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_DYNAMIC_TREE_H |
---|
20 | #define LEMON_DYNAMIC_TREE_H |
---|
21 | |
---|
22 | /// \ingroup auxdata |
---|
23 | /// \file |
---|
24 | /// \brief The dynamic tree data structure of Sleator and Tarjan. |
---|
25 | /// |
---|
26 | |
---|
27 | #include <vector> |
---|
28 | #include <limits> |
---|
29 | #include <lemon/tolerance.h> |
---|
30 | |
---|
31 | namespace lemon { |
---|
32 | |
---|
33 | /// \ingroup auxdata |
---|
34 | /// |
---|
35 | /// \brief The dynamic tree data structure of Sleator and Tarjan. |
---|
36 | /// |
---|
37 | /// This class provides an implementation of the dynamic tree data |
---|
38 | /// structure for maintaining a set of node-disjoint rooted |
---|
39 | /// trees. Each item has an associated value, and the item with |
---|
40 | /// minimum value can be find in \f$O(\log(n)\f$ on the path from a |
---|
41 | /// node to the its root, and the items on such path can be |
---|
42 | /// increased or decreased globally with a certain value in the same |
---|
43 | /// running time. We regard a tree edge as directed toward the root, |
---|
44 | /// that is from child to parent. Its structure can be modified by |
---|
45 | /// two basic operations: \e link(v,w) adds an edge between a root v |
---|
46 | /// and a node w in a different component; \e cut(v) removes the |
---|
47 | /// edge between v and its parent. |
---|
48 | /// |
---|
49 | /// \param _Value The value type of the items. |
---|
50 | /// \param _ItemIntMap Converts item type of node to integer. |
---|
51 | /// \param _Tolerance The tolerance class to handle computation |
---|
52 | /// problems. |
---|
53 | /// \param _enableSize If true then the data structre manatain the |
---|
54 | /// size of each tree. The feature is used in \ref GoldbergTarjan |
---|
55 | /// algorithm. The default value is true. |
---|
56 | /// |
---|
57 | /// \author Hamori Tamas |
---|
58 | #ifdef DOXYGEN |
---|
59 | template <typename _Value, typename _ItemIntMap, |
---|
60 | typename _Tolerance, bool _enableSize> |
---|
61 | #else |
---|
62 | template <typename _Value, typename _ItemIntMap, |
---|
63 | typename _Tolerance = lemon::Tolerance<_Value>, |
---|
64 | bool _enableSize = true> |
---|
65 | #endif |
---|
66 | class DynamicTree { |
---|
67 | public: |
---|
68 | /// \brief The integer map on the items. |
---|
69 | typedef _ItemIntMap ItemIntMap; |
---|
70 | /// \brief The item type of nodes. |
---|
71 | typedef typename ItemIntMap::Key Item; |
---|
72 | /// \brief The value type of the algorithms. |
---|
73 | typedef _Value Value; |
---|
74 | /// \brief The tolerance used by the algorithm. |
---|
75 | typedef _Tolerance Tolerance; |
---|
76 | |
---|
77 | private: |
---|
78 | |
---|
79 | class ItemData; |
---|
80 | |
---|
81 | std::vector<ItemData> _data; |
---|
82 | ItemIntMap &_iim; |
---|
83 | Value _max_value; |
---|
84 | Tolerance _tolerance; |
---|
85 | |
---|
86 | public: |
---|
87 | /// \brief The constructor of the class. |
---|
88 | /// |
---|
89 | /// \param iim The integer map on the items. |
---|
90 | /// \param tolerance Tolerance class. |
---|
91 | DynamicTree(ItemIntMap &iim, const Tolerance& tolerance = Tolerance()) |
---|
92 | : _iim(iim), _max_value(std::numeric_limits<Value>::max()), |
---|
93 | _tolerance(tolerance) {} |
---|
94 | |
---|
95 | ~DynamicTree() {} |
---|
96 | |
---|
97 | /// \brief Clears the data structure |
---|
98 | /// |
---|
99 | /// Clears the data structure |
---|
100 | void clear() { |
---|
101 | _data.clear(); |
---|
102 | } |
---|
103 | |
---|
104 | /// \brief Sets the tolerance used by algorithm. |
---|
105 | /// |
---|
106 | /// Sets the tolerance used by algorithm. |
---|
107 | void tolerance(const Tolerance& tolerance) const { |
---|
108 | _tolerance = tolerance; |
---|
109 | return *this; |
---|
110 | } |
---|
111 | |
---|
112 | /// \brief Returns the tolerance used by algorithm. |
---|
113 | /// |
---|
114 | /// Returns the tolerance used by algorithm. |
---|
115 | const Tolerance& tolerance() const { |
---|
116 | return tolerance; |
---|
117 | } |
---|
118 | |
---|
119 | /// \brief Create a new tree containing a single node with cost zero. |
---|
120 | void makeTree(const Item &item) { |
