1 | // -*- C++ -*- |
---|
2 | #ifndef LEMON_MAX_MATCHING_H |
---|
3 | #define LEMON_MAX_MATCHING_H |
---|
4 | |
---|
5 | ///\ingroup galgs |
---|
6 | ///\file |
---|
7 | ///\brief Maximum matching algorithm. |
---|
8 | |
---|
9 | #include <queue> |
---|
10 | |
---|
11 | #include <invalid.h> |
---|
12 | #include <unionfind.h> |
---|
13 | |
---|
14 | namespace lemon { |
---|
15 | |
---|
16 | /// \addtogroup galgs |
---|
17 | /// @{ |
---|
18 | |
---|
19 | ///Maximum matching algorithms class. |
---|
20 | |
---|
21 | ///This class provides Edmonds' alternating forest matching |
---|
22 | ///algorithm. The starting matching (if any) can be passed to the |
---|
23 | ///algorithm using read-in functions \ref readNMapNode, \ref |
---|
24 | ///readNMapEdge or \ref readEMapBool depending on the container. The |
---|
25 | ///resulting maximum matching can be attained by write-out functions |
---|
26 | ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool |
---|
27 | ///depending on the preferred container. |
---|
28 | /// |
---|
29 | ///The dual side of a mathcing is a map of the nodes to |
---|
30 | ///MaxMatching::pos_enum, having values D, A and C showing the |
---|
31 | ///Gallai-Edmonds decomposition of the graph. The nodes in D induce |
---|
32 | ///a graph with factor-critical components, the nodes in A form the |
---|
33 | ///barrier, and the nodes in C induce a graph having a perfect |
---|
34 | ///matching. This decomposition can be attained by calling \ref |
---|
35 | ///writePos after running the algorithm. Before subsequent runs, |
---|
36 | ///the function \ref resetPos() must be called. |
---|
37 | /// |
---|
38 | ///\param Graph The undirected graph type the algorithm runs on. |
---|
39 | /// |
---|
40 | ///\author Jacint Szabo |
---|
41 | template <typename Graph> |
---|
42 | class MaxMatching { |
---|
43 | typedef typename Graph::Node Node; |
---|
44 | typedef typename Graph::Edge Edge; |
---|
45 | typedef typename Graph::EdgeIt EdgeIt; |
---|
46 | typedef typename Graph::NodeIt NodeIt; |
---|
47 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
48 | |
---|
49 | typedef UnionFindEnum<Node, Graph::template NodeMap> UFE; |
---|
50 | |
---|
51 | public: |
---|
52 | |
---|
53 | ///Indicates the Gallai-Edmonds decomposition of the graph. |
---|
54 | |
---|
55 | ///Indicates the Gallai-Edmonds decomposition of the graph, which |
---|
56 | ///shows an upper bound on the size of a maximum matching. The |
---|
57 | ///nodes with pos_enum \c D induce a graph with factor-critical |
---|
58 | ///components, the nodes in \c A form the canonical barrier, and the |
---|
59 | ///nodes in \c C induce a graph having a perfect matching. |
---|
60 | enum pos_enum { |
---|
61 | D=0, |
---|
62 | A=1, |
---|
63 | C=2 |
---|
64 | }; |
---|
65 | |
---|
66 | private: |
---|
67 | |
---|
68 | const Graph& G; |
---|
69 | typename Graph::template NodeMap<Node> mate; |
---|
70 | typename Graph::template NodeMap<pos_enum> position; |
---|
71 | |
---|
72 | public: |
---|
73 | |
---|
74 | MaxMatching(const Graph& _G) : G(_G), mate(_G,INVALID), position(_G,C) {} |
---|
75 | |
---|
76 | ///Runs Edmonds' algorithm. |
---|
77 | |
---|
78 | ///Runs Edmonds' algorithm for sparse graphs (edgeNum >= |
---|
79 | ///2*nodeNum), and a heuristical Edmonds' algorithm with a |
---|
80 | ///heuristic of postponing shrinks for dense graphs. \pre Before |
---|
81 | ///the subsequent calls \ref resetPos must be called. |
---|
82 | inline void run(); |
---|
83 | |
---|
84 | ///Runs Edmonds' algorithm. |
