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  * SPDX-License-Identifier:     GPL-2.0+
   8
   9   linux/lib/rbtree.c
  10 */
  11
  12 #include <linux/rbtree_augmented.h>
  13 #ifndef __UBOOT__
  14 #include <linux/export.h>
  15 #else
  16 #include <ubi_uboot.h>
  17 #endif
  18 /*
  19  * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
  20  *
  21  *  1) A node is either red or black
  22  *  2) The root is black
  23  *  3) All leaves (NULL) are black
  24  *  4) Both children of every red node are black
  25  *  5) Every simple path from root to leaves contains the same number
  26  *     of black nodes.
  27  *
  28  *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
  29  *  consecutive red nodes in a path and every red node is therefore followed by
  30  *  a black. So if B is the number of black nodes on every simple path (as per
  31  *  5), then the longest possible path due to 4 is 2B.
  32  *
  33  *  We shall indicate color with case, where black nodes are uppercase and red
  34  *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
  35  *  parentheses and have some accompanying text comment.
  36  */
  37
  38 static inline void rb_set_black(struct rb_node *rb)
  39 {
  40         rb->__rb_parent_color |= RB_BLACK;
  41 }
  42
  43 static inline struct rb_node *rb_red_parent(struct rb_node *red)
  44 {
  45         return (struct rb_node *)red->__rb_parent_color;
  46 }
  47
  48 /*
  49  * Helper function for rotations:
  50  * - old's parent and color get assigned to new
  51  * - old gets assigned new as a parent and 'color' as a color.
  52  */
  53 static inline void
  54 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
  55                         struct rb_root *root, int color)
  56 {
  57         struct rb_node *parent = rb_parent(old);
  58         new->__rb_parent_color = old->__rb_parent_color;
  59         rb_set_parent_color(old, new, color);
  60         __rb_change_child(old, new, parent, root);
  61 }
  62
  63 static __always_inline void
  64 __rb_insert(struct rb_node *node, struct rb_root *root,
  65             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
  66 {
  67         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
  68
  69         while (true) {
  70                 /*
  71                  * Loop invariant: node is red
  72                  *
  73                  * If there is a black parent, we are done.
  74                  * Otherwise, take some corrective action as we don't
  75                  * want a red root or two consecutive red nodes.
  76                  */
  77                 if (!parent) {
  78                         rb_set_parent_color(node, NULL, RB_BLACK);
  79                         break;
  80                 } else if (rb_is_black(parent))
  81                         break;
  82
  83                 gparent = rb_red_parent(parent);
  84
  85                 tmp = gparent->rb_right;
  86                 if (parent != tmp) {    /* parent == gparent->rb_left */
  87                         if (tmp && rb_is_red(tmp)) {
  88                                 /*
  89                                  * Case 1 - color flips
  90                                  *
  91                                  *       G            g
  92                                  *      / \          / \
  93                                  *     p   u  -->   P   U
  94                                  *    /            /
  95                                  *   n            N
  96                                  *
  97                                  * However, since g's parent might be red, and
  98                                  * 4) does not allow this, we need to recurse
  99                                  * at g.
 100                                  */
 101                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 102                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 103                                 node = gparent;
 104                                 parent = rb_parent(node);
 105                                 rb_set_parent_color(node, parent, RB_RED);
 106                                 continue;
 107                         }
 108
 109                         tmp = parent->rb_right;
 110                         if (node == tmp) {
 111                                 /*
 112                                  * Case 2 - left rotate at parent
 113                                  *
 114                                  *      G             G
 115                                  *     / \           / \
 116                                  *    p   U  -->    n   U
 117                                  *     \           /
 118                                  *      n         p
 119                                  *
 120                                  * This still leaves us in violation of 4), the
 121                                  * continuation into Case 3 will fix that.
