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 static __always_inline void
 109 __rb_insert(struct rb_node *node, struct rb_root *root,
 110             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 111 {
 112         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
 113
 114         while (true) {
 115                 /*
 116                  * Loop invariant: node is red
 117                  *
 118                  * If there is a black parent, we are done.
 119                  * Otherwise, take some corrective action as we don't
 120                  * want a red root or two consecutive red nodes.
 121                  */
 122                 if (!parent) {
 123                         rb_set_parent_color(node, NULL, RB_BLACK);
 124                         break;
 125                 } else if (rb_is_black(parent))
 126                         break;
 127
 128                 gparent = rb_red_parent(parent);
 129
 130                 tmp = gparent->rb_right;
 131                 if (parent != tmp) {    /* parent == gparent->rb_left */
 132                         if (tmp && rb_is_red(tmp)) {
 133                                 /*
 134                                  * Case 1 - color flips
 135                                  *
 136                                  *       G            g
 137                                  *      / \          / \
 138                                  *     p   u  -->   P   U
 139                                  *    /            /
 140                                  *   n            N
 141                                  *
 142                                  * However, since g's parent might be red, and
 143                                  * 4) does not allow this, we need to recurse
 144                                  * at g.
 145                                  */
 146                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 147                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 148                                 node = gparent;
 149                                 parent = rb_parent(node);
 150                                 rb_set_parent_color(node, parent, RB_RED);
 151                                 continue;
 152                         }
 153
 154                         tmp = parent->rb_right;
 155                         if (node == tmp) {
 156                                 /*
 157                                  * Case 2 - left rotate at parent
 158                                  *
 159                                  *      G             G
 160                                  *     / \           / \
 161                                  *    p   U  -->    n   U
 162                                  *     \           /
 163                                  *      n         p
 164                                  *
 165                                  * This still leaves us in violation of 4), the
 166                                  * continuation into Case 3 will fix that.
 167                                  */
 168                                 parent->rb_right = tmp = node->rb_left;
 169                                 node->rb_left = parent;
 170                                 if (tmp)
 171                                         rb_set_parent_color(tmp, parent,
 172                                                             RB_BLACK);
 173                                 rb_set_parent_color(parent, node, RB_RED);
 174                                 augment_rotate(parent, node);
 175                                 parent = node;
 176                                 tmp = node->rb_right;
 177                         }
 178
 179                         /*
 180                          * Case 3 - right rotate at gparent
 181                          *
 182                          *        G           P
 183                          *       / \         / \
 184                          *      p   U  -->  n   g
 185                          *     /                 \
 186                          *    n                   U
 187                          */
 188                         gparent->rb_left = tmp;  /* == parent->rb_right */
 189                         parent->rb_right = gparent;
 190                         if (tmp)
 191                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 192                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 193                         augment_rotate(gparent, parent);
 194                         break;
 195                 } else {
 196                         tmp = gparent->rb_left;
 197                         if (tmp && rb_is_red(tmp)) {
 198                                 /* Case 1 - color flips */
 199                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 200                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 201                                 node = gparent;
 202                                 parent = rb_parent(node);
 203                                 rb_set_parent_color(node, parent, RB_RED);
 204                                 continue;
 205                         }
 206
 207                         tmp = parent->rb_left;
 208                         if (node == tmp) {
 209                                 /* Case 2 - right rotate at parent */
 210                                 parent->rb_left = tmp = node->rb_right;
 211                                 node->rb_right = parent;
 212                                 if (tmp)
 213                                         rb_set_parent_color(tmp, parent,
 214                                                             RB_BLACK);
 215                                 rb_set_parent_color(parent, node, RB_RED);
 216                                 augment_rotate(parent, node);
 217                                 parent = node;
 218                                 tmp = node->rb_left;
 219                         }
 220
 221                         /* Case 3 - left rotate at gparent */
 222                         gparent->rb_right = tmp;  /* == parent->rb_left */
 223                         parent->rb_left = gparent;
 224                         if (tmp)
 225                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 226                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 227                         augment_rotate(gparent, parent);
 228                         break;
 229                 }
 230         }
 231 }
 232
 233 static __always_inline void
 234 __rb_erase_color(struct rb_node *parent, struct rb_root *root,
 235                  const struct rb_augment_callbacks *augment)
 236 {
 237         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
 238
 239         while (true) {
 240                 /*
 241                  * Loop invariants:
 242                  * - node is black (or NULL on first iteration)
 243                  * - node is not the root (parent is not NULL)
 244                  * - All leaf paths going through parent and node have a
 245                  *   black node count that is 1 lower than other leaf paths.
