| 1 | /* |
| 2 | * Copyright (C) 2008 Apple Inc. All rights reserved. |
| 3 | * |
| 4 | * Based on Abstract AVL Tree Template v1.5 by Walt Karas |
| 5 | * <http://geocities.com/wkaras/gen_cpp/avl_tree.html>. |
| 6 | * |
| 7 | * Redistribution and use in source and binary forms, with or without |
| 8 | * modification, are permitted provided that the following conditions |
| 9 | * are met: |
| 10 | * |
| 11 | * 1. Redistributions of source code must retain the above copyright |
| 12 | * notice, this list of conditions and the following disclaimer. |
| 13 | * 2. Redistributions in binary form must reproduce the above copyright |
| 14 | * notice, this list of conditions and the following disclaimer in the |
| 15 | * documentation and/or other materials provided with the distribution. |
| 16 | * 3. Neither the name of Apple Computer, Inc. ("Apple") nor the names of |
| 17 | * its contributors may be used to endorse or promote products derived |
| 18 | * from this software without specific prior written permission. |
| 19 | * |
| 20 | * THIS SOFTWARE IS PROVIDED BY APPLE AND ITS CONTRIBUTORS "AS IS" AND ANY |
| 21 | * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| 22 | * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| 23 | * DISCLAIMED. IN NO EVENT SHALL APPLE OR ITS CONTRIBUTORS BE LIABLE FOR ANY |
| 24 | * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| 25 | * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| 26 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND |
| 27 | * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| 28 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
| 29 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 30 | */ |
| 31 | |
| 32 | #ifndef AVL_TREE_H_ |
| 33 | #define AVL_TREE_H_ |
| 34 | |
| 35 | #include "Assertions.h" |
| 36 | |
| 37 | namespace WTF { |
| 38 | |
| 39 | // Here is the reference class for BSet. |
| 40 | // |
| 41 | // class BSet |
| 42 | // { |
| 43 | // public: |
| 44 | // |
| 45 | // class ANY_bitref |
| 46 | // { |
| 47 | // public: |
| 48 | // operator bool (); |
| 49 | // void operator = (bool b); |
| 50 | // }; |
| 51 | // |
| 52 | // // Does not have to initialize bits. |
| 53 | // BSet(); |
| 54 | // |
| 55 | // // Must return a valid value for index when 0 <= index < maxDepth |
| 56 | // ANY_bitref operator [] (unsigned index); |
| 57 | // |
| 58 | // // Set all bits to 1. |
| 59 | // void set(); |
| 60 | // |
| 61 | // // Set all bits to 0. |
| 62 | // void reset(); |
| 63 | // }; |
| 64 | |
| 65 | template<unsigned maxDepth> |
| 66 | class AVLTreeDefaultBSet { |
| 67 | public: |
| 68 | bool& operator[](unsigned i) { ASSERT(i < maxDepth); return m_data[i]; } |
| 69 | void set() { for (unsigned i = 0; i < maxDepth; ++i) m_data[i] = true; } |
| 70 | void reset() { for (unsigned i = 0; i < maxDepth; ++i) m_data[i] = false; } |
| 71 | |
| 72 | private: |
| 73 | bool m_data[maxDepth]; |
| 74 | }; |
| 75 | |
| 76 | // How to determine maxDepth: |
| 77 | // d Minimum number of nodes |
| 78 | // 2 2 |
| 79 | // 3 4 |
| 80 | // 4 7 |
| 81 | // 5 12 |
| 82 | // 6 20 |
| 83 | // 7 33 |
| 84 | // 8 54 |
| 85 | // 9 88 |
| 86 | // 10 143 |
| 87 | // 11 232 |
| 88 | // 12 376 |
| 89 | // 13 609 |
| 90 | // 14 986 |
| 91 | // 15 1,596 |
| 92 | // 16 2,583 |
| 93 | // 17 4,180 |
| 94 | // 18 6,764 |
| 95 | // 19 10,945 |
| 96 | // 20 17,710 |
| 97 | // 21 28,656 |
| 98 | // 22 46,367 |
| 99 | // 23 75,024 |
| 100 | // 24 121,392 |
| 101 | // 25 196,417 |
| 102 | // 26 317,810 |
| 103 | // 27 514,228 |
| 104 | // 28 832,039 |
| 105 | // 29 1,346,268 |
| 106 | // 30 2,178,308 |
| 107 | // 31 3,524,577 |
| 108 | // 32 5,702,886 |
| 109 | // 33 9,227,464 |
| 110 | // 34 14,930,351 |
| 111 | // 35 24,157,816 |
