[209] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
---|
[103] | 2 | * |
---|
[209] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
---|
[103] | 4 | * |
---|
[440] | 5 | * Copyright (C) 2003-2009 |
---|
[103] | 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_UNION_FIND_H |
---|
| 20 | #define LEMON_UNION_FIND_H |
---|
| 21 | |
---|
| 22 | //!\ingroup auxdat |
---|
| 23 | //!\file |
---|
| 24 | //!\brief Union-Find data structures. |
---|
| 25 | //! |
---|
| 26 | |
---|
| 27 | #include <vector> |
---|
| 28 | #include <list> |
---|
| 29 | #include <utility> |
---|
| 30 | #include <algorithm> |
---|
| 31 | #include <functional> |
---|
| 32 | |
---|
[220] | 33 | #include <lemon/core.h> |
---|
[103] | 34 | |
---|
| 35 | namespace lemon { |
---|
| 36 | |
---|
| 37 | /// \ingroup auxdat |
---|
| 38 | /// |
---|
| 39 | /// \brief A \e Union-Find data structure implementation |
---|
| 40 | /// |
---|
[209] | 41 | /// The class implements the \e Union-Find data structure. |
---|
[103] | 42 | /// The union operation uses rank heuristic, while |
---|
| 43 | /// the find operation uses path compression. |
---|
[209] | 44 | /// This is a very simple but efficient implementation, providing |
---|
[103] | 45 | /// only four methods: join (union), find, insert and size. |
---|
| 46 | /// For more features see the \ref UnionFindEnum class. |
---|
| 47 | /// |
---|
| 48 | /// It is primarily used in Kruskal algorithm for finding minimal |
---|
| 49 | /// cost spanning tree in a graph. |
---|
| 50 | /// \sa kruskal() |
---|
| 51 | /// |
---|
| 52 | /// \pre You need to add all the elements by the \ref insert() |
---|
[209] | 53 | /// method. |
---|
[103] | 54 | template <typename _ItemIntMap> |
---|
| 55 | class UnionFind { |
---|
| 56 | public: |
---|
| 57 | |
---|
| 58 | typedef _ItemIntMap ItemIntMap; |
---|
| 59 | typedef typename ItemIntMap::Key Item; |
---|
| 60 | |
---|
| 61 | private: |
---|
| 62 | // If the items vector stores negative value for an item then |
---|
| 63 | // that item is root item and it has -items[it] component size. |
---|
| 64 | // Else the items[it] contains the index of the parent. |
---|
| 65 | std::vector<int> items; |
---|
| 66 | ItemIntMap& index; |
---|
| 67 | |
---|
| 68 | bool rep(int idx) const { |
---|
| 69 | return items[idx] < 0; |
---|
| 70 | } |
---|
| 71 | |
---|
| 72 | int repIndex(int idx) const { |
---|
| 73 | int k = idx; |
---|
| 74 | while (!rep(k)) { |
---|
| 75 | k = items[k] ; |
---|
| 76 | } |
---|
| 77 | while (idx != k) { |
---|
| 78 | int next = items[idx]; |
---|
| 79 | const_cast<int&>(items[idx]) = k; |
---|
| 80 | idx = next; |
---|
| 81 | } |
---|
| 82 | return k; |
---|
| 83 | } |
---|
| 84 | |
---|
| 85 | public: |
---|
| 86 | |
---|
| 87 | /// \brief Constructor |
---|
| 88 | /// |
---|
| 89 | /// Constructor of the UnionFind class. You should give an item to |
---|
| 90 | /// integer map which will be used from the data structure. If you |
---|
| 91 | /// modify directly this map that may cause segmentation fault, |
---|
| 92 | /// invalid data structure, or infinite loop when you use again |
---|
| 93 | /// the union-find. |
---|
| 94 | UnionFind(ItemIntMap& m) : index(m) {} |
---|
| 95 | |
---|
| 96 | /// \brief Returns the index of the element's component. |
---|
| 97 | /// |
---|
| 98 | /// The method returns the index of the element's component. |
---|
| 99 | /// This is an integer between zero and the number of inserted elements. |
---|
| 100 | /// |
---|
| 101 | int find(const Item& a) { |
---|
| 102 | return repIndex(index[a]); |
---|
| 103 | } |
---|
| 104 | |
---|
| 105 | /// \brief Clears the union-find data structure |
---|
| 106 | /// |
---|
| 107 | /// Erase each item from the data structure. |
---|
| 108 | void clear() { |
---|
| 109 | items.clear(); |
---|
| 110 | } |
---|
| 111 | |
---|
| 112 | /// \brief Inserts a new element into the structure. |
---|
| 113 | /// |
---|
[209] | 114 | /// This method inserts a new element into the data structure. |
---|
[103] | 115 | /// |
---|
| 116 | /// The method returns the index of the new component. |
---|
| 117 | int insert(const Item& a) { |
---|
| 118 | int n = items.size(); |
---|
| 119 | items.push_back(-1); |
---|
| 120 | index.set(a,n); |
---|
| 121 | return n; |
---|
| 122 | } |
---|
| 123 | |
---|
| 124 | /// \brief Joining the components of element \e a and element \e b. |
---|
| 125 | /// |
---|
[209] | 126 | /// This is the \e union operation of the Union-Find structure. |
---|
[103] | 127 | /// Joins the component of element \e a and component of |
---|
| 128 | /// element \e b. If \e a and \e b are in the same component then |
---|
| 129 | /// it returns false otherwise it returns true. |
---|
| 130 | bool join(const Item& a, const Item& b) { |
---|
| 131 | int ka = repIndex(index[a]); |
---|
| 132 | int kb = repIndex(index[b]); |
---|
| 133 | |
---|
[209] | 134 | if ( ka == kb ) |
---|
| 135 | return false; |
---|
[103] | 136 | |
---|
| 137 | if (items[ka] < items[kb]) { |
---|
[209] | 138 | items[ka] += items[kb]; |
---|
| 139 | items[kb] = ka; |
---|
[103] | 140 | } else { |
---|
[209] | 141 | items[kb] += items[ka]; |
---|
| 142 | items[ka] = kb; |
---|
[103] | 143 | } |
---|
| 144 | return true; |
---|
| 145 | } |
---|
| 146 | |
---|
| 147 | /// \brief Returns the size of the component of element \e a. |
---|
| 148 | /// |
---|
| 149 | /// Returns the size of the component of element \e a. |
---|
| 150 | int size(const Item& a) { |
---|
| 151 | int k = repIndex(index[a]); |
---|
| 152 | return - items[k]; |
---|
| 153 | } |
---|
| 154 | |
---|
| 155 | }; |
---|
| 156 | |
---|
| 157 | /// \ingroup auxdat |
---|
| 158 | /// |
---|
| 159 | /// \brief A \e Union-Find data structure implementation which |
---|
| 160 | /// is able to enumerate the components. |
---|
| 161 | /// |
---|
| 162 | /// The class implements a \e Union-Find data structure |
---|
| 163 | /// which is able to enumerate the components and the items in |
---|
| 164 | /// a component. If you don't need this feature then perhaps it's |
---|
| 165 | /// better to use the \ref UnionFind class which is more efficient. |
---|
| 166 | /// |
---|
| 167 | /// The union operation uses rank heuristic, while |
---|
| 168 | /// the find operation uses path compression. |
---|
| 169 | /// |
---|
| 170 | /// \pre You need to add all the elements by the \ref insert() |
---|
| 171 | /// method. |
---|
| 172 | /// |
---|
| 173 | template <typename _ItemIntMap> |
---|
| 174 | class UnionFindEnum { |
---|
| 175 | public: |
---|
[209] | 176 | |
---|
[103] | 177 | typedef _ItemIntMap ItemIntMap; |
---|
| 178 | typedef typename ItemIntMap::Key Item; |
---|
| 179 | |
---|
| 180 | private: |
---|
[209] | 181 | |
---|
[103] | 182 | ItemIntMap& index; |
---|
| 183 | |
---|
| 184 | // If the parent stores negative value for an item then that item |
---|
| 185 | // is root item and it has ~(items[it].parent) component id. Else |
---|
| 186 | // the items[it].parent contains the index of the parent. |
---|
| 187 | // |
---|
| 188 | // The \c next and \c prev provides the double-linked |
---|
| 189 | // cyclic list of one component's items. |
---|
| 190 | struct ItemT { |
---|
| 191 | int parent; |
---|
| 192 | Item item; |
---|
| 193 | |
---|
| 194 | int next, prev; |
---|
| 195 | }; |
---|
| 196 | |
---|
| 197 | std::vector<ItemT> items; |
---|
| 198 | int firstFreeItem; |
---|
| 199 | |
---|
| 200 | struct ClassT { |
---|
| 201 | int size; |
---|
| 202 | int firstItem; |
---|
| 203 | int next, prev; |
---|
| 204 | }; |
---|
[209] | 205 | |
---|
[103] | 206 | std::vector<ClassT> classes; |
---|
| 207 | int firstClass, firstFreeClass; |
---|
| 208 | |
---|
| 209 | int newClass() { |
---|
| 210 | if (firstFreeClass == -1) { |
---|
[209] | 211 | int cdx = classes.size(); |
---|
| 212 | classes.push_back(ClassT()); |
---|
| 213 | return cdx; |
---|
[103] | 214 | } else { |
---|
[209] | 215 | int cdx = firstFreeClass; |
---|
| 216 | firstFreeClass = classes[firstFreeClass].next; |
---|
| 217 | return cdx; |
---|
[103] | 218 | } |
---|
| 219 | } |
---|
| 220 | |
---|
| 221 | int newItem() { |
---|
| 222 | if (firstFreeItem == -1) { |
---|
[209] | 223 | int idx = items.size(); |
---|
| 224 | items.push_back(ItemT()); |
---|
| 225 | return idx; |
---|
[103] | 226 | } else { |
---|
[209] | 227 | int idx = firstFreeItem; |
---|
| 228 | firstFreeItem = items[firstFreeItem].next; |
---|
| 229 | return idx; |
---|
[103] | 230 | } |
---|
| 231 | } |
---|
| 232 | |
---|
| 233 | |
---|
| 234 | bool rep(int idx) const { |
---|
| 235 | return items[idx].parent < 0; |
---|
