| blob | 0ef40a46b3664304eb561bf0bcdf66f30e11becd |
1 /* $NetBSD: tree.h,v 1.1.1.1 2013/04/11 16:43:33 christos Exp $ */
2 /* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $ */
3 /*
4 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 */
28 #ifndef _SYS_TREE_H_
29 #define _SYS_TREE_H_
31 /*
32 * This file defines data structures for different types of trees:
33 * splay trees and red-black trees.
34 *
35 * A splay tree is a self-organizing data structure. Every operation
36 * on the tree causes a splay to happen. The splay moves the requested
37 * node to the root of the tree and partly rebalances it.
38 *
39 * This has the benefit that request locality causes faster lookups as
40 * the requested nodes move to the top of the tree. On the other hand,
41 * every lookup causes memory writes.
42 *
43 * The Balance Theorem bounds the total access time for m operations
44 * and n inserts on an initially empty tree as O((m + n)lg n). The
45 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
46 *
47 * A red-black tree is a binary search tree with the node color as an
48 * extra attribute. It fulfills a set of conditions:
49 * - every search path from the root to a leaf consists of the
50 * same number of black nodes,
51 * - each red node (except for the root) has a black parent,
52 * - each leaf node is black.
53 *
54 * Every operation on a red-black tree is bounded as O(lg n).
55 * The maximum height of a red-black tree is 2lg (n+1).
56 */
58 #define SPLAY_HEAD(name, type) \
59 struct name { \
61 }
63 #define SPLAY_INITIALIZER(root) \
64 { NULL }
66 #define SPLAY_INIT(root) do { \
67 (root)->sph_root = NULL; \
68 } while (0)
70 #define SPLAY_ENTRY(type) \
71 struct { \
74 }
76 #define SPLAY_LEFT(elm, field) (elm)->field.spe_left
77 #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
78 #define SPLAY_ROOT(head) (head)->sph_root
79 #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)
81 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
82 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \
83 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
84 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
85 (head)->sph_root = tmp; \
86 } while (0)
88 #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \
89 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
90 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
91 (head)->sph_root = tmp; \
92 } while (0)
94 #define SPLAY_LINKLEFT(head, tmp, field) do { \
95 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
96 tmp = (head)->sph_root; \
97 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
98 } while (0)
100 #define SPLAY_LINKRIGHT(head, tmp, field) do { \
101 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
102 tmp = (head)->sph_root; \
103 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
104 } while (0)
106 #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \
107 SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
108 SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
109 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
110 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
111 } while (0)
113 /* Generates prototypes and inline functions */
115 #define SPLAY_PROTOTYPE(name, type, field, cmp) \
116 void name##_SPLAY(struct name *, struct type *); \
117 void name##_SPLAY_MINMAX(struct name *, int); \
118 struct type *name##_SPLAY_INSERT(struct name *, struct type *); \
119 struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \
120 \
122 static __inline struct type * \
123 name##_SPLAY_FIND(struct name *head, struct type *elm) \
124 { \
125 if (SPLAY_EMPTY(head)) \
126 return(NULL); \
127 name##_SPLAY(head, elm); \
128 if ((cmp)(elm, (head)->sph_root) == 0) \
129 return (head->sph_root); \
130 return (NULL); \
131 } \
132 \
133 static __inline struct type * \
134 name##_SPLAY_NEXT(struct name *head, struct type *elm) \
135 { \
136 name##_SPLAY(head, elm); \
137 if (SPLAY_RIGHT(elm, field) != NULL) { \
138 elm = SPLAY_RIGHT(elm, field); \
139 while (SPLAY_LEFT(elm, field) != NULL) { \
140 elm = SPLAY_LEFT(elm, field); \
141 } \
142 } else \
143 elm = NULL; \
144 return (elm); \
145 } \
146 \
147 static __inline struct type * \
148 name##_SPLAY_MIN_MAX(struct name *head, int val) \
149 { \
150 name##_SPLAY_MINMAX(head, val); \
151 return (SPLAY_ROOT(head)); \
152 }
154 /* Main splay operation.
