1 /*
  2   Red Black Trees
  3   (C) 1999  Andrea Arcangeli <[email protected]>
  4   (C) 2002  David Woodhouse <[email protected]>
  5   
  6   This program is free software; you can redistribute it and/or modify
  7   it under the terms of the GNU General Public License as published by
 
  8   the Free Software Foundation; either version 2 of the License, or
  9   (at your option) any later version.
 10 
 11   This program is distributed in the hope that it will be useful,
 12   but WITHOUT ANY WARRANTY; without even the implied warranty of
 13   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 
 14   GNU General Public License for more details.
 15 
 16   You should have received a copy of the GNU General Public License
 17   along with this program; if not, write to the Free Software
 18   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 19 
 20   linux/lib/rbtree.c
 
 21 */
 22 
 23 #include "rbtree.h"
 24 
 25 static void __rb_rotate_left(struct rb_node *node, struct rb_root *root)
 26 {
 27     struct rb_node *right = node->rb_right;
 28     struct rb_node *parent = rb_parent(node);
 29 
 30     if ((node->rb_right = right->rb_left))
 31         rb_set_parent(right->rb_left, node);
 32     right->rb_left = node;
 33 
 34     rb_set_parent(right, parent);
 35 
 36     if (parent)
 37     {
 38         if (node == parent->rb_left)
 39             parent->rb_left = right;
 40         else
 41             parent->rb_right = right;
 42     }
 43     else
 44         root->rb_node = right;
 45     rb_set_parent(node, right);
 46 }
 47 
 48 static void __rb_rotate_right(struct rb_node *node, struct rb_root *root)
 49 {
 50     struct rb_node *left = node->rb_left;
 51     struct rb_node *parent = rb_parent(node);
 52 
 53     if ((node->rb_left = left->rb_right))
 54         rb_set_parent(left->rb_right, node);
 55     left->rb_right = node;
 56 
 57     rb_set_parent(left, parent);
 58 
 59     if (parent)
 60     {
 61         if (node == parent->rb_right)
 62             parent->rb_right = left;
 63         else
 64             parent->rb_left = left;
 65     }
 66     else
 67         root->rb_node = left;
 68     rb_set_parent(node, left);
 69 }
 70 
 71 void rb_insert_color(struct rb_node *node, struct rb_root *root)
 72 {
 73     struct rb_node *parent, *gparent;
 74 
 75     while ((parent = rb_parent(node)) && rb_is_red(parent))
 76     {
 77         gparent = rb_parent(parent);
 78 
 79         if (parent == gparent->rb_left)
 80         {
 81             {
 82                 register struct rb_node *uncle = gparent->rb_right;
 83                 if (uncle && rb_is_red(uncle))
 84                 {
 85                     rb_set_black(uncle);
 86                     rb_set_black(parent);
 87                     rb_set_red(gparent);
 88                     node = gparent;
 89                     continue;
 90                 }
 91             }
 92 
 93             if (parent->rb_right == node)
 94             {
 95                 register struct rb_node *tmp;
 96                 __rb_rotate_left(parent, root);
 97                 tmp = parent;
 98                 parent = node;
 99                 node = tmp;
100             }
101 
102             rb_set_black(parent);
103             rb_set_red(gparent);
104             __rb_rotate_right(gparent, root);
105         } else {
106             {
107                 register struct rb_node *uncle = gparent->rb_left;
108                 if (uncle && rb_is_red(uncle))
109                 {
110                     rb_set_black(uncle);
111                     rb_set_black(parent);
112                     rb_set_red(gparent);
113                     node = gparent;
114                     continue;
115                 }
116             }
117 
118             if (parent->rb_left == node)
119             {
120                 register struct rb_node *tmp;
121                 __rb_rotate_right(parent, root);
122                 tmp = parent;
123                 parent = node;
124                 node = tmp;
125             }
126 
127             rb_set_black(parent);
128             rb_set_red(gparent);
129             __rb_rotate_left(gparent, root);
130         }
131     }
132 
133     rb_set_black(root->rb_node);
134 }
135 
136 static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
137                  struct rb_root *root)
138 {
139     struct rb_node *other;
140 
141     while ((!node || rb_is_black(node)) && node != root->rb_node)
142     {
143         if (parent->rb_left == node)
144         {
145             other = parent->rb_right;
146             if (rb_is_red(other))
