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
   6   This program is free software; you can redistribute it and/or modify
   7   it under the terms of the GNU General Public License as published by
   8   the Free Software Foundation; either version 2 of the License, or
   9   (at your option) any later version.
  10
  11   This program is distributed in the hope that it will be useful,
  12   but WITHOUT ANY WARRANTY; without even the implied warranty of
  13   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14   GNU General Public License for more details.
  15
  16   You should have received a copy of the GNU General Public License
  17   along with this program; if not, write to the Free Software
  18   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  19
  20   linux/lib/rbtree.c
  21 */
  22
  23 #include <linux/rbtree.h>
  24 #include <linux/export.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 #define RB_RED          0
  47 #define RB_BLACK        1
  48
  49 #define rb_color(r)   ((r)->__rb_parent_color & 1)
  50 #define rb_is_red(r)   (!rb_color(r))
  51 #define rb_is_black(r) rb_color(r)
  52
  53 static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
  54 {
  55         rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
  56 }
  57
  58 static inline void rb_set_parent_color(struct rb_node *rb,
  59                                        struct rb_node *p, int color)
  60 {
  61         rb->__rb_parent_color = (unsigned long)p | color;
  62 }
  63
  64 static inline struct rb_node *rb_red_parent(struct rb_node *red)
  65 {
  66         return (struct rb_node *)red->__rb_parent_color;
  67 }
  68
  69 /*
  70  * Helper function for rotations:
  71  * - old's parent and color get assigned to new
  72  * - old gets assigned new as a parent and 'color' as a color.
  73  */
  74 static inline void
  75 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
  76                         struct rb_root *root, int color)
  77 {
  78         struct rb_node *parent = rb_parent(old);
  79         new->__rb_parent_color = old->__rb_parent_color;
  80         rb_set_parent_color(old, new, color);
  81         if (parent) {
  82                 if (parent->rb_left == old)
  83                         parent->rb_left = new;
  84                 else
  85                         parent->rb_right = new;
  86         } else
  87                 root->rb_node = new;
  88 }
  89
  90 void rb_insert_color(struct rb_node *node, struct rb_root *root)
  91 {
  92         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
  93
  94         while (true) {
  95                 /*
  96                  * Loop invariant: node is red
  97                  *
  98                  * If there is a black parent, we are done.
  99                  * Otherwise, take some corrective action as we don't
 100                  * want a red root or two consecutive red nodes.
 101                  */
 102                 if (!parent) {
 103                         rb_set_parent_color(node, NULL, RB_BLACK);
 104                         break;
 105                 } else if (rb_is_black(parent))
 106                         break;
 107
 108                 gparent = rb_red_parent(parent);
 109
 110                 if (parent == gparent->rb_left) {
 111                         tmp = gparent->rb_right;
 112                         if (tmp && rb_is_red(tmp)) {
 113                                 /*
 114                                  * Case 1 - color flips
 115                                  *
 116                                  *       G            g
 117                                  *      / \          / \
 118                                  *     p   u  -->   P   U
 119                                  *    /            /
 120                                  *   n            N
 121                                  *
 122                                  * However, since g's parent might be red, and
 123                                  * 4) does not allow this, we need to recurse
 124                                  * at g.
 125                                  */
 126                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 127                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 128                                 node = gparent;
 129                                 parent = rb_parent(node);
 130                                 rb_set_parent_color(node, parent, RB_RED);
 131                                 continue;
 132                         }
 133
 134                         if (parent->rb_right == node) {
 135                                 /*
 136                                  * Case 2 - left rotate at parent
 137                                  *
 138                                  *      G             G
 139                                  *     / \           / \
 140                                  *    p   U  -->    n   U
 141                                  *     \           /
 142                                  *      n         p
 143                                  *
 144                                  * This still leaves us in violation of 4), the
 145                                  * continuation into Case 3 will fix that.