155 * Moves node close to the key of elm to top
156 */
157 #define SPLAY_GENERATE(name, type, field, cmp) \
158 struct type * \
159 name##_SPLAY_INSERT(struct name *head, struct type *elm) \
160 { \
161 if (SPLAY_EMPTY(head)) { \
162 SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
163 } else { \
164 int __comp; \
165 name##_SPLAY(head, elm); \
166 __comp = (cmp)(elm, (head)->sph_root); \
167 if(__comp < 0) { \
168 SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
169 SPLAY_RIGHT(elm, field) = (head)->sph_root; \
170 SPLAY_LEFT((head)->sph_root, field) = NULL; \
171 } else if (__comp > 0) { \
172 SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
173 SPLAY_LEFT(elm, field) = (head)->sph_root; \
174 SPLAY_RIGHT((head)->sph_root, field) = NULL; \
175 } else \
176 return ((head)->sph_root); \
177 } \
178 (head)->sph_root = (elm); \
179 return (NULL); \
180 } \
181 \
182 struct type * \
183 name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
184 { \
185 struct type *__tmp; \
186 if (SPLAY_EMPTY(head)) \
187 return (NULL); \
188 name##_SPLAY(head, elm); \
189 if ((cmp)(elm, (head)->sph_root) == 0) { \
190 if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \
191 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
192 } else { \
193 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
194 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
195 name##_SPLAY(head, elm); \
196 SPLAY_RIGHT((head)->sph_root, field) = __tmp; \
197 } \
198 return (elm); \
199 } \
200 return (NULL); \
201 } \
202 \
203 void \
204 name##_SPLAY(struct name *head, struct type *elm) \
205 { \
206 struct type __node, *__left, *__right, *__tmp; \
207 int __comp; \
208 \
209 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
210 __left = __right = &__node; \
211 \
212 while ((__comp = (cmp)(elm, (head)->sph_root))) { \
213 if (__comp < 0) { \
214 __tmp = SPLAY_LEFT((head)->sph_root, field); \
215 if (__tmp == NULL) \
216 break; \
217 if ((cmp)(elm, __tmp) < 0){ \
218 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
219 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
220 break; \
221 } \
222 SPLAY_LINKLEFT(head, __right, field); \
223 } else if (__comp > 0) { \
224 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
225 if (__tmp == NULL) \
226 break; \
227 if ((cmp)(elm, __tmp) > 0){ \
228 SPLAY_ROTATE_LEFT(head, __tmp, field); \
229 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
230 break; \
231 } \
232 SPLAY_LINKRIGHT(head, __left, field); \
233 } \
234 } \
235 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
236 } \
237 \
238 /* Splay with either the minimum or the maximum element \
239 * Used to find minimum or maximum element in tree. \
241 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
242 { \
243 struct type __node, *__left, *__right, *__tmp; \
244 \
245 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
246 __left = __right = &__node; \
247 \
248 while (1) { \
249 if (__comp < 0) { \
250 __tmp = SPLAY_LEFT((head)->sph_root, field); \
251 if (__tmp == NULL) \
252 break; \
253 if (__comp < 0){ \
254 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
255 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
256 break; \
257 } \
258 SPLAY_LINKLEFT(head, __right, field); \
259 } else if (__comp > 0) { \
260 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
261 if (__tmp == NULL) \
262 break; \
263 if (__comp > 0) { \
264 SPLAY_ROTATE_LEFT(head, __tmp, field); \
265 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
266 break; \
267 } \
268 SPLAY_LINKRIGHT(head, __left, field); \
269 } \
270 } \
271 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
272 }
274 #define SPLAY_NEGINF -1
275 #define SPLAY_INF 1
277 #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
278 #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
279 #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
280 #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
281 #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \
282 : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
283 #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \
284 : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
286 #define SPLAY_FOREACH(x, name, head) \
287 for ((x) = SPLAY_MIN(name, head); \
288 (x) != NULL; \
289 (x) = SPLAY_NEXT(name, head, x))
291 /* Macros that define a red-back tree */
292 #define RB_HEAD(name, type) \
293 struct name { \
295 }
297 #define RB_INITIALIZER(root) \
298 { NULL }
300 #define RB_INIT(root) do { \
301 (root)->rbh_root = NULL; \
302 } while (0)
304 #define RB_BLACK 0
305 #define RB_RED 1
306 #define RB_ENTRY(type) \
307 struct { \
312 }
314 #define RB_LEFT(elm, field) (elm)->field.rbe_left
315 #define RB_RIGHT(elm, field) (elm)->field.rbe_right
316 #define RB_PARENT(elm, field) (elm)->field.rbe_parent
317 #define RB_COLOR(elm, field) (elm)->field.rbe_color
318 #define RB_ROOT(head) (head)->rbh_root
319 #define RB_EMPTY(head) (RB_ROOT(head) == NULL)
321 #define RB_SET(elm, parent, field) do { \
322 RB_PARENT(elm, field) = parent; \
323 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
324 RB_COLOR(elm, field) = RB_RED; \
325 } while (0)
327 #define RB_SET_BLACKRED(black, red, field) do { \
328 RB_COLOR(black, field) = RB_BLACK; \
329 RB_COLOR(red, field) = RB_RED; \
330 } while (0)
332 #ifndef RB_AUGMENT
333 #define RB_AUGMENT(x)
334 #endif
336 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
337 (tmp) = RB_RIGHT(elm, field); \
338 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) { \
339 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
340 } \
341 RB_AUGMENT(elm); \
342 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) { \
343 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
344 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
345 else \
346 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
347 } else \
348 (head)->rbh_root = (tmp); \
349 RB_LEFT(tmp, field) = (elm); \
350 RB_PARENT(elm, field) = (tmp); \
351 RB_AUGMENT(tmp); \
352 if ((RB_PARENT(tmp, field))) \
353 RB_AUGMENT(RB_PARENT(tmp, field)); \
354 } while (0)
356 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
357 (tmp) = RB_LEFT(elm, field); \
358 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) { \
359 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
360 } \
361 RB_AUGMENT(elm); \
362 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) { \
363 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
364 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
365 else \
366 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
367 } else \
368 (head)->rbh_root = (tmp); \
369 RB_RIGHT(tmp, field) = (elm); \
370 RB_PARENT(elm, field) = (tmp); \
371 RB_AUGMENT(tmp); \
372 if ((RB_PARENT(tmp, field))) \
373 RB_AUGMENT(RB_PARENT(tmp, field)); \
374 } while (0)
376 /* Generates prototypes and inline functions */
377 #define RB_PROTOTYPE(name, type, field, cmp) \
378 void name##_RB_INSERT_COLOR(struct name *, struct type *); \
379 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
380 struct type *name##_RB_REMOVE(struct name *, struct type *); \
381 struct type *name##_RB_INSERT(struct name *, struct type *); \
382 struct type *name##_RB_FIND(struct name *, struct type *); \
383 struct type *name##_RB_NEXT(struct type *); \
384 struct type *name##_RB_MINMAX(struct name *, int); \
385 \
387 /* Main rb operation.