 122                                  */
 123                                 parent->rb_right = tmp = node->rb_left;
 124                                 node->rb_left = parent;
 125                                 if (tmp)
 126                                         rb_set_parent_color(tmp, parent,
 127                                                             RB_BLACK);
 128                                 rb_set_parent_color(parent, node, RB_RED);
 129                                 augment_rotate(parent, node);
 130                                 parent = node;
 131                                 tmp = node->rb_right;
 132                         }
 133
 134                         /*
 135                          * Case 3 - right rotate at gparent
 136                          *
 137                          *        G           P
 138                          *       / \         / \
 139                          *      p   U  -->  n   g
 140                          *     /                 \
 141                          *    n                   U
 142                          */
 143                         gparent->rb_left = tmp;  /* == parent->rb_right */
 144                         parent->rb_right = gparent;
 145                         if (tmp)
 146                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 147                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 148                         augment_rotate(gparent, parent);
 149                         break;
 150                 } else {
 151                         tmp = gparent->rb_left;
 152                         if (tmp && rb_is_red(tmp)) {
 153                                 /* Case 1 - color flips */
 154                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 155                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 156                                 node = gparent;
 157                                 parent = rb_parent(node);
 158                                 rb_set_parent_color(node, parent, RB_RED);
 159                                 continue;
 160                         }
 161
 162                         tmp = parent->rb_left;
 163                         if (node == tmp) {
 164                                 /* Case 2 - right rotate at parent */
 165                                 parent->rb_left = tmp = node->rb_right;
 166                                 node->rb_right = parent;
 167                                 if (tmp)
 168                                         rb_set_parent_color(tmp, parent,
 169                                                             RB_BLACK);
 170                                 rb_set_parent_color(parent, node, RB_RED);
 171                                 augment_rotate(parent, node);
 172                                 parent = node;
 173                                 tmp = node->rb_left;
 174                         }
 175
 176                         /* Case 3 - left rotate at gparent */
 177                         gparent->rb_right = tmp;  /* == parent->rb_left */
 178                         parent->rb_left = gparent;
 179                         if (tmp)
 180                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 181                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 182                         augment_rotate(gparent, parent);
 183                         break;
 184                 }
 185         }
 186 }
 187
 188 /*
 189  * Inline version for rb_erase() use - we want to be able to inline
 190  * and eliminate the dummy_rotate callback there
 191  */
 192 static __always_inline void
 193 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
 194         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 195 {
 196         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
 197
 198         while (true) {
 199                 /*
 200                  * Loop invariants:
 201                  * - node is black (or NULL on first iteration)
 202                  * - node is not the root (parent is not NULL)
 203                  * - All leaf paths going through parent and node have a
 204                  *   black node count that is 1 lower than other leaf paths.
 205                  */
 206                 sibling = parent->rb_right;
 207                 if (node != sibling) {  /* node == parent->rb_left */
 208                         if (rb_is_red(sibling)) {
 209                                 /*
 210                                  * Case 1 - left rotate at parent
 211                                  *
 212                                  *     P               S
 213                                  *    / \             / \
 214                                  *   N   s    -->    p   Sr
 215                                  *      / \         / \
 216                                  *     Sl  Sr      N   Sl
 217                                  */
 218                                 parent->rb_right = tmp1 = sibling->rb_left;
 219                                 sibling->rb_left = parent;
 220                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 221                                 __rb_rotate_set_parents(parent, sibling, root,
 222                                                         RB_RED);
 223                                 augment_rotate(parent, sibling);
 224                                 sibling = tmp1;
 225                         }
 226                         tmp1 = sibling->rb_right;
 227                         if (!tmp1 || rb_is_black(tmp1)) {
 228                                 tmp2 = sibling->rb_left;
 229                                 if (!tmp2 || rb_is_black(tmp2)) {
 230                                         /*
 231                                          * Case 2 - sibling color flip
 232                                          * (p could be either color here)
 233                                          *
 234                                          *    (p)           (p)
 235                                          *    / \           / \
 236                                          *   N   S    -->  N   s
 237                                          *      / \           / \
 238                                          *     Sl  Sr        Sl  Sr
 239                                          *
 240                                          * This leaves us violating 5) which
 241                                          * can be fixed by flipping p to black
 242                                          * if it was red, or by recursing at p.
 243                                          * p is red when coming from Case 1.
 244                                          */
 245                                         rb_set_parent_color(sibling, parent,
 246                                                             RB_RED);
 247                                         if (rb_is_red(parent))
 248                                                 rb_set_black(parent);
 249                                         else {
 250                                                 node = parent;
 251                                                 parent = rb_parent(node);
 252                                                 if (parent)
 253                                                         continue;
 254                                         }
 255                                         break;
 256                                 }
 257                                 /*
 258                                  * Case 3 - right rotate at sibling
 259                                  * (p could be either color here)
 260                                  *
 261                                  *   (p)           (p)
 262                                  *   / \           / \
 263                                  *  N   S    -->  N   Sl
 264                                  *     / \             \
 265                                  *    sl  Sr            s
 266                                  *                       \
 267                                  *                        Sr
 268                                  */
 269                                 sibling->rb_left = tmp1 = tmp2->rb_right;
 270                                 tmp2->rb_right = sibling;
 271                                 parent->rb_right = tmp2;
 272                                 if (tmp1)
 273                                         rb_set_parent_color(tmp1, sibling,
 274                                                             RB_BLACK);
 275                                 augment_rotate(sibling, tmp2);
 276                                 tmp1 = sibling;
 277                                 sibling = tmp2;
 278                         }
 279                         /*
 280                          * Case 4 - left rotate at parent + color flips
 281                          * (p and sl could be either color here.
