; |
---|
280 | typedef typename SrcGraph::template NodeMap<int> HeapCrossRef; |
---|
281 | typedef typename SrcGraph::template NodeMap<UEdge> PredMap; |
---|
282 | HeapCrossRef crossref(graph,-1); |
---|
283 | FibHeap<Node,Value,HeapCrossRef> heap(crossref); |
---|
284 | PredMap pred(graph,INVALID); |
---|
285 | int rate=2*edgenum/countNodes(graph); |
---|
286 | int limit=(rate>std::numeric_limits<int>::digits)? |
---|
287 | std::numeric_limits<int>::max() : (1<<rate); |
---|
288 | for(NodeIt i(graph);i!=INVALID;++i){ |
---|
289 | if(processed[i]==-1){ |
---|
290 | heap.push(i, Value()); |
---|
291 | processNextTree(graph,orig,heap,crossref, |
---|
292 | processed,pred,tree_counter,limit); |
---|
293 | } |
---|
294 | } |
---|
295 | } |
---|
296 | |
---|
297 | template<class SrcGraph,class DestGraph,class SrcOrigMap, |
---|
298 | class DestOrigMap,class ProcessedMap> |
---|
299 | void collect(const SrcGraph& srcgraph,const SrcOrigMap& srcorig, |
---|
300 | DestGraph& destgraph,DestOrigMap& destorig, |
---|
301 | const ProcessedMap& processed,const int tree_counter){ |
---|
302 | typedef typename SrcGraph::Node Node; |
---|
303 | typedef typename DestGraph::Node DNode; |
---|
304 | typedef typename SrcGraph::UEdge UEdge; |
---|
305 | typedef typename DestGraph::UEdge DUEdge; |
---|
306 | typedef typename SrcGraph::Edge Edge; |
---|
307 | typedef typename SrcGraph::EdgeIt EdgeIt; |
---|
308 | std::vector<Edge> edges; |
---|
309 | std::vector<DNode> nodes(tree_counter, INVALID); |
---|
310 | for(EdgeIt i(srcgraph);i!=INVALID;++i){ |
---|
311 | if(processed[srcgraph.source(i)]<processed[srcgraph.target(i)]){ |
---|
312 | edges.push_back(i); |
---|
313 | if(nodes[processed[srcgraph.source(i)]]==INVALID) { |
---|
314 | nodes[processed[srcgraph.source(i)]]=destgraph.addNode(); |
---|
315 | } |
---|
316 | if(nodes[processed[srcgraph.target(i)]]==INVALID) { |
---|
317 | nodes[processed[srcgraph.target(i)]]=destgraph.addNode(); |
---|
318 | } |
---|
319 | } |
---|
320 | } |
---|
321 | |
---|
322 | radixSort(edges.begin(),edges.end(), |
---|
323 | mapFunctor(composeMap(processed,sourceMap(srcgraph)))); |
---|
324 | counterSort(edges.begin(),edges.end(), |
---|
325 | mapFunctor(composeMap(processed,targetMap(srcgraph)))); |
---|
326 | for(int i=0;i!=(int)edges.size();++i){ |
---|
327 | int srcproc=processed[srcgraph.source(edges[i])]; |
---|
328 | int trgproc=processed[srcgraph.target(edges[i])]; |
---|
329 | Value minval=(*cost)[srcorig[edges[i]]]; |
---|
330 | UEdge minpos=edges[i]; |
---|
331 | while (i+1!=(int)edges.size() && |
---|
332 | srcproc==processed[srcgraph.source(edges[i+1])] && |
---|
333 | trgproc==processed[srcgraph.target(edges[i+1])]) { |
---|
334 | if (minval>(*cost)[srcorig[edges[i+1]]]) { |
---|
335 | minval=(*cost)[srcorig[edges[i+1]]]; |
---|
336 | minpos=edges[i+1]; |
---|
337 | } |
---|
338 | ++i; |
---|
339 | } |
---|
340 | destorig[destgraph.addEdge(nodes[srcproc],nodes[trgproc])]= |
---|
341 | srcorig[minpos]; |
---|
342 | } |
---|
343 | } |
---|
344 | |
---|
345 | template<class SrcGraph,class OrigMap> |
---|
346 | void phase(const SrcGraph& graph,const OrigMap& orig,int edgenum){ |
---|
347 | int tree_counter = 0; |
---|
348 | typename SrcGraph::template NodeMap<int> processed(graph,-1); |
---|
349 | SmartUGraph destgraph; |
---|
