wimlib.net Git - wimlib/blob - src/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 #ifdef HAVE_CONFIG_H
  25 #  include "config.h"
  26 #endif
  27
  28 #include "wimlib/rbtree.h"
  29 #include <stdbool.h>
  30
  31 /*
  32  * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
  33  *
  34  *  1) A node is either red or black
  35  *  2) The root is black
  36  *  3) All leaves (NULL) are black
  37  *  4) Both children of every red node are black
  38  *  5) Every simple path from root to leaves contains the same number
  39  *     of black nodes.
  40  *
  41  *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
  42  *  consecutive red nodes in a path and every red node is therefore followed by
  43  *  a black. So if B is the number of black nodes on every simple path (as per
  44  *  5), then the longest possible path due to 4 is 2B.
  45  *
  46  *  We shall indicate color with case, where black nodes are uppercase and red
  47  *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
  48  *  parentheses and have some accompanying text comment.
  49  */
  50
  51 struct rb_augment_callbacks {
  52         void (*propagate)(struct rb_node *node, struct rb_node *stop);
  53         void (*copy)(struct rb_node *old, struct rb_node *new);
  54         void (*rotate)(struct rb_node *old, struct rb_node *new);
  55 };
  56
  57 #define RB_RED          0
  58 #define RB_BLACK        1
  59
  60 #define __rb_parent(pc)    ((struct rb_node *)(pc & ~3))
  61
  62 #define __rb_color(pc)     ((pc) & 1)
  63 #define __rb_is_black(pc)  __rb_color(pc)
  64 #define __rb_is_red(pc)    (!__rb_color(pc))
  65 #define rb_color(rb)       __rb_color((rb)->__rb_parent_color)
  66 #define rb_is_red(rb)      __rb_is_red((rb)->__rb_parent_color)
  67 #define rb_is_black(rb)    __rb_is_black((rb)->__rb_parent_color)
  68
  69 static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
  70 {
  71         rb->__rb_parent_color = rb_color(rb) | (uintptr_t)p;
  72 }
  73
  74 static inline void rb_set_parent_color(struct rb_node *rb,
  75                                        struct rb_node *p, int color)
  76 {
  77         rb->__rb_parent_color = (uintptr_t)p | color;
  78 }
  79
  80 static inline void rb_set_black(struct rb_node *rb)
  81 {
  82         rb->__rb_parent_color |= RB_BLACK;
  83 }
  84
  85 static inline struct rb_node *rb_red_parent(struct rb_node *red)
  86 {
  87         return (struct rb_node *)red->__rb_parent_color;
  88 }
  89
  90 static inline void
  91 __rb_change_child(struct rb_node *old, struct rb_node *new,
  92                   struct rb_node *parent, struct rb_root *root)
  93 {
  94         if (parent) {
  95                 if (parent->rb_left == old)
  96                         parent->rb_left = new;
  97                 else
  98                         parent->rb_right = new;
  99         } else
 100                 root->rb_node = new;
 101 }
 102
 103 /*
 104  * Helper function for rotations:
 105  * - old's parent and color get assigned to new
 106  * - old gets assigned new as a parent and 'color' as a color.
 107  */
 108 static inline void
 109 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
 110                         struct rb_root *root, int color)
 111 {
 112         struct rb_node *parent = rb_parent(old);
 113         new->__rb_parent_color = old->__rb_parent_color;
 114         rb_set_parent_color(old, new, color);
 115         __rb_change_child(old, new, parent, root);
 116 }
 117
 118 static inline void
 119 __rb_erase_color(struct rb_node *parent, struct rb_root *root,
 120         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 121 {
 122         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
 123
 124         while (true) {
 125                 /*
 126                  * Loop invariants:
 127                  * - node is black (or NULL on first iteration)
 128                  * - node is not the root (parent is not NULL)
 129                  * - All leaf paths going through parent and node have a
 130                  *   black node count that is 1 lower than other leaf paths.