---|
121 | _data[makePath(item)].successor = -1; |
---|
122 | } |
---|
123 | |
---|
124 | /// \brief Return the root of the tree containing node with itemtype |
---|
125 | /// \e item. |
---|
126 | Item findRoot(const Item &item) { |
---|
127 | return _data[findTail(expose(_iim[item]))].id; |
---|
128 | } |
---|
129 | |
---|
130 | /// \brief Return the the value of nodes in the tree containing |
---|
131 | /// node with itemtype \e item. |
---|
132 | int findSize(const Item &item) { |
---|
133 | return _data[expose(_iim[item])].size; |
---|
134 | } |
---|
135 | |
---|
136 | /// \brief Return the minimum cost containing node. |
---|
137 | /// |
---|
138 | /// Return into \e d the minimum cost on the tree path from \e item |
---|
139 | /// to findRoot(item). Return the last item (closest to its root) |
---|
140 | /// on this path of the minimum cost. |
---|
141 | Item findCost(const Item &item, Value& d){ |
---|
142 | return _data[findPathCost(expose(_iim[item]),d)].id; |
---|
143 | } |
---|
144 | |
---|
145 | /// \brief Add \e x value to the cost of every node on the path from |
---|
146 | /// \e item to findRoot(item). |
---|
147 | void addCost(const Item &item, Value x) { |
---|
148 | addPathCost(expose(_iim[item]), x); |
---|
149 | } |
---|
150 | |
---|
151 | /// \brief Combine the trees containing nodes \e item1 and \e item2 |
---|
152 | /// by adding an edge from \e item1 \e item2. |
---|
153 | /// |
---|
154 | /// This operation assumes that \e item1 is root and \e item2 is in |
---|
155 | /// a different tree. |
---|
156 | void link(const Item &item1, const Item &item2){ |
---|
157 | int v = _iim[item1]; |
---|
158 | int w = _iim[item2]; |
---|
159 | int p = expose(w); |
---|
160 | join(-1, expose(v), p); |
---|
161 | _data[v].successor = -1; |
---|
162 | _data[v].size += _data[p].size; |
---|
163 | |
---|
164 | } |
---|
165 | |
---|
166 | /// \brief Divide the tree containing node \e item into two trees by |
---|
167 | /// deleting the edge out of \e item. |
---|
168 | /// |
---|
169 | /// This operation assumes that \e item is not a tree root. |
---|
170 | void cut(const Item &item) { |
---|
171 | int v = _iim[item]; |
---|
172 | int p, q; |
---|
173 | expose(v); |
---|
174 | split(p, v, q); |
---|
175 | if (p != -1) { |
---|
176 | _data[p].successor = v; |
---|
177 | } |
---|
178 | _data[v].size -= _data[q].size; |
---|
179 | if (q != -1) { |
---|
180 | _data[q].successor = _data[v].successor; |
---|
181 | } |
---|
182 | _data[v].successor = -1; |
---|
183 | } |
---|
184 | |
---|
185 | ///\brief |
---|
186 | Item parent(const Item &item){ |
---|
187 | return _data[_iim[item].p].id; |
---|
188 | } |
---|
189 | |
---|
190 | ///\brief Return the upper bound of the costs. |
---|
191 | Value maxValue() const { |
---|
192 | return _max_value; |
---|
193 | } |
---|
194 | |
---|
195 | private: |
---|
196 | |
---|
197 | int makePath(const Item &item) { |
---|
198 | _iim.set(item, _data.size()); |
---|
199 | ItemData v(item); |
---|
200 | _data.push_back(v); |
---|
201 | return _iim[item]; |
---|
202 | } |
---|
203 | |
---|
204 | int findPath(int v) { |
---|
205 | splay(v); |
---|
206 | return v; |
---|
207 | } |
---|
208 | |
---|
209 | int findPathCost(int p, Value &d) { |
---|
210 | while ((_data[p].right != -1 && |
---|
211 | !_tolerance.less(0, _data[_data[p].right].dmin)) || |
---|
212 | (_data[p].left != -1 && _tolerance.less(0, _data[p].dcost))) { |
---|
213 | if (_data[p].right != -1 && |
---|
214 | !_tolerance.less(0, _data[_data[p].right].dmin)) { |
---|
215 | p = _data[p].right; |
---|
216 | } else if (_data[p].left != -1 && |
---|
217 | !_tolerance.less(0, _data[_data[p].left].dmin)) { |
---|
218 | p = _data[p].left; |
---|
219 | } |
---|
220 | } |
---|
221 | splay(p); |
---|
222 | d = _data[p].dmin; |
---|
223 | return p; |
---|
224 | } |
---|
225 | |
---|
226 | int findTail(int p){ |
---|
227 | while (_data[p].right != -1) { |
---|
228 | p = _data[p].right; |
---|
229 | } |
---|
230 | splay(p); |
---|
231 | return p; |
---|
232 | } |
---|
233 | |
---|
234 | void addPathCost(int p, Value x) { |
---|
235 | if (!_tolerance.less(x, _max_value)) { |
---|
236 | _data[p].dmin = x; |
---|
237 | _data[p].dcost = x; |
---|