| 112 | // 36 39,088,168 |
| 113 | // 37 63,245,985 |
| 114 | // 38 102,334,154 |
| 115 | // 39 165,580,140 |
| 116 | // 40 267,914,295 |
| 117 | // 41 433,494,436 |
| 118 | // 42 701,408,732 |
| 119 | // 43 1,134,903,169 |
| 120 | // 44 1,836,311,902 |
| 121 | // 45 2,971,215,072 |
| 122 | // |
| 123 | // E.g., if, in a particular instantiation, the maximum number of nodes in a tree instance is 1,000,000, the maximum depth should be 28. |
| 124 | // You pick 28 because MN(28) is 832,039, which is less than or equal to 1,000,000, and MN(29) is 1,346,268, which is strictly greater than 1,000,000. |
| 125 | |
| 126 | template <class Abstractor, unsigned maxDepth = 32, class BSet = AVLTreeDefaultBSet<maxDepth> > |
| 127 | class AVLTree { |
| 128 | public: |
| 129 | |
| 130 | typedef typename Abstractor::key key; |
| 131 | typedef typename Abstractor::handle handle; |
| 132 | typedef typename Abstractor::size size; |
| 133 | |
| 134 | enum SearchType { |
| 135 | EQUAL = 1, |
| 136 | LESS = 2, |
| 137 | GREATER = 4, |
| 138 | LESS_EQUAL = EQUAL | LESS, |
| 139 | GREATER_EQUAL = EQUAL | GREATER |
| 140 | }; |
| 141 | |
| 142 | |
| 143 | Abstractor& abstractor() { return abs; } |
| 144 | |
| 145 | inline handle insert(handle h); |
| 146 | |
| 147 | inline handle search(key k, SearchType st = EQUAL); |
| 148 | inline handle search_least(); |
| 149 | inline handle search_greatest(); |
| 150 | |
| 151 | inline handle remove(key k); |
| 152 | |
| 153 | inline handle subst(handle new_node); |
| 154 | |
| 155 | void purge() { abs.root = null(); } |
| 156 | |
| 157 | bool is_empty() { return abs.root == null(); } |
| 158 | |
| 159 | AVLTree() { abs.root = null(); } |
| 160 | |
| 161 | class Iterator { |
| 162 | public: |
| 163 | |
| 164 | // Initialize depth to invalid value, to indicate iterator is |
| 165 | // invalid. (Depth is zero-base.) |
| 166 | Iterator() { depth = ~0U; } |
| 167 | |
| 168 | void start_iter(AVLTree &tree, key k, SearchType st = EQUAL) |
| 169 | { |
| 170 | // Mask of high bit in an int. |
| 171 | const int MASK_HIGH_BIT = (int) ~ ((~ (unsigned) 0) >> 1); |
| 172 | |
| 173 | // Save the tree that we're going to iterate through in a |
| 174 | // member variable. |
| 175 | tree_ = &tree; |
| 176 | |
| 177 | int cmp, target_cmp; |
| 178 | handle h = tree_->abs.root; |
| 179 | unsigned d = 0; |
| 180 | |
| 181 | depth = ~0U; |
| 182 | |
| 183 | if (h == null()) |
| 184 | // Tree is empty. |
| 185 | return; |
| 186 | |
| 187 | if (st & LESS) |
| 188 | // Key can be greater than key of starting node. |
| 189 | target_cmp = 1; |
| 190 | else if (st & GREATER) |
| 191 | // Key can be less than key of starting node. |
| 192 | target_cmp = -1; |
| 193 | else |
| 194 | // Key must be same as key of starting node. |
| 195 | target_cmp = 0; |
| 196 | |
| 197 | for (;;) { |
| 198 | cmp = cmp_k_n(k, h); |
| 199 | if (cmp == 0) { |
| 200 | if (st & EQUAL) { |
| 201 | // Equal node was sought and found as starting node. |
| 202 | depth = d; |
| 203 | break; |
| 204 | } |
| 205 | cmp = -target_cmp; |
| 206 | } else if (target_cmp != 0) { |
| 207 | if (!((cmp ^ target_cmp) & MASK_HIGH_BIT)) { |
| 208 | // cmp and target_cmp are both negative or both positive. |
| 209 | depth = d; |
| 210 | } |
| 211 | } |
| 212 | h = cmp < 0 ? get_lt(h) : get_gt(h); |
| 213 | if (h == null()) |
| 214 | break; |
| 215 | branch[d] = cmp > 0; |
| 216 | path_h[d++] = h; |
| 217 | } |
| 218 | } |
| 219 | |
| 220 | void start_iter_least(AVLTree &tree) |
| 221 | { |
| 222 | tree_ = &tree; |
| 223 | |
| 224 | handle h = tree_->abs.root; |
| 225 | |
| 226 | depth = ~0U; |
| 227 | |
| 228 | branch.reset(); |
| 229 | |
| 230 | while (h != null()) { |
| 231 | if (depth != ~0U) |
