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) 2007  Andre Noll <maan@systemlinux.org>
   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 "stddef.h"
  25 #include "rbtree.h"
  26
  27 static void __rb_rotate_left(struct rb_node *node, struct rb_root *root)
  28 {
  29         struct rb_node *right = node->rb_right;
  30         struct rb_node *parent = rb_parent(node);
  31
  32         if ((node->rb_right = right->rb_left))
  33                 rb_set_parent(right->rb_left, node);
  34         right->rb_left = node;
  35
  36         rb_set_parent(right, parent);
  37
  38         if (parent)
  39         {
  40                 if (node == parent->rb_left)
  41                         parent->rb_left = right;
  42                 else
  43                         parent->rb_right = right;
  44         }
  45         else
  46                 root->rb_node = right;
  47         rb_set_parent(node, right);
  48         right->size = node->size;
  49         node->size = 1;
  50         if (node->rb_right)
  51                 node->size += node->rb_right->size;
  52         if (node->rb_left)
  53                 node->size += node->rb_left->size;
  54 }
  55
  56 static void __rb_rotate_right(struct rb_node *node, struct rb_root *root)
  57 {
  58         struct rb_node *left = node->rb_left;
  59         struct rb_node *parent = rb_parent(node);
  60
  61         if ((node->rb_left = left->rb_right))
  62                 rb_set_parent(left->rb_right, node);
  63         left->rb_right = node;
  64
  65         rb_set_parent(left, parent);
  66
  67         if (parent)
  68         {
  69                 if (node == parent->rb_right)
  70                         parent->rb_right = left;
  71                 else
  72                         parent->rb_left = left;
  73         }
  74         else
  75                 root->rb_node = left;
  76         rb_set_parent(node, left);
  77         left->size = node->size;
  78         node->size = 1;
  79         if (node->rb_right)
  80                 node->size += node->rb_right->size;
  81         if (node->rb_left)
  82                 node->size += node->rb_left->size;
  83 }
  84
  85 void rb_insert_color(struct rb_node *node, struct rb_root *root)
  86 {
  87         struct rb_node *parent, *gparent;
  88
  89         while ((parent = rb_parent(node)) && rb_is_red(parent))
  90         {
  91                 gparent = rb_parent(parent);
  92
  93                 if (parent == gparent->rb_left)
  94                 {
  95                         {
  96                                 register struct rb_node *uncle = gparent->rb_right;
  97                                 if (uncle && rb_is_red(uncle))
  98                                 {
  99                                         rb_set_black(uncle);
 100                                         rb_set_black(parent);
 101                                         rb_set_red(gparent);
 102                                         node = gparent;
 103                                         continue;
 104                                 }
 105                         }
 106
 107                         if (parent->rb_right == node)
 108                         {
 109                                 register struct rb_node *tmp;
 110                                 __rb_rotate_left(parent, root);
 111                                 tmp = parent;
 112                                 parent = node;
 113                                 node = tmp;
 114                         }
 115
 116                         rb_set_black(parent);
 117                         rb_set_red(gparent);
 118                         __rb_rotate_right(gparent, root);
 119                 } else {
 120                         {
 121                                 register struct rb_node *uncle = gparent->rb_left;
 122                                 if (uncle && rb_is_red(uncle))
 123                                 {
 124                                         rb_set_black(uncle);
 125                                         rb_set_black(parent);
 126                                         rb_set_red(gparent);
 127                                         node = gparent;
 128                                         continue;
 129                                 }
 130                         }
 131
 132                         if (parent->rb_left == node)
 133                         {
 134                                 register struct rb_node *tmp;
 135                                 __rb_rotate_right(parent, root);
 136                                 tmp = parent;
 137                                 parent = node;
 138                                 node = tmp;
 139                         }
 140
 141                         rb_set_black(parent);
 142                         rb_set_red(gparent);
 143                         __rb_rotate_left(gparent, root);
 144                 }
 145         }
 146
 147         rb_set_black(root->rb_node);
 148 }
 149
 150 static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
 151                              struct rb_root *root)
 152 {
 153         struct rb_node *other;
 154
 155         while ((!node || rb_is_black(node)) && node != root->rb_node)
 156         {
 157                 if (parent->rb_left == node)
 158                 {
 159                         other = parent->rb_right;
 160                         if (rb_is_red(other))
 161                         {
 162                                 rb_set_black(other);
 163                                 rb_set_red(parent);
 164                                 __rb_rotate_left(parent, root);
 165                                 other = parent->rb_right;
 166                         }
 167                         if ((!other->rb_left || rb_is_black(other->rb_left)) &&
 168                             (!other->rb_right || rb_is_black(other->rb_right)))
 169                         {