| 236 | } |
---|
| 237 | |
---|
| 238 | int repIndex(int idx) const { |
---|
| 239 | int k = idx; |
---|
| 240 | while (!rep(k)) { |
---|
| 241 | k = items[k].parent; |
---|
| 242 | } |
---|
| 243 | while (idx != k) { |
---|
| 244 | int next = items[idx].parent; |
---|
| 245 | const_cast<int&>(items[idx].parent) = k; |
---|
| 246 | idx = next; |
---|
| 247 | } |
---|
| 248 | return k; |
---|
| 249 | } |
---|
| 250 | |
---|
| 251 | int classIndex(int idx) const { |
---|
| 252 | return ~(items[repIndex(idx)].parent); |
---|
| 253 | } |
---|
| 254 | |
---|
| 255 | void singletonItem(int idx) { |
---|
| 256 | items[idx].next = idx; |
---|
| 257 | items[idx].prev = idx; |
---|
| 258 | } |
---|
| 259 | |
---|
| 260 | void laceItem(int idx, int rdx) { |
---|
| 261 | items[idx].prev = rdx; |
---|
| 262 | items[idx].next = items[rdx].next; |
---|
| 263 | items[items[rdx].next].prev = idx; |
---|
| 264 | items[rdx].next = idx; |
---|
| 265 | } |
---|
| 266 | |
---|
| 267 | void unlaceItem(int idx) { |
---|
| 268 | items[items[idx].prev].next = items[idx].next; |
---|
| 269 | items[items[idx].next].prev = items[idx].prev; |
---|
[209] | 270 | |
---|
[103] | 271 | items[idx].next = firstFreeItem; |
---|
| 272 | firstFreeItem = idx; |
---|
| 273 | } |
---|
| 274 | |
---|
| 275 | void spliceItems(int ak, int bk) { |
---|
| 276 | items[items[ak].prev].next = bk; |
---|
| 277 | items[items[bk].prev].next = ak; |
---|
| 278 | int tmp = items[ak].prev; |
---|
| 279 | items[ak].prev = items[bk].prev; |
---|
| 280 | items[bk].prev = tmp; |
---|
[209] | 281 | |
---|
[103] | 282 | } |
---|
| 283 | |
---|
| 284 | void laceClass(int cls) { |
---|
| 285 | if (firstClass != -1) { |
---|
| 286 | classes[firstClass].prev = cls; |
---|
| 287 | } |
---|
| 288 | classes[cls].next = firstClass; |
---|
| 289 | classes[cls].prev = -1; |
---|
| 290 | firstClass = cls; |
---|
[209] | 291 | } |
---|
[103] | 292 | |
---|
| 293 | void unlaceClass(int cls) { |
---|
| 294 | if (classes[cls].prev != -1) { |
---|
| 295 | classes[classes[cls].prev].next = classes[cls].next; |
---|
| 296 | } else { |
---|
| 297 | firstClass = classes[cls].next; |
---|
| 298 | } |
---|
| 299 | if (classes[cls].next != -1) { |
---|
| 300 | classes[classes[cls].next].prev = classes[cls].prev; |
---|
| 301 | } |
---|
[209] | 302 | |
---|
[103] | 303 | classes[cls].next = firstFreeClass; |
---|
| 304 | firstFreeClass = cls; |
---|
[209] | 305 | } |
---|
[103] | 306 | |
---|
| 307 | public: |
---|
| 308 | |
---|
[209] | 309 | UnionFindEnum(ItemIntMap& _index) |
---|
| 310 | : index(_index), items(), firstFreeItem(-1), |
---|
| 311 | firstClass(-1), firstFreeClass(-1) {} |
---|
| 312 | |
---|
[103] | 313 | /// \brief Inserts the given element into a new component. |
---|
| 314 | /// |
---|
| 315 | /// This method creates a new component consisting only of the |
---|
| 316 | /// given element. |
---|
| 317 | /// |
---|
| 318 | int insert(const Item& item) { |
---|
| 319 | int idx = newItem(); |
---|
| 320 | |
---|
| 321 | index.set(item, idx); |
---|
| 322 | |
---|
| 323 | singletonItem(idx); |
---|
| 324 | items[idx].item = item; |
---|
| 325 | |
---|
| 326 | int cdx = newClass(); |
---|
| 327 | |
---|
| 328 | items[idx].parent = ~cdx; |
---|
| 329 | |
---|
| 330 | laceClass(cdx); |
---|
| 331 | classes[cdx].size = 1; |
---|
| 332 | classes[cdx].firstItem = idx; |
---|
| 333 | |
---|
| 334 | firstClass = cdx; |
---|
[209] | 335 | |
---|
[103] | 336 | return cdx; |
---|
| 337 | } |
---|
| 338 | |
---|
| 339 | /// \brief Inserts the given element into the component of the others. |
---|
| 340 | /// |
---|
| 341 | /// This methods inserts the element \e a into the component of the |
---|
[209] | 342 | /// element \e comp. |
---|
[103] | 343 | void insert(const Item& item, int cls) { |
---|
| 344 | int rdx = classes[cls].firstItem; |
---|
| 345 | int idx = newItem(); |
---|
| 346 | |
---|
| 347 | index.set(item, idx); |
---|
| 348 | |
---|
| 349 | laceItem(idx, rdx); |
---|
| 350 | |
---|
| 351 | items[idx].item = item; |
---|
| 352 | items[idx].parent = rdx; |
---|
| 353 | |
---|
| 354 | ++classes[~(items[rdx].parent)].size; |
---|
| 355 | } |
---|
| 356 | |
---|
| 357 | /// \brief Clears the union-find data structure |
---|
| 358 | /// |
---|
| 359 | /// Erase each item from the data structure. |
---|
| 360 | void clear() { |
---|
| 361 | items.clear(); |
---|
| 362 | firstClass = -1; |
---|
| 363 | firstFreeItem = -1; |
---|
| 364 | } |
---|
| 365 | |
---|
| 366 | /// \brief Finds the component of the given element. |
---|
| 367 | /// |
---|
| 368 | /// The method returns the component id of the given element. |
---|
| 369 | int find(const Item &item) const { |
---|
| 370 | return ~(items[repIndex(index[item])].parent); |
---|
| 371 | } |
---|
| 372 | |
---|
| 373 | /// \brief Joining the component of element \e a and element \e b. |
---|
| 374 | /// |
---|
[209] | 375 | /// This is the \e union operation of the Union-Find structure. |
---|
[103] | 376 | /// Joins the component of element \e a and component of |
---|
| 377 | /// element \e b. If \e a and \e b are in the same component then |
---|
| 378 | /// returns -1 else returns the remaining class. |
---|
| 379 | int join(const Item& a, const Item& b) { |
---|
| 380 | |
---|
| 381 | int ak = repIndex(index[a]); |
---|
| 382 | int bk = repIndex(index[b]); |
---|
| 383 | |
---|
| 384 | if (ak == bk) { |
---|
[209] | 385 | return -1; |
---|
[103] | 386 | } |
---|
| 387 | |
---|
| 388 | int acx = ~(items[ak].parent); |
---|
| 389 | int bcx = ~(items[bk].parent); |
---|
| 390 | |
---|
| 391 | int rcx; |
---|
| 392 | |
---|
| 393 | if (classes[acx].size > classes[bcx].size) { |
---|
[209] | 394 | classes[acx].size += classes[bcx].size; |
---|
| 395 | items[bk].parent = ak; |
---|
[103] | 396 | unlaceClass(bcx); |
---|
[209] | 397 | rcx = acx; |
---|
[103] | 398 | } else { |
---|
[209] | 399 | classes[bcx].size += classes[acx].size; |
---|
| 400 | items[ak].parent = bk; |
---|
[103] | 401 | unlaceClass(acx); |
---|
[209] | 402 | rcx = bcx; |
---|
[103] | 403 | } |
---|
| 404 | spliceItems(ak, bk); |
---|
| 405 | |
---|
| 406 | return rcx; |
---|
| 407 | } |
---|
| 408 | |
---|
| 409 | /// \brief Returns the size of the class. |
---|
| 410 | /// |
---|
| 411 | /// Returns the size of the class. |
---|
| 412 | int size(int cls) const { |
---|
| 413 | return classes[cls].size; |
---|
| 414 | } |
---|
| 415 | |
---|
[209] | 416 | /// \brief Splits up the component. |
---|
[103] | 417 | /// |
---|
| 418 | /// Splitting the component into singleton components (component |
---|
| 419 | /// of size one). |
---|
| 420 | void split(int cls) { |
---|
| 421 | int fdx = classes[cls].firstItem; |
---|
| 422 | int idx = items[fdx].next; |
---|
| 423 | while (idx != fdx) { |
---|
| 424 | int next = items[idx].next; |
---|
| 425 | |
---|
[209] | 426 | singletonItem(idx); |
---|
[103] | 427 | |
---|
[209] | 428 | int cdx = newClass(); |
---|
[103] | 429 | items[idx].parent = ~cdx; |
---|
| 430 | |
---|
[209] | 431 | laceClass(cdx); |
---|
| 432 | classes[cdx].size = 1; |
---|
| 433 | classes[cdx].firstItem = idx; |
---|
| 434 | |
---|
[103] | 435 | idx = next; |
---|
| 436 | } |
---|
| 437 | |
---|
| 438 | items[idx].prev = idx; |
---|
| 439 | items[idx].next = idx; |
---|
| 440 | |
---|
| 441 | classes[~(items[idx].parent)].size = 1; |
---|
[209] | 442 | |
---|
[103] | 443 | } |
---|
| 444 | |
---|
| 445 | /// \brief Removes the given element from the structure. |
---|
| 446 | /// |
---|
| 447 | /// Removes the element from its component and if the component becomes |
---|
| 448 | /// empty then removes that component from the component list. |
---|
| 449 | /// |
---|
| 450 | /// \warning It is an error to remove an element which is not in |
---|
| 451 | /// the structure. |
---|
| 452 | /// \warning This running time of this operation is proportional to the |
---|
| 453 | /// number of the items in this class. |
---|
| 454 | void erase(const Item& item) { |
---|
| 455 | int idx = index[item]; |
---|
| 456 | int fdx = items[idx].next; |
---|
| 457 | |
---|
| 458 | int cdx = classIndex(idx); |
---|
| 459 | if (idx == fdx) { |
---|
[209] | 460 | unlaceClass(cdx); |
---|
| 461 | items[idx].next = firstFreeItem; |
---|
| 462 | firstFreeItem = idx; |
---|
| 463 | return; |
---|
[103] | 464 | } else { |
---|
[209] | 465 | classes[cdx].firstItem = fdx; |
---|
| 466 | --classes[cdx].size; |
---|
| 467 | items[fdx].parent = ~cdx; |
---|
[103] | 468 | |
---|
[209] | 469 | unlaceItem(idx); |
---|
| 470 | idx = items[fdx].next; |
---|
| 471 | while (idx != fdx) { |
---|
| 472 | items[idx].parent = fdx; |
