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