---|
85 | |
---|
86 | ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs |
---|
87 | ///Edmonds' algorithm with a heuristic of postponing shrinks, |
---|
88 | ///giving a faster algorithm for dense graphs. \pre Before the |
---|
89 | ///subsequent calls \ref resetPos must be called. |
---|
90 | void runEdmonds( int heur ); |
---|
91 | |
---|
92 | ///Finds a greedy matching starting from the actual matching. |
---|
93 | |
---|
94 | ///Starting form the actual matching stored, it finds a maximal |
---|
95 | ///greedy matching. |
---|
96 | void greedyMatching(); |
---|
97 | |
---|
98 | ///Returns the size of the actual matching stored. |
---|
99 | |
---|
100 | ///Returns the size of the actual matching stored. After \ref |
---|
101 | ///run() it returns the size of a maximum matching in the graph. |
---|
102 | int size () const; |
---|
103 | |
---|
104 | ///Resets the map storing the Gallai-Edmonds decomposition. |
---|
105 | |
---|
106 | ///Resets the map storing the Gallai-Edmonds decomposition of the |
---|
107 | ///graph, making it possible to run the algorithm. Must be called |
---|
108 | ///before all runs of the Edmonds algorithm, except for the first |
---|
109 | ///run. |
---|
110 | void resetPos(); |
---|
111 | |
---|
112 | ///Resets the actual matching to the empty matching. |
---|
113 | |
---|
114 | ///Resets the actual matching to the empty matching. |
---|
115 | /// |
---|
116 | void resetMatching(); |
---|
117 | |
---|
118 | ///Reads a matching from a \c Node map of \c Nodes. |
---|
119 | |
---|
120 | ///Reads a matching from a \c Node map of \c Nodes. This map must be \e |
---|
121 | ///symmetric, i.e. if \c map[u]=v then \c map[v]=u must hold, and |
---|
122 | ///now \c uv is an edge of the matching. |
---|
123 | template<typename NMapN> |
---|
124 | void readNMapNode(NMapN& map) { |
---|
125 | NodeIt v; |
---|
126 | for( G.first(v); G.valid(v); G.next(v)) { |
---|
127 | mate.set(v,map[v]); |
---|
128 | } |
---|
129 | } |
---|
130 | |
---|
131 | ///Writes the stored matching to a \c Node map of \c Nodes. |
---|
132 | |
---|
133 | ///Writes the stored matching to a \c Node map of \c Nodes. The |
---|
134 | ///resulting map will be \e symmetric, i.e. if \c map[u]=v then \c |
---|
135 | ///map[v]=u will hold, and now \c uv is an edge of the matching. |
---|
136 | template<typename NMapN> |
---|
137 | void writeNMapNode (NMapN& map) const { |
---|
138 | NodeIt v; |
---|
139 | for( G.first(v); G.valid(v); G.next(v)) { |
---|
140 | map.set(v,mate[v]); |
---|
141 | } |
---|
142 | } |
---|
143 | |
---|
144 | ///Reads a matching from a \c Node map of \c Edges. |
---|
145 | |
---|
146 | ///Reads a matching from a \c Node map of incident \c Edges. This |
---|
147 | ///map must have the property that if \c G.bNode(map[u])=v then \c |
---|
148 | ///G.bNode(map[v])=u must hold, and now this edge is an edge of |
---|
149 | ///the matching. |
---|
150 | template<typename NMapE> |
---|
151 | void readNMapEdge(NMapE& map) { |
---|
152 | NodeIt v; |
---|
153 | for( G.first(v); G.valid(v); G.next(v)) { |
---|
154 | Edge e=map[v]; |
---|
155 | if ( G.valid(e) ) |
---|
156 | G.source(e) == v ? mate.set(v,G.target(e)) : mate.set(v,G.source(e)); |
---|
157 | } |
---|
158 | } |
---|
159 | |
---|
160 | ///Writes the matching stored to a \c Node map of \c Edges. |
---|
161 | |
---|
162 | ///Writes the stored matching to a \c Node map of incident \c |
---|
163 | ///Edges. This map will have the property that if \c |
---|