---|
| 473 | idx = items[idx].next; |
---|
| 474 | } |
---|
| 475 | |
---|
[103] | 476 | } |
---|
| 477 | |
---|
| 478 | } |
---|
| 479 | |
---|
| 480 | /// \brief Gives back a representant item of the component. |
---|
| 481 | /// |
---|
| 482 | /// Gives back a representant item of the component. |
---|
| 483 | Item item(int cls) const { |
---|
| 484 | return items[classes[cls].firstItem].item; |
---|
| 485 | } |
---|
| 486 | |
---|
| 487 | /// \brief Removes the component of the given element from the structure. |
---|
| 488 | /// |
---|
| 489 | /// Removes the component of the given element from the structure. |
---|
| 490 | /// |
---|
| 491 | /// \warning It is an error to give an element which is not in the |
---|
| 492 | /// structure. |
---|
| 493 | void eraseClass(int cls) { |
---|
| 494 | int fdx = classes[cls].firstItem; |
---|
| 495 | unlaceClass(cls); |
---|
| 496 | items[items[fdx].prev].next = firstFreeItem; |
---|
| 497 | firstFreeItem = fdx; |
---|
| 498 | } |
---|
| 499 | |
---|
[236] | 500 | /// \brief LEMON style iterator for the representant items. |
---|
[103] | 501 | /// |
---|
| 502 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
| 503 | /// on the ids of the classes. |
---|
| 504 | class ClassIt { |
---|
| 505 | public: |
---|
| 506 | /// \brief Constructor of the iterator |
---|
| 507 | /// |
---|
| 508 | /// Constructor of the iterator |
---|
| 509 | ClassIt(const UnionFindEnum& ufe) : unionFind(&ufe) { |
---|
| 510 | cdx = unionFind->firstClass; |
---|
| 511 | } |
---|
| 512 | |
---|
| 513 | /// \brief Constructor to get invalid iterator |
---|
| 514 | /// |
---|
| 515 | /// Constructor to get invalid iterator |
---|
| 516 | ClassIt(Invalid) : unionFind(0), cdx(-1) {} |
---|
[209] | 517 | |
---|
[103] | 518 | /// \brief Increment operator |
---|
| 519 | /// |
---|
| 520 | /// It steps to the next representant item. |
---|
| 521 | ClassIt& operator++() { |
---|
| 522 | cdx = unionFind->classes[cdx].next; |
---|
| 523 | return *this; |
---|
| 524 | } |
---|
[209] | 525 | |
---|
[103] | 526 | /// \brief Conversion operator |
---|
| 527 | /// |
---|
| 528 | /// It converts the iterator to the current representant item. |
---|
| 529 | operator int() const { |
---|
| 530 | return cdx; |
---|
| 531 | } |
---|
| 532 | |
---|
| 533 | /// \brief Equality operator |
---|
| 534 | /// |
---|
| 535 | /// Equality operator |
---|
[209] | 536 | bool operator==(const ClassIt& i) { |
---|
[103] | 537 | return i.cdx == cdx; |
---|
| 538 | } |
---|
| 539 | |
---|
| 540 | /// \brief Inequality operator |
---|
| 541 | /// |
---|
| 542 | /// Inequality operator |
---|
[209] | 543 | bool operator!=(const ClassIt& i) { |
---|
[103] | 544 | return i.cdx != cdx; |
---|
| 545 | } |
---|
[209] | 546 | |
---|
[103] | 547 | private: |
---|
| 548 | const UnionFindEnum* unionFind; |
---|
| 549 | int cdx; |
---|
| 550 | }; |
---|
| 551 | |
---|
[236] | 552 | /// \brief LEMON style iterator for the items of a component. |
---|
[103] | 553 | /// |
---|
| 554 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
| 555 | /// on the items of a class. By example if you want to iterate on |
---|
| 556 | /// each items of each classes then you may write the next code. |
---|
| 557 | ///\code |
---|
| 558 | /// for (ClassIt cit(ufe); cit != INVALID; ++cit) { |
---|
| 559 | /// std::cout << "Class: "; |
---|
| 560 | /// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) { |
---|
| 561 | /// std::cout << toString(iit) << ' ' << std::endl; |
---|
| 562 | /// } |
---|
| 563 | /// std::cout << std::endl; |
---|
| 564 | /// } |
---|
| 565 | ///\endcode |
---|
| 566 | class ItemIt { |
---|
| 567 | public: |
---|
| 568 | /// \brief Constructor of the iterator |
---|
| 569 | /// |
---|
| 570 | /// Constructor of the iterator. The iterator iterates |
---|
| 571 | /// on the class of the \c item. |
---|
| 572 | ItemIt(const UnionFindEnum& ufe, int cls) : unionFind(&ufe) { |
---|
| 573 | fdx = idx = unionFind->classes[cls].firstItem; |
---|
| 574 | } |
---|
| 575 | |
---|
| 576 | /// \brief Constructor to get invalid iterator |
---|
| 577 | /// |
---|
| 578 | /// Constructor to get invalid iterator |
---|
| 579 | ItemIt(Invalid) : unionFind(0), idx(-1) {} |
---|
[209] | 580 | |
---|
[103] | 581 | /// \brief Increment operator |
---|
| 582 | /// |
---|
| 583 | /// It steps to the next item in the class. |
---|
| 584 | ItemIt& operator++() { |
---|
| 585 | idx = unionFind->items[idx].next; |
---|
| 586 | if (idx == fdx) idx = -1; |
---|
| 587 | return *this; |
---|
| 588 | } |
---|
[209] | 589 | |
---|
[103] | 590 | /// \brief Conversion operator |
---|
| 591 | /// |
---|
| 592 | /// It converts the iterator to the current item. |
---|
| 593 | operator const Item&() const { |
---|
| 594 | return unionFind->items[idx].item; |
---|
| 595 | } |
---|
| 596 | |
---|
| 597 | /// \brief Equality operator |
---|
| 598 | /// |
---|
| 599 | /// Equality operator |
---|
[209] | 600 | bool operator==(const ItemIt& i) { |
---|
[103] | 601 | return i.idx == idx; |
---|
| 602 | } |
---|
| 603 | |
---|
| 604 | /// \brief Inequality operator |
---|
| 605 | /// |
---|
| 606 | /// Inequality operator |
---|
[209] | 607 | bool operator!=(const ItemIt& i) { |
---|
[103] | 608 | return i.idx != idx; |
---|
| 609 | } |
---|
[209] | 610 | |
---|
[103] | 611 | private: |
---|
| 612 | const UnionFindEnum* unionFind; |
---|
| 613 | int idx, fdx; |
---|
| 614 | }; |
---|
| 615 | |
---|
| 616 | }; |
---|
| 617 | |
---|
| 618 | /// \ingroup auxdat |
---|
| 619 | /// |
---|
| 620 | /// \brief A \e Extend-Find data structure implementation which |
---|
| 621 | /// is able to enumerate the components. |
---|
| 622 | /// |
---|
| 623 | /// The class implements an \e Extend-Find data structure which is |
---|
| 624 | /// able to enumerate the components and the items in a |
---|
| 625 | /// component. The data structure is a simplification of the |
---|
| 626 | /// Union-Find structure, and it does not allow to merge two components. |
---|
| 627 | /// |
---|
| 628 | /// \pre You need to add all the elements by the \ref insert() |
---|
| 629 | /// method. |
---|
| 630 | template <typename _ItemIntMap> |
---|
| 631 | class ExtendFindEnum { |
---|
| 632 | public: |
---|
[209] | 633 | |
---|
[103] | 634 | typedef _ItemIntMap ItemIntMap; |
---|
| 635 | typedef typename ItemIntMap::Key Item; |
---|
| 636 | |
---|
| 637 | private: |
---|
[209] | 638 | |
---|
[103] | 639 | ItemIntMap& index; |
---|
| 640 | |
---|
| 641 | struct ItemT { |
---|
| 642 | int cls; |
---|
| 643 | Item item; |
---|
| 644 | int next, prev; |
---|
| 645 | }; |
---|
| 646 | |
---|
| 647 | std::vector<ItemT> items; |
---|
| 648 | int firstFreeItem; |
---|
| 649 | |
---|
| 650 | struct ClassT { |
---|
| 651 | int firstItem; |
---|
| 652 | int next, prev; |
---|
| 653 | }; |
---|
| 654 | |
---|
| 655 | std::vector<ClassT> classes; |
---|
| 656 | |
---|
| 657 | int firstClass, firstFreeClass; |
---|
| 658 | |
---|
| 659 | int newClass() { |
---|
| 660 | if (firstFreeClass != -1) { |
---|
[209] | 661 | int cdx = firstFreeClass; |
---|
| 662 | firstFreeClass = classes[cdx].next; |
---|
| 663 | return cdx; |
---|
[103] | 664 | } else { |
---|
[209] | 665 | classes.push_back(ClassT()); |
---|
| 666 | return classes.size() - 1; |
---|
[103] | 667 | } |
---|
| 668 | } |
---|
| 669 | |
---|
| 670 | int newItem() { |
---|
| 671 | if (firstFreeItem != -1) { |
---|
[209] | 672 | int idx = firstFreeItem; |
---|
| 673 | firstFreeItem = items[idx].next; |
---|
| 674 | return idx; |
---|
[103] | 675 | } else { |
---|
[209] | 676 | items.push_back(ItemT()); |
---|
| 677 | return items.size() - 1; |
---|
[103] | 678 | } |
---|
| 679 | } |
---|
| 680 | |
---|
| 681 | public: |
---|
| 682 | |
---|
| 683 | /// \brief Constructor |
---|
[209] | 684 | ExtendFindEnum(ItemIntMap& _index) |
---|
| 685 | : index(_index), items(), firstFreeItem(-1), |
---|
| 686 | classes(), firstClass(-1), firstFreeClass(-1) {} |
---|
| 687 | |
---|
[103] | 688 | /// \brief Inserts the given element into a new component. |
---|
| 689 | /// |
---|
| 690 | /// This method creates a new component consisting only of the |
---|
| 691 | /// given element. |
---|
| 692 | int insert(const Item& item) { |
---|
| 693 | int cdx = newClass(); |
---|
| 694 | classes[cdx].prev = -1; |
---|
| 695 | classes[cdx].next = firstClass; |
---|
| 696 | if (firstClass != -1) { |
---|
[209] | 697 | classes[firstClass].prev = cdx; |
---|
[103] | 698 | } |
---|
| 699 | firstClass = cdx; |
---|
[209] | 700 | |
---|
[103] | 701 | int idx = newItem(); |
---|
| 702 | items[idx].item = item; |
