lib/rbtree.c

   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.h>
  25 #include <linux/export.h>
  26
  27 /*
  28  * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
  29  *
  30  *  1) A node is either red or black
  31  *  2) The root is black
  32  *  3) All leaves (NULL) are black
  33  *  4) Both children of every red node are black
  34  *  5) Every simple path from root to leaves contains the same number
  35  *     of black nodes.
  36  *
  37  *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
  38  *  consecutive red nodes in a path and every red node is therefore followed by
  39  *  a black. So if B is the number of black nodes on every simple path (as per
  40  *  5), then the longest possible path due to 4 is 2B.
  41  *
  42  *  We shall indicate color with case, where black nodes are uppercase and red
  43  *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
  44  *  parentheses and have some accompanying text comment.
  45  */
  46
  47 #define RB_RED          0
  48 #define RB_BLACK        1
  49
  50 #define __rb_parent(pc)    ((struct rb_node *)(pc & ~3))
  51
  52 #define __rb_color(pc)     ((pc) & 1)
  53 #define __rb_is_black(pc)  __rb_color(pc)
  54 #define __rb_is_red(pc)    (!__rb_color(pc))
  55 #define rb_color(rb)       __rb_color((rb)->__rb_parent_color)
  56 #define rb_is_red(rb)      __rb_is_red((rb)->__rb_parent_color)
  57 #define rb_is_black(rb)    __rb_is_black((rb)->__rb_parent_color)
  58
  59 static inline void rb_set_black(struct rb_node *rb)
  60 {
  61         rb->__rb_parent_color |= RB_BLACK;
  62 }
  63
  64 static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
  65 {
  66         rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
  67 }
  68
  69 static inline void rb_set_parent_color(struct rb_node *rb,
  70                                        struct rb_node *p, int color)
  71 {
  72         rb->__rb_parent_color = (unsigned long)p | color;
  73 }
  74
  75 static inline struct rb_node *rb_red_parent(struct rb_node *red)
  76 {
  77         return (struct rb_node *)red->__rb_parent_color;
  78 }
  79
  80 static inline void
  81 __rb_change_child(struct rb_node *old, struct rb_node *new,
  82                   struct rb_node *parent, struct rb_root *root)
  83 {
  84         if (parent) {
  85                 if (parent->rb_left == old)
  86                         parent->rb_left = new;
  87                 else
  88                         parent->rb_right = new;
  89         } else
  90                 root->rb_node = new;
  91 }
  92
  93 /*
  94  * Helper function for rotations:
  95  * - old's parent and color get assigned to new
  96  * - old gets assigned new as a parent and 'color' as a color.
  97  */
  98 static inline void
  99 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
 100                         struct rb_root *root, int color)
 101 {
 102         struct rb_node *parent = rb_parent(old);
 103         new->__rb_parent_color = old->__rb_parent_color;
 104         rb_set_parent_color(old, new, color);
 105         __rb_change_child(old, new, parent, root);
 106 }
 107
 108 void rb_insert_color(struct rb_node *node, struct rb_root *root)
 109 {
 110         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
 111
 112         while (true) {
 113                 /*
 114                  * Loop invariant: node is red
 115                  *
 116                  * If there is a black parent, we are done.
 117                  * Otherwise, take some corrective action as we don't
 118                  * want a red root or two consecutive red nodes.
 119                  */
 120                 if (!parent) {
 121                         rb_set_parent_color(node, NULL, RB_BLACK);
 122                         break;
 123                 } else if (rb_is_black(parent))
 124                         break;
 125
 126                 gparent = rb_red_parent(parent);
 127
 128                 tmp = gparent->rb_right;
 129                 if (parent != tmp) {    /* parent == gparent->rb_left */
 130                         if (tmp && rb_is_red(tmp)) {
 131                                 /*
 132                                  * Case 1 - color flips
 133                                  *
 134                                  *       G            g
 135                                  *      / \          / \
 136                                  *     p   u  -->   P   U
 137                                  *    /            /
 138                                  *   n            N
 139                                  *
 140                                  * However, since g's parent might be red, and
 141                                  * 4) does not allow this, we need to recurse
 142                                  * at g.