238 | } else if (!_tolerance.less(-x, _max_value)) { |
---|
239 | _data[p].dmin = 0; |
---|
240 | _data[p].dcost = 0; |
---|
241 | } else { |
---|
242 | _data[p].dmin += x; |
---|
243 | } |
---|
244 | } |
---|
245 | |
---|
246 | void join(int p, int v, int q) { |
---|
247 | Value min = _max_value; |
---|
248 | Value pmin = _max_value; |
---|
249 | Value vmin = _data[v].dmin; |
---|
250 | Value qmin = _max_value; |
---|
251 | if (p != -1){ |
---|
252 | pmin = _data[p].dmin; |
---|
253 | } |
---|
254 | if (q != -1){ |
---|
255 | qmin = _data[q].dmin; |
---|
256 | } |
---|
257 | |
---|
258 | if (_tolerance.less(vmin, qmin)) { |
---|
259 | if (_tolerance.less(vmin,pmin)) { |
---|
260 | min = vmin; |
---|
261 | } else { |
---|
262 | min = pmin; |
---|
263 | } |
---|
264 | } else if (_tolerance.less(qmin,pmin)) { |
---|
265 | min = qmin; |
---|
266 | } else { |
---|
267 | min = pmin; |
---|
268 | } |
---|
269 | |
---|
270 | if (p != -1){ |
---|
271 | _data[p].parent = v; |
---|
272 | _data[p].dmin -= min; |
---|
273 | } |
---|
274 | if (q!=-1){ |
---|
275 | _data[q].parent = v; |
---|
276 | if (_tolerance.less(_data[q].dmin,_max_value)) { |
---|
277 | _data[q].dmin -= min; |
---|
278 | } |
---|
279 | } |
---|
280 | _data[v].left = p; |
---|
281 | _data[v].right = q; |
---|
282 | if (_tolerance.less(min,_max_value)) { |
---|
283 | _data[v].dcost = _data[v].dmin - min; |
---|
284 | } |
---|
285 | _data[v].dmin = min; |
---|
286 | } |
---|
287 | |
---|
288 | void split(int &p, int v, int &q){ |
---|
289 | splay(v); |
---|
290 | p = -1; |
---|
291 | if (_data[v].left != -1){ |
---|
292 | p = _data[v].left; |
---|
293 | _data[p].dmin += _data[v].dmin; |
---|
294 | _data[p].parent = -1; |
---|
295 | _data[v].left = -1; |
---|
296 | } |
---|
297 | q = -1; |
---|
298 | if (_data[v].right != -1) { |
---|
299 | q=_data[v].right; |
---|
300 | if (_tolerance.less(_data[q].dmin, _max_value)) { |
---|
301 | _data[q].dmin += _data[v].dmin; |
---|
302 | } |
---|
303 | _data[q].parent = -1; |
---|
304 | _data[v].right = -1; |
---|
305 | } |
---|
306 | if (_tolerance.less(_data[v].dcost, _max_value)) { |
---|
307 | _data[v].dmin += _data[v].dcost; |
---|
308 | _data[v].dcost = 0; |
---|
309 | } else { |
---|
310 | _data[v].dmin = _data[v].dcost; |
---|
311 | } |
---|
312 | } |
---|
313 | |
---|
314 | int expose(int v) { |
---|
315 | int p, q, r, w; |
---|
316 | p = -1; |
---|
317 | while (v != -1) { |
---|
318 | w = _data[findPath(v)].successor; |
---|
319 | split(q, v, r); |
---|
320 | if (q != -1) { |
---|
321 | _data[q].successor = v; |
---|
322 | } |
---|
323 | join(p, v, r); |
---|
324 | p = v; |
---|
325 | v = w; |
---|
326 | } |
---|
327 | _data[p].successor = -1; |
---|
328 | return p; |
---|
329 | } |
---|
330 | |
---|
331 | void splay(int v) { |
---|
332 | while (_data[v].parent != -1) { |
---|
333 | if (v == _data[_data[v].parent].left) { |
---|
334 | if (_data[_data[v].parent].parent == -1) { |
---|
335 | zig(v); |
---|
336 | } else { |
---|
337 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
---|
338 | zig(_data[v].parent); |
---|
339 | zig(v); |
---|
340 | } else { |
---|
341 | zig(v); |
---|
342 | zag(v); |
---|
343 | } |
---|
344 | } |
---|
345 | } else { |
---|
346 | if (_data[_data[v].parent].parent == -1) { |
---|
347 | zag(v); |
---|
348 | } else { |
---|
349 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
---|
350 | zag(v); |
---|
351 | zig(v); |
---|
352 | } else { |
---|
353 | zag(_data[v].parent); |
---|
354 | zag(v); |
---|
355 | } |
---|
356 | } |
---|
357 | } |
---|
358 | } |
---|
359 | } |
---|
360 | |
---|
361 | |
---|
362 | void zig(int v) { |
---|
363 | Value min = _data[_data[v].parent].dmin; |
---|
364 | int a = _data[v].parent; |
---|
365 | |
---|
366 | Value aa = _data[a].dcost; |
---|
367 | if (_tolerance.less(aa, _max_value)) { |
---|
368 | aa += min; |
---|
369 | } |
---|
370 | |
---|
371 | |
---|
372 | int b = v; |
---|
373 | Value ab = min + _data[b].dmin; |
---|
374 | Value bb = _data[b].dcost; |
---|
375 | if (_tolerance.less(bb, _max_value)) { |
---|
376 | bb += ab; |
---|
377 | } |
---|
378 | |
---|
379 | int c = -1; |
---|
380 | Value cc = _max_value; |
---|
381 | if (_data[a].right != -1) { |
---|
382 | c = _data[a].right; |
---|
383 | cc = _data[c].dmin; |