---|
| 703 | items[idx].cls = cdx; |
---|
| 704 | items[idx].prev = idx; |
---|
| 705 | items[idx].next = idx; |
---|
| 706 | |
---|
| 707 | classes[cdx].firstItem = idx; |
---|
| 708 | |
---|
| 709 | index.set(item, idx); |
---|
[209] | 710 | |
---|
[103] | 711 | return cdx; |
---|
| 712 | } |
---|
| 713 | |
---|
| 714 | /// \brief Inserts the given element into the given component. |
---|
| 715 | /// |
---|
| 716 | /// This methods inserts the element \e item a into the \e cls class. |
---|
| 717 | void insert(const Item& item, int cls) { |
---|
| 718 | int idx = newItem(); |
---|
| 719 | int rdx = classes[cls].firstItem; |
---|
| 720 | items[idx].item = item; |
---|
| 721 | items[idx].cls = cls; |
---|
| 722 | |
---|
| 723 | items[idx].prev = rdx; |
---|
| 724 | items[idx].next = items[rdx].next; |
---|
| 725 | items[items[rdx].next].prev = idx; |
---|
| 726 | items[rdx].next = idx; |
---|
| 727 | |
---|
| 728 | index.set(item, idx); |
---|
| 729 | } |
---|
| 730 | |
---|
| 731 | /// \brief Clears the union-find data structure |
---|
| 732 | /// |
---|
| 733 | /// Erase each item from the data structure. |
---|
| 734 | void clear() { |
---|
| 735 | items.clear(); |
---|
| 736 | classes.clear; |
---|
| 737 | firstClass = firstFreeClass = firstFreeItem = -1; |
---|
| 738 | } |
---|
| 739 | |
---|
| 740 | /// \brief Gives back the class of the \e item. |
---|
| 741 | /// |
---|
| 742 | /// Gives back the class of the \e item. |
---|
| 743 | int find(const Item &item) const { |
---|
| 744 | return items[index[item]].cls; |
---|
| 745 | } |
---|
| 746 | |
---|
| 747 | /// \brief Gives back a representant item of the component. |
---|
| 748 | /// |
---|
| 749 | /// Gives back a representant item of the component. |
---|
| 750 | Item item(int cls) const { |
---|
| 751 | return items[classes[cls].firstItem].item; |
---|
| 752 | } |
---|
[209] | 753 | |
---|
[103] | 754 | /// \brief Removes the given element from the structure. |
---|
| 755 | /// |
---|
| 756 | /// Removes the element from its component and if the component becomes |
---|
| 757 | /// empty then removes that component from the component list. |
---|
| 758 | /// |
---|
| 759 | /// \warning It is an error to remove an element which is not in |
---|
| 760 | /// the structure. |
---|
| 761 | void erase(const Item &item) { |
---|
| 762 | int idx = index[item]; |
---|
| 763 | int cdx = items[idx].cls; |
---|
[209] | 764 | |
---|
[103] | 765 | if (idx == items[idx].next) { |
---|
[209] | 766 | if (classes[cdx].prev != -1) { |
---|
| 767 | classes[classes[cdx].prev].next = classes[cdx].next; |
---|
| 768 | } else { |
---|
| 769 | firstClass = classes[cdx].next; |
---|
| 770 | } |
---|
| 771 | if (classes[cdx].next != -1) { |
---|
| 772 | classes[classes[cdx].next].prev = classes[cdx].prev; |
---|
| 773 | } |
---|
| 774 | classes[cdx].next = firstFreeClass; |
---|
| 775 | firstFreeClass = cdx; |
---|
[103] | 776 | } else { |
---|
[209] | 777 | classes[cdx].firstItem = items[idx].next; |
---|
| 778 | items[items[idx].next].prev = items[idx].prev; |
---|
| 779 | items[items[idx].prev].next = items[idx].next; |
---|
[103] | 780 | } |
---|
| 781 | items[idx].next = firstFreeItem; |
---|
| 782 | firstFreeItem = idx; |
---|
| 783 | |
---|
[209] | 784 | } |
---|
| 785 | |
---|
| 786 | |
---|
[103] | 787 | /// \brief Removes the component of the given element from the structure. |
---|
| 788 | /// |
---|
| 789 | /// Removes the component of the given element from the structure. |
---|
| 790 | /// |
---|
| 791 | /// \warning It is an error to give an element which is not in the |
---|
| 792 | /// structure. |
---|
| 793 | void eraseClass(int cdx) { |
---|
| 794 | int idx = classes[cdx].firstItem; |
---|
| 795 | items[items[idx].prev].next = firstFreeItem; |
---|
| 796 | firstFreeItem = idx; |
---|
| 797 | |
---|
| 798 | if (classes[cdx].prev != -1) { |
---|
[209] | 799 | classes[classes[cdx].prev].next = classes[cdx].next; |
---|
[103] | 800 | } else { |
---|
[209] | 801 | firstClass = classes[cdx].next; |
---|
[103] | 802 | } |
---|
| 803 | if (classes[cdx].next != -1) { |
---|
[209] | 804 | classes[classes[cdx].next].prev = classes[cdx].prev; |
---|
[103] | 805 | } |
---|
| 806 | classes[cdx].next = firstFreeClass; |
---|
| 807 | firstFreeClass = cdx; |
---|
| 808 | } |
---|
| 809 | |
---|
[236] | 810 | /// \brief LEMON style iterator for the classes. |
---|
[103] | 811 | /// |
---|
| 812 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
| 813 | /// on the ids of classes. |
---|
| 814 | class ClassIt { |
---|
| 815 | public: |
---|
| 816 | /// \brief Constructor of the iterator |
---|
| 817 | /// |
---|
| 818 | /// Constructor of the iterator |
---|
| 819 | ClassIt(const ExtendFindEnum& ufe) : extendFind(&ufe) { |
---|
| 820 | cdx = extendFind->firstClass; |
---|
| 821 | } |
---|
| 822 | |
---|
| 823 | /// \brief Constructor to get invalid iterator |
---|
| 824 | /// |
---|
| 825 | /// Constructor to get invalid iterator |
---|
| 826 | ClassIt(Invalid) : extendFind(0), cdx(-1) {} |
---|
[209] | 827 | |
---|
[103] | 828 | /// \brief Increment operator |
---|
| 829 | /// |
---|
| 830 | /// It steps to the next representant item. |
---|
| 831 | ClassIt& operator++() { |
---|
| 832 | cdx = extendFind->classes[cdx].next; |
---|
| 833 | return *this; |
---|
| 834 | } |
---|
[209] | 835 | |
---|
[103] | 836 | /// \brief Conversion operator |
---|
| 837 | /// |
---|
| 838 | /// It converts the iterator to the current class id. |
---|
| 839 | operator int() const { |
---|
| 840 | return cdx; |
---|
| 841 | } |
---|
| 842 | |
---|
| 843 | /// \brief Equality operator |
---|
| 844 | /// |
---|
| 845 | /// Equality operator |
---|
[209] | 846 | bool operator==(const ClassIt& i) { |
---|
[103] | 847 | return i.cdx == cdx; |
---|
| 848 | } |
---|
| 849 | |
---|
| 850 | /// \brief Inequality operator |
---|
| 851 | /// |
---|
| 852 | /// Inequality operator |
---|
[209] | 853 | bool operator!=(const ClassIt& i) { |
---|
[103] | 854 | return i.cdx != cdx; |
---|
| 855 | } |
---|
[209] | 856 | |
---|
[103] | 857 | private: |
---|
| 858 | const ExtendFindEnum* extendFind; |
---|
| 859 | int cdx; |
---|
| 860 | }; |
---|
| 861 | |
---|
[236] | 862 | /// \brief LEMON style iterator for the items of a component. |
---|
[103] | 863 | /// |
---|
| 864 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
| 865 | /// on the items of a class. By example if you want to iterate on |
---|
| 866 | /// each items of each classes then you may write the next code. |
---|
| 867 | ///\code |
---|
| 868 | /// for (ClassIt cit(ufe); cit != INVALID; ++cit) { |
---|
| 869 | /// std::cout << "Class: "; |
---|
| 870 | /// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) { |
---|
| 871 | /// std::cout << toString(iit) << ' ' << std::endl; |
---|
| 872 | /// } |
---|
| 873 | /// std::cout << std::endl; |
---|
| 874 | /// } |
---|
| 875 | ///\endcode |
---|
| 876 | class ItemIt { |
---|
| 877 | public: |
---|
| 878 | /// \brief Constructor of the iterator |
---|
| 879 | /// |
---|
| 880 | /// Constructor of the iterator. The iterator iterates |
---|
| 881 | /// on the class of the \c item. |
---|
| 882 | ItemIt(const ExtendFindEnum& ufe, int cls) : extendFind(&ufe) { |
---|
| 883 | fdx = idx = extendFind->classes[cls].firstItem; |
---|
| 884 | } |
---|
| 885 | |
---|
| 886 | /// \brief Constructor to get invalid iterator |
---|
| 887 | /// |
---|
| 888 | /// Constructor to get invalid iterator |
---|
| 889 | ItemIt(Invalid) : extendFind(0), idx(-1) {} |
---|
[209] | 890 | |
---|
[103] | 891 | /// \brief Increment operator |
---|
| 892 | /// |
---|
| 893 | /// It steps to the next item in the class. |
---|
| 894 | ItemIt& operator++() { |
---|
| 895 | idx = extendFind->items[idx].next; |
---|
[209] | 896 | if (fdx == idx) idx = -1; |
---|
[103] | 897 | return *this; |
---|
| 898 | } |
---|
[209] | 899 | |
---|
[103] | 900 | /// \brief Conversion operator |
---|
| 901 | /// |
---|
| 902 | /// It converts the iterator to the current item. |
---|
| 903 | operator const Item&() const { |
---|
| 904 | return extendFind->items[idx].item; |
---|
| 905 | } |
---|
| 906 | |
---|
| 907 | /// \brief Equality operator |
---|
| 908 | /// |
---|
| 909 | /// Equality operator |
---|
[209] | 910 | bool operator==(const ItemIt& i) { |
---|
[103] | 911 | return i.idx == idx; |
---|
| 912 | } |
---|
| 913 | |
---|
| 914 | /// \brief Inequality operator |
---|
| 915 | /// |
---|
| 916 | /// Inequality operator |
---|
[209] | 917 | bool operator!=(const ItemIt& i) { |
---|
[103] | 918 | return i.idx != idx; |
---|
| 919 | } |
---|
[209] | 920 | |
