linux/lib/rbtree.c
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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 <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__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}
 358EXPORT_SYMBOL(__rb_erase_color);
 359
 360/*
 361 * Non-augmented rbtree manipulation functions.
 362 *
 363 * We use dummy augmented callbacks here, and have the compiler optimize them
 364 * out of the rb_insert_color() and rb_erase() function definitions.
 365 */
 366
 367static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
 368static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
 369static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
 370
 371static const struct rb_augment_callbacks dummy_callbacks = {
 372        dummy_propagate, dummy_copy, dummy_rotate
 373};
 374
 375void rb_insert_color(struct rb_node *node, struct rb_root *root)
 376{
 377        __rb_insert(node, root, dummy_rotate);
 378}
 379EXPORT_SYMBOL(rb_insert_color);
 380
 381void rb_erase(struct rb_node *node, struct rb_root *root)
 382{
 383        rb_erase_augmented(node, root, &dummy_callbacks);
 384}
 385EXPORT_SYMBOL(rb_erase);
 386
 387/*
 388 * Augmented rbtree manipulation functions.
 389 *
 390 * This instantiates the same __always_inline functions as in the non-augmented
 391 * case, but this time with user-defined callbacks.
 392 */
 393
 394void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
 395        void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 396{
 397        __rb_insert(node, root, augment_rotate);
 398}
 399EXPORT_SYMBOL(__rb_insert_augmented);
 400
 401/*
 402 * This function returns the first node (in sort order) of the tree.
 403 */
 404struct rb_node *rb_first(const struct rb_root *root)
 405{
 406        struct rb_node  *n;
 407
 408        n = root->rb_node;
 409        if (!n)
 410                return NULL;
 411        while (n->rb_left)
 412                n = n->rb_left;
 413        return n;
 414}
 415EXPORT_SYMBOL(rb_first);
 416
 417struct rb_node *rb_last(const struct rb_root *root)
 418{
 419        struct rb_node  *n;
 420
 421        n = root->rb_node;
 422        if (!n)
 423                return NULL;
 424        while (n->rb_right)
 425                n = n->rb_right;
 426        return n;
 427}
 428EXPORT_SYMBOL(rb_last);
 429
 430struct rb_node *rb_next(const struct rb_node *node)
 431{
 432        struct rb_node *parent;
 433
 434        if (RB_EMPTY_NODE(node))
 435                return NULL;
 436
 437        /*
 438         * If we have a right-hand child, go down and then left as far
 439         * as we can.
 440         */
 441        if (node->rb_right) {
 442                node = node->rb_right; 
 443                while (node->rb_left)
 444                        node=node->rb_left;
 445                return (struct rb_node *)node;
 446        }
 447
 448        /*
 449         * No right-hand children. Everything down and left is smaller than us,
 450         * so any 'next' node must be in the general direction of our parent.
 451         * Go up the tree; any time the ancestor is a right-hand child of its
 452         * parent, keep going up. First time it's a left-hand child of its
 453         * parent, said parent is our 'next' node.
 454         */
 455        while ((parent = rb_parent(node)) && node == parent->rb_right)
 456                node = parent;
 457
 458        return parent;
 459}
 460EXPORT_SYMBOL(rb_next);
 461
 462struct rb_node *rb_prev(const struct rb_node *node)
 463{
 464        struct rb_node *parent;
 465
 466        if (RB_EMPTY_NODE(node))
 467                return NULL;
 468
 469        /*
 470         * If we have a left-hand child, go down and then right as far
 471         * as we can.
 472         */
 473        if (node->rb_left) {
 474                node = node->rb_left; 
 475                while (node->rb_right)
 476                        node=node->rb_right;
 477                return (struct rb_node *)node;
 478        }
 479
 480        /*
 481         * No left-hand children. Go up till we find an ancestor which
 482         * is a right-hand child of its parent.
 483         */
 484        while ((parent = rb_parent(node)) && node == parent->rb_left)
 485                node = parent;
 486
 487        return parent;
 488}
 489EXPORT_SYMBOL(rb_prev);
 490
 491void rb_replace_node(struct rb_node *victim, struct rb_node *new,
 492                     struct rb_root *root)
 493{
 494        struct rb_node *parent = rb_parent(victim);
 495
 496        /* Set the surrounding nodes to point to the replacement */
 497        __rb_change_child(victim, new, parent, root);
 498        if (victim->rb_left)
 499                rb_set_parent(victim->rb_left, new);
 500        if (victim->rb_right)
 501                rb_set_parent(victim->rb_right, new);
 502
 503        /* Copy the pointers/colour from the victim to the replacement */
 504        *new = *victim;
 505}
 506EXPORT_SYMBOL(rb_replace_node);
 507
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