 143                                  */
 144                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 145                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 146                                 node = gparent;
 147                                 parent = rb_parent(node);
 148                                 rb_set_parent_color(node, parent, RB_RED);
 149                                 continue;
 150                         }
 151
 152                         tmp = parent->rb_right;
 153                         if (node == tmp) {
 154                                 /*
 155                                  * Case 2 - left rotate at parent
 156                                  *
 157                                  *      G             G
 158                                  *     / \           / \
 159                                  *    p   U  -->    n   U
 160                                  *     \           /
 161                                  *      n         p
 162                                  *
 163                                  * This still leaves us in violation of 4), the
 164                                  * continuation into Case 3 will fix that.
 165                                  */
 166                                 parent->rb_right = tmp = node->rb_left;
 167                                 node->rb_left = parent;
 168                                 if (tmp)
 169                                         rb_set_parent_color(tmp, parent,
 170                                                             RB_BLACK);
 171                                 rb_set_parent_color(parent, node, RB_RED);
 172                                 parent = node;
 173                                 tmp = node->rb_right;
 174                         }
 175
 176                         /*
 177                          * Case 3 - right rotate at gparent
 178                          *
 179                          *        G           P
 180                          *       / \         / \
 181                          *      p   U  -->  n   g
 182                          *     /                 \
 183                          *    n                   U
 184                          */
 185                         gparent->rb_left = tmp;  /* == parent->rb_right */
 186                         parent->rb_right = gparent;
 187                         if (tmp)
 188                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 189                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 190                         break;
 191                 } else {
 192                         tmp = gparent->rb_left;
 193                         if (tmp && rb_is_red(tmp)) {
 194                                 /* Case 1 - color flips */
 195                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 196                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 197                                 node = gparent;
 198                                 parent = rb_parent(node);
 199                                 rb_set_parent_color(node, parent, RB_RED);
 200                                 continue;
 201                         }
 202
 203                         tmp = parent->rb_left;
 204                         if (node == tmp) {
 205                                 /* Case 2 - right rotate at parent */
 206                                 parent->rb_left = tmp = node->rb_right;
 207                                 node->rb_right = parent;
 208                                 if (tmp)
 209                                         rb_set_parent_color(tmp, parent,
 210                                                             RB_BLACK);
 211                                 rb_set_parent_color(parent, node, RB_RED);
 212                                 parent = node;
 213                                 tmp = node->rb_left;
 214                         }
 215
 216                         /* Case 3 - left rotate at gparent */
 217                         gparent->rb_right = tmp;  /* == parent->rb_left */
 218                         parent->rb_left = gparent;
 219                         if (tmp)
 220                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 221                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 222                         break;
 223                 }
 224         }
 225 }
 226 EXPORT_SYMBOL(rb_insert_color);
 227
 228 static void __rb_erase_color(struct rb_node *parent, struct rb_root *root)
 229 {
 230         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
 231
 232         while (true) {
 233                 /*
 234                  * Loop invariants:
 235                  * - node is black (or NULL on first iteration)
 236                  * - node is not the root (parent is not NULL)
 237                  * - All leaf paths going through parent and node have a
 238                  *   black node count that is 1 lower than other leaf paths.
 239                  */
 240                 sibling = parent->rb_right;
 241                 if (node != sibling) {  /* node == parent->rb_left */
 242                         if (rb_is_red(sibling)) {
 243                                 /*
 244                                  * Case 1 - left rotate at parent
 245                                  *
 246                                  *     P               S
 247                                  *    / \             / \
 248                                  *   N   s    -->    p   Sr
 249                                  *      / \         / \
 250                                  *     Sl  Sr      N   Sl
 251                                  */
 252                                 parent->rb_right = tmp1 = sibling->rb_left;
 253                                 sibling->rb_left = parent;
 254                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 255                                 __rb_rotate_set_parents(parent, sibling, root,
 256                                                         RB_RED);
 257                                 sibling = tmp1;
 258                         }
 259                         tmp1 = sibling->rb_right;
 260                         if (!tmp1 || rb_is_black(tmp1)) {
 261                                 tmp2 = sibling->rb_left;
 262                                 if (!tmp2 || rb_is_black(tmp2)) {
 263                                         /*
 264                                          * Case 2 - sibling color flip
 265                                          * (p could be either color here)
 266                                          *
 267                                          *    (p)           (p)
 268                                          *    / \           / \
 269                                          *   N   S    -->  N   s
 270                                          *      / \           / \
 271                                          *     Sl  Sr        Sl  Sr
 272                                          *
 273                                          * This leaves us violating 5) which
 274                                          * can be fixed by flipping p to black
 275                                          * if it was red, or by recursing at p.