---|
[103] | 921 | private: |
---|
| 922 | const ExtendFindEnum* extendFind; |
---|
| 923 | int idx, fdx; |
---|
| 924 | }; |
---|
| 925 | |
---|
| 926 | }; |
---|
| 927 | |
---|
| 928 | /// \ingroup auxdat |
---|
| 929 | /// |
---|
| 930 | /// \brief A \e Union-Find data structure implementation which |
---|
| 931 | /// is able to store a priority for each item and retrieve the minimum of |
---|
| 932 | /// each class. |
---|
| 933 | /// |
---|
| 934 | /// A \e Union-Find data structure implementation which is able to |
---|
| 935 | /// store a priority for each item and retrieve the minimum of each |
---|
| 936 | /// class. In addition, it supports the joining and splitting the |
---|
| 937 | /// components. If you don't need this feature then you makes |
---|
| 938 | /// better to use the \ref UnionFind class which is more efficient. |
---|
| 939 | /// |
---|
| 940 | /// The union-find data strcuture based on a (2, 16)-tree with a |
---|
| 941 | /// tournament minimum selection on the internal nodes. The insert |
---|
| 942 | /// operation takes O(1), the find, set, decrease and increase takes |
---|
| 943 | /// O(log(n)), where n is the number of nodes in the current |
---|
| 944 | /// component. The complexity of join and split is O(log(n)*k), |
---|
| 945 | /// where n is the sum of the number of the nodes and k is the |
---|
| 946 | /// number of joined components or the number of the components |
---|
| 947 | /// after the split. |
---|
| 948 | /// |
---|
| 949 | /// \pre You need to add all the elements by the \ref insert() |
---|
| 950 | /// method. |
---|
| 951 | /// |
---|
[209] | 952 | template <typename _Value, typename _ItemIntMap, |
---|
[103] | 953 | typename _Comp = std::less<_Value> > |
---|
| 954 | class HeapUnionFind { |
---|
| 955 | public: |
---|
[209] | 956 | |
---|
[103] | 957 | typedef _Value Value; |
---|
| 958 | typedef typename _ItemIntMap::Key Item; |
---|
| 959 | |
---|
| 960 | typedef _ItemIntMap ItemIntMap; |
---|
| 961 | |
---|
| 962 | typedef _Comp Comp; |
---|
| 963 | |
---|
| 964 | private: |
---|
| 965 | |
---|
| 966 | static const int cmax = 16; |
---|
| 967 | |
---|
| 968 | ItemIntMap& index; |
---|
| 969 | |
---|
| 970 | struct ClassNode { |
---|
| 971 | int parent; |
---|
| 972 | int depth; |
---|
| 973 | |
---|
| 974 | int left, right; |
---|
| 975 | int next, prev; |
---|
| 976 | }; |
---|
| 977 | |
---|
| 978 | int first_class; |
---|
| 979 | int first_free_class; |
---|
| 980 | std::vector<ClassNode> classes; |
---|
| 981 | |
---|
| 982 | int newClass() { |
---|
| 983 | if (first_free_class < 0) { |
---|
| 984 | int id = classes.size(); |
---|
| 985 | classes.push_back(ClassNode()); |
---|
| 986 | return id; |
---|
| 987 | } else { |
---|
| 988 | int id = first_free_class; |
---|
| 989 | first_free_class = classes[id].next; |
---|
| 990 | return id; |
---|
| 991 | } |
---|
| 992 | } |
---|
| 993 | |
---|
| 994 | void deleteClass(int id) { |
---|
| 995 | classes[id].next = first_free_class; |
---|
| 996 | first_free_class = id; |
---|
| 997 | } |
---|
| 998 | |
---|
| 999 | struct ItemNode { |
---|
| 1000 | int parent; |
---|
| 1001 | Item item; |
---|
| 1002 | Value prio; |
---|
| 1003 | int next, prev; |
---|
| 1004 | int left, right; |
---|
| 1005 | int size; |
---|
| 1006 | }; |
---|
| 1007 | |
---|
| 1008 | int first_free_node; |
---|
| 1009 | std::vector<ItemNode> nodes; |
---|
| 1010 | |
---|
| 1011 | int newNode() { |
---|
| 1012 | if (first_free_node < 0) { |
---|
| 1013 | int id = nodes.size(); |
---|
| 1014 | nodes.push_back(ItemNode()); |
---|
| 1015 | return id; |
---|
| 1016 | } else { |
---|
| 1017 | int id = first_free_node; |
---|
| 1018 | first_free_node = nodes[id].next; |
---|
| 1019 | return id; |
---|
| 1020 | } |
---|
| 1021 | } |
---|
| 1022 | |
---|
| 1023 | void deleteNode(int id) { |
---|
| 1024 | nodes[id].next = first_free_node; |
---|
| 1025 | first_free_node = id; |
---|
| 1026 | } |
---|
| 1027 | |
---|
| 1028 | Comp comp; |
---|
| 1029 | |
---|
| 1030 | int findClass(int id) const { |
---|
| 1031 | int kd = id; |
---|
| 1032 | while (kd >= 0) { |
---|
| 1033 | kd = nodes[kd].parent; |
---|
| 1034 | } |
---|
| 1035 | return ~kd; |
---|
| 1036 | } |
---|
| 1037 | |
---|
| 1038 | int leftNode(int id) const { |
---|
| 1039 | int kd = ~(classes[id].parent); |
---|
| 1040 | for (int i = 0; i < classes[id].depth; ++i) { |
---|
| 1041 | kd = nodes[kd].left; |
---|
| 1042 | } |
---|
| 1043 | return kd; |
---|
| 1044 | } |
---|
| 1045 | |
---|
| 1046 | int nextNode(int id) const { |
---|
| 1047 | int depth = 0; |
---|
| 1048 | while (id >= 0 && nodes[id].next == -1) { |
---|
| 1049 | id = nodes[id].parent; |
---|
| 1050 | ++depth; |
---|
| 1051 | } |
---|
| 1052 | if (id < 0) { |
---|
| 1053 | return -1; |
---|
| 1054 | } |
---|
| 1055 | id = nodes[id].next; |
---|
| 1056 | while (depth--) { |
---|
[209] | 1057 | id = nodes[id].left; |
---|
[103] | 1058 | } |
---|
| 1059 | return id; |
---|
| 1060 | } |
---|
| 1061 | |
---|
| 1062 | |
---|
| 1063 | void setPrio(int id) { |
---|
| 1064 | int jd = nodes[id].left; |
---|
| 1065 | nodes[id].prio = nodes[jd].prio; |
---|
| 1066 | nodes[id].item = nodes[jd].item; |
---|
| 1067 | jd = nodes[jd].next; |
---|
| 1068 | while (jd != -1) { |
---|
| 1069 | if (comp(nodes[jd].prio, nodes[id].prio)) { |
---|
| 1070 | nodes[id].prio = nodes[jd].prio; |
---|
| 1071 | nodes[id].item = nodes[jd].item; |
---|
| 1072 | } |
---|
| 1073 | jd = nodes[jd].next; |
---|
| 1074 | } |
---|
| 1075 | } |
---|
| 1076 | |
---|
| 1077 | void push(int id, int jd) { |
---|
| 1078 | nodes[id].size = 1; |
---|
| 1079 | nodes[id].left = nodes[id].right = jd; |
---|
| 1080 | nodes[jd].next = nodes[jd].prev = -1; |
---|
| 1081 | nodes[jd].parent = id; |
---|
| 1082 | } |
---|
| 1083 | |
---|
| 1084 | void pushAfter(int id, int jd) { |
---|
| 1085 | int kd = nodes[id].parent; |
---|
| 1086 | if (nodes[id].next != -1) { |
---|
| 1087 | nodes[nodes[id].next].prev = jd; |
---|
| 1088 | if (kd >= 0) { |
---|
| 1089 | nodes[kd].size += 1; |
---|
| 1090 | } |
---|
| 1091 | } else { |
---|
| 1092 | if (kd >= 0) { |
---|
| 1093 | nodes[kd].right = jd; |
---|
| 1094 | nodes[kd].size += 1; |
---|
| 1095 | } |
---|
| 1096 | } |
---|
| 1097 | nodes[jd].next = nodes[id].next; |
---|
| 1098 | nodes[jd].prev = id; |
---|
| 1099 | nodes[id].next = jd; |
---|
| 1100 | nodes[jd].parent = kd; |
---|
| 1101 | } |
---|
| 1102 | |
---|
| 1103 | void pushRight(int id, int jd) { |
---|
| 1104 | nodes[id].size += 1; |
---|
| 1105 | nodes[jd].prev = nodes[id].right; |
---|
| 1106 | nodes[jd].next = -1; |
---|
| 1107 | nodes[nodes[id].right].next = jd; |
---|
| 1108 | nodes[id].right = jd; |
---|
| 1109 | nodes[jd].parent = id; |
---|
| 1110 | } |
---|
| 1111 | |
---|
| 1112 | void popRight(int id) { |
---|
| 1113 | nodes[id].size -= 1; |
---|
| 1114 | int jd = nodes[id].right; |
---|
| 1115 | nodes[nodes[jd].prev].next = -1; |
---|
| 1116 | nodes[id].right = nodes[jd].prev; |
---|
| 1117 | } |
---|
| 1118 | |
---|
| 1119 | void splice(int id, int jd) { |
---|
| 1120 | nodes[id].size += nodes[jd].size; |
---|
| 1121 | nodes[nodes[id].right].next = nodes[jd].left; |
---|
| 1122 | nodes[nodes[jd].left].prev = nodes[id].right; |
---|
| 1123 | int kd = nodes[jd].left; |
---|
| 1124 | while (kd != -1) { |
---|
| 1125 | nodes[kd].parent = id; |
---|
| 1126 | kd = nodes[kd].next; |
---|
| 1127 | } |
---|
| 1128 | nodes[id].right = nodes[jd].right; |
---|
| 1129 | } |
---|
| 1130 | |
---|
| 1131 | void split(int id, int jd) { |
---|
| 1132 | int kd = nodes[id].parent; |
---|
| 1133 | nodes[kd].right = nodes[id].prev; |
---|
| 1134 | nodes[nodes[id].prev].next = -1; |
---|
[209] | 1135 | |
---|
[103] | 1136 | nodes[jd].left = id; |
---|
| 1137 | nodes[id].prev = -1; |
---|
| 1138 | int num = 0; |
---|
| 1139 | while (id != -1) { |
---|
| 1140 | nodes[id].parent = jd; |
---|
| 1141 | nodes[jd].right = id; |
---|
| 1142 | id = nodes[id].next; |
---|
| 1143 | ++num; |
---|
[209] | 1144 | } |
---|
[103] | 1145 | nodes[kd].size -= num; |
---|
| 1146 | nodes[jd].size = num; |
---|
| 1147 | } |
---|
| 1148 | |
---|
| 1149 | void pushLeft(int id, int jd) { |
---|
| 1150 | nodes[id].size += 1; |
---|
| 1151 | nodes[jd].next = nodes[id].left; |
---|
| 1152 | nodes[jd].prev = -1; |
---|
| 1153 | nodes[nodes[id].left].prev = jd; |
---|
| 1154 | nodes[id].left = jd; |
---|
| 1155 | nodes[jd].parent = id; |
---|
| 1156 | } |
---|
| 1157 | |
---|
| 1158 | void popLeft(int id) { |
---|
| 1159 | nodes[id].size -= 1; |
---|
| 1160 | int jd = nodes[id].left; |
---|
| 1161 | nodes[nodes[jd].next].prev = -1; |
---|
