linux/lib/rbtree.c
<<
>>
Prefs
   1/*
   2  Red Black Trees
   3  (C) 1999  Andrea Arcangeli <andrea@suse.de>
   4  (C) 2002  David Woodhouse <dwmw2@infradead.org>
   5  (C) 2012  Michel Lespinasse <walken@google.com>
   6
   7  This program is free software; you can redistribute it and/or modify
   8  it under the terms of the GNU General Public License as published by
   9  the Free Software Foundation; either version 2 of the License, or
  10  (at your option) any later version.
  11
  12  This program is distributed in the hope that it will be useful,
  13  but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15  GNU General Public License for more details.
  16
  17  You should have received a copy of the GNU General Public License
  18  along with this program; if not, write to the Free Software
  19  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  20
  21  linux/lib/rbtree.c
  22*/
  23
  24#include <linux/rbtree_augmented.h>
  25#include <linux/export.h>
  26
  27/*
  28 * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
  29 *
  30 *  1) A node is either red or black
  31 *  2) The root is black
  32 *  3) All leaves (NULL) are black
  33 *  4) Both children of every red node are black
  34 *  5) Every simple path from root to leaves contains the same number
  35 *     of black nodes.
  36 *
  37 *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
  38 *  consecutive red nodes in a path and every red node is therefore followed by
  39 *  a black. So if B is the number of black nodes on every simple path (as per
  40 *  5), then the longest possible path due to 4 is 2B.
  41 *
  42 *  We shall indicate color with case, where black nodes are uppercase and red
  43 *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
  44 *  parentheses and have some accompanying text comment.
  45 */
  46
  47static inline void rb_set_black(struct rb_node *rb)
  48{
  49        rb->__rb_parent_color |= RB_BLACK;
  50}
  51
  52static 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 */
  62static 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
  72static __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/*
 198 * Inline version for rb_erase() use - we want to be able to inline
 199 * and eliminate the dummy_rotate callback there
 200 */
 201static __always_inline void
 202____rb_erase_color(struct rb_node *parent, struct rb_root *root,
 203        void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 204{
 205        struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
 206
 207        while (true) {
 208                /*
 209                 * Loop invariants:
 210                 * - node is black (or NULL on first iteration)
 211                 * - node is not the root (parent is not NULL)
 212                 * - All leaf paths going through parent and node have a
 213                 *   black node count that is 1 lower than other leaf paths.
 214                 */
 215                sibling = parent->rb_right;
 216                if (node != sibling) {  /* node == parent->rb_left */
 217                        if (rb_is_red(sibling)) {
 218                                /*
 219                                 * Case 1 - left rotate at parent
 220                                 *
 221                                 *     P               S
 222                                 *    / \             / \
 223                                 *   N   s    -->    p   Sr
 224                                 *      / \         / \
 225                                 *     Sl  Sr      N   Sl
 226                                 */
 227                                parent->rb_right = tmp1 = sibling->rb_left;
 228                                sibling->rb_left = parent;
 229                                rb_set_parent_color(tmp1, parent, RB_BLACK);
 230                                __rb_rotate_set_parents(parent, sibling, root,
 231                                                        RB_RED);
 232                                augment_rotate(parent, sibling);
 233                                sibling = tmp1;
 234                        }
 235                        tmp1 = sibling->rb_right;
 236                        if (!tmp1 || rb_is_black(tmp1)) {
 237                                tmp2 = sibling->rb_left;
 238                                if (!tmp2 || rb_is_black(tmp2)) {
 239                                        /*
 240                                         * Case 2 - sibling color flip
 241                                         * (p could be either color here)
 242                                         *
 243                                         *    (p)           (p)
 244                                         *    / \           / \
 245                                         *   N   S    -->  N   s
 246                                         *      / \           / \
 247                                         *     Sl  Sr        Sl  Sr
 248                                         *
 249                                         * This leaves us violating 5) which
 250                                         * can be fixed by flipping p to black
 251                                         * if it was red, or by recursing at p.
 252                                         * p is red when coming from Case 1.