| 232 | path_h[depth] = h; |
| 233 | depth++; |
| 234 | h = get_lt(h); |
| 235 | } |
| 236 | } |
| 237 | |
| 238 | void start_iter_greatest(AVLTree &tree) |
| 239 | { |
| 240 | tree_ = &tree; |
| 241 | |
| 242 | handle h = tree_->abs.root; |
| 243 | |
| 244 | depth = ~0U; |
| 245 | |
| 246 | branch.set(); |
| 247 | |
| 248 | while (h != null()) { |
| 249 | if (depth != ~0U) |
| 250 | path_h[depth] = h; |
| 251 | depth++; |
| 252 | h = get_gt(h); |
| 253 | } |
| 254 | } |
| 255 | |
| 256 | handle operator*() |
| 257 | { |
| 258 | if (depth == ~0U) |
| 259 | return null(); |
| 260 | |
| 261 | return depth == 0 ? tree_->abs.root : path_h[depth - 1]; |
| 262 | } |
| 263 | |
| 264 | void operator++() |
| 265 | { |
| 266 | if (depth != ~0U) { |
| 267 | handle h = get_gt(h: **this); |
| 268 | if (h == null()) { |
| 269 | do { |
| 270 | if (depth == 0) { |
| 271 | depth = ~0U; |
| 272 | break; |
| 273 | } |
| 274 | depth--; |
| 275 | } while (branch[depth]); |
| 276 | } else { |
| 277 | branch[depth] = true; |
| 278 | path_h[depth++] = h; |
| 279 | for (;;) { |
| 280 | h = get_lt(h); |
| 281 | if (h == null()) |
| 282 | break; |
| 283 | branch[depth] = false; |
| 284 | path_h[depth++] = h; |
| 285 | } |
| 286 | } |
| 287 | } |
| 288 | } |
| 289 | |
| 290 | void operator--() |
| 291 | { |
| 292 | if (depth != ~0U) { |
| 293 | handle h = get_lt(h: **this); |
| 294 | if (h == null()) |
| 295 | do { |
| 296 | if (depth == 0) { |
| 297 | depth = ~0U; |
| 298 | break; |
| 299 | } |
| 300 | depth--; |
| 301 | } while (!branch[depth]); |
| 302 | else { |
| 303 | branch[depth] = false; |
| 304 | path_h[depth++] = h; |
| 305 | for (;;) { |
| 306 | h = get_gt(h); |
| 307 | if (h == null()) |
| 308 | break; |
| 309 | branch[depth] = true; |
| 310 | path_h[depth++] = h; |
| 311 | } |
| 312 | } |
| 313 | } |
| 314 | } |
| 315 | |
| 316 | void operator++(int) { ++(*this); } |
| 317 | void operator--(int) { --(*this); } |
| 318 | |
| 319 | protected: |
| 320 | |
| 321 | // Tree being iterated over. |
| 322 | AVLTree *tree_; |
| 323 | |
| 324 | // Records a path into the tree. If branch[n] is true, indicates |
| 325 | // take greater branch from the nth node in the path, otherwise |
| 326 | // take the less branch. branch[0] gives branch from root, and |
| 327 | // so on. |
| 328 | BSet branch; |
| 329 | |
| 330 | // Zero-based depth of path into tree. |
| 331 | unsigned depth; |
| 332 | |
| 333 | // Handles of nodes in path from root to current node (returned by *). |
| 334 | handle path_h[maxDepth - 1]; |
| 335 | |
| 336 | int cmp_k_n(key k, handle h) { return tree_->abs.compare_key_node(k, h); } |
| 337 | int cmp_n_n(handle h1, handle h2) { return tree_->abs.compare_node_node(h1, h2); } |
| 338 | handle get_lt(handle h) { return tree_->abs.get_less(h); } |
| 339 | handle get_gt(handle h) { return tree_->abs.get_greater(h); } |
| 340 | handle null() { return tree_->abs.null(); } |
| 341 | }; |
| 342 | |
| 343 | template<typename fwd_iter> |
| 344 | bool build(fwd_iter p, size num_nodes) |
| 345 | { |
| 346 | if (num_nodes == 0) { |
| 347 | abs.root = null(); |
| 348 | return true; |
| 349 | } |
| 350 | |
| 351 | // Gives path to subtree being built. If branch[N] is false, branch |
| 352 | // less from the node at depth N, if true branch greater. |
| 353 | BSet branch; |
| 354 | |
| 355 | // If rem[N] is true, then for the current subtree at depth N, it's |
| 356 | // greater subtree has one more node than it's less subtree. |
| 357 | BSet rem; |
| 358 | |
| 359 | // Depth of root node of current subtree. |
| 360 | unsigned depth = 0; |
| 361 | |
| 362 | // Number of nodes in current subtree. |
| 363 | size num_sub = num_nodes; |
| 364 | |
| 365 | // The algorithm relies on a stack of nodes whose less subtree has |