 246                  */
 247                 sibling = parent->rb_right;
 248                 if (node != sibling) {  /* node == parent->rb_left */
 249                         if (rb_is_red(sibling)) {
 250                                 /*
 251                                  * Case 1 - left rotate at parent
 252                                  *
 253                                  *     P               S
 254                                  *    / \             / \
 255                                  *   N   s    -->    p   Sr
 256                                  *      / \         / \
 257                                  *     Sl  Sr      N   Sl
 258                                  */
 259                                 parent->rb_right = tmp1 = sibling->rb_left;
 260                                 sibling->rb_left = parent;
 261                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 262                                 __rb_rotate_set_parents(parent, sibling, root,
 263                                                         RB_RED);
 264                                 augment->rotate(parent, sibling);
 265                                 sibling = tmp1;
 266                         }
 267                         tmp1 = sibling->rb_right;
 268                         if (!tmp1 || rb_is_black(tmp1)) {
 269                                 tmp2 = sibling->rb_left;
 270                                 if (!tmp2 || rb_is_black(tmp2)) {
 271                                         /*
 272                                          * Case 2 - sibling color flip
 273                                          * (p could be either color here)
 274                                          *
 275                                          *    (p)           (p)
 276                                          *    / \           / \
 277                                          *   N   S    -->  N   s
 278                                          *      / \           / \
 279                                          *     Sl  Sr        Sl  Sr
 280                                          *
 281                                          * This leaves us violating 5) which
 282                                          * can be fixed by flipping p to black
 283                                          * if it was red, or by recursing at p.
 284                                          * p is red when coming from Case 1.
 285                                          */
 286                                         rb_set_parent_color(sibling, parent,
 287                                                             RB_RED);
 288                                         if (rb_is_red(parent))
 289                                                 rb_set_black(parent);
 290                                         else {
 291                                                 node = parent;
 292                                                 parent = rb_parent(node);
 293                                                 if (parent)
 294                                                         continue;
 295                                         }
 296                                         break;
 297                                 }
 298                                 /*
 299                                  * Case 3 - right rotate at sibling
 300                                  * (p could be either color here)
 301                                  *
 302                                  *   (p)           (p)
 303                                  *   / \           / \
 304                                  *  N   S    -->  N   Sl
 305                                  *     / \             \
 306                                  *    sl  Sr            s
 307                                  *                       \
 308                                  *                        Sr
 309                                  */
 310                                 sibling->rb_left = tmp1 = tmp2->rb_right;
 311                                 tmp2->rb_right = sibling;
 312                                 parent->rb_right = tmp2;
 313                                 if (tmp1)
 314                                         rb_set_parent_color(tmp1, sibling,
 315                                                             RB_BLACK);
 316                                 augment->rotate(sibling, tmp2);
 317                                 tmp1 = sibling;
 318                                 sibling = tmp2;
 319                         }
 320                         /*
 321                          * Case 4 - left rotate at parent + color flips
 322                          * (p and sl could be either color here.
 323                          *  After rotation, p becomes black, s acquires
 324                          *  p's color, and sl keeps its color)
 325                          *
 326                          *      (p)             (s)
 327                          *      / \             / \
 328                          *     N   S     -->   P   Sr
 329                          *        / \         / \
 330                          *      (sl) sr      N  (sl)
 331                          */
 332                         parent->rb_right = tmp2 = sibling->rb_left;
 333                         sibling->rb_left = parent;
 334                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 335                         if (tmp2)
 336                                 rb_set_parent(tmp2, parent);
 337                         __rb_rotate_set_parents(parent, sibling, root,
 338                                                 RB_BLACK);
 339                         augment->rotate(parent, sibling);
 340                         break;
 341                 } else {
 342                         sibling = parent->rb_left;
 343                         if (rb_is_red(sibling)) {
 344                                 /* Case 1 - right rotate at parent */
 345                                 parent->rb_left = tmp1 = sibling->rb_right;
 346                                 sibling->rb_right = parent;
 347                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 348                                 __rb_rotate_set_parents(parent, sibling, root,
 349                                                         RB_RED);
 350                                 augment->rotate(parent, sibling);
 351                                 sibling = tmp1;
 352                         }
 353                         tmp1 = sibling->rb_left;
 354                         if (!tmp1 || rb_is_black(tmp1)) {
 355                                 tmp2 = sibling->rb_right;
 356                                 if (!tmp2 || rb_is_black(tmp2)) {
 357                                         /* Case 2 - sibling color flip */
 358                                         rb_set_parent_color(sibling, parent,
 359                                                             RB_RED);
 360                                         if (rb_is_red(parent))
 361                                                 rb_set_black(parent);
 362                                         else {
 363                                                 node = parent;
 364                                                 parent = rb_parent(node);
 365                                                 if (parent)
 366                                                         continue;
 367                                         }
 368                                         break;
 369                                 }
 370                                 /* Case 3 - right rotate at sibling */
 371                                 sibling->rb_right = tmp1 = tmp2->rb_left;
 372                                 tmp2->rb_left = sibling;
 373                                 parent->rb_left = tmp2;
 374                                 if (tmp1)
 375                                         rb_set_parent_color(tmp1, sibling,
 376                                                             RB_BLACK);
 377                                 augment->rotate(sibling, tmp2);
 378                                 tmp1 = sibling;
 379                                 sibling = tmp2;
 380                         }
 381                         /* Case 4 - left rotate at parent + color flips */
 382                         parent->rb_left = tmp2 = sibling->rb_right;
 383                         sibling->rb_right = parent;
 384                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 385                         if (tmp2)
 386                                 rb_set_parent(tmp2, parent);
 387                         __rb_rotate_set_parents(parent, sibling, root,
 388                                                 RB_BLACK);
 389                         augment->rotate(parent, sibling);
 390                         break;
 391                 }
 392         }
 393 }
 394
 395 static __always_inline void
 396 __rb_erase(struct rb_node *node, struct rb_root *root,
 397            const struct rb_augment_callbacks *augment)
 398 {
 399         struct rb_node *child = node->rb_right, *tmp = node->rb_left;
 400         struct rb_node *parent, *rebalance;
 401         unsigned long pc;
 402
 403         if (!tmp) {
 404                 /*
 405                  * Case 1: node to erase has no more than 1 child (easy!)