| 1162 | nodes[id].left = nodes[jd].next; |
---|
| 1163 | } |
---|
| 1164 | |
---|
| 1165 | void repairLeft(int id) { |
---|
| 1166 | int jd = ~(classes[id].parent); |
---|
| 1167 | while (nodes[jd].left != -1) { |
---|
[209] | 1168 | int kd = nodes[jd].left; |
---|
| 1169 | if (nodes[jd].size == 1) { |
---|
| 1170 | if (nodes[jd].parent < 0) { |
---|
| 1171 | classes[id].parent = ~kd; |
---|
| 1172 | classes[id].depth -= 1; |
---|
| 1173 | nodes[kd].parent = ~id; |
---|
| 1174 | deleteNode(jd); |
---|
| 1175 | jd = kd; |
---|
| 1176 | } else { |
---|
| 1177 | int pd = nodes[jd].parent; |
---|
| 1178 | if (nodes[nodes[jd].next].size < cmax) { |
---|
| 1179 | pushLeft(nodes[jd].next, nodes[jd].left); |
---|
[438] | 1180 | if (less(jd, nodes[jd].next) || |
---|
| 1181 | nodes[jd].item == nodes[pd].item) { |
---|
[436] | 1182 | nodes[nodes[jd].next].prio = nodes[jd].prio; |
---|
| 1183 | nodes[nodes[jd].next].item = nodes[jd].item; |
---|
[209] | 1184 | } |
---|
| 1185 | popLeft(pd); |
---|
| 1186 | deleteNode(jd); |
---|
| 1187 | jd = pd; |
---|
| 1188 | } else { |
---|
| 1189 | int ld = nodes[nodes[jd].next].left; |
---|
| 1190 | popLeft(nodes[jd].next); |
---|
| 1191 | pushRight(jd, ld); |
---|
[440] | 1192 | if (less(ld, nodes[jd].left) || |
---|
[436] | 1193 | nodes[ld].item == nodes[pd].item) { |
---|
[209] | 1194 | nodes[jd].item = nodes[ld].item; |
---|
[436] | 1195 | nodes[jd].prio = nodes[ld].prio; |
---|
[209] | 1196 | } |
---|
| 1197 | if (nodes[nodes[jd].next].item == nodes[ld].item) { |
---|
| 1198 | setPrio(nodes[jd].next); |
---|
| 1199 | } |
---|
| 1200 | jd = nodes[jd].left; |
---|
| 1201 | } |
---|
| 1202 | } |
---|
| 1203 | } else { |
---|
| 1204 | jd = nodes[jd].left; |
---|
| 1205 | } |
---|
[103] | 1206 | } |
---|
[209] | 1207 | } |
---|
[103] | 1208 | |
---|
| 1209 | void repairRight(int id) { |
---|
| 1210 | int jd = ~(classes[id].parent); |
---|
| 1211 | while (nodes[jd].right != -1) { |
---|
[209] | 1212 | int kd = nodes[jd].right; |
---|
| 1213 | if (nodes[jd].size == 1) { |
---|
| 1214 | if (nodes[jd].parent < 0) { |
---|
| 1215 | classes[id].parent = ~kd; |
---|
| 1216 | classes[id].depth -= 1; |
---|
| 1217 | nodes[kd].parent = ~id; |
---|
| 1218 | deleteNode(jd); |
---|
| 1219 | jd = kd; |
---|
| 1220 | } else { |
---|
| 1221 | int pd = nodes[jd].parent; |
---|
| 1222 | if (nodes[nodes[jd].prev].size < cmax) { |
---|
| 1223 | pushRight(nodes[jd].prev, nodes[jd].right); |
---|
[438] | 1224 | if (less(jd, nodes[jd].prev) || |
---|
| 1225 | nodes[jd].item == nodes[pd].item) { |
---|
[436] | 1226 | nodes[nodes[jd].prev].prio = nodes[jd].prio; |
---|
| 1227 | nodes[nodes[jd].prev].item = nodes[jd].item; |
---|
[209] | 1228 | } |
---|
| 1229 | popRight(pd); |
---|
| 1230 | deleteNode(jd); |
---|
| 1231 | jd = pd; |
---|
| 1232 | } else { |
---|
| 1233 | int ld = nodes[nodes[jd].prev].right; |
---|
| 1234 | popRight(nodes[jd].prev); |
---|
| 1235 | pushLeft(jd, ld); |
---|
[436] | 1236 | if (less(ld, nodes[jd].right) || |
---|
| 1237 | nodes[ld].item == nodes[pd].item) { |
---|
[209] | 1238 | nodes[jd].item = nodes[ld].item; |
---|
[436] | 1239 | nodes[jd].prio = nodes[ld].prio; |
---|
[209] | 1240 | } |
---|
| 1241 | if (nodes[nodes[jd].prev].item == nodes[ld].item) { |
---|
| 1242 | setPrio(nodes[jd].prev); |
---|
| 1243 | } |
---|
| 1244 | jd = nodes[jd].right; |
---|
| 1245 | } |
---|
| 1246 | } |
---|
| 1247 | } else { |
---|
| 1248 | jd = nodes[jd].right; |
---|
| 1249 | } |
---|
[103] | 1250 | } |
---|
| 1251 | } |
---|
| 1252 | |
---|
| 1253 | |
---|
| 1254 | bool less(int id, int jd) const { |
---|
| 1255 | return comp(nodes[id].prio, nodes[jd].prio); |
---|
| 1256 | } |
---|
| 1257 | |
---|
| 1258 | public: |
---|
| 1259 | |
---|
| 1260 | /// \brief Returns true when the given class is alive. |
---|
| 1261 | /// |
---|
| 1262 | /// Returns true when the given class is alive, ie. the class is |
---|
| 1263 | /// not nested into other class. |
---|
| 1264 | bool alive(int cls) const { |
---|
| 1265 | return classes[cls].parent < 0; |
---|
| 1266 | } |
---|
| 1267 | |
---|
| 1268 | /// \brief Returns true when the given class is trivial. |
---|
| 1269 | /// |
---|
| 1270 | /// Returns true when the given class is trivial, ie. the class |
---|
| 1271 | /// contains just one item directly. |
---|
| 1272 | bool trivial(int cls) const { |
---|
| 1273 | return classes[cls].left == -1; |
---|
| 1274 | } |
---|
| 1275 | |
---|
| 1276 | /// \brief Constructs the union-find. |
---|
| 1277 | /// |
---|
[209] | 1278 | /// Constructs the union-find. |
---|
[103] | 1279 | /// \brief _index The index map of the union-find. The data |
---|
| 1280 | /// structure uses internally for store references. |
---|
[209] | 1281 | HeapUnionFind(ItemIntMap& _index) |
---|
| 1282 | : index(_index), first_class(-1), |
---|
| 1283 | first_free_class(-1), first_free_node(-1) {} |
---|
[103] | 1284 | |
---|
| 1285 | /// \brief Insert a new node into a new component. |
---|
| 1286 | /// |
---|
| 1287 | /// Insert a new node into a new component. |
---|
| 1288 | /// \param item The item of the new node. |
---|
| 1289 | /// \param prio The priority of the new node. |
---|
| 1290 | /// \return The class id of the one-item-heap. |
---|
| 1291 | int insert(const Item& item, const Value& prio) { |
---|
| 1292 | int id = newNode(); |
---|
| 1293 | nodes[id].item = item; |
---|
| 1294 | nodes[id].prio = prio; |
---|
| 1295 | nodes[id].size = 0; |
---|
| 1296 | |
---|
| 1297 | nodes[id].prev = -1; |
---|
| 1298 | nodes[id].next = -1; |
---|
| 1299 | |
---|
| 1300 | nodes[id].left = -1; |
---|
| 1301 | nodes[id].right = -1; |
---|
| 1302 | |
---|
| 1303 | nodes[id].item = item; |
---|
| 1304 | index[item] = id; |
---|
[209] | 1305 | |
---|
[103] | 1306 | int class_id = newClass(); |
---|
| 1307 | classes[class_id].parent = ~id; |
---|
| 1308 | classes[class_id].depth = 0; |
---|
| 1309 | |
---|
| 1310 | classes[class_id].left = -1; |
---|
| 1311 | classes[class_id].right = -1; |
---|
[209] | 1312 | |
---|
[103] | 1313 | if (first_class != -1) { |
---|
| 1314 | classes[first_class].prev = class_id; |
---|
| 1315 | } |
---|
| 1316 | classes[class_id].next = first_class; |
---|
| 1317 | classes[class_id].prev = -1; |
---|
| 1318 | first_class = class_id; |
---|
| 1319 | |
---|
| 1320 | nodes[id].parent = ~class_id; |
---|
[209] | 1321 | |
---|
[103] | 1322 | return class_id; |
---|
| 1323 | } |
---|
| 1324 | |
---|
| 1325 | /// \brief The class of the item. |
---|
| 1326 | /// |
---|
| 1327 | /// \return The alive class id of the item, which is not nested into |
---|
| 1328 | /// other classes. |
---|
| 1329 | /// |
---|
| 1330 | /// The time complexity is O(log(n)). |
---|
| 1331 | int find(const Item& item) const { |
---|
| 1332 | return findClass(index[item]); |
---|
| 1333 | } |
---|
[209] | 1334 | |
---|
[103] | 1335 | /// \brief Joins the classes. |
---|
| 1336 | /// |
---|
| 1337 | /// The current function joins the given classes. The parameter is |
---|
| 1338 | /// an STL range which should be contains valid class ids. The |
---|
| 1339 | /// time complexity is O(log(n)*k) where n is the overall number |
---|
| 1340 | /// of the joined nodes and k is the number of classes. |
---|
| 1341 | /// \return The class of the joined classes. |
---|
| 1342 | /// \pre The range should contain at least two class ids. |
---|
| 1343 | template <typename Iterator> |
---|
| 1344 | int join(Iterator begin, Iterator end) { |
---|
| 1345 | std::vector<int> cs; |
---|
| 1346 | for (Iterator it = begin; it != end; ++it) { |
---|
| 1347 | cs.push_back(*it); |
---|
| 1348 | } |
---|
| 1349 | |
---|
| 1350 | int class_id = newClass(); |
---|
| 1351 | { // creation union-find |
---|
| 1352 | |
---|
| 1353 | if (first_class != -1) { |
---|
| 1354 | classes[first_class].prev = class_id; |
---|
| 1355 | } |
---|
| 1356 | classes[class_id].next = first_class; |
---|
| 1357 | classes[class_id].prev = -1; |
---|
| 1358 | first_class = class_id; |
---|
| 1359 | |
---|
| 1360 | classes[class_id].depth = classes[cs[0]].depth; |
---|
| 1361 | classes[class_id].parent = classes[cs[0]].parent; |
---|
| 1362 | nodes[~(classes[class_id].parent)].parent = ~class_id; |
---|
| 1363 | |
---|
| 1364 | int l = cs[0]; |
---|
| 1365 | |
---|
| 1366 | classes[class_id].left = l; |
---|
| 1367 | classes[class_id].right = l; |
---|
| 1368 | |
---|
| 1369 | if (classes[l].next != -1) { |
---|
| 1370 | classes[classes[l].next].prev = classes[l].prev; |
---|
| 1371 | } |
---|
| 1372 | classes[classes[l].prev].next = classes[l].next; |
---|
[209] | 1373 | |
---|
[103] | 1374 | classes[l].prev = -1; |