---|
384 | if (_tolerance.less(cc, _max_value)) { |
---|
385 | cc += min; |
---|
386 | } |
---|
387 | } |
---|
388 | |
---|
389 | int d = -1; |
---|
390 | Value dd = _max_value; |
---|
391 | if (_data[v].left != -1){ |
---|
392 | d = _data[v].left; |
---|
393 | dd = ab + _data[d].dmin; |
---|
394 | } |
---|
395 | |
---|
396 | int e = -1; |
---|
397 | Value ee = _max_value; |
---|
398 | if (_data[v].right != -1) { |
---|
399 | e = _data[v].right; |
---|
400 | ee = ab + _data[e].dmin; |
---|
401 | } |
---|
402 | |
---|
403 | Value min2; |
---|
404 | if (_tolerance.less(0, _data[b].dmin) || |
---|
405 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
---|
406 | min2 = min; |
---|
407 | } else { |
---|
408 | if (_tolerance.less(aa, cc)) { |
---|
409 | if (_tolerance.less(aa, ee)) { |
---|
410 | min2 = aa; |
---|
411 | } else { |
---|
412 | min2 = ee; |
---|
413 | } |
---|
414 | } else if (_tolerance.less(cc, ee)) { |
---|
415 | min2 = cc; |
---|
416 | } else { |
---|
417 | min2 = ee; |
---|
418 | } |
---|
419 | } |
---|
420 | |
---|
421 | _data[a].dcost = aa; |
---|
422 | if (_tolerance.less(aa, _max_value)) { |
---|
423 | _data[a].dcost -= min2; |
---|
424 | } |
---|
425 | _data[a].dmin = min2; |
---|
426 | if (_tolerance.less(min2,_max_value)) { |
---|
427 | _data[a].dmin -= min; |
---|
428 | } |
---|
429 | _data[a].size -= _data[b].size; |
---|
430 | _data[b].dcost = bb; |
---|
431 | if (_tolerance.less(bb, _max_value)) { |
---|
432 | _data[b].dcost -= min; |
---|
433 | } |
---|
434 | _data[b].dmin = min; |
---|
435 | _data[b].size += _data[a].size; |
---|
436 | if (c != -1) { |
---|
437 | _data[c].dmin = cc; |
---|
438 | if (_tolerance.less(cc, _max_value)) { |
---|
439 | _data[c].dmin -= min2; |
---|
440 | } |
---|
441 | } |
---|
442 | if (d != -1) { |
---|
443 | _data[d].dmin = dd - min; |
---|
444 | _data[a].size += _data[d].size; |
---|
445 | _data[b].size -= _data[d].size; |
---|
446 | } |
---|
447 | if (e != -1) { |
---|
448 | _data[e].dmin = ee - min2; |
---|
449 | } |
---|
450 | |
---|
451 | int w = _data[v].parent; |
---|
452 | _data[v].successor = _data[w].successor; |
---|
453 | _data[w].successor = -1; |
---|
454 | _data[v].parent = _data[w].parent; |
---|
455 | _data[w].parent = v; |
---|
456 | _data[w].left = _data[v].right; |
---|
457 | _data[v].right = w; |
---|
458 | if (_data[v].parent != -1){ |
---|
459 | if (_data[_data[v].parent].right == w) { |
---|
460 | _data[_data[v].parent].right = v; |
---|
461 | } else { |
---|
462 | _data[_data[v].parent].left = v; |
---|
463 | } |
---|
464 | } |
---|
465 | if (_data[w].left != -1){ |
---|
466 | _data[_data[w].left].parent = w; |
---|
467 | } |
---|
468 | } |
---|
469 | |
---|
470 | |
---|
471 | void zag(int v) { |
---|
472 | |
---|
473 | Value min = _data[_data[v].parent].dmin; |
---|
474 | |
---|
475 | int a = _data[v].parent; |
---|
476 | Value aa = _data[a].dcost; |
---|
477 | if (_tolerance.less(aa, _max_value)) { |
---|
478 | aa += min; |
---|
479 | } |
---|
480 | |
---|
481 | int b = v; |
---|
482 | Value ab = min + _data[b].dmin; |
---|
483 | Value bb = _data[b].dcost; |
---|
484 | if (_tolerance.less(bb, _max_value)) { |
---|
485 | bb += ab; |
---|
486 | } |
---|
487 | |
---|
488 | int c = -1; |
---|
489 | Value cc = _max_value; |
---|
490 | if (_data[a].left != -1){ |
---|
491 | c = _data[a].left; |
---|
492 | cc = min + _data[c].dmin; |
---|
493 | } |
---|
494 | |
---|
495 | int d = -1; |
---|
496 | Value dd = _max_value; |
---|
497 | if (_data[v].right!=-1) { |
---|
498 | d = _data[v].right; |
---|
499 | dd = _data[d].dmin; |
---|
500 | if (_tolerance.less(dd, _max_value)) { |
---|
501 | dd += ab; |
---|
502 | } |
---|
503 | } |
---|
504 | |
---|
505 | int e = -1; |
---|
506 | Value ee = _max_value; |
---|
507 | if (_data[v].left != -1){ |
---|
508 | e = _data[v].left; |
---|
509 | ee = ab + _data[e].dmin; |
---|
510 | } |
---|
511 | |
---|
512 | Value min2; |
---|
513 | if (_tolerance.less(0, _data[b].dmin) || |
---|
514 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
---|
515 | min2 = min; |
---|
516 | } else { |
---|
517 | if (_tolerance.less(aa, cc)) { |
---|
518 | if (_tolerance.less(aa, ee)) { |
---|
519 | min2 = aa; |
---|
520 | } else { |
---|