 282                          *  After rotation, p becomes black, s acquires
 283                          *  p's color, and sl keeps its color)
 284                          *
 285                          *      (p)             (s)
 286                          *      / \             / \
 287                          *     N   S     -->   P   Sr
 288                          *        / \         / \
 289                          *      (sl) sr      N  (sl)
 290                          */
 291                         parent->rb_right = tmp2 = sibling->rb_left;
 292                         sibling->rb_left = parent;
 293                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 294                         if (tmp2)
 295                                 rb_set_parent(tmp2, parent);
 296                         __rb_rotate_set_parents(parent, sibling, root,
 297                                                 RB_BLACK);
 298                         augment_rotate(parent, sibling);
 299                         break;
 300                 } else {
 301                         sibling = parent->rb_left;
 302                         if (rb_is_red(sibling)) {
 303                                 /* Case 1 - right rotate at parent */
 304                                 parent->rb_left = tmp1 = sibling->rb_right;
 305                                 sibling->rb_right = parent;
 306                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 307                                 __rb_rotate_set_parents(parent, sibling, root,
 308                                                         RB_RED);
 309                                 augment_rotate(parent, sibling);
 310                                 sibling = tmp1;
 311                         }
 312                         tmp1 = sibling->rb_left;
 313                         if (!tmp1 || rb_is_black(tmp1)) {
 314                                 tmp2 = sibling->rb_right;
 315                                 if (!tmp2 || rb_is_black(tmp2)) {
 316                                         /* Case 2 - sibling color flip */
 317                                         rb_set_parent_color(sibling, parent,
 318                                                             RB_RED);
 319                                         if (rb_is_red(parent))
 320                                                 rb_set_black(parent);
 321                                         else {
 322                                                 node = parent;
 323                                                 parent = rb_parent(node);
 324                                                 if (parent)
 325                                                         continue;
 326                                         }
 327                                         break;
 328                                 }
 329                                 /* Case 3 - right rotate at sibling */
 330                                 sibling->rb_right = tmp1 = tmp2->rb_left;
 331                                 tmp2->rb_left = sibling;
 332                                 parent->rb_left = tmp2;
 333                                 if (tmp1)
 334                                         rb_set_parent_color(tmp1, sibling,
 335                                                             RB_BLACK);
 336                                 augment_rotate(sibling, tmp2);
 337                                 tmp1 = sibling;
 338                                 sibling = tmp2;
 339                         }
 340                         /* Case 4 - left rotate at parent + color flips */
 341                         parent->rb_left = tmp2 = sibling->rb_right;
 342                         sibling->rb_right = parent;
 343                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 344                         if (tmp2)
 345                                 rb_set_parent(tmp2, parent);
 346                         __rb_rotate_set_parents(parent, sibling, root,
 347                                                 RB_BLACK);
 348                         augment_rotate(parent, sibling);
 349                         break;
 350                 }
 351         }
 352 }
 353
 354 /* Non-inline version for rb_erase_augmented() use */
 355 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
 356         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 357 {
 358         ____rb_erase_color(parent, root, augment_rotate);
 359 }
 360 EXPORT_SYMBOL(__rb_erase_color);
 361
 362 /*
 363  * Non-augmented rbtree manipulation functions.
 364  *
 365  * We use dummy augmented callbacks here, and have the compiler optimize them
 366  * out of the rb_insert_color() and rb_erase() function definitions.
 367  */
 368
 369 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
 370 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
 371 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
 372
 373 static const struct rb_augment_callbacks dummy_callbacks = {
 374         dummy_propagate, dummy_copy, dummy_rotate
 375 };
 376
 377 void rb_insert_color(struct rb_node *node, struct rb_root *root)
 378 {
 379         __rb_insert(node, root, dummy_rotate);
 380 }
 381 EXPORT_SYMBOL(rb_insert_color);
 382
 383 void rb_erase(struct rb_node *node, struct rb_root *root)
 384 {
 385         struct rb_node *rebalance;
 386         rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
 387         if (rebalance)
 388                 ____rb_erase_color(rebalance, root, dummy_rotate);
 389 }
 390 EXPORT_SYMBOL(rb_erase);
 391
 392 /*
 393  * Augmented rbtree manipulation functions.