350 | SmartUGraph::UEdgeMap<typename OrigMap::Value> destorig(destgraph); |
---|
351 | createTrees(graph,orig,processed,edgenum,tree_counter); |
---|
352 | collect(graph,orig,destgraph,destorig,processed,tree_counter); |
---|
353 | if (countNodes(destgraph)>1) { |
---|
354 | phase(destgraph,destorig,edgenum); |
---|
355 | } |
---|
356 | } |
---|
357 | |
---|
358 | public: |
---|
359 | |
---|
360 | ///Constructor. |
---|
361 | |
---|
362 | ///\param _graph the graph the algorithm will run on. |
---|
363 | ///\param _cost the cost map used by the algorithm. |
---|
364 | FredmanTarjan(const UGraph& _graph, const CostMap& _cost) : |
---|
365 | graph(&_graph), cost(&_cost), |
---|
366 | _tree(0), local_tree(false) |
---|
367 | { |
---|
368 | checkConcept<concept::UGraph, UGraph>(); |
---|
369 | } |
---|
370 | |
---|
371 | ///Destructor. |
---|
372 | ~FredmanTarjan(){ |
---|
373 | if(local_tree) delete _tree; |
---|
374 | } |
---|
375 | |
---|
376 | ///Sets the cost map. |
---|
377 | |
---|
378 | ///Sets the cost map. |
---|
379 | ///\return <tt> (*this) </tt> |
---|
380 | FredmanTarjan &costMap(const CostMap &m){ |
---|
381 | cost = &m; |
---|
382 | return *this; |
---|
383 | } |
---|
384 | |
---|
385 | ///Sets the map storing the tree edges. |
---|
386 | |
---|
387 | ///Sets the map storing the tree edges. |
---|
388 | ///If you don't use this function before calling \ref run(), |
---|
389 | ///it will allocate one. The destuctor deallocates this |
---|
390 | ///automatically allocated map, of course. |
---|
391 | ///By default this is a BoolEdgeMap. |
---|
392 | ///\return <tt> (*this) </tt> |
---|
393 | FredmanTarjan &treeMap(TreeMap &m){ |
---|
394 | if(local_tree) { |
---|
395 | delete _tree; |
---|
396 | local_tree=false; |
---|
397 | } |
---|
398 | _tree = &m; |
---|
399 | return *this; |
---|
400 | } |
---|
401 | |
---|
402 | public: |
---|
403 | ///\name Execution control |
---|
404 | ///The simplest way to execute the algorithm is to use |
---|
405 | ///one of the member functions called \c run(...). |
---|
406 | |
---|
407 | ///@{ |
---|
408 | |
---|
409 | ///Initializes the internal data structures. |
---|
410 | |
---|
411 | ///Initializes the internal data structures. |
---|
412 | /// |
---|
413 | void init(){ |
---|
414 | create_maps(); |
---|
415 | for(typename Graph::UEdgeIt i(*graph);i!=INVALID;++i){ |
---|
416 | _tree->set(i,false); |
---|
417 | } |
---|
418 | } |
---|
419 | |
---|
420 | ///Executes the algorithm. |
---|
421 | |
---|
422 | ///Executes the algorithm. |
---|
423 | /// |
---|
424 | ///\pre init() must be called and at least one node should be added |
---|
425 | ///with addSource() before using this function. |
---|
426 | /// |
---|
427 | ///This method runs the %FredmanTarjan algorithm from the node(s) |
---|
428 | ///in order to compute the |
---|
429 | ///minimum spanning tree. |
---|
430 | void start(){ |
---|
431 | phase(*graph,identityMap<UEdge>(),countEdges(*graph)); |
---|
432 | } |
---|
433 | |
---|
434 | ///Runs %FredmanTarjan algorithm. |
---|
435 | |
---|
436 | ///This method runs the %FredmanTarjan algorithm |
---|
437 | ///in order to compute the minimum spanning forest. |
---|
438 | /// |
---|
439 | ///\note ft.run() is just a shortcut of the following code. |
---|
440 | ///\code |
---|
441 | /// ft.init(); |
---|
442 | /// ft.start(); |