521 | min2 = ee; |
---|
522 | } |
---|
523 | } else if (_tolerance.less(cc, ee)) { |
---|
524 | min2 = cc; |
---|
525 | } else { |
---|
526 | min2 = ee; |
---|
527 | } |
---|
528 | } |
---|
529 | _data[a].dcost = aa; |
---|
530 | if (_tolerance.less(aa, _max_value)) { |
---|
531 | _data[a].dcost -= min2; |
---|
532 | } |
---|
533 | _data[a].dmin = min2; |
---|
534 | if (_tolerance.less(min2, _max_value)) { |
---|
535 | _data[a].dmin -= min; |
---|
536 | } |
---|
537 | _data[a].size -= _data[b].size; |
---|
538 | _data[b].dcost = bb; |
---|
539 | if (_tolerance.less(bb, _max_value)) { |
---|
540 | _data[b].dcost -= min; |
---|
541 | } |
---|
542 | _data[b].dmin = min; |
---|
543 | _data[b].size += _data[a].size; |
---|
544 | if (c != -1) { |
---|
545 | _data[c].dmin = cc - min2; |
---|
546 | } |
---|
547 | if (d != -1) { |
---|
548 | _data[d].dmin = dd; |
---|
549 | _data[a].size += _data[d].size; |
---|
550 | _data[b].size -= _data[d].size; |
---|
551 | if (_tolerance.less(dd, _max_value)) { |
---|
552 | _data[d].dmin -= min; |
---|
553 | } |
---|
554 | } |
---|
555 | if (e != -1) { |
---|
556 | _data[e].dmin = ee - min2; |
---|
557 | } |
---|
558 | |
---|
559 | int w = _data[v].parent; |
---|
560 | _data[v].successor = _data[w].successor; |
---|
561 | _data[w].successor = -1; |
---|
562 | _data[v].parent = _data[w].parent; |
---|
563 | _data[w].parent = v; |
---|
564 | _data[w].right = _data[v].left; |
---|
565 | _data[v].left = w; |
---|
566 | if (_data[v].parent != -1){ |
---|
567 | if (_data[_data[v].parent].left == w) { |
---|
568 | _data[_data[v].parent].left = v; |
---|
569 | } else { |
---|
570 | _data[_data[v].parent].right = v; |
---|
571 | } |
---|
572 | } |
---|
573 | if (_data[w].right != -1){ |
---|
574 | _data[_data[w].right].parent = w; |
---|
575 | } |
---|
576 | } |
---|
577 | |
---|
578 | private: |
---|
579 | |
---|
580 | class ItemData { |
---|
581 | public: |
---|
582 | Item id; |
---|
583 | int size; |
---|
584 | int successor; |
---|
585 | int parent; |
---|
586 | int left; |
---|
587 | int right; |
---|
588 | Value dmin; |
---|
589 | Value dcost; |
---|
590 | |
---|
591 | public: |
---|
592 | ItemData(const Item &item) |
---|
593 | : id(item), size(1), successor(), parent(-1), |
---|
594 | left(-1), right(-1), dmin(0), dcost(0) {} |
---|
595 | }; |
---|
596 | |
---|
597 | }; |
---|
598 | |
---|
599 | template <typename _Value, typename _ItemIntMap, typename _Tolerance> |
---|
600 | class DynamicTree<_Value, _ItemIntMap, _Tolerance, false> { |
---|
601 | public: |
---|
602 | typedef _ItemIntMap ItemIntMap; |
---|
603 | typedef typename ItemIntMap::Key Item; |
---|
604 | typedef _Value Value; |
---|
605 | typedef _Tolerance Tolerance; |
---|
606 | |
---|
607 | private: |
---|
608 | |
---|
609 | class ItemData; |
---|
610 | |
---|
611 | std::vector<ItemData> _data; |
---|
612 | ItemIntMap &_iim; |
---|
613 | Value _max_value; |
---|
614 | Tolerance _tolerance; |
---|
615 | |
---|
616 | public: |
---|
617 | DynamicTree(ItemIntMap &iim, const Tolerance& tolerance = Tolerance()) |
---|
618 | : _iim(iim), _max_value(std::numeric_limits<Value>::max()), |
---|
619 | _tolerance(tolerance) {} |
---|
620 | |
---|
621 | ~DynamicTree() {} |
---|
622 | |
---|
623 | void clear() { |
---|
624 | _data.clear(); |
---|
625 | } |
---|
626 | |
---|
627 | void tolerance(const Tolerance& tolerance) const { |
---|
628 | _tolerance = tolerance; |
---|
629 | return *this; |
---|
630 | } |
---|
631 | |
---|
632 | const Tolerance& tolerance() const { |
---|
633 | return tolerance; |
---|
634 | } |
---|
635 | |
---|
636 | void makeTree(const Item &item) { |
---|
637 | _data[makePath(item)].successor = -1; |
---|
638 | } |
---|
639 | |
---|
640 | Item findRoot(const Item &item) { |
---|
641 | return _data[findTail(expose(_iim[item]))].id; |
---|
642 | } |
---|
643 | |
---|
644 | Item findCost(const Item &item, Value& d){ |
---|
645 | return _data[findPathCost(expose(_iim[item]),d)].id; |
---|
646 | } |
---|
647 | |
---|
648 | void addCost(const Item &item, Value x){ |
---|
649 | addPathCost(expose(_iim[item]), x); |
---|
650 | } |
---|
651 | |
---|
652 | void link(const Item &item1, const Item &item2){ |
---|
653 | int v = _iim[item1]; |
---|
654 | int w = _iim[item2]; |