 394  *
 395  * This instantiates the same __always_inline functions as in the non-augmented
 396  * case, but this time with user-defined callbacks.
 397  */
 398
 399 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
 400         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 401 {
 402         __rb_insert(node, root, augment_rotate);
 403 }
 404 EXPORT_SYMBOL(__rb_insert_augmented);
 405
 406 /*
 407  * This function returns the first node (in sort order) of the tree.
 408  */
 409 struct rb_node *rb_first(const struct rb_root *root)
 410 {
 411         struct rb_node  *n;
 412
 413         n = root->rb_node;
 414         if (!n)
 415                 return NULL;
 416         while (n->rb_left)
 417                 n = n->rb_left;
 418         return n;
 419 }
 420 EXPORT_SYMBOL(rb_first);
 421
 422 struct rb_node *rb_last(const struct rb_root *root)
 423 {
 424         struct rb_node  *n;
 425
 426         n = root->rb_node;
 427         if (!n)
 428                 return NULL;
 429         while (n->rb_right)
 430                 n = n->rb_right;
 431         return n;
 432 }
 433 EXPORT_SYMBOL(rb_last);
 434
 435 struct rb_node *rb_next(const struct rb_node *node)
 436 {
 437         struct rb_node *parent;
 438
 439         if (RB_EMPTY_NODE(node))
 440                 return NULL;
 441
 442         /*
 443          * If we have a right-hand child, go down and then left as far
 444          * as we can.
 445          */
 446         if (node->rb_right) {
 447                 node = node->rb_right;
 448                 while (node->rb_left)
 449                         node=node->rb_left;
 450                 return (struct rb_node *)node;
 451         }
 452
 453         /*
 454          * No right-hand children. Everything down and left is smaller than us,
 455          * so any 'next' node must be in the general direction of our parent.
 456          * Go up the tree; any time the ancestor is a right-hand child of its
 457          * parent, keep going up. First time it's a left-hand child of its
 458          * parent, said parent is our 'next' node.
 459          */
 460         while ((parent = rb_parent(node)) && node == parent->rb_right)
 461                 node = parent;
 462
 463         return parent;
 464 }
 465 EXPORT_SYMBOL(rb_next);
 466
 467 struct rb_node *rb_prev(const struct rb_node *node)
 468 {
 469         struct rb_node *parent;
 470
 471         if (RB_EMPTY_NODE(node))
 472                 return NULL;
 473
 474         /*
 475          * If we have a left-hand child, go down and then right as far
 476          * as we can.
 477          */
 478         if (node->rb_left) {
 479                 node = node->rb_left;
 480                 while (node->rb_right)
 481                         node=node->rb_right;
 482                 return (struct rb_node *)node;
 483         }
 484
 485         /*
 486          * No left-hand children. Go up till we find an ancestor which
 487          * is a right-hand child of its parent.
 488          */
 489         while ((parent = rb_parent(node)) && node == parent->rb_left)
 490                 node = parent;
 491
 492         return parent;
 493 }
 494 EXPORT_SYMBOL(rb_prev);
 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 EXPORT_SYMBOL(rb_replace_node);
 512
 513 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
 514 {
 515         for (;;) {
 516                 if (node->rb_left)
 517                         node = node->rb_left;
 518                 else if (node->rb_right)
 519                         node = node->rb_right;
 520                 else
 521                         return (struct rb_node *)node;
 522         }
 523 }
 524
 525 struct rb_node *rb_next_postorder(const struct rb_node *node)
 526 {
 527         const struct rb_node *parent;
 528         if (!node)
 529                 return NULL;
 530         parent = rb_parent(node);
 531
 532         /* If we're sitting on node, we've already seen our children */
 533         if (parent && node == parent->rb_left && parent->rb_right) {
 534                 /* If we are the parent's left node, go to the parent's right
 535                  * node then all the way down to the left */
 536                 return rb_left_deepest_node(parent->rb_right);
 537         } else
 538                 /* Otherwise we are the parent's right node, and the parent
 539                  * should be next */
 540                 return (struct rb_node *)parent;
 541 }
 542 EXPORT_SYMBOL(rb_next_postorder);
 543
 544 struct rb_node *rb_first_postorder(const struct rb_root *root)
 545 {
 546         if (!root->rb_node)
 547                 return NULL;
 548
 549         return rb_left_deepest_node(root->rb_node);
 550 }
 551 EXPORT_SYMBOL(rb_first_postorder);