---|
| 1375 | classes[l].next = -1; |
---|
| 1376 | |
---|
| 1377 | classes[l].depth = leftNode(l); |
---|
| 1378 | classes[l].parent = class_id; |
---|
[209] | 1379 | |
---|
[103] | 1380 | } |
---|
| 1381 | |
---|
| 1382 | { // merging of heap |
---|
| 1383 | int l = class_id; |
---|
| 1384 | for (int ci = 1; ci < int(cs.size()); ++ci) { |
---|
| 1385 | int r = cs[ci]; |
---|
| 1386 | int rln = leftNode(r); |
---|
| 1387 | if (classes[l].depth > classes[r].depth) { |
---|
| 1388 | int id = ~(classes[l].parent); |
---|
| 1389 | for (int i = classes[r].depth + 1; i < classes[l].depth; ++i) { |
---|
| 1390 | id = nodes[id].right; |
---|
| 1391 | } |
---|
| 1392 | while (id >= 0 && nodes[id].size == cmax) { |
---|
| 1393 | int new_id = newNode(); |
---|
| 1394 | int right_id = nodes[id].right; |
---|
| 1395 | |
---|
| 1396 | popRight(id); |
---|
| 1397 | if (nodes[id].item == nodes[right_id].item) { |
---|
| 1398 | setPrio(id); |
---|
| 1399 | } |
---|
| 1400 | push(new_id, right_id); |
---|
| 1401 | pushRight(new_id, ~(classes[r].parent)); |
---|
[436] | 1402 | |
---|
| 1403 | if (less(~classes[r].parent, right_id)) { |
---|
| 1404 | nodes[new_id].item = nodes[~classes[r].parent].item; |
---|
| 1405 | nodes[new_id].prio = nodes[~classes[r].parent].prio; |
---|
| 1406 | } else { |
---|
| 1407 | nodes[new_id].item = nodes[right_id].item; |
---|
| 1408 | nodes[new_id].prio = nodes[right_id].prio; |
---|
| 1409 | } |
---|
[103] | 1410 | |
---|
| 1411 | id = nodes[id].parent; |
---|
| 1412 | classes[r].parent = ~new_id; |
---|
| 1413 | } |
---|
| 1414 | if (id < 0) { |
---|
| 1415 | int new_parent = newNode(); |
---|
| 1416 | nodes[new_parent].next = -1; |
---|
| 1417 | nodes[new_parent].prev = -1; |
---|
| 1418 | nodes[new_parent].parent = ~l; |
---|
| 1419 | |
---|
| 1420 | push(new_parent, ~(classes[l].parent)); |
---|
| 1421 | pushRight(new_parent, ~(classes[r].parent)); |
---|
| 1422 | setPrio(new_parent); |
---|
| 1423 | |
---|
| 1424 | classes[l].parent = ~new_parent; |
---|
| 1425 | classes[l].depth += 1; |
---|
| 1426 | } else { |
---|
| 1427 | pushRight(id, ~(classes[r].parent)); |
---|
| 1428 | while (id >= 0 && less(~(classes[r].parent), id)) { |
---|
| 1429 | nodes[id].prio = nodes[~(classes[r].parent)].prio; |
---|
| 1430 | nodes[id].item = nodes[~(classes[r].parent)].item; |
---|
| 1431 | id = nodes[id].parent; |
---|
| 1432 | } |
---|
| 1433 | } |
---|
| 1434 | } else if (classes[r].depth > classes[l].depth) { |
---|
| 1435 | int id = ~(classes[r].parent); |
---|
| 1436 | for (int i = classes[l].depth + 1; i < classes[r].depth; ++i) { |
---|
| 1437 | id = nodes[id].left; |
---|
| 1438 | } |
---|
| 1439 | while (id >= 0 && nodes[id].size == cmax) { |
---|
| 1440 | int new_id = newNode(); |
---|
| 1441 | int left_id = nodes[id].left; |
---|
| 1442 | |
---|
| 1443 | popLeft(id); |
---|
| 1444 | if (nodes[id].prio == nodes[left_id].prio) { |
---|
| 1445 | setPrio(id); |
---|
| 1446 | } |
---|
| 1447 | push(new_id, left_id); |
---|
| 1448 | pushLeft(new_id, ~(classes[l].parent)); |
---|
[436] | 1449 | |
---|
| 1450 | if (less(~classes[l].parent, left_id)) { |
---|
| 1451 | nodes[new_id].item = nodes[~classes[l].parent].item; |
---|
| 1452 | nodes[new_id].prio = nodes[~classes[l].parent].prio; |
---|
| 1453 | } else { |
---|
| 1454 | nodes[new_id].item = nodes[left_id].item; |
---|
| 1455 | nodes[new_id].prio = nodes[left_id].prio; |
---|
| 1456 | } |
---|
[103] | 1457 | |
---|
| 1458 | id = nodes[id].parent; |
---|
| 1459 | classes[l].parent = ~new_id; |
---|
| 1460 | |
---|
| 1461 | } |
---|
| 1462 | if (id < 0) { |
---|
| 1463 | int new_parent = newNode(); |
---|
| 1464 | nodes[new_parent].next = -1; |
---|
| 1465 | nodes[new_parent].prev = -1; |
---|
| 1466 | nodes[new_parent].parent = ~l; |
---|
| 1467 | |
---|
| 1468 | push(new_parent, ~(classes[r].parent)); |
---|
| 1469 | pushLeft(new_parent, ~(classes[l].parent)); |
---|
| 1470 | setPrio(new_parent); |
---|
[209] | 1471 | |
---|
[103] | 1472 | classes[r].parent = ~new_parent; |
---|
| 1473 | classes[r].depth += 1; |
---|
| 1474 | } else { |
---|
| 1475 | pushLeft(id, ~(classes[l].parent)); |
---|
| 1476 | while (id >= 0 && less(~(classes[l].parent), id)) { |
---|
| 1477 | nodes[id].prio = nodes[~(classes[l].parent)].prio; |
---|
| 1478 | nodes[id].item = nodes[~(classes[l].parent)].item; |
---|
| 1479 | id = nodes[id].parent; |
---|
| 1480 | } |
---|
| 1481 | } |
---|
| 1482 | nodes[~(classes[r].parent)].parent = ~l; |
---|
| 1483 | classes[l].parent = classes[r].parent; |
---|
| 1484 | classes[l].depth = classes[r].depth; |
---|
| 1485 | } else { |
---|
[209] | 1486 | if (classes[l].depth != 0 && |
---|
| 1487 | nodes[~(classes[l].parent)].size + |
---|
[103] | 1488 | nodes[~(classes[r].parent)].size <= cmax) { |
---|
| 1489 | splice(~(classes[l].parent), ~(classes[r].parent)); |
---|
| 1490 | deleteNode(~(classes[r].parent)); |
---|
| 1491 | if (less(~(classes[r].parent), ~(classes[l].parent))) { |
---|
[209] | 1492 | nodes[~(classes[l].parent)].prio = |
---|
[103] | 1493 | nodes[~(classes[r].parent)].prio; |
---|
[209] | 1494 | nodes[~(classes[l].parent)].item = |
---|
[103] | 1495 | nodes[~(classes[r].parent)].item; |
---|
| 1496 | } |
---|
| 1497 | } else { |
---|
| 1498 | int new_parent = newNode(); |
---|
| 1499 | nodes[new_parent].next = nodes[new_parent].prev = -1; |
---|
| 1500 | push(new_parent, ~(classes[l].parent)); |
---|
| 1501 | pushRight(new_parent, ~(classes[r].parent)); |
---|
| 1502 | setPrio(new_parent); |
---|
[209] | 1503 | |
---|
[103] | 1504 | classes[l].parent = ~new_parent; |
---|
| 1505 | classes[l].depth += 1; |
---|
| 1506 | nodes[new_parent].parent = ~l; |
---|
| 1507 | } |
---|
| 1508 | } |
---|
| 1509 | if (classes[r].next != -1) { |
---|
| 1510 | classes[classes[r].next].prev = classes[r].prev; |
---|
| 1511 | } |
---|
| 1512 | classes[classes[r].prev].next = classes[r].next; |
---|
| 1513 | |
---|
| 1514 | classes[r].prev = classes[l].right; |
---|
| 1515 | classes[classes[l].right].next = r; |
---|
| 1516 | classes[l].right = r; |
---|
| 1517 | classes[r].parent = l; |
---|
| 1518 | |
---|
| 1519 | classes[r].next = -1; |
---|
| 1520 | classes[r].depth = rln; |
---|
| 1521 | } |
---|
| 1522 | } |
---|
| 1523 | return class_id; |
---|
| 1524 | } |
---|
| 1525 | |
---|
| 1526 | /// \brief Split the class to subclasses. |
---|
| 1527 | /// |
---|
| 1528 | /// The current function splits the given class. The join, which |
---|
| 1529 | /// made the current class, stored a reference to the |
---|
| 1530 | /// subclasses. The \c splitClass() member restores the classes |
---|
| 1531 | /// and creates the heaps. The parameter is an STL output iterator |
---|
| 1532 | /// which will be filled with the subclass ids. The time |
---|
| 1533 | /// complexity is O(log(n)*k) where n is the overall number of |
---|
| 1534 | /// nodes in the splitted classes and k is the number of the |
---|
| 1535 | /// classes. |
---|
| 1536 | template <typename Iterator> |
---|
| 1537 | void split(int cls, Iterator out) { |
---|
| 1538 | std::vector<int> cs; |
---|
| 1539 | { // splitting union-find |
---|
| 1540 | int id = cls; |
---|
| 1541 | int l = classes[id].left; |
---|
| 1542 | |
---|
| 1543 | classes[l].parent = classes[id].parent; |
---|
| 1544 | classes[l].depth = classes[id].depth; |
---|
| 1545 | |
---|
| 1546 | nodes[~(classes[l].parent)].parent = ~l; |
---|
| 1547 | |
---|
| 1548 | *out++ = l; |
---|
| 1549 | |
---|
| 1550 | while (l != -1) { |
---|
| 1551 | cs.push_back(l); |
---|
| 1552 | l = classes[l].next; |
---|
| 1553 | } |
---|
| 1554 | |
---|
| 1555 | classes[classes[id].right].next = first_class; |
---|
| 1556 | classes[first_class].prev = classes[id].right; |
---|
| 1557 | first_class = classes[id].left; |
---|
[209] | 1558 | |
---|
[103] | 1559 | if (classes[id].next != -1) { |
---|
| 1560 | classes[classes[id].next].prev = classes[id].prev; |
---|
| 1561 | } |
---|
| 1562 | classes[classes[id].prev].next = classes[id].next; |
---|
[209] | 1563 | |
---|
[103] | 1564 | deleteClass(id); |
---|
| 1565 | } |
---|
| 1566 | |
---|
| 1567 | { |
---|
| 1568 | for (int i = 1; i < int(cs.size()); ++i) { |
---|
| 1569 | int l = classes[cs[i]].depth; |
---|
| 1570 | while (nodes[nodes[l].parent].left == l) { |
---|
| 1571 | l = nodes[l].parent; |
---|
| 1572 | } |
---|
[209] | 1573 | int r = l; |
---|
[103] | 1574 | while (nodes[l].parent >= 0) { |
---|
| 1575 | l = nodes[l].parent; |
---|
| 1576 | int new_node = newNode(); |
---|
| 1577 | |
---|
| 1578 | nodes[new_node].prev = -1; |
---|
| 1579 | nodes[new_node].next = -1; |
---|
| 1580 | |
---|