 131                  */
 132                 sibling = parent->rb_right;
 133                 if (node != sibling) {  /* node == parent->rb_left */
 134                         if (rb_is_red(sibling)) {
 135                                 /*
 136                                  * Case 1 - left rotate at parent
 137                                  *
 138                                  *     P               S
 139                                  *    / \             / \
 140                                  *   N   s    -->    p   Sr
 141                                  *      / \         / \
 142                                  *     Sl  Sr      N   Sl
 143                                  */
 144                                 parent->rb_right = tmp1 = sibling->rb_left;
 145                                 sibling->rb_left = parent;
 146                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 147                                 __rb_rotate_set_parents(parent, sibling, root,
 148                                                         RB_RED);
 149                                 augment_rotate(parent, sibling);
 150                                 sibling = tmp1;
 151                         }
 152                         tmp1 = sibling->rb_right;
 153                         if (!tmp1 || rb_is_black(tmp1)) {
 154                                 tmp2 = sibling->rb_left;
 155                                 if (!tmp2 || rb_is_black(tmp2)) {
 156                                         /*
 157                                          * Case 2 - sibling color flip
 158                                          * (p could be either color here)
 159                                          *
 160                                          *    (p)           (p)
 161                                          *    / \           / \
 162                                          *   N   S    -->  N   s
 163                                          *      / \           / \
 164                                          *     Sl  Sr        Sl  Sr
 165                                          *
 166                                          * This leaves us violating 5) which
 167                                          * can be fixed by flipping p to black
 168                                          * if it was red, or by recursing at p.
 169                                          * p is red when coming from Case 1.
 170                                          */
 171                                         rb_set_parent_color(sibling, parent,
 172                                                             RB_RED);
 173                                         if (rb_is_red(parent))
 174                                                 rb_set_black(parent);
 175                                         else {
 176                                                 node = parent;
 177                                                 parent = rb_parent(node);
 178                                                 if (parent)
 179                                                         continue;
 180                                         }
 181                                         break;
 182                                 }
 183                                 /*
 184                                  * Case 3 - right rotate at sibling
 185                                  * (p could be either color here)
 186                                  *
 187                                  *   (p)           (p)
 188                                  *   / \           / \
 189                                  *  N   S    -->  N   Sl
 190                                  *     / \             \
 191                                  *    sl  Sr            s
 192                                  *                       \
 193                                  *                        Sr
 194                                  */
 195                                 sibling->rb_left = tmp1 = tmp2->rb_right;
 196                                 tmp2->rb_right = sibling;
 197                                 parent->rb_right = tmp2;
 198                                 if (tmp1)
 199                                         rb_set_parent_color(tmp1, sibling,
 200                                                             RB_BLACK);
 201                                 augment_rotate(sibling, tmp2);
 202                                 tmp1 = sibling;
 203                                 sibling = tmp2;
 204                         }
 205                         /*
 206                          * Case 4 - left rotate at parent + color flips
 207                          * (p and sl could be either color here.
 208                          *  After rotation, p becomes black, s acquires
 209                          *  p's color, and sl keeps its color)
 210                          *
 211                          *      (p)             (s)
 212                          *      / \             / \
 213                          *     N   S     -->   P   Sr
 214                          *        / \         / \
 215                          *      (sl) sr      N  (sl)
 216                          */
 217                         parent->rb_right = tmp2 = sibling->rb_left;
 218                         sibling->rb_left = parent;
 219                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 220                         if (tmp2)
 221                                 rb_set_parent(tmp2, parent);
 222                         __rb_rotate_set_parents(parent, sibling, root,
 223                                                 RB_BLACK);
 224                         augment_rotate(parent, sibling);
 225                         break;
 226                 } else {
 227                         sibling = parent->rb_left;
 228                         if (rb_is_red(sibling)) {
 229                                 /* Case 1 - right rotate at parent */
 230                                 parent->rb_left = tmp1 = sibling->rb_right;
 231                                 sibling->rb_right = parent;
 232                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 233                                 __rb_rotate_set_parents(parent, sibling, root,
 234                                                         RB_RED);
 235                                 augment_rotate(parent, sibling);
 236                                 sibling = tmp1;
 237                         }
 238                         tmp1 = sibling->rb_left;
 239                         if (!tmp1 || rb_is_black(tmp1)) {
 240                                 tmp2 = sibling->rb_right;
 241                                 if (!tmp2 || rb_is_black(tmp2)) {
 242                                         /* Case 2 - sibling color flip */
 243                                         rb_set_parent_color(sibling, parent,
 244                                                             RB_RED);
 245                                         if (rb_is_red(parent))
 246                                                 rb_set_black(parent);
 247                                         else {
 248                                                 node = parent;
 249                                                 parent = rb_parent(node);
 250                                                 if (parent)
 251                                                         continue;
 252                                         }
 253                                         break;
 254                                 }
 255                                 /* Case 3 - right rotate at sibling */
 256                                 sibling->rb_right = tmp1 = tmp2->rb_left;
 257                                 tmp2->rb_left = sibling;
 258                                 parent->rb_left = tmp2;
 259                                 if (tmp1)
 260                                         rb_set_parent_color(tmp1, sibling,
 261                                                             RB_BLACK);
 262                                 augment_rotate(sibling, tmp2);
 263                                 tmp1 = sibling;
 264                                 sibling = tmp2;
 265                         }
 266                         /* Case 4 - left rotate at parent + color flips */
 267                         parent->rb_left = tmp2 = sibling->rb_right;
 268                         sibling->rb_right = parent;
 269                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 270                         if (tmp2)
 271                                 rb_set_parent(tmp2, parent);
 272                         __rb_rotate_set_parents(parent, sibling, root,
 273                                                 RB_BLACK);
 274                         augment_rotate(parent, sibling);
 275                         break;
 276                 }
 277         }
 278 }
 279
 280 static inline void
 281 rb_erase_augmented(struct rb_node *node, struct rb_root *root,
 282                    const struct rb_augment_callbacks *augment)
 283 {
 284         struct rb_node *child = node->rb_right, *tmp = node->rb_left;
 285         struct rb_node *parent, *rebalance;
 286         uintptr_t pc;
 287
 288         if (!tmp) {
 289                 /*
 290                  * Case 1: node to erase has no more than 1 child (easy!)