| 366 | // been built, but whose right subtree has not yet been built. The |
| 367 | // stack is implemented as linked list. The nodes are linked |
| 368 | // together by having the "greater" handle of a node set to the |
| 369 | // next node in the list. "less_parent" is the handle of the first |
| 370 | // node in the list. |
| 371 | handle less_parent = null(); |
| 372 | |
| 373 | // h is root of current subtree, child is one of its children. |
| 374 | handle h, child; |
| 375 | |
| 376 | for (;;) { |
| 377 | while (num_sub > 2) { |
| 378 | // Subtract one for root of subtree. |
| 379 | num_sub--; |
| 380 | rem[depth] = !!(num_sub & 1); |
| 381 | branch[depth++] = false; |
| 382 | num_sub >>= 1; |
| 383 | } |
| 384 | |
| 385 | if (num_sub == 2) { |
| 386 | // Build a subtree with two nodes, slanting to greater. |
| 387 | // I arbitrarily chose to always have the extra node in the |
| 388 | // greater subtree when there is an odd number of nodes to |
| 389 | // split between the two subtrees. |
| 390 | |
| 391 | h = *p; |
| 392 | p++; |
| 393 | child = *p; |
| 394 | p++; |
| 395 | set_lt(h: child, lh: null()); |
| 396 | set_gt(h: child, gh: null()); |
| 397 | set_bf(h: child, bf: 0); |
| 398 | set_gt(h, gh: child); |
| 399 | set_lt(h, lh: null()); |
| 400 | set_bf(h, bf: 1); |
| 401 | } else { // num_sub == 1 |
| 402 | // Build a subtree with one node. |
| 403 | |
| 404 | h = *p; |
| 405 | p++; |
| 406 | set_lt(h, lh: null()); |
| 407 | set_gt(h, gh: null()); |
| 408 | set_bf(h, bf: 0); |
| 409 | } |
| 410 | |
| 411 | while (depth) { |
| 412 | depth--; |
| 413 | if (!branch[depth]) |
| 414 | // We've completed a less subtree. |
| 415 | break; |
| 416 | |
| 417 | // We've completed a greater subtree, so attach it to |
| 418 | // its parent (that is less than it). We pop the parent |
| 419 | // off the stack of less parents. |
| 420 | child = h; |
| 421 | h = less_parent; |
| 422 | less_parent = get_gt(h); |
| 423 | set_gt(h, gh: child); |
| 424 | // num_sub = 2 * (num_sub - rem[depth]) + rem[depth] + 1 |
| 425 | num_sub <<= 1; |
| 426 | num_sub += 1 - rem[depth]; |
| 427 | if (num_sub & (num_sub - 1)) |
| 428 | // num_sub is not a power of 2 |
| 429 | set_bf(h, bf: 0); |
| 430 | else |
| 431 | // num_sub is a power of 2 |
| 432 | set_bf(h, bf: 1); |
| 433 | } |
| 434 | |
| 435 | if (num_sub == num_nodes) |
| 436 | // We've completed the full tree. |
| 437 | break; |
| 438 | |
| 439 | // The subtree we've completed is the less subtree of the |
| 440 | // next node in the sequence. |
| 441 | |
| 442 | child = h; |
| 443 | h = *p; |
| 444 | p++; |
| 445 | set_lt(h, lh: child); |
| 446 | |
| 447 | // Put h into stack of less parents. |
| 448 | set_gt(h, gh: less_parent); |
| 449 | less_parent = h; |
| 450 | |
| 451 | // Proceed to creating greater than subtree of h. |
| 452 | branch[depth] = true; |
| 453 | num_sub += rem[depth++]; |
| 454 | |
| 455 | } // end for (;;) |
| 456 | |
| 457 | abs.root = h; |
| 458 | |
| 459 | return true; |
| 460 | } |
| 461 | |
| 462 | protected: |
| 463 | |
| 464 | friend class Iterator; |
| 465 | |
| 466 | // Create a class whose sole purpose is to take advantage of |
| 467 | // the "empty member" optimization. |
| 468 | struct abs_plus_root : public Abstractor { |
| 469 | // The handle of the root element in the AVL tree. |
| 470 | handle root; |
| 471 | }; |
| 472 | |
| 473 | abs_plus_root abs; |
| 474 | |
| 475 | |
| 476 | handle get_lt(handle h) { return abs.get_less(h); } |
| 477 | void set_lt(handle h, handle lh) { abs.set_less(h, lh); } |
| 478 | |
| 479 | handle get_gt(handle h) { return abs.get_greater(h); } |
| 480 | void set_gt(handle h, handle gh) { abs.set_greater(h, gh); } |
| 481 | |
