[1724] | 1 | /* -*- C++ -*- |
---|
| 2 | * lemon/linear_heap.h - Part of LEMON, a generic C++ optimization library |
---|
| 3 | * |
---|
| 4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
| 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
| 6 | * |
---|
| 7 | * Permission to use, modify and distribute this software is granted |
---|
| 8 | * provided that this copyright notice appears in all copies. For |
---|
| 9 | * precise terms see the accompanying LICENSE file. |
---|
| 10 | * |
---|
| 11 | * This software is provided "AS IS" with no warranty of any kind, |
---|
| 12 | * express or implied, and with no claim as to its suitability for any |
---|
| 13 | * purpose. |
---|
| 14 | * |
---|
| 15 | */ |
---|
| 16 | |
---|
| 17 | #ifndef LEMON_LINEAR_HEAP_H |
---|
| 18 | #define LEMON_LINEAR_HEAP_H |
---|
| 19 | |
---|
| 20 | ///\ingroup auxdat |
---|
| 21 | ///\file |
---|
| 22 | ///\brief Binary Heap implementation. |
---|
| 23 | |
---|
| 24 | #include <vector> |
---|
| 25 | #include <utility> |
---|
| 26 | #include <functional> |
---|
| 27 | |
---|
| 28 | namespace lemon { |
---|
| 29 | |
---|
| 30 | /// \addtogroup auxdat |
---|
| 31 | /// @{ |
---|
| 32 | |
---|
| 33 | /// \brief A Linear Heap implementation. |
---|
| 34 | /// |
---|
| 35 | /// This class implements the \e linear \e heap data structure. A \e heap |
---|
| 36 | /// is a data structure for storing items with specified values called \e |
---|
| 37 | /// priorities in such a way that finding the item with minimum priority is |
---|
| 38 | /// efficient. The linear heap is very simple implementation, it can store |
---|
| 39 | /// only integer priorities and it stores for each priority in the [0..C] |
---|
| 40 | /// range a list of items. So it should be used only when the priorities |
---|
| 41 | /// are small. It is not intended to use as dijkstra heap. |
---|
| 42 | /// |
---|
| 43 | /// \param _Item Type of the items to be stored. |
---|
| 44 | /// \param _ItemIntMap A read and writable Item int map, used internally |
---|
| 45 | /// to handle the cross references. |
---|
| 46 | /// \param minimize If the given parameter is true then the heap gives back |
---|
| 47 | /// the lowest priority. |
---|
| 48 | template <typename _Item, typename _ItemIntMap, bool minimize = true > |
---|
| 49 | class LinearHeap { |
---|
| 50 | |
---|
| 51 | public: |
---|
| 52 | typedef _Item Item; |
---|
| 53 | typedef int Prio; |
---|
| 54 | typedef std::pair<Item, Prio> Pair; |
---|
| 55 | typedef _ItemIntMap ItemIntMap; |
---|
| 56 | |
---|
| 57 | /// \brief Type to represent the items states. |
---|
| 58 | /// |
---|
| 59 | /// Each Item element have a state associated to it. It may be "in heap", |
---|
| 60 | /// "pre heap" or "post heap". The latter two are indifferent from the |
---|
| 61 | /// heap's point of view, but may be useful to the user. |
---|
| 62 | /// |
---|
| 63 | /// The ItemIntMap \e should be initialized in such way that it maps |
---|
| 64 | /// PRE_HEAP (-1) to any element to be put in the heap... |
---|
| 65 | enum state_enum { |
---|
| 66 | IN_HEAP = 0, |
---|
| 67 | PRE_HEAP = -1, |
---|
| 68 | POST_HEAP = -2 |
---|
| 69 | }; |
---|
| 70 | |
---|
| 71 | public: |
---|
| 72 | /// \brief The constructor. |
---|
| 73 | /// |
---|
| 74 | /// The constructor. |
---|
| 75 | /// \param _index should be given to the constructor, since it is used |
---|
| 76 | /// internally to handle the cross references. The value of the map |
---|
| 77 | /// should be PRE_HEAP (-1) for each element. |
---|