 291                  *
 292                  * Note that if there is one child it must be red due to 5)
 293                  * and node must be black due to 4). We adjust colors locally
 294                  * so as to bypass __rb_erase_color() later on.
 295                  */
 296                 pc = node->__rb_parent_color;
 297                 parent = __rb_parent(pc);
 298                 __rb_change_child(node, child, parent, root);
 299                 if (child) {
 300                         child->__rb_parent_color = pc;
 301                         rebalance = NULL;
 302                 } else
 303                         rebalance = __rb_is_black(pc) ? parent : NULL;
 304                 tmp = parent;
 305         } else if (!child) {
 306                 /* Still case 1, but this time the child is node->rb_left */
 307                 tmp->__rb_parent_color = pc = node->__rb_parent_color;
 308                 parent = __rb_parent(pc);
 309                 __rb_change_child(node, tmp, parent, root);
 310                 rebalance = NULL;
 311                 tmp = parent;
 312         } else {
 313                 struct rb_node *successor = child, *child2;
 314                 tmp = child->rb_left;
 315                 if (!tmp) {
 316                         /*
 317                          * Case 2: node's successor is its right child
 318                          *
 319                          *    (n)          (s)
 320                          *    / \          / \
 321                          *  (x) (s)  ->  (x) (c)
 322                          *        \
 323                          *        (c)
 324                          */
 325                         parent = successor;
 326                         child2 = successor->rb_right;
 327                         augment->copy(node, successor);
 328                 } else {
 329                         /*
 330                          * Case 3: node's successor is leftmost under
 331                          * node's right child subtree
 332                          *
 333                          *    (n)          (s)
 334                          *    / \          / \
 335                          *  (x) (y)  ->  (x) (y)
 336                          *      /            /
 337                          *    (p)          (p)
 338                          *    /            /
 339                          *  (s)          (c)
 340                          *    \
 341                          *    (c)
 342                          */
 343                         do {
 344                                 parent = successor;
 345                                 successor = tmp;
 346                                 tmp = tmp->rb_left;
 347                         } while (tmp);
 348                         parent->rb_left = child2 = successor->rb_right;
 349                         successor->rb_right = child;
 350                         rb_set_parent(child, successor);
 351                         augment->copy(node, successor);
 352                         augment->propagate(parent, successor);
 353                 }
 354
 355                 successor->rb_left = tmp = node->rb_left;
 356                 rb_set_parent(tmp, successor);
 357
 358                 pc = node->__rb_parent_color;
 359                 tmp = __rb_parent(pc);
 360                 __rb_change_child(node, successor, tmp, root);
 361                 if (child2) {
 362                         successor->__rb_parent_color = pc;
 363                         rb_set_parent_color(child2, parent, RB_BLACK);
 364                         rebalance = NULL;
 365                 } else {
 366                         uintptr_t pc2 = successor->__rb_parent_color;
 367                         successor->__rb_parent_color = pc;
 368                         rebalance = __rb_is_black(pc2) ? parent : NULL;
 369                 }
 370                 tmp = successor;
 371         }
 372
 373         augment->propagate(tmp, NULL);
 374         if (rebalance)
 375                 __rb_erase_color(rebalance, root, augment->rotate);
 376 }
 377
 378
 379 static inline void
 380 __rb_insert(struct rb_node *node, struct rb_root *root,
 381             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 382 {
 383         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
 384
 385         while (true) {
 386                 /*
 387                  * Loop invariant: node is red
 388                  *
 389                  * If there is a black parent, we are done.
