1 /* 2 Red Black Trees 3 (C) 1999 Andrea Arcangeli <andrea@suse.de> 4 (C) 2002 David Woodhouse <dwmw2@infradead.org> 5 (C) 2012 Michel Lespinasse <walken@google.com> 6 7 This program is free software; you can redistribute it and/or modify 8 it under the terms of the GNU General Public License as published by 9 the Free Software Foundation; either version 2 of the License, or 10 (at your option) any later version. 11 12 This program is distributed in the hope that it will be useful, 13 but WITHOUT ANY WARRANTY; without even the implied warranty of 14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 GNU General Public License for more details. 16 17 You should have received a copy of the GNU General Public License 18 along with this program; if not, write to the Free Software 19 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 20 21 linux/lib/rbtree.c 22 */ 23 24 #include <linux/rbtree_augmented.h> 25 26 /* 27 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree 28 * 29 * 1) A node is either red or black 30 * 2) The root is black 31 * 3) All leaves (NULL) are black 32 * 4) Both children of every red node are black 33 * 5) Every simple path from root to leaves contains the same number 34 * of black nodes. 35 * 36 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two 37 * consecutive red nodes in a path and every red node is therefore followed by 38 * a black. So if B is the number of black nodes on every simple path (as per 39 * 5), then the longest possible path due to 4 is 2B. 40 * 41 * We shall indicate color with case, where black nodes are uppercase and red 42 * nodes will be lowercase. Unknown color nodes shall be drawn as red within 43 * parentheses and have some accompanying text comment. 44 */ 45 46 static inline void rb_set_black(struct rb_node *rb) 47 { 48 rb->__rb_parent_color |= RB_BLACK; 49 } 50 51 static inline struct rb_node *rb_red_parent(struct rb_node *red) 52 { 53 return (struct rb_node *)red->__rb_parent_color; 54 } 55 56 /* 57 * Helper function for rotations: 58 * - old's parent and color get assigned to new 59 * - old gets assigned new as a parent and 'color' as a color. 60 */ 61 static inline void 62 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, 63 struct rb_root *root, int color) 64 { 65 struct rb_node *parent = rb_parent(old); 66 new->__rb_parent_color = old->__rb_parent_color; 67 rb_set_parent_color(old, new, color); 68 __rb_change_child(old, new, parent, root); 69 } 70 71 static __always_inline void 72 __rb_insert(struct rb_node *node, struct rb_root *root, 73 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 74 { 75 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; 76 77 while (true) { 78 /* 79 * Loop invariant: node is red 80 * 81 * If there is a black parent, we are done. 82 * Otherwise, take some corrective action as we don't 83 * want a red root or two consecutive red nodes. 84 */ 85 if (!parent) { 86 rb_set_parent_color(node, NULL, RB_BLACK); 87 break; 88 } else if (rb_is_black(parent)) 89 break; 90 91 gparent = rb_red_parent(parent); 92 93 tmp = gparent->rb_right; 94 if (parent != tmp) { /* parent == gparent->rb_left */ 95 if (tmp && rb_is_red(tmp)) { 96 /* 97 * Case 1 - color flips 98 * 99 * G g 100 * / \ / \ 101 * p u --> P U 102 * / / 103 * n n 104 * 105 * However, since g's parent might be red, and 106 * 4) does not allow this, we need to recurse 107 * at g. 108 */ 109 rb_set_parent_color(tmp, gparent, RB_BLACK); 110 rb_set_parent_color(parent, gparent, RB_BLACK); 111 node = gparent; 112 parent = rb_parent(node); 113 rb_set_parent_color(node, parent, RB_RED); 114 continue; 115 } 116 117 tmp = parent->rb_right; 118 if (node == tmp) { 119 /* 120 * Case 2 - left rotate at parent 121 * 122 * G G 123 * / \ / \ 124 * p U --> n U 125 * \ / 126 * n p 127 * 128 * This still leaves us in violation of 4), the 129 * continuation into Case 3 will fix that. 130 */ 131 parent->rb_right = tmp = node->rb_left; 132 node->rb_left = parent; 133 if (tmp) 134 rb_set_parent_color(tmp, parent, 135 RB_BLACK); 136 rb_set_parent_color(parent, node, RB_RED); 137 augment_rotate(parent, node); 138 parent = node; 139 tmp = node->rb_right; 140 } 141 142 /* 143 * Case 3 - right rotate at gparent 144 * 145 * G P 146 * / \ / \ 147 * p U --> n g 148 * / \ 149 * n U 150 */ 151 gparent->rb_left = tmp; /* == parent->rb_right */ 152 parent->rb_right = gparent; 153 if (tmp) 154 rb_set_parent_color(tmp, gparent, RB_BLACK); 155 __rb_rotate_set_parents(gparent, parent, root, RB_RED); 156 augment_rotate(gparent, parent); 157 break; 158 } else { 159 tmp = gparent->rb_left; 160 if (tmp && rb_is_red(tmp)) { 161 /* Case 1 - color flips */ 162 rb_set_parent_color(tmp, gparent, RB_BLACK); 163 rb_set_parent_color(parent, gparent, RB_BLACK); 164 node = gparent; 165 parent = rb_parent(node); 166 rb_set_parent_color(node, parent, RB_RED); 167 continue; 168 } 169 170 tmp = parent->rb_left; 171 if (node == tmp) { 172 /* Case 2 - right rotate at parent */ 173 parent->rb_left = tmp = node->rb_right; 174 node->rb_right = parent; 175 if (tmp) 176 rb_set_parent_color(tmp, parent, 177 RB_BLACK); 178 rb_set_parent_color(parent, node, RB_RED); 179 augment_rotate(parent, node); 180 parent = node; 181 tmp = node->rb_left; 182 } 183 184 /* Case 3 - left rotate at gparent */ 185 gparent->rb_right = tmp; /* == parent->rb_left */ 186 parent->rb_left = gparent; 187 if (tmp) 188 rb_set_parent_color(tmp, gparent, RB_BLACK); 189 __rb_rotate_set_parents(gparent, parent, root, RB_RED); 190 augment_rotate(gparent, parent); 191 break; 192 } 193 } 194 } 195 196 /* 197 * Inline version for rb_erase() use - we want to be able to inline 198 * and eliminate the dummy_rotate callback there 199 */ 200 static __always_inline void 201 ____rb_erase_color(struct rb_node *parent, struct rb_root *root, 202 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 203 { 204 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; 205 206 while (true) { 207 /* 208 * Loop invariants: 209 * - node is black (or NULL on first iteration) 210 * - node is not the root (parent is not NULL) 211 * - All leaf paths going through parent and node have a 212 * black node count that is 1 lower than other leaf paths. 213 */ 214 sibling = parent->rb_right; 215 if (node != sibling) { /* node == parent->rb_left */ 216 if (rb_is_red(sibling)) { 217 /* 218 * Case 1 - left rotate at parent 219 * 220 * P S 221 * / \ / \ 222 * N s --> p Sr 223 * / \ / \ 224 * Sl Sr N Sl 225 */ 226 parent->rb_right = tmp1 = sibling->rb_left; 227 sibling->rb_left = parent; 228 rb_set_parent_color(tmp1, parent, RB_BLACK); 229 __rb_rotate_set_parents(parent, sibling, root, 230 RB_RED); 231 augment_rotate(parent, sibling); 232 sibling = tmp1; 233 } 234 tmp1 = sibling->rb_right; 235 if (!tmp1 || rb_is_black(tmp1)) { 236 tmp2 = sibling->rb_left; 237 if (!tmp2 || rb_is_black(tmp2)) { 238 /* 239 * Case 2 - sibling color flip 240 * (p could be either color here) 241 * 242 * (p) (p) 243 * / \ / \ 244 * N S --> N s 245 * / \ / \ 246 * Sl Sr Sl Sr 247 * 248 * This leaves us violating 5) which 249 * can be fixed by flipping p to black 250 * if it was red, or by recursing at p. 251 * p is red when coming from Case 1. 