 276                                          * p is red when coming from Case 1.
 277                                          */
 278                                         rb_set_parent_color(sibling, parent,
 279                                                             RB_RED);
 280                                         if (rb_is_red(parent))
 281                                                 rb_set_black(parent);
 282                                         else {
 283                                                 node = parent;
 284                                                 parent = rb_parent(node);
 285                                                 if (parent)
 286                                                         continue;
 287                                         }
 288                                         break;
 289                                 }
 290                                 /*
 291                                  * Case 3 - right rotate at sibling
 292                                  * (p could be either color here)
 293                                  *
 294                                  *   (p)           (p)
 295                                  *   / \           / \
 296                                  *  N   S    -->  N   Sl
 297                                  *     / \             \
 298                                  *    sl  Sr            s
 299                                  *                       \
 300                                  *                        Sr
 301                                  */
 302                                 sibling->rb_left = tmp1 = tmp2->rb_right;
 303                                 tmp2->rb_right = sibling;
 304                                 parent->rb_right = tmp2;
 305                                 if (tmp1)
 306                                         rb_set_parent_color(tmp1, sibling,
 307                                                             RB_BLACK);
 308                                 tmp1 = sibling;
 309                                 sibling = tmp2;
 310                         }
 311                         /*
 312                          * Case 4 - left rotate at parent + color flips
 313                          * (p and sl could be either color here.
 314                          *  After rotation, p becomes black, s acquires
 315                          *  p's color, and sl keeps its color)
 316                          *
 317                          *      (p)             (s)
 318                          *      / \             / \
 319                          *     N   S     -->   P   Sr
 320                          *        / \         / \
 321                          *      (sl) sr      N  (sl)
 322                          */
 323                         parent->rb_right = tmp2 = sibling->rb_left;
 324                         sibling->rb_left = parent;
 325                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 326                         if (tmp2)
 327                                 rb_set_parent(tmp2, parent);
 328                         __rb_rotate_set_parents(parent, sibling, root,
 329                                                 RB_BLACK);
 330                         break;
 331                 } else {
 332                         sibling = parent->rb_left;
 333                         if (rb_is_red(sibling)) {
 334                                 /* Case 1 - right rotate at parent */
 335                                 parent->rb_left = tmp1 = sibling->rb_right;
 336                                 sibling->rb_right = parent;
 337                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 338                                 __rb_rotate_set_parents(parent, sibling, root,
 339                                                         RB_RED);
 340                                 sibling = tmp1;
 341                         }
 342                         tmp1 = sibling->rb_left;
 343                         if (!tmp1 || rb_is_black(tmp1)) {
 344                                 tmp2 = sibling->rb_right;
 345                                 if (!tmp2 || rb_is_black(tmp2)) {
 346                                         /* Case 2 - sibling color flip */
 347                                         rb_set_parent_color(sibling, parent,
 348                                                             RB_RED);
 349                                         if (rb_is_red(parent))
 350                                                 rb_set_black(parent);
 351                                         else {
 352                                                 node = parent;
 353                                                 parent = rb_parent(node);
 354                                                 if (parent)
 355                                                         continue;
 356                                         }
 357                                         break;
 358                                 }
 359                                 /* Case 3 - right rotate at sibling */
 360                                 sibling->rb_right = tmp1 = tmp2->rb_left;
 361                                 tmp2->rb_left = sibling;
 362                                 parent->rb_left = tmp2;
 363                                 if (tmp1)
 364                                         rb_set_parent_color(tmp1, sibling,
 365                                                             RB_BLACK);
 366                                 tmp1 = sibling;
 367                                 sibling = tmp2;
 368                         }
 369                         /* Case 4 - left rotate at parent + color flips */
 370                         parent->rb_left = tmp2 = sibling->rb_right;
 371                         sibling->rb_right = parent;
 372                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 373                         if (tmp2)
 374                                 rb_set_parent(tmp2, parent);
 375                         __rb_rotate_set_parents(parent, sibling, root,
 376                                                 RB_BLACK);
 377                         break;
 378                 }
 379         }
 380 }
 381
 382 void rb_erase(struct rb_node *node, struct rb_root *root)
 383 {
 384         struct rb_node *child = node->rb_right, *tmp = node->rb_left;
 385         struct rb_node *parent, *rebalance;
 386         unsigned long pc;
 387
 388         if (!tmp) {
 389                 /*
 390                  * Case 1: node to erase has no more than 1 child (easy!)