| 78 | explicit LinearHeap(ItemIntMap &_index) : index(_index), minimal(0) {} |
---|
| 79 | |
---|
| 80 | /// The number of items stored in the heap. |
---|
| 81 | /// |
---|
| 82 | /// \brief Returns the number of items stored in the heap. |
---|
| 83 | int size() const { return data.size(); } |
---|
| 84 | |
---|
| 85 | /// \brief Checks if the heap stores no items. |
---|
| 86 | /// |
---|
| 87 | /// Returns \c true if and only if the heap stores no items. |
---|
| 88 | bool empty() const { return data.empty(); } |
---|
| 89 | |
---|
| 90 | /// \brief Make empty this heap. |
---|
| 91 | /// |
---|
| 92 | /// Make empty this heap. |
---|
| 93 | void clear() { |
---|
| 94 | for (int i = 0; i < (int)data.size(); ++i) { |
---|
| 95 | index[data[i].item] = -2; |
---|
| 96 | } |
---|
| 97 | data.clear(); first.clear(); minimal = 0; |
---|
| 98 | } |
---|
| 99 | |
---|
| 100 | private: |
---|
| 101 | |
---|
| 102 | void relocate_last(int idx) { |
---|
| 103 | if (idx + 1 < (int)data.size()) { |
---|
| 104 | data[idx] = data.back(); |
---|
| 105 | if (data[idx].prev != -1) { |
---|
| 106 | data[data[idx].prev].next = idx; |
---|
| 107 | } else { |
---|
| 108 | first[data[idx].value] = idx; |
---|
| 109 | } |
---|
| 110 | if (data[idx].next != -1) { |
---|
| 111 | data[data[idx].next].prev = idx; |
---|
| 112 | } |
---|
| 113 | index[data[idx].item] = idx; |
---|
| 114 | } |
---|
| 115 | data.pop_back(); |
---|
| 116 | } |
---|
| 117 | |
---|
| 118 | void unlace(int idx) { |
---|
| 119 | if (data[idx].prev != -1) { |
---|
| 120 | data[data[idx].prev].next = data[idx].next; |
---|
| 121 | } else { |
---|
| 122 | first[data[idx].value] = data[idx].next; |
---|
| 123 | } |
---|
| 124 | if (data[idx].next != -1) { |
---|
| 125 | data[data[idx].next].prev = data[idx].prev; |
---|
| 126 | } |
---|
| 127 | } |
---|
| 128 | |
---|
| 129 | void lace(int idx) { |
---|
| 130 | if ((int)first.size() <= data[idx].value) { |
---|
| 131 | first.resize(data[idx].value + 1, -1); |
---|
| 132 | } |
---|
| 133 | data[idx].next = first[data[idx].value]; |
---|
| 134 | if (data[idx].next != -1) { |
---|
| 135 | data[data[idx].next].prev = idx; |
---|
| 136 | } |
---|
| 137 | first[data[idx].value] = idx; |
---|
| 138 | data[idx].prev = -1; |
---|
| 139 | } |
---|
| 140 | |
---|
| 141 | public: |
---|
| 142 | /// \brief Insert a pair of item and priority into the heap. |
---|
| 143 | /// |
---|
| 144 | /// Adds \c p.first to the heap with priority \c p.second. |
---|
| 145 | /// \param p The pair to insert. |
---|
| 146 | void push(const Pair& p) { |
---|
| 147 | push(p.first, p.second); |
---|
| 148 | } |
---|
| 149 | |
---|
| 150 | /// \brief Insert an item into the heap with the given priority. |
---|
| 151 | /// |
---|
| 152 | /// Adds \c i to the heap with priority \c p. |
---|
| 153 | /// \param i The item to insert. |
---|
| 154 | /// \param p The priority of the item. |
---|
| 155 | void push(const Item &i, const Prio &p) { |
---|
| 156 | int idx = data.size(); |
---|
| 157 | index[i] = idx; |
---|
| 158 | data.push_back(LinearItem(i, p)); |
---|
| 159 | lace(idx); |
---|
| 160 | if (p < minimal) { |
---|
| 161 | minimal = p; |
---|
| 162 | } |
---|
| 163 | } |
---|
| 164 | |
---|
| 165 | /// \brief Returns the item with minimum priority relative to \c Compare. |
---|
| 166 | /// |
---|
| 167 | /// This method returns the item with minimum priority relative to \c |
---|
| 168 | /// Compare. |
---|
| 169 | /// \pre The heap must be nonempty. |
---|
| 170 | Item top() const { |
---|
| 171 | while (first[minimal] == -1) { |
---|
| 172 | ++minimal; |
---|
