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