 146                                  */
 147                                 parent->rb_right = tmp = node->rb_left;
 148                                 node->rb_left = parent;
 149                                 if (tmp)
 150                                         rb_set_parent_color(tmp, parent,
 151                                                             RB_BLACK);
 152                                 rb_set_parent_color(parent, node, RB_RED);
 153                                 parent = node;
 154                         }
 155
 156                         /*
 157                          * Case 3 - right rotate at gparent
 158                          *
 159                          *        G           P
 160                          *       / \         / \
 161                          *      p   U  -->  n   g
 162                          *     /                 \
 163                          *    n                   U
 164                          */
 165                         gparent->rb_left = tmp = parent->rb_right;
 166                         parent->rb_right = gparent;
 167                         if (tmp)
 168                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 169                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 170                         break;
 171                 } else {
 172                         tmp = gparent->rb_left;
 173                         if (tmp && rb_is_red(tmp)) {
 174                                 /* Case 1 - color flips */
 175                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 176                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 177                                 node = gparent;
 178                                 parent = rb_parent(node);
 179                                 rb_set_parent_color(node, parent, RB_RED);
 180                                 continue;
 181                         }
 182
 183                         if (parent->rb_left == node) {
 184                                 /* Case 2 - right rotate at parent */
 185                                 parent->rb_left = tmp = node->rb_right;
 186                                 node->rb_right = parent;
 187                                 if (tmp)
 188                                         rb_set_parent_color(tmp, parent,
 189                                                             RB_BLACK);
 190                                 rb_set_parent_color(parent, node, RB_RED);
 191                                 parent = node;
 192                         }
 193
 194                         /* Case 3 - left rotate at gparent */
 195                         gparent->rb_right = tmp = parent->rb_left;
 196                         parent->rb_left = gparent;
 197                         if (tmp)
 198                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 199                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 200                         break;
 201                 }
 202         }
 203 }
 204 EXPORT_SYMBOL(rb_insert_color);
 205
 206 static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
 207                              struct rb_root *root)
 208 {
 209         struct rb_node *sibling, *tmp1, *tmp2;
 210
 211         while (true) {
 212                 /*
 213                  * Loop invariant: all leaf paths going through node have a
 214                  * black node count that is 1 lower than other leaf paths.
 215                  *
 216                  * If node is red, we can flip it to black to adjust.
 217                  * If node is the root, all leaf paths go through it.
 218                  * Otherwise, we need to adjust the tree through color flips
 219                  * and tree rotations as per one of the 4 cases below.
 220                  */
 221                 if (node && rb_is_red(node)) {
 222                         rb_set_parent_color(node, parent, RB_BLACK);
 223                         break;
 224                 } else if (!parent) {
 225                         break;
 226                 } else if (parent->rb_left == node) {
 227                         sibling = parent->rb_right;
 228                         if (rb_is_red(sibling)) {
 229                                 /*
 230                                  * Case 1 - left rotate at parent
 231                                  *
 232                                  *     P               S
 233                                  *    / \             / \
 234                                  *   N   s    -->    p   Sr
 235                                  *      / \         / \
 236                                  *     Sl  Sr      N   Sl
 237                                  */
 238                                 parent->rb_right = tmp1 = sibling->rb_left;
 239                                 sibling->rb_left = parent;
 240                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 241                                 __rb_rotate_set_parents(parent, sibling, root,
 242                                                         RB_RED);
 243                                 sibling = tmp1;
 244                         }
 245                         tmp1 = sibling->rb_right;
 246                         if (!tmp1 || rb_is_black(tmp1)) {
 247                                 tmp2 = sibling->rb_left;
 248                                 if (!tmp2 || rb_is_black(tmp2)) {
 249                                         /*
 250                                          * Case 2 - sibling color flip
 251                                          * (p could be either color here)
 252                                          *
 253                                          *    (p)           (p)
 254                                          *    / \           / \
 255                                          *   N   S    -->  N   s
 256                                          *      / \           / \
 257                                          *     Sl  Sr        Sl  Sr
 258                                          *
 259                                          * This leaves us violating 5), so
 260                                          * recurse at p. If p is red, the
 261                                          * recursion will just flip it to black
 262                                          * and exit. If coming from Case 1,
 263                                          * p is known to be red.