| 173 | } |
---|
| 174 | return data[first[minimal]].item; |
---|
| 175 | } |
---|
| 176 | |
---|
| 177 | /// \brief Returns the minimum priority relative to \c Compare. |
---|
| 178 | /// |
---|
| 179 | /// It returns the minimum priority relative to \c Compare. |
---|
| 180 | /// \pre The heap must be nonempty. |
---|
| 181 | Prio prio() const { |
---|
| 182 | while (first[minimal] == -1) { |
---|
| 183 | ++minimal; |
---|
| 184 | } |
---|
| 185 | return minimal; |
---|
| 186 | } |
---|
| 187 | |
---|
| 188 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
---|
| 189 | /// |
---|
| 190 | /// This method deletes the item with minimum priority relative to \c |
---|
| 191 | /// Compare from the heap. |
---|
| 192 | /// \pre The heap must be non-empty. |
---|
| 193 | void pop() { |
---|
| 194 | while (first[minimal] == -1) { |
---|
| 195 | ++minimal; |
---|
| 196 | } |
---|
| 197 | int idx = first[minimal]; |
---|
| 198 | index[data[idx].item] = -2; |
---|
| 199 | unlace(idx); |
---|
| 200 | relocate_last(idx); |
---|
| 201 | } |
---|
| 202 | |
---|
| 203 | /// \brief Deletes \c i from the heap. |
---|
| 204 | /// |
---|
| 205 | /// This method deletes item \c i from the heap, if \c i was |
---|
| 206 | /// already stored in the heap. |
---|
| 207 | /// \param i The item to erase. |
---|
| 208 | void erase(const Item &i) { |
---|
| 209 | int idx = index[i]; |
---|
| 210 | index[data[idx].item] = -2; |
---|
| 211 | unlace(idx); |
---|
| 212 | relocate_last(idx); |
---|
| 213 | } |
---|
| 214 | |
---|
| 215 | |
---|
| 216 | /// \brief Returns the priority of \c i. |
---|
| 217 | /// |
---|
| 218 | /// This function returns the priority of item \c i. |
---|
| 219 | /// \pre \c i must be in the heap. |
---|
| 220 | /// \param i The item. |
---|
| 221 | Prio operator[](const Item &i) const { |
---|
| 222 | int idx = index[i]; |
---|
| 223 | return data[idx].value; |
---|
| 224 | } |
---|
| 225 | |
---|
| 226 | /// \brief \c i gets to the heap with priority \c p independently |
---|
| 227 | /// if \c i was already there. |
---|
| 228 | /// |
---|
| 229 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
---|
| 230 | /// in the heap and sets the priority of \c i to \c p otherwise. |
---|
| 231 | /// \param i The item. |
---|
| 232 | /// \param p The priority. |
---|
| 233 | void set(const Item &i, const Prio &p) { |
---|
| 234 | int idx = index[i]; |
---|
| 235 | if (idx < 0) { |
---|
| 236 | push(i,p); |
---|
| 237 | } else if (p > data[idx].value) { |
---|
| 238 | increase(i, p); |
---|
| 239 | } else { |
---|
| 240 | decrease(i, p); |
---|
| 241 | } |
---|
| 242 | } |
---|
| 243 | |
---|
| 244 | /// \brief Decreases the priority of \c i to \c p. |
---|
| 245 | |
---|
| 246 | /// This method decreases the priority of item \c i to \c p. |
---|
| 247 | /// \pre \c i must be stored in the heap with priority at least \c |
---|
| 248 | /// p relative to \c Compare. |
---|
| 249 | /// \param i The item. |
---|
| 250 | /// \param p The priority. |
---|
| 251 | void decrease(const Item &i, const Prio &p) { |
---|
| 252 | int idx = index[i]; |
---|
| 253 | unlace(idx); |
---|
| 254 | data[idx].value = p; |
---|
| 255 | if (p < minimal) { |
---|
| 256 | minimal = p; |
---|
| 257 | } |
---|
| 258 | lace(idx); |
---|
| 259 | } |
---|
| 260 | |
---|
| 261 | /// \brief Increases the priority of \c i to \c p. |
---|
| 262 | /// |
---|
| 263 | /// This method sets the priority of item \c i to \c p. |
---|
| 264 | /// \pre \c i must be stored in the heap with priority at most \c |
---|
| 265 | /// p relative to \c Compare. |