 406                  *
 407                  * Note that if there is one child it must be red due to 5)
 408                  * and node must be black due to 4). We adjust colors locally
 409                  * so as to bypass __rb_erase_color() later on.
 410                  */
 411                 pc = node->__rb_parent_color;
 412                 parent = __rb_parent(pc);
 413                 __rb_change_child(node, child, parent, root);
 414                 if (child) {
 415                         child->__rb_parent_color = pc;
 416                         rebalance = NULL;
 417                 } else
 418                         rebalance = __rb_is_black(pc) ? parent : NULL;
 419                 tmp = parent;
 420         } else if (!child) {
 421                 /* Still case 1, but this time the child is node->rb_left */
 422                 tmp->__rb_parent_color = pc = node->__rb_parent_color;
 423                 parent = __rb_parent(pc);
 424                 __rb_change_child(node, tmp, parent, root);
 425                 rebalance = NULL;
 426                 tmp = parent;
 427         } else {
 428                 struct rb_node *successor = child, *child2;
 429                 tmp = child->rb_left;
 430                 if (!tmp) {
 431                         /*
 432                          * Case 2: node's successor is its right child
 433                          *
 434                          *    (n)          (s)
 435                          *    / \          / \
 436                          *  (x) (s)  ->  (x) (c)
 437                          *        \
 438                          *        (c)
 439                          */
 440                         parent = successor;
 441                         child2 = successor->rb_right;
 442                         augment->copy(node, successor);
 443                 } else {
 444                         /*
 445                          * Case 3: node's successor is leftmost under
 446                          * node's right child subtree
 447                          *
 448                          *    (n)          (s)
 449                          *    / \          / \
 450                          *  (x) (y)  ->  (x) (y)
 451                          *      /            /
 452                          *    (p)          (p)
 453                          *    /            /
 454                          *  (s)          (c)
 455                          *    \
 456                          *    (c)
 457                          */
 458                         do {
 459                                 parent = successor;
 460                                 successor = tmp;
 461                                 tmp = tmp->rb_left;
 462                         } while (tmp);
 463                         parent->rb_left = child2 = successor->rb_right;
 464                         successor->rb_right = child;
 465                         rb_set_parent(child, successor);
 466                         augment->copy(node, successor);
 467                         augment->propagate(parent, successor);
 468                 }
 469
 470                 successor->rb_left = tmp = node->rb_left;
 471                 rb_set_parent(tmp, successor);
 472
 473                 pc = node->__rb_parent_color;
 474                 tmp = __rb_parent(pc);
 475                 __rb_change_child(node, successor, tmp, root);
 476                 if (child2) {
 477                         successor->__rb_parent_color = pc;
 478                         rb_set_parent_color(child2, parent, RB_BLACK);
 479                         rebalance = NULL;
 480                 } else {
 481                         unsigned long pc2 = successor->__rb_parent_color;
 482                         successor->__rb_parent_color = pc;
 483                         rebalance = __rb_is_black(pc2) ? parent : NULL;
 484                 }
 485                 tmp = successor;
 486         }
 487
 488         augment->propagate(tmp, NULL);
 489         if (rebalance)
 490                 __rb_erase_color(rebalance, root, augment);
 491 }
 492
 493 /*
 494  * Non-augmented rbtree manipulation functions.