 264                                          */
 265                                         rb_set_parent_color(sibling, parent,
 266                                                             RB_RED);
 267                                         node = parent;
 268                                         parent = rb_parent(node);
 269                                         continue;
 270                                 }
 271                                 /*
 272                                  * Case 3 - right rotate at sibling
 273                                  * (p could be either color here)
 274                                  *
 275                                  *   (p)           (p)
 276                                  *   / \           / \
 277                                  *  N   S    -->  N   Sl
 278                                  *     / \             \
 279                                  *    sl  Sr            s
 280                                  *                       \
 281                                  *                        Sr
 282                                  */
 283                                 sibling->rb_left = tmp1 = tmp2->rb_right;
 284                                 tmp2->rb_right = sibling;
 285                                 parent->rb_right = tmp2;
 286                                 if (tmp1)
 287                                         rb_set_parent_color(tmp1, sibling,
 288                                                             RB_BLACK);
 289                                 tmp1 = sibling;
 290                                 sibling = tmp2;
 291                         }
 292                         /*
 293                          * Case 4 - left rotate at parent + color flips
 294                          * (p and sl could be either color here.
 295                          *  After rotation, p becomes black, s acquires
 296                          *  p's color, and sl keeps its color)
 297                          *
 298                          *      (p)             (s)
 299                          *      / \             / \
 300                          *     N   S     -->   P   Sr
 301                          *        / \         / \
 302                          *      (sl) sr      N  (sl)
 303                          */
 304                         parent->rb_right = tmp2 = sibling->rb_left;
 305                         sibling->rb_left = parent;
 306                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 307                         if (tmp2)
 308                                 rb_set_parent(tmp2, parent);
 309                         __rb_rotate_set_parents(parent, sibling, root,
 310                                                 RB_BLACK);
 311                         break;
 312                 } else {
 313                         sibling = parent->rb_left;
 314                         if (rb_is_red(sibling)) {
 315                                 /* Case 1 - right rotate at parent */
 316                                 parent->rb_left = tmp1 = sibling->rb_right;
 317                                 sibling->rb_right = parent;
 318                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 319                                 __rb_rotate_set_parents(parent, sibling, root,
 320                                                         RB_RED);
 321                                 sibling = tmp1;
 322                         }
 323                         tmp1 = sibling->rb_left;
 324                         if (!tmp1 || rb_is_black(tmp1)) {
 325                                 tmp2 = sibling->rb_right;
 326                                 if (!tmp2 || rb_is_black(tmp2)) {
 327                                         /* Case 2 - sibling color flip */
 328                                         rb_set_parent_color(sibling, parent,
 329                                                             RB_RED);
 330                                         node = parent;
 331                                         parent = rb_parent(node);
 332                                         continue;
 333                                 }
 334                                 /* Case 3 - right rotate at sibling */
 335                                 sibling->rb_right = tmp1 = tmp2->rb_left;
 336                                 tmp2->rb_left = sibling;
 337                                 parent->rb_left = tmp2;
 338                                 if (tmp1)
 339                                         rb_set_parent_color(tmp1, sibling,
 340                                                             RB_BLACK);
 341                                 tmp1 = sibling;
 342                                 sibling = tmp2;
 343                         }
 344                         /* Case 4 - left rotate at parent + color flips */