147             {
148                 rb_set_black(other);
149                 rb_set_red(parent);
150                 __rb_rotate_left(parent, root);
151                 other = parent->rb_right;
152             }
153             if ((!other->rb_left || rb_is_black(other->rb_left)) &&
154                 (!other->rb_right || rb_is_black(other->rb_right)))
155             {
156                 rb_set_red(other);
157                 node = parent;
158                 parent = rb_parent(node);
159             }
160             else
161             {
162                 if (!other->rb_right || rb_is_black(other->rb_right))
163                 {
164                     rb_set_black(other->rb_left);
165                     rb_set_red(other);
166                     __rb_rotate_right(other, root);
167                     other = parent->rb_right;
168                 }
169                 rb_set_color(other, rb_color(parent));
170                 rb_set_black(parent);
171                 rb_set_black(other->rb_right);
172                 __rb_rotate_left(parent, root);
173                 node = root->rb_node;
174                 break;
175             }
176         }
177         else
178         {
179             other = parent->rb_left;
180             if (rb_is_red(other))
181             {
182                 rb_set_black(other);
183                 rb_set_red(parent);
184                 __rb_rotate_right(parent, root);
185                 other = parent->rb_left;
186             }
187             if ((!other->rb_left || rb_is_black(other->rb_left)) &&
188                 (!other->rb_right || rb_is_black(other->rb_right)))
189             {
190                 rb_set_red(other);
191                 node = parent;
192                 parent = rb_parent(node);
193             }
194             else
195             {
196                 if (!other->rb_left || rb_is_black(other->rb_left))
197                 {
198                     rb_set_black(other->rb_right);
199                     rb_set_red(other);
200                     __rb_rotate_left(other, root);
201                     other = parent->rb_left;
202                 }
203                 rb_set_color(other, rb_color(parent));
204                 rb_set_black(parent);
205                 rb_set_black(other->rb_left);
206                 __rb_rotate_right(parent, root);
207                 node = root->rb_node;
208                 break;
209             }
210         }
211     }
212     if (node)
213         rb_set_black(node);
214 }
215 
216 void rb_erase(struct rb_node *node, struct rb_root *root)
217 {
218     struct rb_node *child, *parent;
219     int color;
220 
221     if (!node->rb_left)
222         child = node->rb_right;
223     else if (!node->rb_right)
224         child = node->rb_left;
225     else
226     {
227         struct rb_node *old = node, *left;
228 
229         node = node->rb_right;
230         while ((left = node->rb_left) != NULL)
231             node = left;
232 
233         if (rb_parent(old)) {
234             if (rb_parent(old)->rb_left == old)
235                 rb_parent(old)->rb_left = node;
236             else
237                 rb_parent(old)->rb_right = node;
238         } else
239             root->rb_node = node;
240 
241         child = node->rb_right;
242         parent = rb_parent(node);
243         color = rb_color(node);
244 
245         if (parent == old) {
246             parent = node;
247         } else {
248             if (child)
249                 rb_set_parent(child, parent);
250             parent->rb_left = child;
251 
252             node->rb_right = old->rb_right;
253             rb_set_parent(old->rb_right, node);
254         }
255 
256         node->rb_parent_color = old->rb_parent_color;
257         node->rb_left = old->rb_left;
258         rb_set_parent(old->rb_left, node);
259 
260         goto color;
261     }
262 
263     parent = rb_parent(node);
264     color = rb_color(node);
265 
266     if (child)
267         rb_set_parent(child, parent);
268     if (parent)
269     {
270         if (parent->rb_left == node)
271             parent->rb_left = child;
272         else
273             parent->rb_right = child;
274     }
275     else
276         root->rb_node = child;
277 
278  color:
279     if (color == RB_BLACK)
280         __rb_erase_color(child, parent, root);
281 }
282 
283 static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data)
284 {
285     struct rb_node *parent;
286 
287 up:
288     func(node, data);
289     parent = rb_parent(node);
290     if (!parent)
291         return;
292 