252 */ 253 rb_set_parent_color(sibling, parent, 254 RB_RED); 255 if (rb_is_red(parent)) 256 rb_set_black(parent); 257 else { 258 node = parent; 259 parent = rb_parent(node); 260 if (parent) 261 continue; 262 } 263 break; 264 } 265 /* 266 * Case 3 - right rotate at sibling 267 * (p could be either color here) 268 * 269 * (p) (p) 270 * / \ / \ 271 * N S --> N Sl 272 * / \ \ 273 * sl Sr s 274 * \ 275 * Sr 276 */ 277 sibling->rb_left = tmp1 = tmp2->rb_right; 278 tmp2->rb_right = sibling; 279 parent->rb_right = tmp2; 280 if (tmp1) 281 rb_set_parent_color(tmp1, sibling, 282 RB_BLACK); 283 augment_rotate(sibling, tmp2); 284 tmp1 = sibling; 285 sibling = tmp2; 286 } 287 /* 288 * Case 4 - left rotate at parent + color flips 289 * (p and sl could be either color here. 290 * After rotation, p becomes black, s acquires 291 * p's color, and sl keeps its color) 292 * 293 * (p) (s) 294 * / \ / \ 295 * N S --> P Sr 296 * / \ / \ 297 * (sl) sr N (sl) 298 */ 299 parent->rb_right = tmp2 = sibling->rb_left; 300 sibling->rb_left = parent; 301 rb_set_parent_color(tmp1, sibling, RB_BLACK); 302 if (tmp2) 303 rb_set_parent(tmp2, parent); 304 __rb_rotate_set_parents(parent, sibling, root, 305 RB_BLACK); 306 augment_rotate(parent, sibling); 307 break; 308 } else { 309 sibling = parent->rb_left; 310 if (rb_is_red(sibling)) { 311 /* Case 1 - right rotate at parent */ 312 parent->rb_left = tmp1 = sibling->rb_right; 313 sibling->rb_right = parent; 314 rb_set_parent_color(tmp1, parent, RB_BLACK); 315 __rb_rotate_set_parents(parent, sibling, root, 316 RB_RED); 317 augment_rotate(parent, sibling); 318 sibling = tmp1; 319 } 320 tmp1 = sibling->rb_left; 321 if (!tmp1 || rb_is_black(tmp1)) { 322 tmp2 = sibling->rb_right; 323 if (!tmp2 || rb_is_black(tmp2)) { 324 /* Case 2 - sibling color flip */ 325 rb_set_parent_color(sibling, parent, 326 RB_RED); 327 if (rb_is_red(parent)) 328 rb_set_black(parent); 329 else { 330 node = parent; 331 parent = rb_parent(node); 332 if (parent) 333 continue; 334 } 335 break; 336 } 337 /* Case 3 - right rotate at sibling */ 338 sibling->rb_right = tmp1 = tmp2->rb_left; 339 tmp2->rb_left = sibling; 340 parent->rb_left = tmp2; 341 if (tmp1) 342 rb_set_parent_color(tmp1, sibling, 343 RB_BLACK); 344 augment_rotate(sibling, tmp2); 345 tmp1 = sibling; 346 sibling = tmp2; 347 } 348 /* Case 4 - left rotate at parent + color flips */ 349 parent->rb_left = tmp2 = sibling->rb_right; 350 sibling->rb_right = parent; 351 rb_set_parent_color(tmp1, sibling, RB_BLACK); 352 if (tmp2) 353 rb_set_parent(tmp2, parent); 354 __rb_rotate_set_parents(parent, sibling, root, 355 RB_BLACK); 356 augment_rotate(parent, sibling); 357 break; 358 } 359 } 360 } 361 362 /* Non-inline version for rb_erase_augmented() use */ 363 void __rb_erase_color(struct rb_node *parent, struct rb_root *root, 364 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 365 { 366 ____rb_erase_color(parent, root, augment_rotate); 367 } 368 369 /* 370 * Non-augmented rbtree manipulation functions. 371 * 372 * We use dummy augmented callbacks here, and have the compiler optimize them 373 * out of the rb_insert_color() and rb_erase() function definitions. 374 */ 375 376 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} 377 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} 378 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} 379 380 static const struct rb_augment_callbacks dummy_callbacks = { 381 dummy_propagate, dummy_copy, dummy_rotate 382 }; 383 384 void rb_insert_color(struct rb_node *node, struct rb_root *root) 385 { 386 __rb_insert(node, root, dummy_rotate); 387 } 388 389 void rb_erase(struct rb_node *node, struct rb_root *root) 390 { 391 struct rb_node *rebalance; 392 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); 393 if (rebalance) 394 ____rb_erase_color(rebalance, root, dummy_rotate); 395 } 396 397 /* 398 * Augmented rbtree manipulation functions. 399 * 400 * This instantiates the same __always_inline functions as in the non-augmented 401 * case, but this time with user-defined callbacks. 