 345                         parent->rb_left = tmp2 = sibling->rb_right;
 346                         sibling->rb_right = parent;
 347                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 348                         if (tmp2)
 349                                 rb_set_parent(tmp2, parent);
 350                         __rb_rotate_set_parents(parent, sibling, root,
 351                                                 RB_BLACK);
 352                         break;
 353                 }
 354         }
 355 }
 356
 357 void rb_erase(struct rb_node *node, struct rb_root *root)
 358 {
 359         struct rb_node *child, *parent;
 360         int color;
 361
 362         if (!node->rb_left)
 363                 child = node->rb_right;
 364         else if (!node->rb_right)
 365                 child = node->rb_left;
 366         else {
 367                 struct rb_node *old = node, *left;
 368
 369                 node = node->rb_right;
 370                 while ((left = node->rb_left) != NULL)
 371                         node = left;
 372
 373                 if (rb_parent(old)) {
 374                         if (rb_parent(old)->rb_left == old)
 375                                 rb_parent(old)->rb_left = node;
 376                         else
 377                                 rb_parent(old)->rb_right = node;
 378                 } else
 379                         root->rb_node = node;
 380
 381                 child = node->rb_right;
 382                 parent = rb_parent(node);
 383                 color = rb_color(node);
 384
 385                 if (parent == old) {
 386                         parent = node;
 387                 } else {
 388                         if (child)
 389                                 rb_set_parent(child, parent);
 390                         parent->rb_left = child;
 391
 392                         node->rb_right = old->rb_right;
 393                         rb_set_parent(old->rb_right, node);
 394                 }
 395
 396                 node->__rb_parent_color = old->__rb_parent_color;
 397                 node->rb_left = old->rb_left;
 398                 rb_set_parent(old->rb_left, node);
 399
 400                 goto color;
 401         }
 402
 403         parent = rb_parent(node);
 404         color = rb_color(node);
 405
 406         if (child)
 407                 rb_set_parent(child, parent);
 408         if (parent) {
 409                 if (parent->rb_left == node)
 410                         parent->rb_left = child;
 411                 else
 412                         parent->rb_right = child;
 413         } else
 414                 root->rb_node = child;
 415
 416 color:
 417         if (color == RB_BLACK)
 418                 __rb_erase_color(child, parent, root);
 419 }
 420 EXPORT_SYMBOL(rb_erase);
 421
 422 static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data)
 423 {
 424         struct rb_node *parent;
 425
 426 up:
 427         func(node, data);
 428         parent = rb_parent(node);
 429         if (!parent)
 430                 return;
 431
 432         if (node == parent->rb_left && parent->rb_right)
 433                 func(parent->rb_right, data);
 434         else if (parent->rb_left)
 435                 func(parent->rb_left, data);
 436
 437         node = parent;
 438         goto up;
 439 }
 440
 441 /*
 442  * after inserting @node into the tree, update the tree to account for
 443  * both the new entry and any damage done by rebalance
 444  */
 445 void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data)
 446 {
 447         if (node->rb_left)
 448                 node = node->rb_left;
 449         else if (node->rb_right)
 450                 node = node->rb_right;
 451
 452         rb_augment_path(node, func, data);
 453 }
 454 EXPORT_SYMBOL(rb_augment_insert);
 455
 456 /*
 457  * before removing the node, find the deepest node on the rebalance path
 458  * that will still be there after @node gets removed
 459  */
 460 struct rb_node *rb_augment_erase_begin(struct rb_node *node)
 461 {
 462         struct rb_node *deepest;
 463
 464         if (!node->rb_right && !node->rb_left)
 465                 deepest = rb_parent(node);
 466         else if (!node->rb_right)
 467                 deepest = node->rb_left;
 468         else if (!node->rb_left)
 469                 deepest = node->rb_right;
 470         else {
 471                 deepest = rb_next(node);
 472                 if (deepest->rb_right)
 473                         deepest = deepest->rb_right;
 474                 else if (rb_parent(deepest) != node)
 475                         deepest = rb_parent(deepest);
 476         }
 477
 478         return deepest;
 479 }
 480 EXPORT_SYMBOL(rb_augment_erase_begin);
 481
 482 /*
 483  * after removal, update the tree to account for the removed entry
 484  * and any rebalance damage.