 391                  *
 392                  * Note that if there is one child it must be red due to 5)
 393                  * and node must be black due to 4). We adjust colors locally
 394                  * so as to bypass __rb_erase_color() later on.
 395                  */
 396                 pc = node->__rb_parent_color;
 397                 parent = __rb_parent(pc);
 398                 __rb_change_child(node, child, parent, root);
 399                 if (child) {
 400                         child->__rb_parent_color = pc;
 401                         rebalance = NULL;
 402                 } else
 403                         rebalance = __rb_is_black(pc) ? parent : NULL;
 404         } else if (!child) {
 405                 /* Still case 1, but this time the child is node->rb_left */
 406                 tmp->__rb_parent_color = pc = node->__rb_parent_color;
 407                 parent = __rb_parent(pc);
 408                 __rb_change_child(node, tmp, parent, root);
 409                 rebalance = NULL;
 410         } else {
 411                 struct rb_node *successor = child, *child2;
 412                 tmp = child->rb_left;
 413                 if (!tmp) {
 414                         /*
 415                          * Case 2: node's successor is its right child
 416                          *
 417                          *    (n)          (s)
 418                          *    / \          / \
 419                          *  (x) (s)  ->  (x) (c)
 420                          *        \
 421                          *        (c)
 422                          */
 423                         parent = child;
 424                         child2 = child->rb_right;
 425                 } else {
 426                         /*
 427                          * Case 3: node's successor is leftmost under
 428                          * node's right child subtree
 429                          *
 430                          *    (n)          (s)
 431                          *    / \          / \
 432                          *  (x) (y)  ->  (x) (y)
 433                          *      /            /
 434                          *    (p)          (p)
 435                          *    /            /
 436                          *  (s)          (c)
 437                          *    \
 438                          *    (c)
 439                          */
 440                         do {
 441                                 parent = successor;
 442                                 successor = tmp;
 443                                 tmp = tmp->rb_left;
 444                         } while (tmp);
 445                         parent->rb_left = child2 = successor->rb_right;
 446                         successor->rb_right = child;
 447                         rb_set_parent(child, successor);
 448                 }
 449
 450                 successor->rb_left = tmp = node->rb_left;
 451                 rb_set_parent(tmp, successor);
 452
 453                 pc = node->__rb_parent_color;
 454                 tmp = __rb_parent(pc);
 455                 __rb_change_child(node, successor, tmp, root);
 456                 if (child2) {
 457                         successor->__rb_parent_color = pc;
 458                         rb_set_parent_color(child2, parent, RB_BLACK);
 459                         rebalance = NULL;
 460                 } else {
 461                         unsigned long pc2 = successor->__rb_parent_color;
 462                         successor->__rb_parent_color = pc;
 463                         rebalance = __rb_is_black(pc2) ? parent : NULL;
 464                 }
 465         }
 466
 467         if (rebalance)
 468                 __rb_erase_color(rebalance, root);
 469 }
 470 EXPORT_SYMBOL(rb_erase);
 471
 472 static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data)
 473 {
 474         struct rb_node *parent;
 475
 476 up:
 477         func(node, data);
 478         parent = rb_parent(node);
 479         if (!parent)
 480                 return;
 481
 482         if (node == parent->rb_left && parent->rb_right)
 483                 func(parent->rb_right, data);
 484         else if (parent->rb_left)
 485                 func(parent->rb_left, data);
 486
 487         node = parent;
 488         goto up;
 489 }
 490
 491 /*
 492  * after inserting @node into the tree, update the tree to account for
 493  * both the new entry and any damage done by rebalance
 494  */
 495 void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data)
 496 {
 497         if (node->rb_left)
 498                 node = node->rb_left;
 499         else if (node->rb_right)
 500                 node = node->rb_right;
 501
 502         rb_augment_path(node, func, data);
 503 }
 504 EXPORT_SYMBOL(rb_augment_insert);
 505
 506 /*
 507  * before removing the node, find the deepest node on the rebalance path
 508  * that will still be there after @node gets removed
 509  */
 510 struct rb_node *rb_augment_erase_begin(struct rb_node *node)
 511 {
 512         struct rb_node *deepest;
 513
 514         if (!node->rb_right && !node->rb_left)
 515                 deepest = rb_parent(node);
 516         else if (!node->rb_right)
 517                 deepest = node->rb_left;
 518         else if (!node->rb_left)
 519                 deepest = node->rb_right;
 520         else {
 521                 deepest = rb_next(node);
 522                 if (deepest->rb_right)
 523                         deepest = deepest->rb_right;
 524                 else if (rb_parent(deepest) != node)
 525                         deepest = rb_parent(deepest);
 526         }
 527
 528         return deepest;
 529 }
 530 EXPORT_SYMBOL(rb_augment_erase_begin);
 531
 532 /*
 533  * after removal, update the tree to account for the removed entry
 534  * and any rebalance damage.