 495  *
 496  * We use dummy augmented callbacks here, and have the compiler optimize them
 497  * out of the rb_insert_color() and rb_erase() function definitions.
 498  */
 499
 500 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
 501 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
 502 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
 503
 504 static const struct rb_augment_callbacks dummy_callbacks = {
 505         dummy_propagate, dummy_copy, dummy_rotate
 506 };
 507
 508 void rb_insert_color(struct rb_node *node, struct rb_root *root)
 509 {
 510         __rb_insert(node, root, dummy_rotate);
 511 }
 512 EXPORT_SYMBOL(rb_insert_color);
 513
 514 void rb_erase(struct rb_node *node, struct rb_root *root)
 515 {
 516         __rb_erase(node, root, &dummy_callbacks);
 517 }
 518 EXPORT_SYMBOL(rb_erase);
 519
 520 /*
 521  * Augmented rbtree manipulation functions.
 522  *
 523  * This instantiates the same __always_inline functions as in the non-augmented
 524  * case, but this time with user-defined callbacks.
 525  */
 526
 527 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
 528         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 529 {
 530         __rb_insert(node, root, augment_rotate);
 531 }
 532 EXPORT_SYMBOL(__rb_insert_augmented);
 533
 534 void rb_erase_augmented(struct rb_node *node, struct rb_root *root,
 535                         const struct rb_augment_callbacks *augment)
 536 {
 537         __rb_erase(node, root, augment);
 538 }
 539 EXPORT_SYMBOL(rb_erase_augmented);
 540
 541 /*
 542  * This function returns the first node (in sort order) of the tree.
 543  */
 544 struct rb_node *rb_first(const struct rb_root *root)
 545 {
 546         struct rb_node  *n;
 547
 548         n = root->rb_node;
 549         if (!n)
 550                 return NULL;
 551         while (n->rb_left)
 552                 n = n->rb_left;
 553         return n;
 554 }
 555 EXPORT_SYMBOL(rb_first);
 556
 557 struct rb_node *rb_last(const struct rb_root *root)
 558 {
 559         struct rb_node  *n;
 560
 561         n = root->rb_node;
 562         if (!n)
 563                 return NULL;
 564         while (n->rb_right)
 565                 n = n->rb_right;
 566         return n;
 567 }
 568 EXPORT_SYMBOL(rb_last);
 569
 570 struct rb_node *rb_next(const struct rb_node *node)
 571 {
 572         struct rb_node *parent;
 573
 574         if (RB_EMPTY_NODE(node))
 575                 return NULL;
 576
 577         /*
 578          * If we have a right-hand child, go down and then left as far
 579          * as we can.
 580          */
 581         if (node->rb_right) {
 582                 node = node->rb_right;
 583                 while (node->rb_left)
 584                         node=node->rb_left;
 585                 return (struct rb_node *)node;
 586         }
 587
 588         /*
 589          * No right-hand children. Everything down and left is smaller than us,
 590          * so any 'next' node must be in the general direction of our parent.
 591          * Go up the tree; any time the ancestor is a right-hand child of its
 592          * parent, keep going up. First time it's a left-hand child of its
 593          * parent, said parent is our 'next' node.
 594          */
 595         while ((parent = rb_parent(node)) && node == parent->rb_right)
 596                 node = parent;
 597
 598         return parent;
 599 }
 600 EXPORT_SYMBOL(rb_next);
 601
 602 struct rb_node *rb_prev(const struct rb_node *node)
 603 {
 604         struct rb_node *parent;
 605
 606         if (RB_EMPTY_NODE(node))
 607                 return NULL;
 608
 609         /*
 610          * If we have a left-hand child, go down and then right as far
 611          * as we can.
 612          */
 613         if (node->rb_left) {
 614                 node = node->rb_left;
 615                 while (node->rb_right)
 616                         node=node->rb_right;
 617                 return (struct rb_node *)node;
 618         }
 619
 620         /*
 621          * No left-hand children. Go up till we find an ancestor which
 622          * is a right-hand child of its parent.
 623          */
 624         while ((parent = rb_parent(node)) && node == parent->rb_left)
 625                 node = parent;
 626
 627         return parent;
 628 }
 629 EXPORT_SYMBOL(rb_prev);
 630
 631 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
 632                      struct rb_root *root)
 633 {
 634         struct rb_node *parent = rb_parent(victim);
 635
 636         /* Set the surrounding nodes to point to the replacement */
 637         __rb_change_child(victim, new, parent, root);
 638         if (victim->rb_left)
 639                 rb_set_parent(victim->rb_left, new);
 640         if (victim->rb_right)
 641                 rb_set_parent(victim->rb_right, new);
 642
 643         /* Copy the pointers/colour from the victim to the replacement */
 644         *new = *victim;
 645 }
 646 EXPORT_SYMBOL(rb_replace_node);