| 482 | int get_bf(handle h) { return abs.get_balance_factor(h); } |
| 483 | void set_bf(handle h, int bf) { abs.set_balance_factor(h, bf); } |
| 484 | |
| 485 | int cmp_k_n(key k, handle h) { return abs.compare_key_node(k, h); } |
| 486 | int cmp_n_n(handle h1, handle h2) { return abs.compare_node_node(h1, h2); } |
| 487 | |
| 488 | handle null() { return abs.null(); } |
| 489 | |
| 490 | private: |
| 491 | |
| 492 | // Balances subtree, returns handle of root node of subtree |
| 493 | // after balancing. |
| 494 | handle balance(handle bal_h) |
| 495 | { |
| 496 | handle deep_h; |
| 497 | |
| 498 | // Either the "greater than" or the "less than" subtree of |
| 499 | // this node has to be 2 levels deeper (or else it wouldn't |
| 500 | // need balancing). |
| 501 | |
| 502 | if (get_bf(h: bal_h) > 0) { |
| 503 | // "Greater than" subtree is deeper. |
| 504 | |
| 505 | deep_h = get_gt(h: bal_h); |
| 506 | |
| 507 | if (get_bf(h: deep_h) < 0) { |
| 508 | handle old_h = bal_h; |
| 509 | bal_h = get_lt(h: deep_h); |
| 510 | |
| 511 | set_gt(h: old_h, gh: get_lt(h: bal_h)); |
| 512 | set_lt(h: deep_h, lh: get_gt(h: bal_h)); |
| 513 | set_lt(h: bal_h, lh: old_h); |
| 514 | set_gt(h: bal_h, gh: deep_h); |
| 515 | |
| 516 | int bf = get_bf(h: bal_h); |
| 517 | if (bf != 0) { |
| 518 | if (bf > 0) { |
| 519 | set_bf(h: old_h, bf: -1); |
| 520 | set_bf(h: deep_h, bf: 0); |
| 521 | } else { |
| 522 | set_bf(h: deep_h, bf: 1); |
| 523 | set_bf(h: old_h, bf: 0); |
| 524 | } |
| 525 | set_bf(h: bal_h, bf: 0); |
| 526 | } else { |
| 527 | set_bf(h: old_h, bf: 0); |
| 528 | set_bf(h: deep_h, bf: 0); |
| 529 | } |
| 530 | } else { |
| 531 | set_gt(h: bal_h, gh: get_lt(h: deep_h)); |
| 532 | set_lt(h: deep_h, lh: bal_h); |
| 533 | if (get_bf(h: deep_h) == 0) { |
| 534 | set_bf(h: deep_h, bf: -1); |
| 535 | set_bf(h: bal_h, bf: 1); |
| 536 | } else { |
| 537 | set_bf(h: deep_h, bf: 0); |
| 538 | set_bf(h: bal_h, bf: 0); |
| 539 | } |
| 540 | bal_h = deep_h; |
| 541 | } |
| 542 | } else { |
| 543 | // "Less than" subtree is deeper. |
| 544 | |
| 545 | deep_h = get_lt(h: bal_h); |
| 546 | |
| 547 | if (get_bf(h: deep_h) > 0) { |
| 548 | handle old_h = bal_h; |
| 549 | bal_h = get_gt(h: deep_h); |
| 550 | set_lt(h: old_h, lh: get_gt(h: bal_h)); |
| 551 | set_gt(h: deep_h, gh: get_lt(h: bal_h)); |
| 552 | set_gt(h: bal_h, gh: old_h); |
| 553 | set_lt(h: bal_h, lh: deep_h); |
| 554 | |
| 555 | int bf = get_bf(h: bal_h); |
| 556 | if (bf != 0) { |
| 557 | if (bf < 0) { |
| 558 | set_bf(h: old_h, bf: 1); |
| 559 | set_bf(h: deep_h, bf: 0); |
| 560 | } else { |
| 561 | set_bf(h: deep_h, bf: -1); |
| 562 | set_bf(h: old_h, bf: 0); |
| 563 | } |
| 564 | set_bf(h: bal_h, bf: 0); |
| 565 | } else { |
| 566 | set_bf(h: old_h, bf: 0); |
| 567 | set_bf(h: deep_h, bf: 0); |
| 568 | } |
| 569 | } else { |
| 570 | set_lt(h: bal_h, lh: get_gt(h: deep_h)); |
| 571 | set_gt(h: deep_h, gh: bal_h); |
| 572 | if (get_bf(h: deep_h) == 0) { |
| 573 | set_bf(h: deep_h, bf: 1); |
| 574 | set_bf(h: bal_h, bf: -1); |
| 575 | } else { |
| 576 | set_bf(h: deep_h, bf: 0); |
| 577 | set_bf(h: bal_h, bf: 0); |
| 578 | } |
| 579 | bal_h = deep_h; |
| 580 | } |
| 581 | } |
| 582 | |
| 583 | return bal_h; |
| 584 | } |
| 585 | |
| 586 | }; |
| 587 | |
| 588 | template <class Abstractor, unsigned maxDepth, class BSet> |
| 589 | inline typename AVLTree<Abstractor, maxDepth, BSet>::handle |
| 590 | AVLTree<Abstractor, maxDepth, BSet>::insert(handle h) |
| 591 | { |
| 592 | set_lt(h, lh: null()); |
| 593 | set_gt(h, gh: null()); |
| 594 | set_bf(h, bf: 0); |
| 595 | |
| 596 | if (abs.root == null()) |
| 597 | abs.root = h; |
| 598 | else { |
| 599 | // Last unbalanced node encountered in search for insertion point. |
| 600 | handle unbal = null(); |