---|
655 | int p = expose(w); |
---|
656 | join(-1, expose(v), p); |
---|
657 | _data[v].successor = -1; |
---|
658 | } |
---|
659 | |
---|
660 | void cut(const Item &item) { |
---|
661 | int v = _iim[item]; |
---|
662 | int p, q; |
---|
663 | expose(v); |
---|
664 | split(p, v, q); |
---|
665 | if (p != -1) { |
---|
666 | _data[p].successor = v; |
---|
667 | } |
---|
668 | if (q != -1) { |
---|
669 | _data[q].successor = _data[v].successor; |
---|
670 | } |
---|
671 | _data[v].successor = -1; |
---|
672 | } |
---|
673 | |
---|
674 | Item parent(const Item &item){ |
---|
675 | return _data[_iim[item].p].id; |
---|
676 | } |
---|
677 | |
---|
678 | Value maxValue() const { |
---|
679 | return _max_value; |
---|
680 | } |
---|
681 | |
---|
682 | private: |
---|
683 | |
---|
684 | int makePath(const Item &item) { |
---|
685 | _iim.set(item, _data.size()); |
---|
686 | ItemData v(item); |
---|
687 | _data.push_back(v); |
---|
688 | return _iim[item]; |
---|
689 | } |
---|
690 | |
---|
691 | int findPath(int v) { |
---|
692 | splay(v); |
---|
693 | return v; |
---|
694 | } |
---|
695 | |
---|
696 | int findPathCost(int p, Value &d) { |
---|
697 | while ((_data[p].right != -1 && |
---|
698 | !_tolerance.less(0, _data[_data[p].right].dmin)) || |
---|
699 | (_data[p].left != -1 && _tolerance.less(0, _data[p].dcost))) { |
---|
700 | if (_data[p].right != -1 && |
---|
701 | !_tolerance.less(0, _data[_data[p].right].dmin)) { |
---|
702 | p = _data[p].right; |
---|
703 | } else if (_data[p].left != -1 && |
---|
704 | !_tolerance.less(0, _data[_data[p].left].dmin)){ |
---|
705 | p = _data[p].left; |
---|
706 | } |
---|
707 | } |
---|
708 | splay(p); |
---|
709 | d = _data[p].dmin; |
---|
710 | return p; |
---|
711 | } |
---|
712 | |
---|
713 | int findTail(int p) { |
---|
714 | while (_data[p].right != -1) { |
---|
715 | p = _data[p].right; |
---|
716 | } |
---|
717 | splay(p); |
---|
718 | return p; |
---|
719 | } |
---|
720 | |
---|
721 | void addPathCost(int p, Value x) { |
---|
722 | if (!_tolerance.less(x, _max_value)) { |
---|
723 | _data[p].dmin = x;_data[p].dcost = x; |
---|
724 | } else if (!_tolerance.less(-x, _max_value)) { |
---|
725 | _data[p].dmin = 0; |
---|
726 | _data[p].dcost = 0; |
---|
727 | } else { |
---|
728 | _data[p].dmin += x; |
---|
729 | } |
---|
730 | } |
---|
731 | |
---|
732 | void join(int p, int v, int q) { |
---|
733 | Value min = _max_value; |
---|
734 | Value pmin = _max_value; |
---|
735 | Value vmin = _data[v].dmin; |
---|
736 | Value qmin = _max_value; |
---|
737 | if (p != -1){ |
---|
738 | pmin = _data[p].dmin; |
---|
739 | } |
---|
740 | if (q != -1){ |
---|
741 | qmin = _data[q].dmin; |
---|
742 | } |
---|
743 | |
---|
744 | if (_tolerance.less(vmin, qmin)) { |
---|
745 | if (_tolerance.less(vmin,pmin)) { |
---|
746 | min = vmin; |
---|
747 | } else { |
---|
748 | min = pmin; |
---|
749 | } |
---|
750 | } else if (_tolerance.less(qmin,pmin)) { |
---|
751 | min = qmin; |
---|
752 | } else { |
---|
753 | min = pmin; |
---|
754 | } |
---|
755 | |
---|
756 | if (p != -1){ |
---|
757 | _data[p].parent = v; |
---|
758 | _data[p].dmin -= min; |
---|
759 | } |
---|
760 | if (q != -1){ |
---|
761 | _data[q].parent = v; |
---|
762 | if (_tolerance.less(_data[q].dmin,_max_value)) { |
---|
763 | _data[q].dmin -= min; |
---|
764 | } |
---|
765 | } |
---|
766 | _data[v].left = p; |
---|
767 | _data[v].right = q; |
---|
768 | if (_tolerance.less(min, _max_value)) { |
---|
769 | _data[v].dcost = _data[v].dmin - min; |
---|
770 | } |
---|
771 | _data[v].dmin = min; |
---|
772 | } |
---|
773 | |
---|
774 | void split(int &p, int v, int &q){ |
---|
775 | splay(v); |
---|
776 | p = -1; |
---|
777 | if (_data[v].left != -1){ |
---|
778 | p = _data[v].left; |
---|
779 | _data[p].dmin += _data[v].dmin; |
---|
780 | _data[p].parent = -1; |
---|
781 | _data[v].left = -1; |
---|
782 | } |
---|
783 | q = -1; |
---|
784 | if (_data[v].right != -1) { |
---|
785 | q=_data[v].right; |
---|
786 | if (_tolerance.less(_data[q].dmin, _max_value)) { |
---|
787 | _data[q].dmin += _data[v].dmin; |
---|
788 | } |
---|
789 | _data[q].parent = -1; |
---|
790 | _data[v].right = -1; |
---|
791 | } |
---|
792 | if (_tolerance.less(_data[v].dcost, _max_value)) { |
