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Linux/tools/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 
 26 /*
 27  * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
 28  *
 29  *  1) A node is either red or black
 30  *  2) The root is black
 31  *  3) All leaves (NULL) are black
 32  *  4) Both children of every red node are black
 33  *  5) Every simple path from root to leaves contains the same number
 34  *     of black nodes.
 35  *
 36  *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
 37  *  consecutive red nodes in a path and every red node is therefore followed by
 38  *  a black. So if B is the number of black nodes on every simple path (as per
 39  *  5), then the longest possible path due to 4 is 2B.
 40  *
 41  *  We shall indicate color with case, where black nodes are uppercase and red
 42  *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
 43  *  parentheses and have some accompanying text comment.
 44  */
 45 
 46 static inline void rb_set_black(struct rb_node *rb)
 47 {
 48         rb->__rb_parent_color |= RB_BLACK;
 49 }
 50 
 51 static inline struct rb_node *rb_red_parent(struct rb_node *red)
 52 {
 53         return (struct rb_node *)red->__rb_parent_color;
 54 }
 55 
 56 /*
 57  * Helper function for rotations:
 58  * - old's parent and color get assigned to new
 59  * - old gets assigned new as a parent and 'color' as a color.
 60  */
 61 static inline void
 62 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
 63                         struct rb_root *root, int color)
 64 {
 65         struct rb_node *parent = rb_parent(old);
 66         new->__rb_parent_color = old->__rb_parent_color;
 67         rb_set_parent_color(old, new, color);
 68         __rb_change_child(old, new, parent, root);
 69 }
 70 
 71 static __always_inline void
 72 __rb_insert(struct rb_node *node, struct rb_root *root,
 73             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 74 {
 75         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
 76 
 77         while (true) {
 78                 /*
 79                  * Loop invariant: node is red
 80                  *
 81                  * If there is a black parent, we are done.
 82                  * Otherwise, take some corrective action as we don't
 83                  * want a red root or two consecutive red nodes.
 84                  */
 85                 if (!parent) {
 86                         rb_set_parent_color(node, NULL, RB_BLACK);
 87                         break;
 88                 } else if (rb_is_black(parent))
 89                         break;
 90 
 91                 gparent = rb_red_parent(parent);
 92 
 93                 tmp = gparent->rb_right;
 94                 if (parent != tmp) {    /* parent == gparent->rb_left */
 95                         if (tmp && rb_is_red(tmp)) {
 96                                 /*
 97                                  * Case 1 - color flips
 98                                  *
 99                                  *       G            g
100                                  *      / \          / \
101                                  *     p   u  -->   P   U
102                                  *    /            /
103                                  *   n            n
104                                  *
105                                  * However, since g's parent might be red, and
106                                  * 4) does not allow this, we need to recurse
107                                  * at g.
108                                  */
109                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
110                                 rb_set_parent_color(parent, gparent, RB_BLACK);
111                                 node = gparent;
112                                 parent = rb_parent(node);
113                                 rb_set_parent_color(node, parent, RB_RED);
114                                 continue;
115                         }
116 
117                         tmp = parent->rb_right;
118                         if (node == tmp) {
119                                 /*
120                                  * Case 2 - left rotate at parent
121                                  *
122                                  *      G             G
123                                  *     / \           / \
124                                  *    p   U  -->    n   U
125                                  *     \           /
126                                  *      n         p
127                                  *
128                                  * This still leaves us in violation of 4), the
129                                  * continuation into Case 3 will fix that.