388 * Moves node close to the key of elm to top
389 */
390 #define RB_GENERATE(name, type, field, cmp) \
391 void \
392 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
393 { \
394 struct type *parent, *gparent, *tmp; \
395 while ((parent = RB_PARENT(elm, field)) && \
396 RB_COLOR(parent, field) == RB_RED) { \
397 gparent = RB_PARENT(parent, field); \
398 if (parent == RB_LEFT(gparent, field)) { \
399 tmp = RB_RIGHT(gparent, field); \
400 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
401 RB_COLOR(tmp, field) = RB_BLACK; \
402 RB_SET_BLACKRED(parent, gparent, field);\
403 elm = gparent; \
404 continue; \
405 } \
406 if (RB_RIGHT(parent, field) == elm) { \
407 RB_ROTATE_LEFT(head, parent, tmp, field);\
408 tmp = parent; \
409 parent = elm; \
410 elm = tmp; \
411 } \
412 RB_SET_BLACKRED(parent, gparent, field); \
413 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
414 } else { \
415 tmp = RB_LEFT(gparent, field); \
416 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
417 RB_COLOR(tmp, field) = RB_BLACK; \
418 RB_SET_BLACKRED(parent, gparent, field);\
419 elm = gparent; \
420 continue; \
421 } \
422 if (RB_LEFT(parent, field) == elm) { \
423 RB_ROTATE_RIGHT(head, parent, tmp, field);\
424 tmp = parent; \
425 parent = elm; \
426 elm = tmp; \
427 } \
428 RB_SET_BLACKRED(parent, gparent, field); \
429 RB_ROTATE_LEFT(head, gparent, tmp, field); \
430 } \
431 } \
432 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
433 } \
434 \
435 void \
436 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
437 { \
438 struct type *tmp; \
439 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
440 elm != RB_ROOT(head)) { \
441 if (RB_LEFT(parent, field) == elm) { \
442 tmp = RB_RIGHT(parent, field); \
443 if (RB_COLOR(tmp, field) == RB_RED) { \
444 RB_SET_BLACKRED(tmp, parent, field); \
445 RB_ROTATE_LEFT(head, parent, tmp, field);\
446 tmp = RB_RIGHT(parent, field); \
447 } \
448 if ((RB_LEFT(tmp, field) == NULL || \
449 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
450 (RB_RIGHT(tmp, field) == NULL || \
451 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
452 RB_COLOR(tmp, field) = RB_RED; \
453 elm = parent; \
454 parent = RB_PARENT(elm, field); \
455 } else { \
456 if (RB_RIGHT(tmp, field) == NULL || \
457 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
458 struct type *oleft; \
459 if ((oleft = RB_LEFT(tmp, field)))\
460 RB_COLOR(oleft, field) = RB_BLACK;\
461 RB_COLOR(tmp, field) = RB_RED; \
462 RB_ROTATE_RIGHT(head, tmp, oleft, field);\
463 tmp = RB_RIGHT(parent, field); \
464 } \
465 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
466 RB_COLOR(parent, field) = RB_BLACK; \
467 if (RB_RIGHT(tmp, field)) \
468 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
469 RB_ROTATE_LEFT(head, parent, tmp, field);\
470 elm = RB_ROOT(head); \
471 break; \
472 } \
473 } else { \
474 tmp = RB_LEFT(parent, field); \
475 if (RB_COLOR(tmp, field) == RB_RED) { \
476 RB_SET_BLACKRED(tmp, parent, field); \
477 RB_ROTATE_RIGHT(head, parent, tmp, field);\
478 tmp = RB_LEFT(parent, field); \
479 } \
480 if ((RB_LEFT(tmp, field) == NULL || \
481 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
482 (RB_RIGHT(tmp, field) == NULL || \
483 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
484 RB_COLOR(tmp, field) = RB_RED; \
485 elm = parent; \
486 parent = RB_PARENT(elm, field); \
487 } else { \
488 if (RB_LEFT(tmp, field) == NULL || \
489 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
490 struct type *oright; \
491 if ((oright = RB_RIGHT(tmp, field)))\
492 RB_COLOR(oright, field) = RB_BLACK;\
493 RB_COLOR(tmp, field) = RB_RED; \
494 RB_ROTATE_LEFT(head, tmp, oright, field);\
495 tmp = RB_LEFT(parent, field); \
496 } \
497 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
498 RB_COLOR(parent, field) = RB_BLACK; \
499 if (RB_LEFT(tmp, field)) \
500 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
501 RB_ROTATE_RIGHT(head, parent, tmp, field);\
502 elm = RB_ROOT(head); \
503 break; \
504 } \
505 } \
506 } \
507 if (elm) \
508 RB_COLOR(elm, field) = RB_BLACK; \
509 } \
510 \
511 struct type * \
512 name##_RB_REMOVE(struct name *head, struct type *elm) \
513 { \
514 struct type *child, *parent, *old = elm; \
515 int color; \
516 if (RB_LEFT(elm, field) == NULL) \
517 child = RB_RIGHT(elm, field); \
518 else if (RB_RIGHT(elm, field) == NULL) \
519 child = RB_LEFT(elm, field); \
520 else { \
521 struct type *left; \
522 elm = RB_RIGHT(elm, field); \
523 while ((left = RB_LEFT(elm, field))) \
524 elm = left; \
525 child = RB_RIGHT(elm, field); \
526 parent = RB_PARENT(elm, field); \
527 color = RB_COLOR(elm, field); \