---|
793 | _data[v].dmin += _data[v].dcost; |
---|
794 | _data[v].dcost = 0; |
---|
795 | } else { |
---|
796 | _data[v].dmin = _data[v].dcost; |
---|
797 | } |
---|
798 | } |
---|
799 | |
---|
800 | int expose(int v) { |
---|
801 | int p, q, r, w; |
---|
802 | p = -1; |
---|
803 | while (v != -1) { |
---|
804 | w = _data[findPath(v)].successor; |
---|
805 | split(q, v, r); |
---|
806 | if (q != -1) { |
---|
807 | _data[q].successor = v; |
---|
808 | } |
---|
809 | join(p, v, r); |
---|
810 | p = v; |
---|
811 | v = w; |
---|
812 | } |
---|
813 | _data[p].successor = -1; |
---|
814 | return p; |
---|
815 | } |
---|
816 | |
---|
817 | void splay(int v) { |
---|
818 | while (_data[v].parent != -1) { |
---|
819 | if (v == _data[_data[v].parent].left) { |
---|
820 | if (_data[_data[v].parent].parent == -1) { |
---|
821 | zig(v); |
---|
822 | } else { |
---|
823 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
---|
824 | zig(_data[v].parent); |
---|
825 | zig(v); |
---|
826 | } else { |
---|
827 | zig(v); |
---|
828 | zag(v); |
---|
829 | } |
---|
830 | } |
---|
831 | } else { |
---|
832 | if (_data[_data[v].parent].parent == -1) { |
---|
833 | zag(v); |
---|
834 | } else { |
---|
835 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
---|
836 | zag(v); |
---|
837 | zig(v); |
---|
838 | } else { |
---|
839 | zag(_data[v].parent); |
---|
840 | zag(v); |
---|
841 | } |
---|
842 | } |
---|
843 | } |
---|
844 | } |
---|
845 | } |
---|
846 | |
---|
847 | |
---|
848 | void zig(int v) { |
---|
849 | Value min = _data[_data[v].parent].dmin; |
---|
850 | int a = _data[v].parent; |
---|
851 | |
---|
852 | Value aa = _data[a].dcost; |
---|
853 | if (_tolerance.less(aa, _max_value)) { |
---|
854 | aa+= min; |
---|
855 | } |
---|
856 | |
---|
857 | |
---|
858 | int b = v; |
---|
859 | Value ab = min + _data[b].dmin; |
---|
860 | Value bb = _data[b].dcost; |
---|
861 | if (_tolerance.less(bb, _max_value)) { |
---|
862 | bb+= ab; |
---|
863 | } |
---|
864 | |
---|
865 | int c = -1; |
---|
866 | Value cc = _max_value; |
---|
867 | if (_data[a].right != -1) { |
---|
868 | c = _data[a].right; |
---|
869 | cc = _data[c].dmin; |
---|
870 | if (_tolerance.less(cc, _max_value)) { |
---|
871 | cc+=min; |
---|
872 | } |
---|
873 | } |
---|
874 | |
---|
875 | int d = -1; |
---|
876 | Value dd = _max_value; |
---|
877 | if (_data[v].left != -1){ |
---|
878 | d = _data[v].left; |
---|
879 | dd = ab + _data[d].dmin; |
---|
880 | } |
---|
881 | |
---|
882 | int e = -1; |
---|
883 | Value ee = _max_value; |
---|
884 | if (_data[v].right != -1) { |
---|
885 | e = _data[v].right; |
---|
886 | ee = ab + _data[e].dmin; |
---|
887 | } |
---|
888 | |
---|
889 | Value min2; |
---|
890 | if (_tolerance.less(0, _data[b].dmin) || |
---|
891 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
---|
892 | min2 = min; |
---|
893 | } else { |
---|
894 | if (_tolerance.less(aa, cc)) { |
---|
895 | if (_tolerance.less(aa, ee)) { |
---|
896 | min2 = aa; |
---|
897 | } else { |
---|
898 | min2 = ee; |
---|
899 | } |
---|
900 | } else if (_tolerance.less(cc, ee)) { |
---|
901 | min2 = cc; |
---|
902 | } else { |
---|
903 | min2 = ee; |
---|
904 | } |
---|
905 | } |
---|
906 | |
---|
907 | _data[a].dcost = aa; |
---|
908 | if (_tolerance.less(aa, _max_value)) { |
---|
909 | _data[a].dcost -= min2; |
---|
910 | } |
---|
911 | _data[a].dmin = min2; |
---|
912 | if (_tolerance.less(min2,_max_value)) { |
---|
913 | _data[a].dmin -= min; |
---|
914 | } |
---|
915 | _data[b].dcost = bb; |
---|
916 | if (_tolerance.less(bb, _max_value)) { |
---|
917 | _data[b].dcost -= min; |
---|
918 | } |
---|
919 | _data[b].dmin = min; |
---|
920 | if (c != -1) { |
---|
921 | _data[c].dmin = cc; |
---|
922 | if (_tolerance.less(cc, _max_value)) { |
---|
923 | _data[c].dmin -= min2; |
---|
924 | } |
---|
925 | } |
---|
926 | if (d != -1) { |
---|
927 | _data[d].dmin = dd - min; |
---|
928 | } |
---|
929 | if (e != -1) { |
---|
930 | _data[e].dmin = ee - min2; |
---|
931 | } |
---|
932 | |
---|
933 | int w = _data[v].parent; |
---|
934 | _data[v].successor = _data[w].successor; |
---|
935 | _data[w].successor = -1; |
---|
936 | _data[v].parent = _data[w].parent; |
---|
937 | _data[w].parent = v; |
---|