130                                  */
131                                 parent->rb_right = tmp = node->rb_left;
132                                 node->rb_left = parent;
133                                 if (tmp)
134                                         rb_set_parent_color(tmp, parent,
135                                                             RB_BLACK);
136                                 rb_set_parent_color(parent, node, RB_RED);
137                                 augment_rotate(parent, node);
138                                 parent = node;
139                                 tmp = node->rb_right;
140                         }
141 
142                         /*
143                          * Case 3 - right rotate at gparent
144                          *
145                          *        G           P
146                          *       / \         / \
147                          *      p   U  -->  n   g
148                          *     /                 \
149                          *    n                   U
150                          */
151                         gparent->rb_left = tmp;  /* == parent->rb_right */
152                         parent->rb_right = gparent;
153                         if (tmp)
154                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
155                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
156                         augment_rotate(gparent, parent);
157                         break;
158                 } else {
159                         tmp = gparent->rb_left;
160                         if (tmp && rb_is_red(tmp)) {
161                                 /* Case 1 - color flips */
162                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
163                                 rb_set_parent_color(parent, gparent, RB_BLACK);
164                                 node = gparent;
165                                 parent = rb_parent(node);
166                                 rb_set_parent_color(node, parent, RB_RED);
167                                 continue;
168                         }
169 
170                         tmp = parent->rb_left;
171                         if (node == tmp) {
172                                 /* Case 2 - right rotate at parent */
173                                 parent->rb_left = tmp = node->rb_right;
174                                 node->rb_right = parent;
175                                 if (tmp)
176                                         rb_set_parent_color(tmp, parent,
177                                                             RB_BLACK);
178                                 rb_set_parent_color(parent, node, RB_RED);
179                                 augment_rotate(parent, node);
180                                 parent = node;
181                                 tmp = node->rb_left;
182                         }
183 
184                         /* Case 3 - left rotate at gparent */
185                         gparent->rb_right = tmp;  /* == parent->rb_left */
186                         parent->rb_left = gparent;
187                         if (tmp)
188                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
189                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
190                         augment_rotate(gparent, parent);
191                         break;
192                 }
193         }
194 }
195 
196 /*
197  * Inline version for rb_erase() use - we want to be able to inline
198  * and eliminate the dummy_rotate callback there
199  */
200 static __always_inline void
201 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
202         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
203 {
204         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
205 
206         while (true) {
207                 /*
208                  * Loop invariants:
209                  * - node is black (or NULL on first iteration)
210                  * - node is not the root (parent is not NULL)
211                  * - All leaf paths going through parent and node have a
212                  *   black node count that is 1 lower than other leaf paths.
213                  */
214                 sibling = parent->rb_right;
215                 if (node != sibling) {  /* node == parent->rb_left */
216                         if (rb_is_red(sibling)) {
217                                 /*
218                                  * Case 1 - left rotate at parent
219                                  *
220                                  *     P               S
221                                  *    / \             / \
222                                  *   N   s    -->    p   Sr
223                                  *      / \         / \
224                                  *     Sl  Sr      N   Sl
225                                  */
226                                 parent->rb_right = tmp1 = sibling->rb_left;
227                                 sibling->rb_left = parent;
228                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
229                                 __rb_rotate_set_parents(parent, sibling, root,
230                                                         RB_RED);
231                                 augment_rotate(parent, sibling);
232                                 sibling = tmp1;
233                         }
234                         tmp1 = sibling->rb_right;
235                         if (!tmp1 || rb_is_black(tmp1)) {
236                                 tmp2 = sibling->rb_left;
237                                 if (!tmp2 || rb_is_black(tmp2)) {
238                                         /*
239                                          * Case 2 - sibling color flip
240                                          * (p could be either color here)
241                                          *
242                                          *    (p)           (p)
243                                          *    / \           / \
244                                          *   N   S    -->  N   s
245                                          *      / \           / \
246                                          *     Sl  Sr        Sl  Sr
247                                          *
248                                          * This leaves us violating 5) which
249                                          * can be fixed by flipping p to black
250                                          * if it was red, or by recursing at p.
251                                          * p is red when coming from Case 1.
252                                          */
253                                         rb_set_parent_color(sibling, parent,
254                                                             RB_RED);
255                                         if (rb_is_red(parent))
256                                                 rb_set_black(parent);
257                                         else {
258                                                 node = parent;
259                                                 parent = rb_parent(node);
260                                                 if (parent)
261                                                         continue;
262                                         }
263                                         break;
264                                 }
265                                 /*
266                                  * Case 3 - right rotate at sibling
267                                  * (p could be either color here)
268                                  *
269                                  *   (p)           (p)
270                                  *   / \           / \
271                                  *  N   S    -->  N   Sl
272                                  *     / \             \
273                                  *    sl  Sr            s
274                                  *                       \
275                                  *                        Sr
276                                  */
277                                 sibling->rb_left = tmp1 = tmp2->rb_right;
278                                 tmp2->rb_right = sibling;
279                                 parent->rb_right = tmp2;
280                                 if (tmp1)
281                                         rb_set_parent_color(tmp1, sibling,
282                                                             RB_BLACK);
283                                 augment_rotate(sibling, tmp2);
284                                 tmp1 = sibling;
285                                 sibling = tmp2;
286                         }
287                         /*
288                          * Case 4 - left rotate at parent + color flips
289                          * (p and sl could be either color here.