528 if (child) \
529 RB_PARENT(child, field) = parent; \
530 if (parent) { \
531 if (RB_LEFT(parent, field) == elm) \
532 RB_LEFT(parent, field) = child; \
533 else \
534 RB_RIGHT(parent, field) = child; \
535 RB_AUGMENT(parent); \
536 } else \
537 RB_ROOT(head) = child; \
538 if (RB_PARENT(elm, field) == old) \
539 parent = elm; \
540 (elm)->field = (old)->field; \
541 if (RB_PARENT(old, field)) { \
542 if (RB_LEFT(RB_PARENT(old, field), field) == old)\
543 RB_LEFT(RB_PARENT(old, field), field) = elm;\
544 else \
545 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
546 RB_AUGMENT(RB_PARENT(old, field)); \
547 } else \
548 RB_ROOT(head) = elm; \
549 RB_PARENT(RB_LEFT(old, field), field) = elm; \
550 if (RB_RIGHT(old, field)) \
551 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
552 if (parent) { \
553 left = parent; \
554 do { \
555 RB_AUGMENT(left); \
556 } while ((left = RB_PARENT(left, field))); \
557 } \
558 goto color; \
559 } \
560 parent = RB_PARENT(elm, field); \
561 color = RB_COLOR(elm, field); \
562 if (child) \
563 RB_PARENT(child, field) = parent; \
564 if (parent) { \
565 if (RB_LEFT(parent, field) == elm) \
566 RB_LEFT(parent, field) = child; \
567 else \
568 RB_RIGHT(parent, field) = child; \
569 RB_AUGMENT(parent); \
570 } else \
571 RB_ROOT(head) = child; \
572 color: \
573 if (color == RB_BLACK) \
574 name##_RB_REMOVE_COLOR(head, parent, child); \
575 return (old); \
576 } \
577 \
579 struct type * \
580 name##_RB_INSERT(struct name *head, struct type *elm) \
581 { \
582 struct type *tmp; \
583 struct type *parent = NULL; \
584 int comp = 0; \
585 tmp = RB_ROOT(head); \
586 while (tmp) { \
587 parent = tmp; \
588 comp = (cmp)(elm, parent); \
589 if (comp < 0) \
590 tmp = RB_LEFT(tmp, field); \
591 else if (comp > 0) \
592 tmp = RB_RIGHT(tmp, field); \
593 else \
594 return (tmp); \
595 } \
596 RB_SET(elm, parent, field); \
597 if (parent != NULL) { \
598 if (comp < 0) \
599 RB_LEFT(parent, field) = elm; \
600 else \
601 RB_RIGHT(parent, field) = elm; \
602 RB_AUGMENT(parent); \
603 } else \
604 RB_ROOT(head) = elm; \
605 name##_RB_INSERT_COLOR(head, elm); \
606 return (NULL); \
607 } \
608 \
610 struct type * \
611 name##_RB_FIND(struct name *head, struct type *elm) \
612 { \
613 struct type *tmp = RB_ROOT(head); \
614 int comp; \
615 while (tmp) { \
616 comp = cmp(elm, tmp); \
617 if (comp < 0) \
618 tmp = RB_LEFT(tmp, field); \
619 else if (comp > 0) \
620 tmp = RB_RIGHT(tmp, field); \
621 else \
622 return (tmp); \
623 } \
624 return (NULL); \
625 } \
626 \
627 struct type * \
628 name##_RB_NEXT(struct type *elm) \
629 { \
630 if (RB_RIGHT(elm, field)) { \
631 elm = RB_RIGHT(elm, field); \
632 while (RB_LEFT(elm, field)) \
633 elm = RB_LEFT(elm, field); \
634 } else { \
635 if (RB_PARENT(elm, field) && \
636 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
637 elm = RB_PARENT(elm, field); \
638 else { \
639 while (RB_PARENT(elm, field) && \
640 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
641 elm = RB_PARENT(elm, field); \
642 elm = RB_PARENT(elm, field); \
643 } \
644 } \
645 return (elm); \
646 } \
647 \
648 struct type * \
649 name##_RB_MINMAX(struct name *head, int val) \
650 { \
651 struct type *tmp = RB_ROOT(head); \
652 struct type *parent = NULL; \
653 while (tmp) { \
654 parent = tmp; \
655 if (val < 0) \
656 tmp = RB_LEFT(tmp, field); \
657 else \
658 tmp = RB_RIGHT(tmp, field); \
659 } \
660 return (parent); \
661 }
663 #define RB_NEGINF -1
664 #define RB_INF 1
666 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
667 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
668 #define RB_FIND(name, x, y) name##_RB_FIND(x, y)
669 #define RB_NEXT(name, x, y) name##_RB_NEXT(y)
670 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
671 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
673 #define RB_FOREACH(x, name, head) \
674 for ((x) = RB_MIN(name, head); \
675 (x) != NULL; \
676 (x) = name##_RB_NEXT(x))
679 /* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $ */
680 /*
681 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
682 * All rights reserved.
683 *
684 * Redistribution and use in source and binary forms, with or without
685 * modification, are permitted provided that the following conditions
686 * are met:
687 * 1. Redistributions of source code must retain the above copyright
688 * notice, this list of conditions and the following disclaimer.
689 * 2. Redistributions in binary form must reproduce the above copyright
690 * notice, this list of conditions and the following disclaimer in the
691 * documentation and/or other materials provided with the distribution.