 535  */
 536 void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data)
 537 {
 538         if (node)
 539                 rb_augment_path(node, func, data);
 540 }
 541 EXPORT_SYMBOL(rb_augment_erase_end);
 542
 543 /*
 544  * This function returns the first node (in sort order) of the tree.
 545  */
 546 struct rb_node *rb_first(const struct rb_root *root)
 547 {
 548         struct rb_node  *n;
 549
 550         n = root->rb_node;
 551         if (!n)
 552                 return NULL;
 553         while (n->rb_left)
 554                 n = n->rb_left;
 555         return n;
 556 }
 557 EXPORT_SYMBOL(rb_first);
 558
 559 struct rb_node *rb_last(const struct rb_root *root)
 560 {
 561         struct rb_node  *n;
 562
 563         n = root->rb_node;
 564         if (!n)
 565                 return NULL;
 566         while (n->rb_right)
 567                 n = n->rb_right;
 568         return n;
 569 }
 570 EXPORT_SYMBOL(rb_last);
 571
 572 struct rb_node *rb_next(const struct rb_node *node)
 573 {
 574         struct rb_node *parent;
 575
 576         if (RB_EMPTY_NODE(node))
 577                 return NULL;
 578
 579         /*
 580          * If we have a right-hand child, go down and then left as far
 581          * as we can.
 582          */
 583         if (node->rb_right) {
 584                 node = node->rb_right;
 585                 while (node->rb_left)
 586                         node=node->rb_left;
 587                 return (struct rb_node *)node;
 588         }
 589
 590         /*
 591          * No right-hand children. Everything down and left is smaller than us,
 592          * so any 'next' node must be in the general direction of our parent.
 593          * Go up the tree; any time the ancestor is a right-hand child of its
 594          * parent, keep going up. First time it's a left-hand child of its
 595          * parent, said parent is our 'next' node.
 596          */
 597         while ((parent = rb_parent(node)) && node == parent->rb_right)
 598                 node = parent;
 599
 600         return parent;
 601 }
 602 EXPORT_SYMBOL(rb_next);
 603
 604 struct rb_node *rb_prev(const struct rb_node *node)
 605 {
 606         struct rb_node *parent;
 607
 608         if (RB_EMPTY_NODE(node))
 609                 return NULL;
 610
 611         /*
 612          * If we have a left-hand child, go down and then right as far
 613          * as we can.
 614          */
 615         if (node->rb_left) {
 616                 node = node->rb_left;
 617                 while (node->rb_right)
 618                         node=node->rb_right;
 619                 return (struct rb_node *)node;
 620         }
 621
 622         /*
 623          * No left-hand children. Go up till we find an ancestor which
 624          * is a right-hand child of its parent.
 625          */
 626         while ((parent = rb_parent(node)) && node == parent->rb_left)
 627                 node = parent;
 628
 629         return parent;
 630 }
 631 EXPORT_SYMBOL(rb_prev);
 632
 633 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
 634                      struct rb_root *root)
 635 {
 636         struct rb_node *parent = rb_parent(victim);
 637
 638         /* Set the surrounding nodes to point to the replacement */
 639         __rb_change_child(victim, new, parent, root);
 640         if (victim->rb_left)
 641                 rb_set_parent(victim->rb_left, new);
 642         if (victim->rb_right)
 643                 rb_set_parent(victim->rb_right, new);
 644
 645         /* Copy the pointers/colour from the victim to the replacement */
 646         *new = *victim;
 647 }
 648 EXPORT_SYMBOL(rb_replace_node);