 170                                 rb_set_red(other);
 171                                 node = parent;
 172                                 parent = rb_parent(node);
 173                         }
 174                         else
 175                         {
 176                                 if (!other->rb_right || rb_is_black(other->rb_right))
 177                                 {
 178                                         struct rb_node *o_left;
 179                                         if ((o_left = other->rb_left))
 180                                                 rb_set_black(o_left);
 181                                         rb_set_red(other);
 182                                         __rb_rotate_right(other, root);
 183                                         other = parent->rb_right;
 184                                 }
 185                                 rb_set_color(other, rb_color(parent));
 186                                 rb_set_black(parent);
 187                                 if (other->rb_right)
 188                                         rb_set_black(other->rb_right);
 189                                 __rb_rotate_left(parent, root);
 190                                 node = root->rb_node;
 191                                 break;
 192                         }
 193                 }
 194                 else
 195                 {
 196                         other = parent->rb_left;
 197                         if (rb_is_red(other))
 198                         {
 199                                 rb_set_black(other);
 200                                 rb_set_red(parent);
 201                                 __rb_rotate_right(parent, root);
 202                                 other = parent->rb_left;
 203                         }
 204                         if ((!other->rb_left || rb_is_black(other->rb_left)) &&
 205                             (!other->rb_right || rb_is_black(other->rb_right)))
 206                         {
 207                                 rb_set_red(other);
 208                                 node = parent;
 209                                 parent = rb_parent(node);
 210                         }
 211                         else
 212                         {
 213                                 if (!other->rb_left || rb_is_black(other->rb_left))
 214                                 {
 215                                         register struct rb_node *o_right;
 216                                         if ((o_right = other->rb_right))
 217                                                 rb_set_black(o_right);
 218                                         rb_set_red(other);
 219                                         __rb_rotate_left(other, root);
 220                                         other = parent->rb_left;
 221                                 }
 222                                 rb_set_color(other, rb_color(parent));
 223                                 rb_set_black(parent);
 224                                 if (other->rb_left)
 225                                         rb_set_black(other->rb_left);
 226                                 __rb_rotate_right(parent, root);
 227                                 node = root->rb_node;
 228                                 break;
 229                         }
 230                 }
 231         }
 232         if (node)
 233                 rb_set_black(node);
 234 }
 235
 236 void rb_erase(struct rb_node *node, struct rb_root *root)
 237 {
 238         struct rb_node *child, *parent;
 239         int color;
 240
 241         if (!node->rb_left)
 242                 child = node->rb_right;
 243         else if (!node->rb_right)
 244                 child = node->rb_left;
 245         else
 246         {
 247                 struct rb_node *old = node, *left;
 248
 249                 node = node->rb_right;
 250                 while ((left = node->rb_left) != NULL)
 251                         node = left;
 252                 child = node->rb_right;
 253                 parent = rb_parent(node);
 254                 color = rb_color(node);
 255
 256                 if (child)
 257                         rb_set_parent(child, parent);
 258                 if (parent == old) {
 259                         parent->rb_right = child;
 260                         parent = node;
 261                 } else
 262                         parent->rb_left = child;
 263
 264                 node->rb_parent_color = old->rb_parent_color;
 265                 node->rb_right = old->rb_right;
 266                 node->rb_left = old->rb_left;
 267                 node->size = old->size;
 268
 269                 if (rb_parent(old))
 270                 {
 271                         if (rb_parent(old)->rb_left == old)
 272                                 rb_parent(old)->rb_left = node;
 273                         else
 274                                 rb_parent(old)->rb_right = node;
 275                 } else
 276                         root->rb_node = node;
 277
 278                 rb_set_parent(old->rb_left, node);
 279                 if (old->rb_right)
 280                         rb_set_parent(old->rb_right, node);
 281                 goto color;
 282         }
 283
 284         parent = rb_parent(node);
 285         color = rb_color(node);
 286
 287         if (child)
 288                 rb_set_parent(child, parent);
 289         if (parent)
 290         {
 291                 if (parent->rb_left == node)
 292                         parent->rb_left = child;
 293                 else
 294                         parent->rb_right = child;
 295         }
 296         else
 297                 root->rb_node = child;
 298
 299  color:
 300         if (color == RB_BLACK)
 301                 __rb_erase_color(child, parent, root);
 302 }
 303
 304 /*
 305  * This function returns the first node (in sort order) of the tree.