 485  */
 486 void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data)
 487 {
 488         if (node)
 489                 rb_augment_path(node, func, data);
 490 }
 491 EXPORT_SYMBOL(rb_augment_erase_end);
 492
 493 /*
 494  * This function returns the first node (in sort order) of the tree.
 495  */
 496 struct rb_node *rb_first(const struct rb_root *root)
 497 {
 498         struct rb_node  *n;
 499
 500         n = root->rb_node;
 501         if (!n)
 502                 return NULL;
 503         while (n->rb_left)
 504                 n = n->rb_left;
 505         return n;
 506 }
 507 EXPORT_SYMBOL(rb_first);
 508
 509 struct rb_node *rb_last(const struct rb_root *root)
 510 {
 511         struct rb_node  *n;
 512
 513         n = root->rb_node;
 514         if (!n)
 515                 return NULL;
 516         while (n->rb_right)
 517                 n = n->rb_right;
 518         return n;
 519 }
 520 EXPORT_SYMBOL(rb_last);
 521
 522 struct rb_node *rb_next(const struct rb_node *node)
 523 {
 524         struct rb_node *parent;
 525
 526         if (RB_EMPTY_NODE(node))
 527                 return NULL;
 528
 529         /*
 530          * If we have a right-hand child, go down and then left as far
 531          * as we can.
 532          */
 533         if (node->rb_right) {
 534                 node = node->rb_right;
 535                 while (node->rb_left)
 536                         node=node->rb_left;
 537                 return (struct rb_node *)node;
 538         }
 539
 540         /*
 541          * No right-hand children. Everything down and left is smaller than us,
 542          * so any 'next' node must be in the general direction of our parent.
 543          * Go up the tree; any time the ancestor is a right-hand child of its
 544          * parent, keep going up. First time it's a left-hand child of its
 545          * parent, said parent is our 'next' node.
 546          */
 547         while ((parent = rb_parent(node)) && node == parent->rb_right)
 548                 node = parent;
 549
 550         return parent;
 551 }
 552 EXPORT_SYMBOL(rb_next);
 553
 554 struct rb_node *rb_prev(const struct rb_node *node)
 555 {
 556         struct rb_node *parent;
 557
 558         if (RB_EMPTY_NODE(node))
 559                 return NULL;
 560
 561         /*
 562          * If we have a left-hand child, go down and then right as far
 563          * as we can.
 564          */
 565         if (node->rb_left) {
 566                 node = node->rb_left;
 567                 while (node->rb_right)
 568                         node=node->rb_right;
 569                 return (struct rb_node *)node;
 570         }
 571
 572         /*
 573          * No left-hand children. Go up till we find an ancestor which
 574          * is a right-hand child of its parent.
 575          */
 576         while ((parent = rb_parent(node)) && node == parent->rb_left)
 577                 node = parent;
 578
 579         return parent;
 580 }
 581 EXPORT_SYMBOL(rb_prev);
 582
 583 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
 584                      struct rb_root *root)
 585 {
 586         struct rb_node *parent = rb_parent(victim);
 587
 588         /* Set the surrounding nodes to point to the replacement */
 589         if (parent) {
 590                 if (victim == parent->rb_left)
 591                         parent->rb_left = new;
 592                 else
 593                         parent->rb_right = new;
 594         } else {
 595                 root->rb_node = new;
 596         }
 597         if (victim->rb_left)
 598                 rb_set_parent(victim->rb_left, new);
 599         if (victim->rb_right)
 600                 rb_set_parent(victim->rb_right, new);
 601
 602         /* Copy the pointers/colour from the victim to the replacement */
 603         *new = *victim;
 604 }
 605 EXPORT_SYMBOL(rb_replace_node);