 253                                         */
 254                                        rb_set_parent_color(sibling, parent,
 255                                                            RB_RED);
 256                                        if (rb_is_red(parent))
 257                                                rb_set_black(parent);
 258                                        else {
 259                                                node = parent;
 260                                                parent = rb_parent(node);
 261                                                if (parent)
 262                                                        continue;
 263                                        }
 264                                        break;
 265                                }
 266                                /*
 267                                 * Case 3 - right rotate at sibling
 268                                 * (p could be either color here)
 269                                 *
 270                                 *   (p)           (p)
 271                                 *   / \           / \
 272                                 *  N   S    -->  N   Sl
 273                                 *     / \             \
 274                                 *    sl  Sr            s
 275                                 *                       \
 276                                 *                        Sr
 277                                 */
 278                                sibling->rb_left = tmp1 = tmp2->rb_right;
 279                                tmp2->rb_right = sibling;
 280                                parent->rb_right = tmp2;
 281                                if (tmp1)
 282                                        rb_set_parent_color(tmp1, sibling,
 283                                                            RB_BLACK);
 284                                augment_rotate(sibling, tmp2);
 285                                tmp1 = sibling;
 286                                sibling = tmp2;
 287                        }
 288                        /*
 289                         * Case 4 - left rotate at parent + color flips
 290                         * (p and sl could be either color here.
 291                         *  After rotation, p becomes black, s acquires
 292                         *  p's color, and sl keeps its color)
 293                         *
 294                         *      (p)             (s)
 295                         *      / \             / \
 296                         *     N   S     -->   P   Sr
 297                         *        / \         / \
 298                         *      (sl) sr      N  (sl)
 299                         */
 300                        parent->rb_right = tmp2 = sibling->rb_left;
 301                        sibling->rb_left = parent;
 302                        rb_set_parent_color(tmp1, sibling, RB_BLACK);
 303                        if (tmp2)
 304                                rb_set_parent(tmp2, parent);
 305                        __rb_rotate_set_parents(parent, sibling, root,
 306                                                RB_BLACK);
 307                        augment_rotate(parent, sibling);
 308                        break;
 309                } else {
 310                        sibling = parent->rb_left;
 311                        if (rb_is_red(sibling)) {
 312                                /* Case 1 - right rotate at parent */
 313                                parent->rb_left = tmp1 = sibling->rb_right;
 314                                sibling->rb_right = parent;
 315                                rb_set_parent_color(tmp1, parent, RB_BLACK);
 316                                __rb_rotate_set_parents(parent, sibling, root,
 317                                                        RB_RED);
 318                                augment_rotate(parent, sibling);
 319                                sibling = tmp1;
 320                        }
 321                        tmp1 = sibling->rb_left;
 322                        if (!tmp1 || rb_is_black(tmp1)) {
 323                                tmp2 = sibling->rb_right;
 324                                if (!tmp2 || rb_is_black(tmp2)) {
 325                                        /* Case 2 - sibling color flip */
 326                                        rb_set_parent_color(sibling, parent,
 327                                                            RB_RED);
 328                                        if (rb_is_red(parent))
 329                                                rb_set_black(parent);
 330                                        else {
 331                                                node = parent;
 332                                                parent = rb_parent(node);
 333                                                if (parent)
 334                                                        continue;
 335                                        }
 336                                        break;
 337                                }
 338                                /* Case 3 - right rotate at sibling */
 339                                sibling->rb_right = tmp1 = tmp2->rb_left;
 340                                tmp2->rb_left = sibling;
 341                                parent->rb_left = tmp2;
 342                                if (tmp1)
 343                                        rb_set_parent_color(tmp1, sibling,
 344                                                            RB_BLACK);
 345                                augment_rotate(sibling, tmp2);
 346                                tmp1 = sibling;
 347                                sibling = tmp2;
 348                        }
 349                        /* Case 4 - left rotate at parent + color flips */
 350                        parent->rb_left = tmp2 = sibling->rb_right;
 351                        sibling->rb_right = parent;
 352                        rb_set_parent_color(tmp1, sibling, RB_BLACK);
 353                        if (tmp2)
 354                                rb_set_parent(tmp2, parent);
 355                        __rb_rotate_set_parents(parent, sibling, root,
 356                                                RB_BLACK);
 357                        augment_rotate(parent, sibling);
 358                        break;
 359                }
 360        }
 361}
 362
 363/* Non-inline version for rb_erase_augmented() use */
 364void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
 365        void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 366{
 367        ____rb_erase_color(parent, root, augment_rotate);
 368}
 369EXPORT_SYMBOL(__rb_erase_color);
 370
 371/*
 372 * Non-augmented rbtree manipulation functions.
 373 *
 374 * We use dummy augmented callbacks here, and have the compiler optimize them
 375 * out of the rb_insert_color() and rb_erase() function definitions.