| 601 | // Parent of last unbalanced node. |
| 602 | handle parent_unbal = null(); |
| 603 | // Balance factor of last unbalanced node. |
| 604 | int unbal_bf; |
| 605 | |
| 606 | // Zero-based depth in tree. |
| 607 | unsigned depth = 0, unbal_depth = 0; |
| 608 | |
| 609 | // Records a path into the tree. If branch[n] is true, indicates |
| 610 | // take greater branch from the nth node in the path, otherwise |
| 611 | // take the less branch. branch[0] gives branch from root, and |
| 612 | // so on. |
| 613 | BSet branch; |
| 614 | |
| 615 | handle hh = abs.root; |
| 616 | handle parent = null(); |
| 617 | int cmp; |
| 618 | |
| 619 | do { |
| 620 | if (get_bf(h: hh) != 0) { |
| 621 | unbal = hh; |
| 622 | parent_unbal = parent; |
| 623 | unbal_depth = depth; |
| 624 | } |
| 625 | cmp = cmp_n_n(h1: h, h2: hh); |
| 626 | if (cmp == 0) |
| 627 | // Duplicate key. |
| 628 | return hh; |
| 629 | parent = hh; |
| 630 | hh = cmp < 0 ? get_lt(h: hh) : get_gt(h: hh); |
| 631 | branch[depth++] = cmp > 0; |
| 632 | } while (hh != null()); |
| 633 | |
| 634 | // Add node to insert as leaf of tree. |
| 635 | if (cmp < 0) |
| 636 | set_lt(h: parent, lh: h); |
| 637 | else |
| 638 | set_gt(h: parent, gh: h); |
| 639 | |
| 640 | depth = unbal_depth; |
| 641 | |
| 642 | if (unbal == null()) |
| 643 | hh = abs.root; |
| 644 | else { |
| 645 | cmp = branch[depth++] ? 1 : -1; |
| 646 | unbal_bf = get_bf(h: unbal); |
| 647 | if (cmp < 0) |
| 648 | unbal_bf--; |
| 649 | else // cmp > 0 |
| 650 | unbal_bf++; |
| 651 | hh = cmp < 0 ? get_lt(h: unbal) : get_gt(h: unbal); |
| 652 | if ((unbal_bf != -2) && (unbal_bf != 2)) { |
| 653 | // No rebalancing of tree is necessary. |
| 654 | set_bf(h: unbal, bf: unbal_bf); |
| 655 | unbal = null(); |
| 656 | } |
| 657 | } |
| 658 | |
| 659 | if (hh != null()) |
| 660 | while (h != hh) { |
| 661 | cmp = branch[depth++] ? 1 : -1; |
| 662 | if (cmp < 0) { |
| 663 | set_bf(h: hh, bf: -1); |
| 664 | hh = get_lt(h: hh); |
| 665 | } else { // cmp > 0 |
| 666 | set_bf(h: hh, bf: 1); |
| 667 | hh = get_gt(h: hh); |
| 668 | } |
| 669 | } |
| 670 | |
| 671 | if (unbal != null()) { |
| 672 | unbal = balance(bal_h: unbal); |
| 673 | if (parent_unbal == null()) |
| 674 | abs.root = unbal; |
| 675 | else { |
| 676 | depth = unbal_depth - 1; |
| 677 | cmp = branch[depth] ? 1 : -1; |
| 678 | if (cmp < 0) |
| 679 | set_lt(h: parent_unbal, lh: unbal); |
| 680 | else // cmp > 0 |
| 681 | set_gt(h: parent_unbal, gh: unbal); |
| 682 | } |
| 683 | } |
| 684 | } |
| 685 | |
| 686 | return h; |
| 687 | } |
| 688 | |
| 689 | template <class Abstractor, unsigned maxDepth, class BSet> |
| 690 | inline typename AVLTree<Abstractor, maxDepth, BSet>::handle |
| 691 | AVLTree<Abstractor, maxDepth, BSet>::search(key k, typename AVLTree<Abstractor, maxDepth, BSet>::SearchType st) |
| 692 | { |
| 693 | const int MASK_HIGH_BIT = (int) ~ ((~ (unsigned) 0) >> 1); |
| 694 | |
| 695 | int cmp, target_cmp; |
| 696 | handle match_h = null(); |
| 697 | handle h = abs.root; |
| 698 | |
| 699 | if (st & LESS) |
| 700 | target_cmp = 1; |
| 701 | else if (st & GREATER) |
| 702 | target_cmp = -1; |
| 703 | else |
| 704 | target_cmp = 0; |
| 705 | |
| 706 | while (h != null()) { |
| 707 | cmp = cmp_k_n(k, h); |
| 708 | if (cmp == 0) { |
| 709 | if (st & EQUAL) { |
| 710 | match_h = h; |
| 711 | break; |
| 712 | } |
| 713 | cmp = -target_cmp; |
| 714 | } else if (target_cmp != 0) |
| 715 | if (!((cmp ^ target_cmp) & MASK_HIGH_BIT)) |
| 716 | // cmp and target_cmp are both positive or both negative. |
| 717 | match_h = h; |
| 718 | h = cmp < 0 ? get_lt(h) : get_gt(h); |
| 719 | } |
| 720 | |
| 721 | return match_h; |
| 722 | } |
| 723 | |
| 724 | template <class Abstractor, unsigned maxDepth, class BSet> |