| 1581 | split(r, new_node); |
---|
| 1582 | pushAfter(l, new_node); |
---|
| 1583 | setPrio(l); |
---|
| 1584 | setPrio(new_node); |
---|
| 1585 | r = new_node; |
---|
| 1586 | } |
---|
| 1587 | classes[cs[i]].parent = ~r; |
---|
| 1588 | classes[cs[i]].depth = classes[~(nodes[l].parent)].depth; |
---|
| 1589 | nodes[r].parent = ~cs[i]; |
---|
| 1590 | |
---|
| 1591 | nodes[l].next = -1; |
---|
| 1592 | nodes[r].prev = -1; |
---|
| 1593 | |
---|
| 1594 | repairRight(~(nodes[l].parent)); |
---|
| 1595 | repairLeft(cs[i]); |
---|
[209] | 1596 | |
---|
[103] | 1597 | *out++ = cs[i]; |
---|
| 1598 | } |
---|
| 1599 | } |
---|
| 1600 | } |
---|
| 1601 | |
---|
| 1602 | /// \brief Gives back the priority of the current item. |
---|
| 1603 | /// |
---|
| 1604 | /// \return Gives back the priority of the current item. |
---|
| 1605 | const Value& operator[](const Item& item) const { |
---|
| 1606 | return nodes[index[item]].prio; |
---|
| 1607 | } |
---|
| 1608 | |
---|
| 1609 | /// \brief Sets the priority of the current item. |
---|
| 1610 | /// |
---|
| 1611 | /// Sets the priority of the current item. |
---|
| 1612 | void set(const Item& item, const Value& prio) { |
---|
| 1613 | if (comp(prio, nodes[index[item]].prio)) { |
---|
| 1614 | decrease(item, prio); |
---|
| 1615 | } else if (!comp(prio, nodes[index[item]].prio)) { |
---|
| 1616 | increase(item, prio); |
---|
| 1617 | } |
---|
| 1618 | } |
---|
[209] | 1619 | |
---|
[103] | 1620 | /// \brief Increase the priority of the current item. |
---|
| 1621 | /// |
---|
| 1622 | /// Increase the priority of the current item. |
---|
| 1623 | void increase(const Item& item, const Value& prio) { |
---|
| 1624 | int id = index[item]; |
---|
| 1625 | int kd = nodes[id].parent; |
---|
| 1626 | nodes[id].prio = prio; |
---|
| 1627 | while (kd >= 0 && nodes[kd].item == item) { |
---|
| 1628 | setPrio(kd); |
---|
| 1629 | kd = nodes[kd].parent; |
---|
| 1630 | } |
---|
| 1631 | } |
---|
| 1632 | |
---|
| 1633 | /// \brief Increase the priority of the current item. |
---|
| 1634 | /// |
---|
| 1635 | /// Increase the priority of the current item. |
---|
| 1636 | void decrease(const Item& item, const Value& prio) { |
---|
| 1637 | int id = index[item]; |
---|
| 1638 | int kd = nodes[id].parent; |
---|
| 1639 | nodes[id].prio = prio; |
---|
| 1640 | while (kd >= 0 && less(id, kd)) { |
---|
| 1641 | nodes[kd].prio = prio; |
---|
| 1642 | nodes[kd].item = item; |
---|
| 1643 | kd = nodes[kd].parent; |
---|
| 1644 | } |
---|
| 1645 | } |
---|
[209] | 1646 | |
---|
[103] | 1647 | /// \brief Gives back the minimum priority of the class. |
---|
| 1648 | /// |
---|
| 1649 | /// \return Gives back the minimum priority of the class. |
---|
| 1650 | const Value& classPrio(int cls) const { |
---|
| 1651 | return nodes[~(classes[cls].parent)].prio; |
---|
| 1652 | } |
---|
| 1653 | |
---|
| 1654 | /// \brief Gives back the minimum priority item of the class. |
---|
| 1655 | /// |
---|
| 1656 | /// \return Gives back the minimum priority item of the class. |
---|
| 1657 | const Item& classTop(int cls) const { |
---|
| 1658 | return nodes[~(classes[cls].parent)].item; |
---|
| 1659 | } |
---|
| 1660 | |
---|
| 1661 | /// \brief Gives back a representant item of the class. |
---|
[209] | 1662 | /// |
---|
[103] | 1663 | /// The representant is indpendent from the priorities of the |
---|
[209] | 1664 | /// items. |
---|
[103] | 1665 | /// \return Gives back a representant item of the class. |
---|
| 1666 | const Item& classRep(int id) const { |
---|
| 1667 | int parent = classes[id].parent; |
---|
| 1668 | return nodes[parent >= 0 ? classes[id].depth : leftNode(id)].item; |
---|
| 1669 | } |
---|
| 1670 | |
---|
[236] | 1671 | /// \brief LEMON style iterator for the items of a class. |
---|
[103] | 1672 | /// |
---|
| 1673 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
| 1674 | /// on the items of a class. By example if you want to iterate on |
---|
| 1675 | /// each items of each classes then you may write the next code. |
---|
| 1676 | ///\code |
---|
| 1677 | /// for (ClassIt cit(huf); cit != INVALID; ++cit) { |
---|
| 1678 | /// std::cout << "Class: "; |
---|
| 1679 | /// for (ItemIt iit(huf, cit); iit != INVALID; ++iit) { |
---|
| 1680 | /// std::cout << toString(iit) << ' ' << std::endl; |
---|
| 1681 | /// } |
---|
| 1682 | /// std::cout << std::endl; |
---|
| 1683 | /// } |
---|
| 1684 | ///\endcode |
---|
| 1685 | class ItemIt { |
---|
| 1686 | private: |
---|
| 1687 | |
---|
| 1688 | const HeapUnionFind* _huf; |
---|
| 1689 | int _id, _lid; |
---|
[209] | 1690 | |
---|
[103] | 1691 | public: |
---|
| 1692 | |
---|
[209] | 1693 | /// \brief Default constructor |
---|
[103] | 1694 | /// |
---|
[209] | 1695 | /// Default constructor |
---|
[103] | 1696 | ItemIt() {} |
---|
| 1697 | |
---|
| 1698 | ItemIt(const HeapUnionFind& huf, int cls) : _huf(&huf) { |
---|
| 1699 | int id = cls; |
---|
| 1700 | int parent = _huf->classes[id].parent; |
---|
| 1701 | if (parent >= 0) { |
---|
| 1702 | _id = _huf->classes[id].depth; |
---|
| 1703 | if (_huf->classes[id].next != -1) { |
---|
| 1704 | _lid = _huf->classes[_huf->classes[id].next].depth; |
---|
| 1705 | } else { |
---|
| 1706 | _lid = -1; |
---|
| 1707 | } |
---|
| 1708 | } else { |
---|
| 1709 | _id = _huf->leftNode(id); |
---|
| 1710 | _lid = -1; |
---|
[209] | 1711 | } |
---|
[103] | 1712 | } |
---|
[209] | 1713 | |
---|
[103] | 1714 | /// \brief Increment operator |
---|
| 1715 | /// |
---|
| 1716 | /// It steps to the next item in the class. |
---|
| 1717 | ItemIt& operator++() { |
---|
| 1718 | _id = _huf->nextNode(_id); |
---|
| 1719 | return *this; |
---|
| 1720 | } |
---|
| 1721 | |
---|
| 1722 | /// \brief Conversion operator |
---|
| 1723 | /// |
---|
| 1724 | /// It converts the iterator to the current item. |
---|
| 1725 | operator const Item&() const { |
---|
| 1726 | return _huf->nodes[_id].item; |
---|
| 1727 | } |
---|
[209] | 1728 | |
---|
[103] | 1729 | /// \brief Equality operator |
---|
| 1730 | /// |
---|
| 1731 | /// Equality operator |
---|
[209] | 1732 | bool operator==(const ItemIt& i) { |
---|
[103] | 1733 | return i._id == _id; |
---|
| 1734 | } |
---|
| 1735 | |
---|
| 1736 | /// \brief Inequality operator |
---|
| 1737 | /// |
---|
| 1738 | /// Inequality operator |
---|
[209] | 1739 | bool operator!=(const ItemIt& i) { |
---|
[103] | 1740 | return i._id != _id; |
---|
| 1741 | } |
---|
| 1742 | |
---|
| 1743 | /// \brief Equality operator |
---|
| 1744 | /// |
---|
| 1745 | /// Equality operator |
---|
[209] | 1746 | bool operator==(Invalid) { |
---|
[103] | 1747 | return _id == _lid; |
---|
| 1748 | } |
---|
| 1749 | |
---|
| 1750 | /// \brief Inequality operator |
---|
| 1751 | /// |
---|
| 1752 | /// Inequality operator |
---|
[209] | 1753 | bool operator!=(Invalid) { |
---|
[103] | 1754 | return _id != _lid; |
---|
| 1755 | } |
---|
[209] | 1756 | |
---|
[103] | 1757 | }; |
---|
| 1758 | |
---|
| 1759 | /// \brief Class iterator |
---|
| 1760 | /// |
---|
[209] | 1761 | /// The iterator stores |
---|
[103] | 1762 | class ClassIt { |
---|
| 1763 | private: |
---|
| 1764 | |
---|
| 1765 | const HeapUnionFind* _huf; |
---|
| 1766 | int _id; |
---|
| 1767 | |
---|
| 1768 | public: |
---|
| 1769 | |
---|
[209] | 1770 | ClassIt(const HeapUnionFind& huf) |
---|
[103] | 1771 | : _huf(&huf), _id(huf.first_class) {} |
---|
| 1772 | |
---|
[209] | 1773 | ClassIt(const HeapUnionFind& huf, int cls) |
---|
[103] | 1774 | : _huf(&huf), _id(huf.classes[cls].left) {} |
---|
| 1775 | |
---|
| 1776 | ClassIt(Invalid) : _huf(0), _id(-1) {} |
---|
[209] | 1777 | |
---|
[103] | 1778 | const ClassIt& operator++() { |
---|
| 1779 | _id = _huf->classes[_id].next; |
---|
[209] | 1780 | return *this; |
---|
[103] | 1781 | } |
---|
| 1782 | |
---|
| 1783 | /// \brief Equality operator |
---|
| 1784 | /// |
---|
| 1785 | /// Equality operator |
---|
[209] | 1786 | bool operator==(const ClassIt& i) { |
---|
[103] | 1787 | return i._id == _id; |
---|
| 1788 | } |
---|
| 1789 | |
---|
| 1790 | /// \brief Inequality operator |
---|
| 1791 | /// |
---|
| 1792 | /// Inequality operator |
---|
[209] | 1793 | bool operator!=(const ClassIt& i) { |
---|
[103] | 1794 | return i._id != _id; |
---|
[209] | 1795 | } |
---|
| 1796 | |
---|
[103] | 1797 | operator int() const { |
---|
[209] | 1798 | return _id; |
---|
[103] | 1799 | } |
---|
[209] | 1800 | |
---|
[103] | 1801 | }; |
---|
| 1802 | |
---|
| 1803 | }; |
---|
| 1804 | |
---|
| 1805 | //! @} |
---|
| 1806 | |
---|
| 1807 | } //namespace lemon |
---|
| 1808 | |
---|
| 1809 | #endif //LEMON_UNION_FIND_H |
---|