290                          *  After rotation, p becomes black, s acquires
291                          *  p's color, and sl keeps its color)
292                          *
293                          *      (p)             (s)
294                          *      / \             / \
295                          *     N   S     -->   P   Sr
296                          *        / \         / \
297                          *      (sl) sr      N  (sl)
298                          */
299                         parent->rb_right = tmp2 = sibling->rb_left;
300                         sibling->rb_left = parent;
301                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
302                         if (tmp2)
303                                 rb_set_parent(tmp2, parent);
304                         __rb_rotate_set_parents(parent, sibling, root,
305                                                 RB_BLACK);
306                         augment_rotate(parent, sibling);
307                         break;
308                 } else {
309                         sibling = parent->rb_left;
310                         if (rb_is_red(sibling)) {
311                                 /* Case 1 - right rotate at parent */
312                                 parent->rb_left = tmp1 = sibling->rb_right;
313                                 sibling->rb_right = parent;
314                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
315                                 __rb_rotate_set_parents(parent, sibling, root,
316                                                         RB_RED);
317                                 augment_rotate(parent, sibling);
318                                 sibling = tmp1;
319                         }
320                         tmp1 = sibling->rb_left;
321                         if (!tmp1 || rb_is_black(tmp1)) {
322                                 tmp2 = sibling->rb_right;
323                                 if (!tmp2 || rb_is_black(tmp2)) {
324                                         /* Case 2 - sibling color flip */
325                                         rb_set_parent_color(sibling, parent,
326                                                             RB_RED);
327                                         if (rb_is_red(parent))
328                                                 rb_set_black(parent);
329                                         else {
330                                                 node = parent;
331                                                 parent = rb_parent(node);
332                                                 if (parent)
333                                                         continue;
334                                         }
335                                         break;
336                                 }
337                                 /* Case 3 - right rotate at sibling */
338                                 sibling->rb_right = tmp1 = tmp2->rb_left;
339                                 tmp2->rb_left = sibling;
340                                 parent->rb_left = tmp2;
341                                 if (tmp1)
342                                         rb_set_parent_color(tmp1, sibling,
343                                                             RB_BLACK);
344                                 augment_rotate(sibling, tmp2);
345                                 tmp1 = sibling;
346                                 sibling = tmp2;
347                         }
348                         /* Case 4 - left rotate at parent + color flips */
349                         parent->rb_left = tmp2 = sibling->rb_right;
350                         sibling->rb_right = parent;
351                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
352                         if (tmp2)
353                                 rb_set_parent(tmp2, parent);
354                         __rb_rotate_set_parents(parent, sibling, root,
355                                                 RB_BLACK);
356                         augment_rotate(parent, sibling);
357                         break;
358                 }
359         }
360 }
361 
362 /* Non-inline version for rb_erase_augmented() use */
363 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
364         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
365 {
366         ____rb_erase_color(parent, root, augment_rotate);
367 }
368 
369 /*
370  * Non-augmented rbtree manipulation functions.
371  *
372  * We use dummy augmented callbacks here, and have the compiler optimize them
373  * out of the rb_insert_color() and rb_erase() function definitions.
374  */
375 
376 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
377 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
378 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
379 
380 static const struct rb_augment_callbacks dummy_callbacks = {
381         dummy_propagate, dummy_copy, dummy_rotate
382 };
383 
384 void rb_insert_color(struct rb_node *node, struct rb_root *root)
385 {
386         __rb_insert(node, root, dummy_rotate);
387 }
388 
389 void rb_erase(struct rb_node *node, struct rb_root *root)
390 {
391         struct rb_node *rebalance;
392         rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
393         if (rebalance)
394                 ____rb_erase_color(rebalance, root, dummy_rotate);
395 }
396 
397 /*
398  * Augmented rbtree manipulation functions.