692 *
693 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
694 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
695 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
696 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
697 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
698 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
699 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
700 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
701 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
702 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
703 */
705 #ifndef _SYS_TREE_H_
706 #define _SYS_TREE_H_
708 /*
709 * This file defines data structures for different types of trees:
710 * splay trees and red-black trees.
711 *
712 * A splay tree is a self-organizing data structure. Every operation
713 * on the tree causes a splay to happen. The splay moves the requested
714 * node to the root of the tree and partly rebalances it.
715 *
716 * This has the benefit that request locality causes faster lookups as
717 * the requested nodes move to the top of the tree. On the other hand,
718 * every lookup causes memory writes.
719 *
720 * The Balance Theorem bounds the total access time for m operations
721 * and n inserts on an initially empty tree as O((m + n)lg n). The
722 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
723 *
724 * A red-black tree is a binary search tree with the node color as an
725 * extra attribute. It fulfills a set of conditions:
726 * - every search path from the root to a leaf consists of the
727 * same number of black nodes,
728 * - each red node (except for the root) has a black parent,
729 * - each leaf node is black.
730 *
731 * Every operation on a red-black tree is bounded as O(lg n).
732 * The maximum height of a red-black tree is 2lg (n+1).
733 */
735 #define SPLAY_HEAD(name, type) \
736 struct name { \
738 }
740 #define SPLAY_INITIALIZER(root) \
741 { NULL }
743 #define SPLAY_INIT(root) do { \
744 (root)->sph_root = NULL; \
745 } while (0)
747 #define SPLAY_ENTRY(type) \
748 struct { \
751 }
753 #define SPLAY_LEFT(elm, field) (elm)->field.spe_left
754 #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
755 #define SPLAY_ROOT(head) (head)->sph_root
756 #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)
758 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
759 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \
760 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
761 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
762 (head)->sph_root = tmp; \
763 } while (0)
765 #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \
766 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
767 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
768 (head)->sph_root = tmp; \
769 } while (0)
771 #define SPLAY_LINKLEFT(head, tmp, field) do { \
772 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
773 tmp = (head)->sph_root; \
774 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
775 } while (0)
777 #define SPLAY_LINKRIGHT(head, tmp, field) do { \
778 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
779 tmp = (head)->sph_root; \
780 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
781 } while (0)
783 #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \
784 SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
785 SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
786 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
787 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
788 } while (0)
790 /* Generates prototypes and inline functions */
792 #define SPLAY_PROTOTYPE(name, type, field, cmp) \
793 void name##_SPLAY(struct name *, struct type *); \
794 void name##_SPLAY_MINMAX(struct name *, int); \
795 struct type *name##_SPLAY_INSERT(struct name *, struct type *); \
796 struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \
797 \
799 static __inline struct type * \
800 name##_SPLAY_FIND(struct name *head, struct type *elm) \
801 { \
802 if (SPLAY_EMPTY(head)) \
803 return(NULL); \
804 name##_SPLAY(head, elm); \
805 if ((cmp)(elm, (head)->sph_root) == 0) \
806 return (head->sph_root); \
807 return (NULL); \
808 } \
809 \
810 static __inline struct type * \
811 name##_SPLAY_NEXT(struct name *head, struct type *elm) \
812 { \
813 name##_SPLAY(head, elm); \
814 if (SPLAY_RIGHT(elm, field) != NULL) { \
815 elm = SPLAY_RIGHT(elm, field); \
816 while (SPLAY_LEFT(elm, field) != NULL) { \
817 elm = SPLAY_LEFT(elm, field); \
818 } \
819 } else \
820 elm = NULL; \
821 return (elm); \
822 } \
823 \
824 static __inline struct type * \
825 name##_SPLAY_MIN_MAX(struct name *head, int val) \
826 { \
827 name##_SPLAY_MINMAX(head, val); \
828 return (SPLAY_ROOT(head)); \
829 }
831 /* Main splay operation.
832 * Moves node close to the key of elm to top
833 */
834 #define SPLAY_GENERATE(name, type, field, cmp) \
835 struct type * \
836 name##_SPLAY_INSERT(struct name *head, struct type *elm) \
837 { \
838 if (SPLAY_EMPTY(head)) { \
839 SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
840 } else { \
841 int __comp; \
842 name##_SPLAY(head, elm); \
843 __comp = (cmp)(elm, (head)->sph_root); \
844 if(__comp < 0) { \
845 SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
846 SPLAY_RIGHT(elm, field) = (head)->sph_root; \
847 SPLAY_LEFT((head)->sph_root, field) = NULL; \
848 } else if (__comp > 0) { \
849 SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
850 SPLAY_LEFT(elm, field) = (head)->sph_root; \
851 SPLAY_RIGHT((head)->sph_root, field) = NULL; \
852 } else \
853 return ((head)->sph_root); \
854 } \
855 (head)->sph_root = (elm); \
856 return (NULL); \
857 } \
858 \
859 struct type * \
860 name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
861 { \
862 struct type *__tmp; \
863 if (SPLAY_EMPTY(head)) \
864 return (NULL); \
865 name##_SPLAY(head, elm); \
866 if ((cmp)(elm, (head)->sph_root) == 0) { \
867 if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \
868 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
869 } else { \
870 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