---|
| 266 | /// \param i The item. |
---|
| 267 | /// \param p The priority. |
---|
| 268 | void increase(const Item &i, const Prio &p) { |
---|
| 269 | int idx = index[i]; |
---|
| 270 | unlace(idx); |
---|
| 271 | data[idx].value = p; |
---|
| 272 | lace(idx); |
---|
| 273 | } |
---|
| 274 | |
---|
| 275 | /// \brief Returns if \c item is in, has already been in, or has |
---|
| 276 | /// never been in the heap. |
---|
| 277 | /// |
---|
| 278 | /// This method returns PRE_HEAP if \c item has never been in the |
---|
| 279 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
---|
| 280 | /// otherwise. In the latter case it is possible that \c item will |
---|
| 281 | /// get back to the heap again. |
---|
| 282 | /// \param i The item. |
---|
| 283 | state_enum state(const Item &i) const { |
---|
| 284 | int idx = index[i]; |
---|
| 285 | if (idx >= 0) idx = 0; |
---|
| 286 | return state_enum(idx); |
---|
| 287 | } |
---|
| 288 | |
---|
| 289 | private: |
---|
| 290 | |
---|
| 291 | struct LinearItem { |
---|
| 292 | LinearItem(const Item& _item, int _value) |
---|
| 293 | : item(_item), value(_value) {} |
---|
| 294 | |
---|
| 295 | Item item; |
---|
| 296 | int value; |
---|
| 297 | |
---|
| 298 | int prev, next; |
---|
| 299 | }; |
---|
| 300 | |
---|
| 301 | ItemIntMap& index; |
---|
| 302 | std::vector<int> first; |
---|
| 303 | std::vector<LinearItem> data; |
---|
| 304 | mutable int minimal; |
---|
| 305 | |
---|
| 306 | }; // class LinearHeap |
---|
| 307 | |
---|
| 308 | |
---|
| 309 | template <typename _Item, typename _ItemIntMap> |
---|
| 310 | class LinearHeap<_Item, _ItemIntMap, false> { |
---|
| 311 | |
---|
| 312 | public: |
---|
| 313 | typedef _Item Item; |
---|
| 314 | typedef int Prio; |
---|
| 315 | typedef std::pair<Item, Prio> Pair; |
---|
| 316 | typedef _ItemIntMap ItemIntMap; |
---|
| 317 | |
---|
| 318 | enum state_enum { |
---|
| 319 | IN_HEAP = 0, |
---|
| 320 | PRE_HEAP = -1, |
---|
| 321 | POST_HEAP = -2 |
---|
| 322 | }; |
---|
| 323 | |
---|
| 324 | public: |
---|
| 325 | |
---|
| 326 | explicit LinearHeap(ItemIntMap &_index) : index(_index), maximal(-1) {} |
---|
| 327 | |
---|
| 328 | int size() const { return data.size(); } |
---|
| 329 | bool empty() const { return data.empty(); } |
---|
| 330 | |
---|
| 331 | void clear() { |
---|
| 332 | for (int i = 0; i < (int)data.size(); ++i) { |
---|
| 333 | index[data[i].item] = -2; |
---|
| 334 | } |
---|
| 335 | data.clear(); first.clear(); maximal = -1; |
---|
| 336 | } |
---|
| 337 | |
---|
| 338 | private: |
---|
| 339 | |
---|
| 340 | void relocate_last(int idx) { |
---|
| 341 | if (idx + 1 != (int)data.size()) { |
---|
| 342 | data[idx] = data.back(); |
---|
| 343 | if (data[idx].prev != -1) { |
---|
| 344 | data[data[idx].prev].next = idx; |
---|
| 345 | } else { |
---|
| 346 | first[data[idx].value] = idx; |
---|
| 347 | } |
---|
| 348 | if (data[idx].next != -1) { |
---|
| 349 | data[data[idx].next].prev = idx; |
---|
| 350 | } |
---|
| 351 | index[data[idx].item] = idx; |
---|
| 352 | } |
---|
| 353 | data.pop_back(); |
---|
| 354 | } |
---|
| 355 | |
---|
| 356 | void unlace(int idx) { |
---|
| 357 | if (data[idx].prev != -1) { |
---|
| 358 | data[data[idx].prev].next = data[idx].next; |
---|
| 359 | } else { |
---|
| 360 | first[data[idx].value] = data[idx].next; |
---|
| 361 | } |
---|
| 362 | if (data[idx].next != -1) { |
---|
| 363 | data[data[idx].next].prev = data[idx].prev; |
---|
| 364 | } |
---|
| 365 | } |
---|
| 366 | |
---|
| 367 | void lace(int idx) { |
---|
| 368 | if ((int)first.size() <= data[idx].value) { |