399  *
400  * This instantiates the same __always_inline functions as in the non-augmented
401  * case, but this time with user-defined callbacks.
402  */
403 
404 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
405         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
406 {
407         __rb_insert(node, root, augment_rotate);
408 }
409 
410 /*
411  * This function returns the first node (in sort order) of the tree.
412  */
413 struct rb_node *rb_first(const struct rb_root *root)
414 {
415         struct rb_node  *n;
416 
417         n = root->rb_node;
418         if (!n)
419                 return NULL;
420         while (n->rb_left)
421                 n = n->rb_left;
422         return n;
423 }
424 
425 struct rb_node *rb_last(const struct rb_root *root)
426 {
427         struct rb_node  *n;
428 
429         n = root->rb_node;
430         if (!n)
431                 return NULL;
432         while (n->rb_right)
433                 n = n->rb_right;
434         return n;
435 }
436 
437 struct rb_node *rb_next(const struct rb_node *node)
438 {
439         struct rb_node *parent;
440 
441         if (RB_EMPTY_NODE(node))
442                 return NULL;
443 
444         /*
445          * If we have a right-hand child, go down and then left as far
446          * as we can.
447          */
448         if (node->rb_right) {
449                 node = node->rb_right;
450                 while (node->rb_left)
451                         node=node->rb_left;
452                 return (struct rb_node *)node;
453         }
454 
455         /*
456          * No right-hand children. Everything down and left is smaller than us,
457          * so any 'next' node must be in the general direction of our parent.
458          * Go up the tree; any time the ancestor is a right-hand child of its
459          * parent, keep going up. First time it's a left-hand child of its
460          * parent, said parent is our 'next' node.
461          */
462         while ((parent = rb_parent(node)) && node == parent->rb_right)
463                 node = parent;
464 
465         return parent;
466 }
467 
468 struct rb_node *rb_prev(const struct rb_node *node)
469 {
470         struct rb_node *parent;
471 
472         if (RB_EMPTY_NODE(node))
473                 return NULL;
474 
475         /*
476          * If we have a left-hand child, go down and then right as far
477          * as we can.
478          */
479         if (node->rb_left) {
480                 node = node->rb_left;
481                 while (node->rb_right)
482                         node=node->rb_right;
483                 return (struct rb_node *)node;
484         }
485 
486         /*
487          * No left-hand children. Go up till we find an ancestor which
488          * is a right-hand child of its parent.
489          */
490         while ((parent = rb_parent(node)) && node == parent->rb_left)
491                 node = parent;
492 
493         return parent;
494 }
495 
496 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
497                      struct rb_root *root)
498 {
499         struct rb_node *parent = rb_parent(victim);
500 
501         /* Set the surrounding nodes to point to the replacement */
502         __rb_change_child(victim, new, parent, root);
503         if (victim->rb_left)
504                 rb_set_parent(victim->rb_left, new);
505         if (victim->rb_right)
506                 rb_set_parent(victim->rb_right, new);
507 
508         /* Copy the pointers/colour from the victim to the replacement */
509         *new = *victim;
510 }
511 
512 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
513 {
514         for (;;) {
515                 if (node->rb_left)
516                         node = node->rb_left;
517                 else if (node->rb_right)
518                         node = node->rb_right;
519                 else
520                         return (struct rb_node *)node;
521         }
522 }
523 
524 struct rb_node *rb_next_postorder(const struct rb_node *node)
525 {
526         const struct rb_node *parent;
527         if (!node)
528                 return NULL;
529         parent = rb_parent(node);
530 
531         /* If we're sitting on node, we've already seen our children */
532         if (parent && node == parent->rb_left && parent->rb_right) {
533                 /* If we are the parent's left node, go to the parent's right
534                  * node then all the way down to the left */
535                 return rb_left_deepest_node(parent->rb_right);
536         } else
537                 /* Otherwise we are the parent's right node, and the parent
538                  * should be next */
539                 return (struct rb_node *)parent;
540 }
541 
542 struct rb_node *rb_first_postorder(const struct rb_root *root)
543 {
544         if (!root->rb_node)
545                 return NULL;
546 
547         return rb_left_deepest_node(root->rb_node);
548 }
549 

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