871 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
872 name##_SPLAY(head, elm); \
873 SPLAY_RIGHT((head)->sph_root, field) = __tmp; \
874 } \
875 return (elm); \
876 } \
877 return (NULL); \
878 } \
879 \
880 void \
881 name##_SPLAY(struct name *head, struct type *elm) \
882 { \
883 struct type __node, *__left, *__right, *__tmp; \
884 int __comp; \
885 \
886 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
887 __left = __right = &__node; \
888 \
889 while ((__comp = (cmp)(elm, (head)->sph_root))) { \
890 if (__comp < 0) { \
891 __tmp = SPLAY_LEFT((head)->sph_root, field); \
892 if (__tmp == NULL) \
893 break; \
894 if ((cmp)(elm, __tmp) < 0){ \
895 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
896 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
897 break; \
898 } \
899 SPLAY_LINKLEFT(head, __right, field); \
900 } else if (__comp > 0) { \
901 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
902 if (__tmp == NULL) \
903 break; \
904 if ((cmp)(elm, __tmp) > 0){ \
905 SPLAY_ROTATE_LEFT(head, __tmp, field); \
906 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
907 break; \
908 } \
909 SPLAY_LINKRIGHT(head, __left, field); \
910 } \
911 } \
912 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
913 } \
914 \
915 /* Splay with either the minimum or the maximum element \
916 * Used to find minimum or maximum element in tree. \
918 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
919 { \
920 struct type __node, *__left, *__right, *__tmp; \
921 \
922 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
923 __left = __right = &__node; \
924 \
925 while (1) { \
926 if (__comp < 0) { \
927 __tmp = SPLAY_LEFT((head)->sph_root, field); \
928 if (__tmp == NULL) \
929 break; \
930 if (__comp < 0){ \
931 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
932 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
933 break; \
934 } \
935 SPLAY_LINKLEFT(head, __right, field); \
936 } else if (__comp > 0) { \
937 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
938 if (__tmp == NULL) \
939 break; \
940 if (__comp > 0) { \
941 SPLAY_ROTATE_LEFT(head, __tmp, field); \
942 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
943 break; \
944 } \
945 SPLAY_LINKRIGHT(head, __left, field); \
946 } \
947 } \
948 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
949 }
951 #define SPLAY_NEGINF -1
952 #define SPLAY_INF 1
954 #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
955 #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
956 #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
957 #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
958 #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \
959 : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
960 #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \
961 : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
963 #define SPLAY_FOREACH(x, name, head) \
964 for ((x) = SPLAY_MIN(name, head); \
965 (x) != NULL; \
966 (x) = SPLAY_NEXT(name, head, x))
968 /* Macros that define a red-back tree */
969 #define RB_HEAD(name, type) \
970 struct name { \
972 }
974 #define RB_INITIALIZER(root) \
975 { NULL }
977 #define RB_INIT(root) do { \
978 (root)->rbh_root = NULL; \
979 } while (0)
981 #define RB_BLACK 0
982 #define RB_RED 1
983 #define RB_ENTRY(type) \
984 struct { \
989 }
991 #define RB_LEFT(elm, field) (elm)->field.rbe_left
992 #define RB_RIGHT(elm, field) (elm)->field.rbe_right
993 #define RB_PARENT(elm, field) (elm)->field.rbe_parent
994 #define RB_COLOR(elm, field) (elm)->field.rbe_color
995 #define RB_ROOT(head) (head)->rbh_root
996 #define RB_EMPTY(head) (RB_ROOT(head) == NULL)
998 #define RB_SET(elm, parent, field) do { \
999 RB_PARENT(elm, field) = parent; \
1000 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
1001 RB_COLOR(elm, field) = RB_RED; \
1002 } while (0)
1004 #define RB_SET_BLACKRED(black, red, field) do { \
1005 RB_COLOR(black, field) = RB_BLACK; \
1006 RB_COLOR(red, field) = RB_RED; \
1007 } while (0)
1009 #ifndef RB_AUGMENT
1010 #define RB_AUGMENT(x)
1011 #endif
1013 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
1014 (tmp) = RB_RIGHT(elm, field); \
1015 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) { \
1016 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
1017 } \
1018 RB_AUGMENT(elm); \
1019 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) { \
1020 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
1021 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
1022 else \
1023 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
1024 } else \
1025 (head)->rbh_root = (tmp); \
1026 RB_LEFT(tmp, field) = (elm); \
1027 RB_PARENT(elm, field) = (tmp); \
1028 RB_AUGMENT(tmp); \
1029 if ((RB_PARENT(tmp, field))) \
1030 RB_AUGMENT(RB_PARENT(tmp, field)); \
1031 } while (0)
1033 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
1034 (tmp) = RB_LEFT(elm, field); \
1035 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) { \
1036 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
1037 } \
1038 RB_AUGMENT(elm); \
1039 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) { \
1040 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
1041 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
1042 else \
1043 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
1044 } else \
1045 (head)->rbh_root = (tmp); \
1046 RB_RIGHT(tmp, field) = (elm); \
1047 RB_PARENT(elm, field) = (tmp); \
1048 RB_AUGMENT(tmp); \
1049 if ((RB_PARENT(tmp, field))) \
1050 RB_AUGMENT(RB_PARENT(tmp, field)); \
1051 } while (0)
1053 /* Generates prototypes and inline functions */
1054 #define RB_PROTOTYPE(name, type, field, cmp) \
1055 void name##_RB_INSERT_COLOR(struct name *, struct type *); \
1056 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
1057 struct type *name##_RB_REMOVE(struct name *, struct type *); \
1058 struct type *name##_RB_INSERT(struct name *, struct type *); \
1059 struct type *name##_RB_FIND(struct name *, struct type *); \
1060 struct type *name##_RB_NEXT(struct type *); \
1061 struct type *name##_RB_MINMAX(struct name *, int); \
1062 \
1064 /* Main rb operation.