164 | ///G.bNode(map[u])=v then \c G.bNode(map[v])=u holds, and now this |
---|
165 | ///edge is an edge of the matching. |
---|
166 | template<typename NMapE> |
---|
167 | void writeNMapEdge (NMapE& map) const { |
---|
168 | typename Graph::template NodeMap<bool> todo(G,false); |
---|
169 | NodeIt v; |
---|
170 | for( G.first(v); G.valid(v); G.next(v)) { |
---|
171 | if ( mate[v]!=INVALID ) todo.set(v,true); |
---|
172 | } |
---|
173 | NodeIt e; |
---|
174 | for( G.first(e); G.valid(e); G.next(e)) { |
---|
175 | if ( todo[G.target(e)] && todo[G.source(e)] ) { |
---|
176 | Node u=G.source(e); |
---|
177 | Node v=G.target(e); |
---|
178 | if ( mate[u]=v && mate[v]=u ) { |
---|
179 | map.set(u,e); |
---|
180 | map.set(v,e); |
---|
181 | todo.set(u,false); |
---|
182 | todo.set(v,false); |
---|
183 | } |
---|
184 | } |
---|
185 | } |
---|
186 | } |
---|
187 | |
---|
188 | ///Reads a matching from an \c Edge map of \c bools. |
---|
189 | |
---|
190 | ///Reads a matching from an \c Edge map of \c bools. This map must |
---|
191 | ///have the property that there are no two adjacent edges \c e, \c |
---|
192 | ///f with \c map[e]=map[f]=true. The edges \c e with \c |
---|
193 | ///map[e]=true form the matching. |
---|
194 | template<typename EMapB> |
---|
195 | void readEMapBool(EMapB& map) { |
---|
196 | EdgeIt e; |
---|
197 | for( G.first(e); G.valid(e); G.next(e)) { |
---|
198 | if ( G.valid(e) ) { |
---|
199 | Node u=G.source(e); |
---|
200 | Node v=G.target(e); |
---|
201 | mate.set(u,v); |
---|
202 | mate.set(v,u); |
---|
203 | } |
---|
204 | } |
---|
205 | } |
---|
206 | |
---|
207 | |
---|
208 | ///Writes the matching stored to an \c Edge map of \c bools. |
---|
209 | |
---|
210 | ///Writes the matching stored to an \c Edge map of \c bools. This |
---|
211 | ///map will have the property that there are no two adjacent edges |
---|
212 | ///\c e, \c f with \c map[e]=map[f]=true. The edges \c e with \c |
---|
213 | ///map[e]=true form the matching. |
---|
214 | template<typename EMapB> |
---|
215 | void writeEMapBool (EMapB& map) const { |
---|
216 | typename Graph::template NodeMap<bool> todo(G,false); |
---|
217 | NodeIt v; |
---|
218 | for( G.first(v); G.valid(v); G.next(v)) { |
---|
219 | if ( mate[v]!=INVALID ) todo.set(v,true); |
---|
220 | } |
---|
221 | |
---|
222 | NodeIt e; |
---|
223 | for( G.first(e); G.valid(e); G.next(e)) { |
---|
224 | map.set(e,false); |
---|
225 | if ( todo[G.target(e)] && todo[G.source(e)] ) { |
---|
226 | Node u=G.source(e); |
---|
227 | Node v=G.target(e); |
---|
228 | if ( mate[u]=v && mate[v]=u ) { |
---|
229 | map.set(e,true); |
---|
230 | todo.set(u,false); |
---|
231 | todo.set(v,false); |
---|
232 | } |
---|
233 | } |
---|
234 | } |
---|
235 | } |
---|
236 | |
---|
237 | ///Writes the canonical decomposition of the graph after running |
---|
238 | ///the algorithm. |
---|
239 | |
---|
240 | ///After calling any run methods of the class, and before calling |
---|
241 | ///\ref resetPos(), it writes the Gallai-Edmonds canonical |
---|
242 | ///decomposition of the graph. \c map must be a node map |
---|
243 | ///of \ref pos_enum 's. |
---|
244 | template<typename NMapEnum> |
---|
245 | void writePos (NMapEnum& map) const { |
---|
246 | NodeIt v; |
---|
247 | for( G.first(v); G.valid(v); G.next(v)) map.set(v,position[v]); |
---|
248 | } |
---|
249 | |
---|
250 | private: |
---|
251 | |
---|
252 | void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
---|
253 | UFE& blossom, UFE& tree); |
---|
254 | |
---|
255 | void normShrink(Node v, typename Graph::NodeMap<Node>& ear, |
