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