1065 * Moves node close to the key of elm to top
1066 */
1067 #define RB_GENERATE(name, type, field, cmp) \
1068 void \
1069 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
1070 { \
1071 struct type *parent, *gparent, *tmp; \
1072 while ((parent = RB_PARENT(elm, field)) && \
1073 RB_COLOR(parent, field) == RB_RED) { \
1074 gparent = RB_PARENT(parent, field); \
1075 if (parent == RB_LEFT(gparent, field)) { \
1076 tmp = RB_RIGHT(gparent, field); \
1077 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
1078 RB_COLOR(tmp, field) = RB_BLACK; \
1079 RB_SET_BLACKRED(parent, gparent, field);\
1080 elm = gparent; \
1081 continue; \
1082 } \
1083 if (RB_RIGHT(parent, field) == elm) { \
1084 RB_ROTATE_LEFT(head, parent, tmp, field);\
1085 tmp = parent; \
1086 parent = elm; \
1087 elm = tmp; \
1088 } \
1089 RB_SET_BLACKRED(parent, gparent, field); \
1090 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
1091 } else { \
1092 tmp = RB_LEFT(gparent, field); \
1093 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
1094 RB_COLOR(tmp, field) = RB_BLACK; \
1095 RB_SET_BLACKRED(parent, gparent, field);\
1096 elm = gparent; \
1097 continue; \
1098 } \
1099 if (RB_LEFT(parent, field) == elm) { \
1100 RB_ROTATE_RIGHT(head, parent, tmp, field);\
1101 tmp = parent; \
1102 parent = elm; \
1103 elm = tmp; \
1104 } \
1105 RB_SET_BLACKRED(parent, gparent, field); \
1106 RB_ROTATE_LEFT(head, gparent, tmp, field); \
1107 } \
1108 } \
1109 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
1110 } \
1111 \
1112 void \
1113 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
1114 { \
1115 struct type *tmp; \
1116 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
1117 elm != RB_ROOT(head)) { \
1118 if (RB_LEFT(parent, field) == elm) { \
1119 tmp = RB_RIGHT(parent, field); \
1120 if (RB_COLOR(tmp, field) == RB_RED) { \
1121 RB_SET_BLACKRED(tmp, parent, field); \
1122 RB_ROTATE_LEFT(head, parent, tmp, field);\
1123 tmp = RB_RIGHT(parent, field); \
1124 } \
1125 if ((RB_LEFT(tmp, field) == NULL || \
1126 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
1127 (RB_RIGHT(tmp, field) == NULL || \
1128 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
1129 RB_COLOR(tmp, field) = RB_RED; \
1130 elm = parent; \
1131 parent = RB_PARENT(elm, field); \
1132 } else { \
1133 if (RB_RIGHT(tmp, field) == NULL || \
1134 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
1135 struct type *oleft; \
1136 if ((oleft = RB_LEFT(tmp, field)))\
1137 RB_COLOR(oleft, field) = RB_BLACK;\
1138 RB_COLOR(tmp, field) = RB_RED; \
1139 RB_ROTATE_RIGHT(head, tmp, oleft, field);\
1140 tmp = RB_RIGHT(parent, field); \
1141 } \
1142 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
1143 RB_COLOR(parent, field) = RB_BLACK; \
1144 if (RB_RIGHT(tmp, field)) \
1145 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
1146 RB_ROTATE_LEFT(head, parent, tmp, field);\
1147 elm = RB_ROOT(head); \
1148 break; \
1149 } \
1150 } else { \
1151 tmp = RB_LEFT(parent, field); \
1152 if (RB_COLOR(tmp, field) == RB_RED) { \
1153 RB_SET_BLACKRED(tmp, parent, field); \
1154 RB_ROTATE_RIGHT(head, parent, tmp, field);\
1155 tmp = RB_LEFT(parent, field); \
1156 } \
1157 if ((RB_LEFT(tmp, field) == NULL || \
1158 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
1159 (RB_RIGHT(tmp, field) == NULL || \
1160 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
1161 RB_COLOR(tmp, field) = RB_RED; \
1162 elm = parent; \
1163 parent = RB_PARENT(elm, field); \
1164 } else { \
1165 if (RB_LEFT(tmp, field) == NULL || \
1166 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
1167 struct type *oright; \
1168 if ((oright = RB_RIGHT(tmp, field)))\
1169 RB_COLOR(oright, field) = RB_BLACK;\
1170 RB_COLOR(tmp, field) = RB_RED; \
1171 RB_ROTATE_LEFT(head, tmp, oright, field);\
1172 tmp = RB_LEFT(parent, field); \
1173 } \
1174 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
1175 RB_COLOR(parent, field) = RB_BLACK; \
1176 if (RB_LEFT(tmp, field)) \
1177 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
1178 RB_ROTATE_RIGHT(head, parent, tmp, field);\
1179 elm = RB_ROOT(head); \
1180 break; \
1181 } \
1182 } \
1183 } \
1184 if (elm) \
1185 RB_COLOR(elm, field) = RB_BLACK; \
1186 } \
1187 \
1188 struct type * \
1189 name##_RB_REMOVE(struct name *head, struct type *elm) \
1190 { \
1191 struct type *child, *parent, *old = elm; \
1192 int color; \
1193 if (RB_LEFT(elm, field) == NULL) \
1194 child = RB_RIGHT(elm, field); \