402 */ 403 404 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, 405 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 406 { 407 __rb_insert(node, root, augment_rotate); 408 } 409 410 /* 411 * This function returns the first node (in sort order) of the tree. 412 */ 413 struct rb_node *rb_first(const struct rb_root *root) 414 { 415 struct rb_node *n; 416 417 n = root->rb_node; 418 if (!n) 419 return NULL; 420 while (n->rb_left) 421 n = n->rb_left; 422 return n; 423 } 424 425 struct rb_node *rb_last(const struct rb_root *root) 426 { 427 struct rb_node *n; 428 429 n = root->rb_node; 430 if (!n) 431 return NULL; 432 while (n->rb_right) 433 n = n->rb_right; 434 return n; 435 } 436 437 struct rb_node *rb_next(const struct rb_node *node) 438 { 439 struct rb_node *parent; 440 441 if (RB_EMPTY_NODE(node)) 442 return NULL; 443 444 /* 445 * If we have a right-hand child, go down and then left as far 446 * as we can. 447 */ 448 if (node->rb_right) { 449 node = node->rb_right; 450 while (node->rb_left) 451 node=node->rb_left; 452 return (struct rb_node *)node; 453 } 454 455 /* 456 * No right-hand children. Everything down and left is smaller than us, 457 * so any 'next' node must be in the general direction of our parent. 458 * Go up the tree; any time the ancestor is a right-hand child of its 459 * parent, keep going up. First time it's a left-hand child of its 460 * parent, said parent is our 'next' node. 461 */ 462 while ((parent = rb_parent(node)) && node == parent->rb_right) 463 node = parent; 464 465 return parent; 466 } 467 468 struct rb_node *rb_prev(const struct rb_node *node) 469 { 470 struct rb_node *parent; 471 472 if (RB_EMPTY_NODE(node)) 473 return NULL; 474 475 /* 476 * If we have a left-hand child, go down and then right as far 477 * as we can. 478 */ 479 if (node->rb_left) { 480 node = node->rb_left; 481 while (node->rb_right) 482 node=node->rb_right; 483 return (struct rb_node *)node; 484 } 485 486 /* 487 * No left-hand children. Go up till we find an ancestor which 488 * is a right-hand child of its parent. 489 */ 490 while ((parent = rb_parent(node)) && node == parent->rb_left) 491 node = parent; 492 493 return parent; 494 } 495 496 void rb_replace_node(struct rb_node *victim, struct rb_node *new, 497 struct rb_root *root) 498 { 499 struct rb_node *parent = rb_parent(victim); 500 501 /* Set the surrounding nodes to point to the replacement */ 502 __rb_change_child(victim, new, parent, root); 503 if (victim->rb_left) 504 rb_set_parent(victim->rb_left, new); 505 if (victim->rb_right) 506 rb_set_parent(victim->rb_right, new); 507 508 /* Copy the pointers/colour from the victim to the replacement */ 509 *new = *victim; 510 } 511 512 static struct rb_node *rb_left_deepest_node(const struct rb_node *node) 513 { 514 for (;;) { 515 if (node->rb_left) 516 node = node->rb_left; 517 else if (node->rb_right) 518 node = node->rb_right; 519 else 520 return (struct rb_node *)node; 521 } 522 } 523 524 struct rb_node *rb_next_postorder(const struct rb_node *node) 525 { 526 const struct rb_node *parent; 527 if (!node) 528 return NULL; 529 parent = rb_parent(node); 530 531 /* If we're sitting on node, we've already seen our children */ 532 if (parent && node == parent->rb_left && parent->rb_right) { 533 /* If we are the parent's left node, go to the parent's right 534 * node then all the way down to the left */ 535 return rb_left_deepest_node(parent->rb_right); 536 } else 537 /* Otherwise we are the parent's right node, and the parent 538 * should be next */ 539 return (struct rb_node *)parent; 540 } 541 542 struct rb_node *rb_first_postorder(const struct rb_root *root) 543 { 544 if (!root->rb_node) 545 return NULL; 546 547 return rb_left_deepest_node(root->rb_node); 548 } 549