293     if (node == parent->rb_left && parent->rb_right)
294         func(parent->rb_right, data);
295     else if (parent->rb_left)
296         func(parent->rb_left, data);
297 
298     node = parent;
299     goto up;
300 }
301 
302 /*
303  * after inserting @node into the tree, update the tree to account for
304  * both the new entry and any damage done by rebalance
305  */
306 void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data)
307 {
308     if (node->rb_left)
309         node = node->rb_left;
310     else if (node->rb_right)
311         node = node->rb_right;
312 
313     rb_augment_path(node, func, data);
314 }
315 
316 /*
317  * before removing the node, find the deepest node on the rebalance path
318  * that will still be there after @node gets removed
319  */
320 struct rb_node *rb_augment_erase_begin(struct rb_node *node)
321 {
322     struct rb_node *deepest;
323 
324     if (!node->rb_right && !node->rb_left)
325         deepest = rb_parent(node);
326     else if (!node->rb_right)
327         deepest = node->rb_left;
328     else if (!node->rb_left)
329         deepest = node->rb_right;
330     else {
331         deepest = rb_next(node);
332         if (deepest->rb_right)
333             deepest = deepest->rb_right;
334         else if (rb_parent(deepest) != node)
335             deepest = rb_parent(deepest);
336     }
337 
338     return deepest;
339 }
340 
341 /*
342  * after removal, update the tree to account for the removed entry
343  * and any rebalance damage.
344  */
345 void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data)
346 {
347     if (node)
348         rb_augment_path(node, func, data);
349 }
350 
351 /*
352  * This function returns the first node (in sort order) of the tree.
353  */
354 struct rb_node *rb_first(const struct rb_root *root)
355 {
356     struct rb_node    *n;
357 
358     n = root->rb_node;
359     if (!n)
360         return NULL;
361     while (n->rb_left)
362         n = n->rb_left;
363     return n;
364 }
365 
366 struct rb_node *rb_last(const struct rb_root *root)
367 {
368     struct rb_node    *n;
369 
370     n = root->rb_node;
371     if (!n)
372         return NULL;
373     while (n->rb_right)
374         n = n->rb_right;
375     return n;
376 }
377 
378 struct rb_node *rb_next(const struct rb_node *node)
379 {
380     struct rb_node *parent;
381 
382     if (rb_parent(node) == node)
383         return NULL;
384 
385     /* If we have a right-hand child, go down and then left as far
386        as we can. */
387     if (node->rb_right) {
388         node = node->rb_right; 
389         while (node->rb_left)
390             node=node->rb_left;
391         return (struct rb_node *)node;
392     }
393 
394     /* No right-hand children.  Everything down and left is
395        smaller than us, so any 'next' node must be in the general
396        direction of our parent. Go up the tree; any time the
397        ancestor is a right-hand child of its parent, keep going
398        up. First time it's a left-hand child of its parent, said
399        parent is our 'next' node. */
400     while ((parent = rb_parent(node)) && node == parent->rb_right)
401         node = parent;
402 
403     return parent;
404 }
405 
406 struct rb_node *rb_prev(const struct rb_node *node)
407 {
408     struct rb_node *parent;
409 
410     if (rb_parent(node) == node)
411         return NULL;
412 
413     /* If we have a left-hand child, go down and then right as far
414        as we can. */
415     if (node->rb_left) {
416         node = node->rb_left; 
417         while (node->rb_right)
418             node=node->rb_right;
419         return (struct rb_node *)node;
420     }
421 
422     /* No left-hand children. Go up till we find an ancestor which
423        is a right-hand child of its parent */
424     while ((parent = rb_parent(node)) && node == parent->rb_left)
425         node = parent;
426 
427     return parent;
428 }
429 
430 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
431              struct rb_root *root)
432 {
433     struct rb_node *parent = rb_parent(victim);
434 
435     /* Set the surrounding nodes to point to the replacement */
436     if (parent) {
437         if (victim == parent->rb_left)
438             parent->rb_left = new;
439         else
440             parent->rb_right = new;
441     } else {
442         root->rb_node = new;
443     }
444     if (victim->rb_left)
445         rb_set_parent(victim->rb_left, new);
446     if (victim->rb_right)
447         rb_set_parent(victim->rb_right, new);
448 
449     /* Copy the pointers/colour from the victim to the replacement */
450     *new = *victim;
451 }