---|
256 | UFE& blossom, UFE& tree); |
---|
257 | |
---|
258 | bool noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear, |
---|
259 | UFE& blossom, UFE& tree, std::queue<Node>& Q); |
---|
260 | |
---|
261 | void shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear, |
---|
262 | UFE& blossom, UFE& tree, std::queue<Node>& Q); |
---|
263 | |
---|
264 | void augment(Node x, typename Graph::NodeMap<Node>& ear, |
---|
265 | UFE& blossom, UFE& tree); |
---|
266 | |
---|
267 | }; |
---|
268 | |
---|
269 | |
---|
270 | // ********************************************************************** |
---|
271 | // IMPLEMENTATIONS |
---|
272 | // ********************************************************************** |
---|
273 | |
---|
274 | |
---|
275 | template <typename Graph> |
---|
276 | void MaxMatching<Graph>::run() { |
---|
277 | if ( G.edgeNum() > 2*G.nodeNum() ) { |
---|
278 | greedyMatching(); |
---|
279 | runEdmonds(1); |
---|
280 | } else runEdmonds(0); |
---|
281 | } |
---|
282 | |
---|
283 | template <typename Graph> |
---|
284 | void MaxMatching<Graph>::runEdmonds( int heur=1 ) { |
---|
285 | |
---|
286 | typename Graph::template NodeMap<Node> ear(G,INVALID); |
---|
287 | //undefined for the base nodes of the blossoms (i.e. for the |
---|
288 | //representative elements of UFE blossom) and for the nodes in C |
---|
289 | |
---|
290 | typename UFE::MapType blossom_base(G); |
---|
291 | UFE blossom(blossom_base); |
---|
292 | typename UFE::MapType tree_base(G); |
---|
293 | UFE tree(tree_base); |
---|
294 | |
---|
295 | NodeIt v; |
---|
296 | for( G.first(v); G.valid(v); G.next(v) ) { |
---|
297 | if ( position[v]==C && mate[v]==INVALID ) { |
---|
298 | blossom.insert(v); |
---|
299 | tree.insert(v); |
---|
300 | position.set(v,D); |
---|
301 | if ( heur == 1 ) lateShrink( v, ear, blossom, tree ); |
---|
302 | else normShrink( v, ear, blossom, tree ); |
---|
303 | } |
---|
304 | } |
---|
305 | } |
---|
306 | |
---|
307 | template <typename Graph> |
---|
308 | void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
---|
309 | UFE& blossom, UFE& tree) { |
---|
310 | |
---|
311 | std::queue<Node> Q; //queue of the totally unscanned nodes |
---|
312 | Q.push(v); |
---|
313 | std::queue<Node> R; |
---|
314 | //queue of the nodes which must be scanned for a possible shrink |
---|
315 | |
---|
316 | while ( !Q.empty() ) { |
---|
317 | Node x=Q.front(); |
---|
318 | Q.pop(); |
---|
319 | if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return; |
---|
320 | else R.push(x); |
---|
321 | } |
---|
322 | |
---|
323 | while ( !R.empty() ) { |
---|
324 | Node x=R.front(); |
---|
325 | R.pop(); |
---|
326 | |
---|
327 | OutEdgeIt e; |
---|
328 | for( G.first(e,x); G.valid(e); G.next(e) ) { |
---|
329 | Node y=G.bNode(e); |
---|
330 | |
---|
331 | if ( position[y] == D && blossom.find(x) != blossom.find(y) ) { |
---|
332 | //x and y must be in the same tree |
---|
333 | |
---|
334 | typename Graph::template NodeMap<bool> path(G,false); |
---|
335 | |
---|
336 | Node b=blossom.find(x); |
---|
337 | path.set(b,true); |
---|
338 | b=mate[b]; |
---|
339 | while ( b!=INVALID ) { |
---|
340 | b=blossom.find(ear[b]); |
---|
341 | path.set(b,true); |
---|
342 | b=mate[b]; |
---|
343 | } //going till the root |
---|
344 | |
---|
345 | Node top=y; |
---|
346 | Node middle=blossom.find(top); |
---|
347 | Node bottom=x; |
---|
348 | while ( !path[middle] ) |
---|
349 | shrinkStep(top, middle, bottom, ear, blossom, tree, Q); |
---|