938 | _data[w].left = _data[v].right; |
---|
939 | _data[v].right = w; |
---|
940 | if (_data[v].parent != -1){ |
---|
941 | if (_data[_data[v].parent].right == w) { |
---|
942 | _data[_data[v].parent].right = v; |
---|
943 | } else { |
---|
944 | _data[_data[v].parent].left = v; |
---|
945 | } |
---|
946 | } |
---|
947 | if (_data[w].left != -1){ |
---|
948 | _data[_data[w].left].parent = w; |
---|
949 | } |
---|
950 | } |
---|
951 | |
---|
952 | |
---|
953 | void zag(int v) { |
---|
954 | |
---|
955 | Value min = _data[_data[v].parent].dmin; |
---|
956 | |
---|
957 | int a = _data[v].parent; |
---|
958 | Value aa = _data[a].dcost; |
---|
959 | if (_tolerance.less(aa, _max_value)) { |
---|
960 | aa += min; |
---|
961 | } |
---|
962 | |
---|
963 | int b = v; |
---|
964 | Value ab = min + _data[b].dmin; |
---|
965 | Value bb = _data[b].dcost; |
---|
966 | if (_tolerance.less(bb, _max_value)) { |
---|
967 | bb += ab; |
---|
968 | } |
---|
969 | |
---|
970 | int c = -1; |
---|
971 | Value cc = _max_value; |
---|
972 | if (_data[a].left != -1){ |
---|
973 | c = _data[a].left; |
---|
974 | cc = min + _data[c].dmin; |
---|
975 | } |
---|
976 | |
---|
977 | int d = -1; |
---|
978 | Value dd = _max_value; |
---|
979 | if (_data[v].right!=-1) { |
---|
980 | d = _data[v].right; |
---|
981 | dd = _data[d].dmin; |
---|
982 | if (_tolerance.less(dd, _max_value)) { |
---|
983 | dd += ab; |
---|
984 | } |
---|
985 | } |
---|
986 | |
---|
987 | int e = -1; |
---|
988 | Value ee = _max_value; |
---|
989 | if (_data[v].left != -1){ |
---|
990 | e = _data[v].left; |
---|
991 | ee = ab + _data[e].dmin; |
---|
992 | } |
---|
993 | |
---|
994 | Value min2; |
---|
995 | if (_tolerance.less(0, _data[b].dmin) || |
---|
996 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
---|
997 | min2 = min; |
---|
998 | } else { |
---|
999 | if (_tolerance.less(aa, cc)) { |
---|
1000 | if (_tolerance.less(aa, ee)) { |
---|
1001 | min2 = aa; |
---|
1002 | } else { |
---|
1003 | min2 = ee; |
---|
1004 | } |
---|
1005 | } else if (_tolerance.less(cc, ee)) { |
---|
1006 | min2 = cc; |
---|
1007 | } else { |
---|
1008 | min2 = ee; |
---|
1009 | } |
---|
1010 | } |
---|
1011 | _data[a].dcost = aa; |
---|
1012 | if (_tolerance.less(aa, _max_value)) { |
---|
1013 | _data[a].dcost -= min2; |
---|
1014 | } |
---|
1015 | _data[a].dmin = min2; |
---|
1016 | if (_tolerance.less(min2, _max_value)) { |
---|
1017 | _data[a].dmin -= min; |
---|
1018 | } |
---|
1019 | _data[b].dcost = bb; |
---|
1020 | if (_tolerance.less(bb, _max_value)) { |
---|
1021 | _data[b].dcost -= min; |
---|
1022 | } |
---|
1023 | _data[b].dmin = min; |
---|
1024 | if (c != -1) { |
---|
1025 | _data[c].dmin = cc - min2; |
---|
1026 | } |
---|
1027 | if (d != -1) { |
---|
1028 | _data[d].dmin = dd; |
---|
1029 | if (_tolerance.less(dd, _max_value)) { |
---|
1030 | _data[d].dmin -= min; |
---|
1031 | } |
---|
1032 | } |
---|
1033 | if (e != -1) { |
---|
1034 | _data[e].dmin = ee - min2; |
---|
1035 | } |
---|
1036 | |
---|
1037 | int w = _data[v].parent; |
---|
1038 | _data[v].successor = _data[w].successor; |
---|
1039 | _data[w].successor = -1; |
---|
1040 | _data[v].parent = _data[w].parent; |
---|
1041 | _data[w].parent = v; |
---|
1042 | _data[w].right = _data[v].left; |
---|
1043 | _data[v].left = w; |
---|
1044 | if (_data[v].parent != -1){ |
---|
1045 | if (_data[_data[v].parent].left == w) { |
---|
1046 | _data[_data[v].parent].left = v; |
---|
1047 | } else { |
---|
1048 | _data[_data[v].parent].right = v; |
---|
1049 | } |
---|
1050 | } |
---|
1051 | if (_data[w].right != -1){ |
---|
1052 | _data[_data[w].right].parent = w; |
---|
1053 | } |
---|
1054 | } |
---|
1055 | |
---|
1056 | private: |
---|
1057 | |
---|
1058 | class ItemData { |
---|
1059 | public: |
---|
1060 | Item id; |
---|
1061 | int successor; |
---|
1062 | int parent; |
---|
1063 | int left; |
---|
1064 | int right; |
---|
1065 | Value dmin; |
---|
1066 | Value dcost; |
---|
1067 | |
---|
1068 | public: |
---|
1069 | ItemData(const Item &item) |
---|
1070 | : id(item), successor(), parent(-1), |
---|
1071 | left(-1), right(-1), dmin(0), dcost(0) {} |
---|
1072 | }; |
---|
1073 | |
---|
1074 | }; |
---|
1075 | |
---|
1076 | } |
---|
1077 | |
---|
1078 | #endif |
---|