 390                  * Otherwise, take some corrective action as we don't
 391                  * want a red root or two consecutive red nodes.
 392                  */
 393                 if (!parent) {
 394                         rb_set_parent_color(node, NULL, RB_BLACK);
 395                         break;
 396                 } else if (rb_is_black(parent))
 397                         break;
 398
 399                 gparent = rb_red_parent(parent);
 400
 401                 tmp = gparent->rb_right;
 402                 if (parent != tmp) {    /* parent == gparent->rb_left */
 403                         if (tmp && rb_is_red(tmp)) {
 404                                 /*
 405                                  * Case 1 - color flips
 406                                  *
 407                                  *       G            g
 408                                  *      / \          / \
 409                                  *     p   u  -->   P   U
 410                                  *    /            /
 411                                  *   n            N
 412                                  *
 413                                  * However, since g's parent might be red, and
 414                                  * 4) does not allow this, we need to recurse
 415                                  * at g.
 416                                  */
 417                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 418                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 419                                 node = gparent;
 420                                 parent = rb_parent(node);
 421                                 rb_set_parent_color(node, parent, RB_RED);
 422                                 continue;
 423                         }
 424
 425                         tmp = parent->rb_right;
 426                         if (node == tmp) {
 427                                 /*
 428                                  * Case 2 - left rotate at parent
 429                                  *
 430                                  *      G             G
 431                                  *     / \           / \
 432                                  *    p   U  -->    n   U
 433                                  *     \           /
 434                                  *      n         p
 435                                  *
 436                                  * This still leaves us in violation of 4), the
 437                                  * continuation into Case 3 will fix that.
 438                                  */
 439                                 parent->rb_right = tmp = node->rb_left;
 440                                 node->rb_left = parent;
 441                                 if (tmp)
 442                                         rb_set_parent_color(tmp, parent,
 443                                                             RB_BLACK);
 444                                 rb_set_parent_color(parent, node, RB_RED);
 445                                 augment_rotate(parent, node);
 446                                 parent = node;
 447                                 tmp = node->rb_right;
 448                         }
 449
 450                         /*
 451                          * Case 3 - right rotate at gparent
 452                          *
 453                          *        G           P
 454                          *       / \         / \
 455                          *      p   U  -->  n   g
 456                          *     /                 \
 457                          *    n                   U
 458                          */
 459                         gparent->rb_left = tmp;  /* == parent->rb_right */
 460                         parent->rb_right = gparent;
 461                         if (tmp)
 462                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 463                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 464                         augment_rotate(gparent, parent);
 465                         break;
 466                 } else {
 467                         tmp = gparent->rb_left;
 468                         if (tmp && rb_is_red(tmp)) {
 469                                 /* Case 1 - color flips */
 470                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 471                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 472                                 node = gparent;
 473                                 parent = rb_parent(node);
 474                                 rb_set_parent_color(node, parent, RB_RED);
 475                                 continue;
 476                         }
 477
 478                         tmp = parent->rb_left;
 479                         if (node == tmp) {
 480                                 /* Case 2 - right rotate at parent */
 481                                 parent->rb_left = tmp = node->rb_right;
 482                                 node->rb_right = parent;
 483                                 if (tmp)
 484                                         rb_set_parent_color(tmp, parent,
 485                                                             RB_BLACK);
 486                                 rb_set_parent_color(parent, node, RB_RED);
 487                                 augment_rotate(parent, node);
 488                                 parent = node;
 489                                 tmp = node->rb_left;
 490                         }
 491
 492                         /* Case 3 - left rotate at gparent */
 493                         gparent->rb_right = tmp;  /* == parent->rb_left */
 494                         parent->rb_left = gparent;
 495                         if (tmp)
 496                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 497                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 498                         augment_rotate(gparent, parent);
 499                         break;
 500                 }
 501         }
 502 }
 503
 504
 505 /*
 506  * Non-augmented rbtree manipulation functions.
 507  *
 508  * We use dummy augmented callbacks here, and have the compiler optimize them
 509  * out of the rb_insert_color() and rb_erase() function definitions.
 510  */
 511
 512 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
 513 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
 514 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
 515
 516 static const struct rb_augment_callbacks dummy_callbacks = {
 517         dummy_propagate, dummy_copy, dummy_rotate
 518 };
 519
 520 void rb_insert_color(struct rb_node *node, struct rb_root *root)
 521 {
 522         __rb_insert(node, root, dummy_rotate);
 523 }
 524
 525 void rb_erase(struct rb_node *node, struct rb_root *root)
 526 {
 527         rb_erase_augmented(node, root, &dummy_callbacks);
 528 }