350 | |
---|
351 | Node base=middle; |
---|
352 | top=x; |
---|
353 | middle=blossom.find(top); |
---|
354 | bottom=y; |
---|
355 | Node blossom_base=blossom.find(base); |
---|
356 | while ( middle!=blossom_base ) |
---|
357 | shrinkStep(top, middle, bottom, ear, blossom, tree, Q); |
---|
358 | |
---|
359 | blossom.makeRep(base); |
---|
360 | } // if shrink is needed |
---|
361 | |
---|
362 | while ( !Q.empty() ) { |
---|
363 | Node x=Q.front(); |
---|
364 | Q.pop(); |
---|
365 | if ( noShrinkStep(x, ear, blossom, tree, Q) ) return; |
---|
366 | else R.push(x); |
---|
367 | } |
---|
368 | } //for e |
---|
369 | } // while ( !R.empty() ) |
---|
370 | } |
---|
371 | |
---|
372 | template <typename Graph> |
---|
373 | void MaxMatching<Graph>::normShrink(Node v, typename Graph::NodeMap<Node>& ear, |
---|
374 | UFE& blossom, UFE& tree) { |
---|
375 | |
---|
376 | std::queue<Node> Q; //queue of the unscanned nodes |
---|
377 | Q.push(v); |
---|
378 | while ( !Q.empty() ) { |
---|
379 | Node x=Q.front(); |
---|
380 | Q.pop(); |
---|
381 | |
---|
382 | OutEdgeIt e; |
---|
383 | for( G.first(e,x); G.valid(e); G.next(e) ) { |
---|
384 | Node y=G.bNode(e); |
---|
385 | |
---|
386 | switch ( position[y] ) { |
---|
387 | case D: //x and y must be in the same tree |
---|
388 | if ( blossom.find(x) != blossom.find(y) ) { //shrink |
---|
389 | typename Graph::template NodeMap<bool> path(G,false); |
---|
390 | |
---|
391 | Node b=blossom.find(x); |
---|
392 | path.set(b,true); |
---|
393 | b=mate[b]; |
---|
394 | while ( b!=INVALID ) { |
---|
395 | b=blossom.find(ear[b]); |
---|
396 | path.set(b,true); |
---|
397 | b=mate[b]; |
---|
398 | } //going till the root |
---|
399 | |
---|
400 | Node top=y; |
---|
401 | Node middle=blossom.find(top); |
---|
402 | Node bottom=x; |
---|
403 | while ( !path[middle] ) |
---|
404 | shrinkStep(top, middle, bottom, ear, blossom, tree, Q); |
---|
405 | |
---|
406 | Node base=middle; |
---|
407 | top=x; |
---|
408 | middle=blossom.find(top); |
---|
409 | bottom=y; |
---|
410 | Node blossom_base=blossom.find(base); |
---|
411 | while ( middle!=blossom_base ) |
---|
412 | shrinkStep(top, middle, bottom, ear, blossom, tree, Q); |
---|
413 | |
---|
414 | blossom.makeRep(base); |
---|
415 | } |
---|
416 | break; |
---|
417 | case C: |
---|
418 | if ( mate[y]!=INVALID ) { //grow |
---|
419 | ear.set(y,x); |
---|
420 | Node w=mate[y]; |
---|
421 | blossom.insert(w); |
---|
422 | position.set(y,A); |
---|
423 | position.set(w,D); |
---|
424 | tree.insert(y); |
---|
425 | tree.insert(w); |
---|
426 | tree.join(y,blossom.find(x)); |
---|
427 | tree.join(w,y); |
---|
428 | Q.push(w); |
---|
429 | } else { //augment |
---|
430 | augment(x, ear, blossom, tree); |
---|
431 | mate.set(x,y); |
---|
432 | mate.set(y,x); |
---|
433 | return; |
---|
434 | } //if |
---|
435 | break; |
---|
436 | default: break; |
---|
437 | } |
---|
438 | } |
---|
439 | } |
---|
440 | } |
---|
441 | |
---|
442 | template <typename Graph> |
---|
443 | void MaxMatching<Graph>::greedyMatching() { |
---|
444 | NodeIt v; |
---|
445 | for( G.first(v); G.valid(v); G.next(v) ) |
---|
446 | if ( mate[v]==INVALID ) { |
---|
447 | OutEdgeIt e; |
---|
448 | for( G.first(e,v); G.valid(e); G.next(e) ) { |
---|
449 | Node y=G.bNode(e); |
---|
450 | if ( mate[y]==INVALID && y!=v ) { |
---|
451 | mate.set(v,y); |
---|
452 | mate.set(y,v); |
---|
453 | break; |
---|
454 | } |
---|
455 | } |
---|
456 | } |
---|
457 | } |
---|
458 | |
---|
459 | template <typename Graph> |
---|