| 725 | inline typename AVLTree<Abstractor, maxDepth, BSet>::handle |
| 726 | AVLTree<Abstractor, maxDepth, BSet>::search_least() |
| 727 | { |
| 728 | handle h = abs.root, parent = null(); |
| 729 | |
| 730 | while (h != null()) { |
| 731 | parent = h; |
| 732 | h = get_lt(h); |
| 733 | } |
| 734 | |
| 735 | return parent; |
| 736 | } |
| 737 | |
| 738 | template <class Abstractor, unsigned maxDepth, class BSet> |
| 739 | inline typename AVLTree<Abstractor, maxDepth, BSet>::handle |
| 740 | AVLTree<Abstractor, maxDepth, BSet>::search_greatest() |
| 741 | { |
| 742 | handle h = abs.root, parent = null(); |
| 743 | |
| 744 | while (h != null()) { |
| 745 | parent = h; |
| 746 | h = get_gt(h); |
| 747 | } |
| 748 | |
| 749 | return parent; |
| 750 | } |
| 751 | |
| 752 | template <class Abstractor, unsigned maxDepth, class BSet> |
| 753 | inline typename AVLTree<Abstractor, maxDepth, BSet>::handle |
| 754 | AVLTree<Abstractor, maxDepth, BSet>::remove(key k) |
| 755 | { |
| 756 | // Zero-based depth in tree. |
| 757 | unsigned depth = 0, rm_depth; |
| 758 | |
| 759 | // Records a path into the tree. If branch[n] is true, indicates |
| 760 | // take greater branch from the nth node in the path, otherwise |
| 761 | // take the less branch. branch[0] gives branch from root, and |
| 762 | // so on. |
| 763 | BSet branch; |
| 764 | |
| 765 | handle h = abs.root; |
| 766 | handle parent = null(), child; |
| 767 | int cmp, cmp_shortened_sub_with_path = 0; |
| 768 | |
| 769 | for (;;) { |
| 770 | if (h == null()) |
| 771 | // No node in tree with given key. |
| 772 | return null(); |
| 773 | cmp = cmp_k_n(k, h); |
| 774 | if (cmp == 0) |
| 775 | // Found node to remove. |
| 776 | break; |
| 777 | parent = h; |
| 778 | h = cmp < 0 ? get_lt(h) : get_gt(h); |
| 779 | branch[depth++] = cmp > 0; |
| 780 | cmp_shortened_sub_with_path = cmp; |
| 781 | } |
| 782 | handle rm = h; |
| 783 | handle parent_rm = parent; |
| 784 | rm_depth = depth; |
| 785 | |
| 786 | // If the node to remove is not a leaf node, we need to get a |
| 787 | // leaf node, or a node with a single leaf as its child, to put |
| 788 | // in the place of the node to remove. We will get the greatest |
| 789 | // node in the less subtree (of the node to remove), or the least |
| 790 | // node in the greater subtree. We take the leaf node from the |
| 791 | // deeper subtree, if there is one. |
| 792 | |
| 793 | if (get_bf(h) < 0) { |
| 794 | child = get_lt(h); |
| 795 | branch[depth] = false; |
| 796 | cmp = -1; |
| 797 | } else { |
| 798 | child = get_gt(h); |
| 799 | branch[depth] = true; |
| 800 | cmp = 1; |
| 801 | } |
| 802 | depth++; |
| 803 | |
| 804 | if (child != null()) { |
| 805 | cmp = -cmp; |
| 806 | do { |
| 807 | parent = h; |
| 808 | h = child; |
| 809 | if (cmp < 0) { |
| 810 | child = get_lt(h); |
| 811 | branch[depth] = false; |
| 812 | } else { |
| 813 | child = get_gt(h); |
| 814 | branch[depth] = true; |
| 815 | } |
| 816 | depth++; |
| 817 | } while (child != null()); |
| 818 | |
| 819 | if (parent == rm) |
| 820 | // Only went through do loop once. Deleted node will be replaced |
| 821 | // in the tree structure by one of its immediate children. |
| 822 | cmp_shortened_sub_with_path = -cmp; |
| 823 | else |
| 824 | cmp_shortened_sub_with_path = cmp; |
| 825 | |
| 826 | // Get the handle of the opposite child, which may not be null. |
| 827 | child = cmp > 0 ? get_lt(h) : get_gt(h); |
| 828 | } |
| 829 | |
| 830 | if (parent == null()) |
| 831 | // There were only 1 or 2 nodes in this tree. |
| 832 | abs.root = child; |
| 833 | else if (cmp_shortened_sub_with_path < 0) |
| 834 | set_lt(h: parent, lh: child); |
| 835 | else |
| 836 | set_gt(h: parent, gh: child); |
| 837 | |