1195 else if (RB_RIGHT(elm, field) == NULL) \
1196 child = RB_LEFT(elm, field); \
1197 else { \
1198 struct type *left; \
1199 elm = RB_RIGHT(elm, field); \
1200 while ((left = RB_LEFT(elm, field))) \
1201 elm = left; \
1202 child = RB_RIGHT(elm, field); \
1203 parent = RB_PARENT(elm, field); \
1204 color = RB_COLOR(elm, field); \
1205 if (child) \
1206 RB_PARENT(child, field) = parent; \
1207 if (parent) { \
1208 if (RB_LEFT(parent, field) == elm) \
1209 RB_LEFT(parent, field) = child; \
1210 else \
1211 RB_RIGHT(parent, field) = child; \
1212 RB_AUGMENT(parent); \
1213 } else \
1214 RB_ROOT(head) = child; \
1215 if (RB_PARENT(elm, field) == old) \
1216 parent = elm; \
1217 (elm)->field = (old)->field; \
1218 if (RB_PARENT(old, field)) { \
1219 if (RB_LEFT(RB_PARENT(old, field), field) == old)\
1220 RB_LEFT(RB_PARENT(old, field), field) = elm;\
1221 else \
1222 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
1223 RB_AUGMENT(RB_PARENT(old, field)); \
1224 } else \
1225 RB_ROOT(head) = elm; \
1226 RB_PARENT(RB_LEFT(old, field), field) = elm; \
1227 if (RB_RIGHT(old, field)) \
1228 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
1229 if (parent) { \
1230 left = parent; \
1231 do { \
1232 RB_AUGMENT(left); \
1233 } while ((left = RB_PARENT(left, field))); \
1234 } \
1235 goto color; \
1236 } \
1237 parent = RB_PARENT(elm, field); \
1238 color = RB_COLOR(elm, field); \
1239 if (child) \
1240 RB_PARENT(child, field) = parent; \
1241 if (parent) { \
1242 if (RB_LEFT(parent, field) == elm) \
1243 RB_LEFT(parent, field) = child; \
1244 else \
1245 RB_RIGHT(parent, field) = child; \
1246 RB_AUGMENT(parent); \
1247 } else \
1248 RB_ROOT(head) = child; \
1249 color: \
1250 if (color == RB_BLACK) \
1251 name##_RB_REMOVE_COLOR(head, parent, child); \
1252 return (old); \
1253 } \
1254 \
1256 struct type * \
1257 name##_RB_INSERT(struct name *head, struct type *elm) \
1258 { \
1259 struct type *tmp; \
1260 struct type *parent = NULL; \
1261 int comp = 0; \
1262 tmp = RB_ROOT(head); \
1263 while (tmp) { \
1264 parent = tmp; \
1265 comp = (cmp)(elm, parent); \
1266 if (comp < 0) \
1267 tmp = RB_LEFT(tmp, field); \
1268 else if (comp > 0) \
1269 tmp = RB_RIGHT(tmp, field); \
1270 else \
1271 return (tmp); \
1272 } \
1273 RB_SET(elm, parent, field); \
1274 if (parent != NULL) { \
1275 if (comp < 0) \
1276 RB_LEFT(parent, field) = elm; \
1277 else \
1278 RB_RIGHT(parent, field) = elm; \
1279 RB_AUGMENT(parent); \
1280 } else \
1281 RB_ROOT(head) = elm; \
1282 name##_RB_INSERT_COLOR(head, elm); \
1283 return (NULL); \
1284 } \
1285 \
1287 struct type * \
1288 name##_RB_FIND(struct name *head, struct type *elm) \
1289 { \
1290 struct type *tmp = RB_ROOT(head); \
1291 int comp; \
1292 while (tmp) { \
1293 comp = cmp(elm, tmp); \
1294 if (comp < 0) \
1295 tmp = RB_LEFT(tmp, field); \
1296 else if (comp > 0) \
1297 tmp = RB_RIGHT(tmp, field); \
1298 else \
1299 return (tmp); \
1300 } \
1301 return (NULL); \
1302 } \
1303 \
1304 struct type * \
1305 name##_RB_NEXT(struct type *elm) \
1306 { \
1307 if (RB_RIGHT(elm, field)) { \
1308 elm = RB_RIGHT(elm, field); \
1309 while (RB_LEFT(elm, field)) \
1310 elm = RB_LEFT(elm, field); \
1311 } else { \
1312 if (RB_PARENT(elm, field) && \
1313 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
1314 elm = RB_PARENT(elm, field); \
1315 else { \
1316 while (RB_PARENT(elm, field) && \
1317 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
1318 elm = RB_PARENT(elm, field); \
1319 elm = RB_PARENT(elm, field); \
1320 } \
1321 } \
1322 return (elm); \
1323 } \
1324 \
1325 struct type * \
1326 name##_RB_MINMAX(struct name *head, int val) \
1327 { \
1328 struct type *tmp = RB_ROOT(head); \
1329 struct type *parent = NULL; \
1330 while (tmp) { \
1331 parent = tmp; \
1332 if (val < 0) \
1333 tmp = RB_LEFT(tmp, field); \
1334 else \
1335 tmp = RB_RIGHT(tmp, field); \
1336 } \
1337 return (parent); \
1338 }
1340 #define RB_NEGINF -1
1341 #define RB_INF 1
1343 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
1344 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
1345 #define RB_FIND(name, x, y) name##_RB_FIND(x, y)
1346 #define RB_NEXT(name, x, y) name##_RB_NEXT(y)
1347 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
1348 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
1350 #define RB_FOREACH(x, name, head) \
1351 for ((x) = RB_MIN(name, head); \
1352 (x) != NULL; \
1353 (x) = name##_RB_NEXT(x))