460 | int MaxMatching<Graph>::size() const { |
---|
461 | int s=0; |
---|
462 | NodeIt v; |
---|
463 | for(G.first(v); G.valid(v); G.next(v) ) { |
---|
464 | if ( G.valid(mate[v]) ) { |
---|
465 | ++s; |
---|
466 | } |
---|
467 | } |
---|
468 | return (int)s/2; |
---|
469 | } |
---|
470 | |
---|
471 | template <typename Graph> |
---|
472 | void MaxMatching<Graph>::resetPos() { |
---|
473 | NodeIt v; |
---|
474 | for( G.first(v); G.valid(v); G.next(v)) |
---|
475 | position.set(v,C); |
---|
476 | } |
---|
477 | |
---|
478 | template <typename Graph> |
---|
479 | void MaxMatching<Graph>::resetMatching() { |
---|
480 | NodeIt v; |
---|
481 | for( G.first(v); G.valid(v); G.next(v)) |
---|
482 | mate.set(v,INVALID); |
---|
483 | } |
---|
484 | |
---|
485 | template <typename Graph> |
---|
486 | bool MaxMatching<Graph>::noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear, |
---|
487 | UFE& blossom, UFE& tree, std::queue<Node>& Q) { |
---|
488 | OutEdgeIt e; |
---|
489 | for( G.first(e,x); G.valid(e); G.next(e) ) { |
---|
490 | Node y=G.bNode(e); |
---|
491 | |
---|
492 | if ( position[y]==C ) { |
---|
493 | if ( mate[y]!=INVALID ) { //grow |
---|
494 | ear.set(y,x); |
---|
495 | Node w=mate[y]; |
---|
496 | blossom.insert(w); |
---|
497 | position.set(y,A); |
---|
498 | position.set(w,D); |
---|
499 | tree.insert(y); |
---|
500 | tree.insert(w); |
---|
501 | tree.join(y,blossom.find(x)); |
---|
502 | tree.join(w,y); |
---|
503 | Q.push(w); |
---|
504 | } else { //augment |
---|
505 | augment(x, ear, blossom, tree); |
---|
506 | mate.set(x,y); |
---|
507 | mate.set(y,x); |
---|
508 | return true; |
---|
509 | } |
---|
510 | } |
---|
511 | } |
---|
512 | return false; |
---|
513 | } |
---|
514 | |
---|
515 | template <typename Graph> |
---|
516 | void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear, |
---|
517 | UFE& blossom, UFE& tree, std::queue<Node>& Q) { |
---|
518 | ear.set(top,bottom); |
---|
519 | Node t=top; |
---|
520 | while ( t!=middle ) { |
---|
521 | Node u=mate[t]; |
---|
522 | t=ear[u]; |
---|
523 | ear.set(t,u); |
---|
524 | } |
---|
525 | bottom=mate[middle]; |
---|
526 | position.set(bottom,D); |
---|
527 | Q.push(bottom); |
---|
528 | top=ear[bottom]; |
---|
529 | Node oldmiddle=middle; |
---|
530 | middle=blossom.find(top); |
---|
531 | tree.erase(bottom); |
---|
532 | tree.erase(oldmiddle); |
---|
533 | blossom.insert(bottom); |
---|
534 | blossom.join(bottom, oldmiddle); |
---|
535 | blossom.join(top, oldmiddle); |
---|
536 | } |
---|
537 | |
---|
538 | template <typename Graph> |
---|
539 | void MaxMatching<Graph>::augment(Node x, typename Graph::NodeMap<Node>& ear, |
---|
540 | UFE& blossom, UFE& tree) { |
---|
541 | Node v=mate[x]; |
---|
542 | while ( G.valid(v) ) { |
---|
543 | |
---|
544 | Node u=ear[v]; |
---|
545 | mate.set(v,u); |
---|
546 | Node tmp=v; |
---|
547 | v=mate[u]; |
---|
548 | mate.set(u,tmp); |
---|
549 | } |
---|
550 | typename UFE::ItemIt it; |
---|
551 | for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) { |
---|
552 | if ( position[it] == D ) { |
---|
553 | typename UFE::ItemIt b_it; |
---|
554 | for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) { |
---|
555 | position.set( b_it ,C); |
---|
556 | } |
---|
557 | blossom.eraseClass(it); |
---|
558 | } else position.set( it ,C); |
---|
559 | } |
---|
560 | tree.eraseClass(x); |
---|
561 | } |
---|
562 | |
---|
563 | |
---|
564 | |
---|
565 | /// @} |
---|
566 | |
---|
567 | } //END OF NAMESPACE LEMON |
---|
568 | |
---|
569 | #endif //EDMONDS_H |
---|