---|
| 369 | first.resize(data[idx].value + 1, -1); |
---|
| 370 | } |
---|
| 371 | data[idx].next = first[data[idx].value]; |
---|
| 372 | if (data[idx].next != -1) { |
---|
| 373 | data[data[idx].next].prev = idx; |
---|
| 374 | } |
---|
| 375 | first[data[idx].value] = idx; |
---|
| 376 | data[idx].prev = -1; |
---|
| 377 | } |
---|
| 378 | |
---|
| 379 | public: |
---|
| 380 | |
---|
| 381 | void push(const Pair& p) { |
---|
| 382 | push(p.first, p.second); |
---|
| 383 | } |
---|
| 384 | |
---|
| 385 | void push(const Item &i, const Prio &p) { |
---|
| 386 | int idx = data.size(); |
---|
| 387 | index[i] = idx; |
---|
| 388 | data.push_back(LinearItem(i, p)); |
---|
| 389 | lace(idx); |
---|
| 390 | if (data[idx].value > maximal) { |
---|
| 391 | maximal = data[idx].value; |
---|
| 392 | } |
---|
| 393 | } |
---|
| 394 | |
---|
| 395 | Item top() const { |
---|
| 396 | while (first[maximal] == -1) { |
---|
| 397 | --maximal; |
---|
| 398 | } |
---|
| 399 | return data[first[maximal]].item; |
---|
| 400 | } |
---|
| 401 | |
---|
| 402 | Prio prio() const { |
---|
| 403 | while (first[maximal] == -1) { |
---|
| 404 | --maximal; |
---|
| 405 | } |
---|
| 406 | return maximal; |
---|
| 407 | } |
---|
| 408 | |
---|
| 409 | void pop() { |
---|
| 410 | while (first[maximal] == -1) { |
---|
| 411 | --maximal; |
---|
| 412 | } |
---|
| 413 | int idx = first[maximal]; |
---|
| 414 | index[data[idx].item] = -2; |
---|
| 415 | unlace(idx); |
---|
| 416 | relocate_last(idx); |
---|
| 417 | } |
---|
| 418 | |
---|
| 419 | void erase(const Item &i) { |
---|
| 420 | int idx = index[i]; |
---|
| 421 | index[data[idx].item] = -2; |
---|
| 422 | unlace(idx); |
---|
| 423 | relocate_last(idx); |
---|
| 424 | } |
---|
| 425 | |
---|
| 426 | Prio operator[](const Item &i) const { |
---|
| 427 | int idx = index[i]; |
---|
| 428 | return data[idx].value; |
---|
| 429 | } |
---|
| 430 | |
---|
| 431 | void set(const Item &i, const Prio &p) { |
---|
| 432 | int idx = index[i]; |
---|
| 433 | if (idx < 0) { |
---|
| 434 | push(i,p); |
---|
| 435 | } else if (p > data[idx].value) { |
---|
| 436 | decrease(i, p); |
---|
| 437 | } else { |
---|
| 438 | increase(i, p); |
---|
| 439 | } |
---|
| 440 | } |
---|
| 441 | |
---|
| 442 | void decrease(const Item &i, const Prio &p) { |
---|
| 443 | int idx = index[i]; |
---|
| 444 | unlace(idx); |
---|
| 445 | data[idx].value = p; |
---|
| 446 | if (p > maximal) { |
---|
| 447 | maximal = p; |
---|
| 448 | } |
---|
| 449 | lace(idx); |
---|
| 450 | } |
---|
| 451 | |
---|
| 452 | void increase(const Item &i, const Prio &p) { |
---|
| 453 | int idx = index[i]; |
---|
| 454 | unlace(idx); |
---|
| 455 | data[idx].value = p; |
---|
| 456 | lace(idx); |
---|
| 457 | } |
---|
| 458 | |
---|
| 459 | state_enum state(const Item &i) const { |
---|
| 460 | int idx = index[i]; |
---|
| 461 | if (idx >= 0) idx = 0; |
---|
| 462 | return state_enum(idx); |
---|
| 463 | } |
---|
| 464 | |
---|
| 465 | private: |
---|
| 466 | |
---|
| 467 | struct LinearItem { |
---|
| 468 | LinearItem(const Item& _item, int _value) |
---|
| 469 | : item(_item), value(_value) {} |
---|
| 470 | |
---|
| 471 | Item item; |
---|
| 472 | int value; |
---|
| 473 | |
---|
| 474 | int prev, next; |
---|
| 475 | }; |
---|
| 476 | |
---|
| 477 | ItemIntMap& index; |
---|
| 478 | std::vector<int> first; |
---|
| 479 | std::vector<LinearItem> data; |
---|
| 480 | mutable int maximal; |
---|
| 481 | |
---|
| 482 | }; // class LinearHeap |
---|
| 483 | |
---|
| 484 | } |
---|
| 485 | |
---|
| 486 | #endif |
---|