| 838 | // "path" is the parent of the subtree being eliminated or reduced |
| 839 | // from a depth of 2 to 1. If "path" is the node to be removed, we |
| 840 | // set path to the node we're about to poke into the position of the |
| 841 | // node to be removed. |
| 842 | handle path = parent == rm ? h : parent; |
| 843 | |
| 844 | if (h != rm) { |
| 845 | // Poke in the replacement for the node to be removed. |
| 846 | set_lt(h, lh: get_lt(h: rm)); |
| 847 | set_gt(h, gh: get_gt(h: rm)); |
| 848 | set_bf(h, bf: get_bf(h: rm)); |
| 849 | if (parent_rm == null()) |
| 850 | abs.root = h; |
| 851 | else { |
| 852 | depth = rm_depth - 1; |
| 853 | if (branch[depth]) |
| 854 | set_gt(h: parent_rm, gh: h); |
| 855 | else |
| 856 | set_lt(h: parent_rm, lh: h); |
| 857 | } |
| 858 | } |
| 859 | |
| 860 | if (path != null()) { |
| 861 | // Create a temporary linked list from the parent of the path node |
| 862 | // to the root node. |
| 863 | h = abs.root; |
| 864 | parent = null(); |
| 865 | depth = 0; |
| 866 | while (h != path) { |
| 867 | if (branch[depth++]) { |
| 868 | child = get_gt(h); |
| 869 | set_gt(h, gh: parent); |
| 870 | } else { |
| 871 | child = get_lt(h); |
| 872 | set_lt(h, lh: parent); |
| 873 | } |
| 874 | parent = h; |
| 875 | h = child; |
| 876 | } |
| 877 | |
| 878 | // Climb from the path node to the root node using the linked |
| 879 | // list, restoring the tree structure and rebalancing as necessary. |
| 880 | bool reduced_depth = true; |
| 881 | int bf; |
| 882 | cmp = cmp_shortened_sub_with_path; |
| 883 | for (;;) { |
| 884 | if (reduced_depth) { |
| 885 | bf = get_bf(h); |
| 886 | if (cmp < 0) |
| 887 | bf++; |
| 888 | else // cmp > 0 |
| 889 | bf--; |
| 890 | if ((bf == -2) || (bf == 2)) { |
| 891 | h = balance(bal_h: h); |
| 892 | bf = get_bf(h); |
| 893 | } else |
| 894 | set_bf(h, bf); |
| 895 | reduced_depth = (bf == 0); |
| 896 | } |
| 897 | if (parent == null()) |
| 898 | break; |
| 899 | child = h; |
| 900 | h = parent; |
| 901 | cmp = branch[--depth] ? 1 : -1; |
| 902 | if (cmp < 0) { |
| 903 | parent = get_lt(h); |
| 904 | set_lt(h, lh: child); |
| 905 | } else { |
| 906 | parent = get_gt(h); |
| 907 | set_gt(h, gh: child); |
| 908 | } |
| 909 | } |
| 910 | abs.root = h; |
| 911 | } |
| 912 | |
| 913 | return rm; |
| 914 | } |
| 915 | |
| 916 | template <class Abstractor, unsigned maxDepth, class BSet> |
| 917 | inline typename AVLTree<Abstractor, maxDepth, BSet>::handle |
| 918 | AVLTree<Abstractor, maxDepth, BSet>::subst(handle new_node) |
| 919 | { |
| 920 | handle h = abs.root; |
| 921 | handle parent = null(); |
| 922 | int cmp, last_cmp; |
| 923 | |
| 924 | /* Search for node already in tree with same key. */ |
| 925 | for (;;) { |
| 926 | if (h == null()) |
| 927 | /* No node in tree with same key as new node. */ |
| 928 | return null(); |
| 929 | cmp = cmp_n_n(h1: new_node, h2: h); |
| 930 | if (cmp == 0) |
| 931 | /* Found the node to substitute new one for. */ |
| 932 | break; |
| 933 | last_cmp = cmp; |
| 934 | parent = h; |
| 935 | h = cmp < 0 ? get_lt(h) : get_gt(h); |
| 936 | } |
| 937 | |
| 938 | /* Copy tree housekeeping fields from node in tree to new node. */ |
| 939 | set_lt(h: new_node, lh: get_lt(h)); |
| 940 | set_gt(h: new_node, gh: get_gt(h)); |
| 941 | set_bf(h: new_node, bf: get_bf(h)); |
| 942 | |
| 943 | if (parent == null()) |
| 944 | /* New node is also new root. */ |
| 945 | abs.root = new_node; |
| 946 | else { |
| 947 | /* Make parent point to new node. */ |
| 948 | if (last_cmp < 0) |
| 949 | set_lt(h: parent, lh: new_node); |
| 950 | else |
| 951 | set_gt(h: parent, gh: new_node); |
| 952 | } |
| 953 | |
| 954 | return h; |
| 955 | } |
| 956 | |
| 957 | } |
| 958 | |
| 959 | #endif |
| 960 | |