 306  */
 307 struct rb_node *rb_first(struct rb_root *root)
 308 {
 309         struct rb_node  *n;
 310
 311         n = root->rb_node;
 312         if (!n)
 313                 return NULL;
 314         while (n->rb_left)
 315                 n = n->rb_left;
 316         return n;
 317 }
 318
 319 struct rb_node *rb_last(struct rb_root *root)
 320 {
 321         struct rb_node  *n;
 322
 323         n = root->rb_node;
 324         if (!n)
 325                 return NULL;
 326         while (n->rb_right)
 327                 n = n->rb_right;
 328         return n;
 329 }
 330
 331 struct rb_node *rb_next(struct rb_node *node)
 332 {
 333         struct rb_node *parent;
 334
 335         if (rb_parent(node) == node)
 336                 return NULL;
 337
 338         /* If we have a right-hand child, go down and then left as far
 339            as we can. */
 340         if (node->rb_right) {
 341                 node = node->rb_right;
 342                 while (node->rb_left)
 343                         node=node->rb_left;
 344                 return node;
 345         }
 346
 347         /* No right-hand children.  Everything down and left is
 348            smaller than us, so any 'next' node must be in the general
 349            direction of our parent. Go up the tree; any time the
 350            ancestor is a right-hand child of its parent, keep going
 351            up. First time it's a left-hand child of its parent, said
 352            parent is our 'next' node. */
 353         while ((parent = rb_parent(node)) && node == parent->rb_right)
 354                 node = parent;
 355
 356         return parent;
 357 }
 358
 359 struct rb_node *rb_prev(struct rb_node *node)
 360 {
 361         struct rb_node *parent;
 362
 363         if (rb_parent(node) == node)
 364                 return NULL;
 365
 366         /* If we have a left-hand child, go down and then right as far
 367            as we can. */
 368         if (node->rb_left) {
 369                 node = node->rb_left;
 370                 while (node->rb_right)
 371                         node=node->rb_right;
 372                 return node;
 373         }
 374
 375         /* No left-hand children. Go up till we find an ancestor which
 376            is a right-hand child of its parent */
 377         while ((parent = rb_parent(node)) && node == parent->rb_left)
 378                 node = parent;
 379
 380         return parent;
 381 }
 382
 383 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
 384                      struct rb_root *root)
 385 {
 386         struct rb_node *parent = rb_parent(victim);
 387
 388         /* Set the surrounding nodes to point to the replacement */
 389         if (parent) {
 390                 if (victim == parent->rb_left)
 391                         parent->rb_left = new;
 392                 else
 393                         parent->rb_right = new;
 394         } else {
 395                 root->rb_node = new;
 396         }
 397         if (victim->rb_left)
 398                 rb_set_parent(victim->rb_left, new);
 399         if (victim->rb_right)
 400                 rb_set_parent(victim->rb_right, new);
 401
 402         /* Copy the pointers/colour from the victim to the replacement */
 403         *new = *victim;
 404 }
 405
 406 /**
 407  * Get the n-th node (in sort order) of the tree.
 408  *
 409  * \param node The root of the subtree to consider.
 410  * \param n The order statistic to compute.
 411  *
 412  * \return Pointer to the \a n th greatest node on success, \p NULL on errors.
 413  */
 414 struct rb_node *rb_nth(struct rb_node *node, unsigned n)
 415 {
 416         unsigned size = 1;
 417
 418         if (!node)
 419                 return NULL;
 420         if (node->rb_left)
 421                 size += node->rb_left->size;
 422         if (n == size)
 423                 return node;
 424         if (n < size)
 425                 return rb_nth(node->rb_left, n);
 426         return rb_nth(node->rb_right, n - size);
 427 }
 428
 429 /**
 430  * Get the rank of a node in O(log n) time.
 431  *
 432  * \param node The node to get the rank of.
 433  * \param rank Result pointer.
 434  *
 435  * \return Positive on success, -1 on errors.
 436  */
 437 int rb_rank(struct rb_node *node, unsigned *rank)
 438 {
 439         *rank = 1;
 440         struct rb_node *parent;
 441
 442         if (!node)
 443                 return -1;
 444         if (node->rb_left)
 445                 *rank += node->rb_left->size;
 446         while ((parent = rb_parent(node))) {
 447                 if (node == parent->rb_right) {
 448                         (*rank)++;
 449                         if (parent->rb_left)
 450                                 *rank += parent->rb_left->size;
 451                 }
 452                 node = parent;
 453         }
 454         return 1;
 455 }