 376 */
 377
 378static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
 379static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
 380static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
 381
 382static const struct rb_augment_callbacks dummy_callbacks = {
 383        dummy_propagate, dummy_copy, dummy_rotate
 384};
 385
 386void rb_insert_color(struct rb_node *node, struct rb_root *root)
 387{
 388        __rb_insert(node, root, dummy_rotate);
 389}
 390EXPORT_SYMBOL(rb_insert_color);
 391
 392void rb_erase(struct rb_node *node, struct rb_root *root)
 393{
 394        struct rb_node *rebalance;
 395        rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
 396        if (rebalance)
 397                ____rb_erase_color(rebalance, root, dummy_rotate);
 398}
 399EXPORT_SYMBOL(rb_erase);
 400
 401/*
 402 * Augmented rbtree manipulation functions.
 403 *
 404 * This instantiates the same __always_inline functions as in the non-augmented
 405 * case, but this time with user-defined callbacks.
 406 */
 407
 408void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
 409        void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 410{
 411        __rb_insert(node, root, augment_rotate);
 412}
 413EXPORT_SYMBOL(__rb_insert_augmented);
 414
 415/*
 416 * This function returns the first node (in sort order) of the tree.
 417 */
 418struct rb_node *rb_first(const struct rb_root *root)
 419{
 420        struct rb_node  *n;
 421
 422        n = root->rb_node;
 423        if (!n)
 424                return NULL;
 425        while (n->rb_left)
 426                n = n->rb_left;
 427        return n;
 428}
 429EXPORT_SYMBOL(rb_first);
 430
 431struct rb_node *rb_last(const struct rb_root *root)
 432{
 433        struct rb_node  *n;
 434
 435        n = root->rb_node;
 436        if (!n)
 437                return NULL;
 438        while (n->rb_right)
 439                n = n->rb_right;
 440        return n;
 441}
 442EXPORT_SYMBOL(rb_last);
 443
 444struct rb_node *rb_next(const struct rb_node *node)
 445{
 446        struct rb_node *parent;
 447
 448        if (RB_EMPTY_NODE(node))
 449                return NULL;
 450
 451        /*
 452         * If we have a right-hand child, go down and then left as far
 453         * as we can.
 454         */
 455        if (node->rb_right) {
 456                node = node->rb_right; 
 457                while (node->rb_left)
 458                        node=node->rb_left;
 459                return (struct rb_node *)node;
 460        }
 461
 462        /*
 463         * No right-hand children. Everything down and left is smaller than us,
 464         * so any 'next' node must be in the general direction of our parent.
 465         * Go up the tree; any time the ancestor is a right-hand child of its
 466         * parent, keep going up. First time it's a left-hand child of its
 467         * parent, said parent is our 'next' node.
 468         */
 469        while ((parent = rb_parent(node)) && node == parent->rb_right)
 470                node = parent;
 471
 472        return parent;
 473}
 474EXPORT_SYMBOL(rb_next);
 475
 476struct rb_node *rb_prev(const struct rb_node *node)
 477{
 478        struct rb_node *parent;
 479
 480        if (RB_EMPTY_NODE(node))
 481                return NULL;
 482
 483        /*
 484         * If we have a left-hand child, go down and then right as far
 485         * as we can.
 486         */
 487        if (node->rb_left) {
 488                node = node->rb_left; 
 489                while (node->rb_right)
 490                        node=node->rb_right;
 491                return (struct rb_node *)node;
 492        }
 493
 494        /*
 495         * No left-hand children. Go up till we find an ancestor which
 496         * is a right-hand child of its parent.
 497         */
 498        while ((parent = rb_parent(node)) && node == parent->rb_left)
 499                node = parent;
 500
 501        return parent;
 502}
 503EXPORT_SYMBOL(rb_prev);
 504
 505void rb_replace_node(struct rb_node *victim, struct rb_node *new,
 506                     struct rb_root *root)
 507{
 508        struct rb_node *parent = rb_parent(victim);
 509
 510        /* Set the surrounding nodes to point to the replacement */
 511        __rb_change_child(victim, new, parent, root);
 512        if (victim->rb_left)
 513                rb_set_parent(victim->rb_left, new);
 514        if (victim->rb_right)
 515                rb_set_parent(victim->rb_right, new);
 516
 517        /* Copy the pointers/colour from the victim to the replacement */
 518        *new = *victim;
 519}
 520EXPORT_SYMBOL(rb_replace_node);
 521
lxr.linux.no kindly hosted by Redpill Linpro AS, provider of Linux consulting and operations services since 1995.