---|
443 | ///\endcode |
---|
444 | void run() { |
---|
445 | init(); |
---|
446 | start(); |
---|
447 | } |
---|
448 | |
---|
449 | ///@} |
---|
450 | |
---|
451 | ///\name Query Functions |
---|
452 | ///The result of the %FredmanTarjan algorithm can be obtained using these |
---|
453 | ///functions.\n |
---|
454 | ///Before the use of these functions, |
---|
455 | ///either run() or start() must be called. |
---|
456 | |
---|
457 | ///@{ |
---|
458 | |
---|
459 | ///Returns a reference to the tree edges map. |
---|
460 | |
---|
461 | ///Returns a reference to the TreeEdgeMap of the edges of the |
---|
462 | ///minimum spanning tree. The value of the map is \c true only if the |
---|
463 | ///edge is in the minimum spanning tree. |
---|
464 | /// |
---|
465 | ///\pre \ref run() or \ref start() must be called before using this |
---|
466 | ///function. |
---|
467 | const TreeMap &treeMap() const { return *_tree;} |
---|
468 | |
---|
469 | ///Sets the tree edges map. |
---|
470 | |
---|
471 | ///Sets the TreeMap of the edges of the minimum spanning tree. |
---|
472 | ///The map values belonging to the edges of the minimum |
---|
473 | ///spanning tree are set to \c tree_edge_value or \c true by default |
---|
474 | ///while the edge values not belonging to the minimum spanning tree are |
---|
475 | ///set to |
---|
476 | ///\c tree_default_value or \c false by default. |
---|
477 | /// |
---|
478 | ///\pre \ref run() or \ref start() must be called before using this |
---|
479 | ///function. |
---|
480 | |
---|
481 | template<class TreeMap> |
---|
482 | void treeEdges( |
---|
483 | TreeMap& tree, |
---|
484 | const typename TreeMap::Value& tree_edge_value=true, |
---|
485 | const typename TreeMap::Value& tree_default_value=false) const { |
---|
486 | for(typename UGraph::UEdgeIt i(*graph);i!=INVALID;++i){ |
---|
487 | (*_tree)[i]?tree.set(i,tree_edge_value):tree.set(i,tree_default_value); |
---|
488 | } |
---|
489 | } |
---|
490 | |
---|
491 | ///\brief Checks if an edge is in the spanning tree or not. |
---|
492 | |
---|
493 | ///Checks if an edge is in the spanning tree or not. |
---|
494 | ///\param e is the edge that will be checked |
---|
495 | ///\return \c true if e is in the spanning tree, \c false otherwise |
---|
496 | bool tree(UEdge e){ |
---|
497 | return (*_tree)[e]; |
---|
498 | } |
---|
499 | ///@} |
---|
500 | }; |
---|
501 | |
---|
502 | /// \ingroup spantree |
---|
503 | /// |
---|
504 | /// \brief Function type interface for FredmanTarjan algorithm. |
---|
505 | /// |
---|
506 | /// Function type interface for FredmanTarjan algorithm. |
---|
507 | /// \param graph the UGraph that the algorithm runs on |
---|
508 | /// \param cost the CostMap of the edges |
---|
509 | /// \retval tree the EdgeMap that contains whether an edge is in the |
---|
510 | /// spanning tree or not |
---|
511 | /// |
---|
512 | /// \sa Prim |
---|
513 | template<class Graph,class CostMap,class TreeMap> |
---|
514 | void fredmanTarjan(const Graph& graph, const CostMap& cost,TreeMap& tree){ |
---|
515 | typename FredmanTarjan<Graph,CostMap>::template DefTreeMap<TreeMap>:: |
---|
516 | Create ft(graph,cost); |
---|
517 | ft.treeMap(tree); |
---|
518 | ft.run(); |
---|
519 | } |
---|
520 | |
---|
521 | } //END OF NAMESPACE LEMON |
---|
522 | |
---|
523 | #endif |
---|