1 /* $OpenBSD: tree.h,v 1.9 2004/11/24 18:10:42 tdeval Exp $ */
2 /*
3 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25 */
26
27 #ifndef _SYS_TREE_H_
28 #define _SYS_TREE_H_
29
30 /*
31 * This file defines data structures for different types of trees:
32 * splay trees and red-black trees.
33 *
34 * A splay tree is a self-organizing data structure. Every operation
35 * on the tree causes a splay to happen. The splay moves the requested
36 * node to the root of the tree and partly rebalances it.
37 *
38 * This has the benefit that request locality causes faster lookups as
39 * the requested nodes move to the top of the tree. On the other hand,
40 * every lookup causes memory writes.
41 *
42 * The Balance Theorem bounds the total access time for m operations
43 * and n inserts on an initially empty tree as O((m + n)lg n). The
44 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
45 *
46 * A red-black tree is a binary search tree with the node color as an
47 * extra attribute. It fulfills a set of conditions:
48 * - every search path from the root to a leaf consists of the
49 * same number of black nodes,
50 * - each red node (except for the root) has a black parent,
51 * - each leaf node is black.
52 *
53 * Every operation on a red-black tree is bounded as O(lg n).
54 * The maximum height of a red-black tree is 2lg (n+1).
55 */
56
57 #define SPLAY_HEAD(name, type) \
58 struct name { \
59 struct type *sph_root; /* root of the tree */ \
60 }
61
62 #define SPLAY_INITIALIZER(root) \
63 { NULL }
64
65 #define SPLAY_INIT(root) do { \
66 (root)->sph_root = NULL; \
67 } while (0)
68
69 #define SPLAY_ENTRY(type) \
70 struct { \
71 struct type *spe_left; /* left element */ \
72 struct type *spe_right; /* right element */ \
73 }
74
75 #define SPLAY_LEFT(elm, field) (elm)->field.spe_left
76 #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
77 #define SPLAY_ROOT(head) (head)->sph_root
78 #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)
79
80 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
81 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \
82 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
83 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
84 (head)->sph_root = tmp; \
85 } while (0)
86
87 #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \
88 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
89 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
90 (head)->sph_root = tmp; \
91 } while (0)
92
93 #define SPLAY_LINKLEFT(head, tmp, field) do { \
94 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
95 tmp = (head)->sph_root; \
96 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
97 } while (0)
98
99 #define SPLAY_LINKRIGHT(head, tmp, field) do { \
100 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
101 tmp = (head)->sph_root; \
102 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
103 } while (0)
104
105 #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \
106 SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
107 SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
108 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
109 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
110 } while (0)
111
112 /* Generates prototypes and inline functions */
113
114 #define SPLAY_PROTOTYPE(name, type, field, cmp) \
115 void name##_SPLAY(struct name *, struct type *); \
116 void name##_SPLAY_MINMAX(struct name *, int); \
117 struct type *name##_SPLAY_INSERT(struct name *, struct type *); \
118 struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \
119 \
120 /* Finds the node with the same key as elm */ \
121 static __inline struct type * \
122 name##_SPLAY_FIND(struct name *head, struct type *elm) \
123 { \
124 if (SPLAY_EMPTY(head)) \
125 return(NULL); \
126 name##_SPLAY(head, elm); \
127 if ((cmp)(elm, (head)->sph_root) == 0) \
128 return (head->sph_root); \
129 return (NULL); \
130 } \
131 \
132 static __inline struct type * \
133 name##_SPLAY_NEXT(struct name *head, struct type *elm) \
134 { \
135 name##_SPLAY(head, elm); \
136 if (SPLAY_RIGHT(elm, field) != NULL) { \
137 elm = SPLAY_RIGHT(elm, field); \
138 while (SPLAY_LEFT(elm, field) != NULL) { \
139 elm = SPLAY_LEFT(elm, field); \
140 } \
141 } else \
142 elm = NULL; \
143 return (elm); \
144 } \
145 \
146 static __inline struct type * \
147 name##_SPLAY_MIN_MAX(struct name *head, int val) \
148 { \
149 name##_SPLAY_MINMAX(head, val); \
150 return (SPLAY_ROOT(head)); \
151 }
152
153 /* Main splay operation.
154 * Moves node close to the key of elm to top
155 */
156 #define SPLAY_GENERATE(name, type, field, cmp) \
157 struct type * \
158 name##_SPLAY_INSERT(struct name *head, struct type *elm) \
159 { \
160 if (SPLAY_EMPTY(head)) { \
161 SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
162 } else { \
163 int __comp; \
164 name##_SPLAY(head, elm); \
165 __comp = (cmp)(elm, (head)->sph_root); \
166 if(__comp < 0) { \
167 SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
168 SPLAY_RIGHT(elm, field) = (head)->sph_root; \
169 SPLAY_LEFT((head)->sph_root, field) = NULL; \
170 } else if (__comp > 0) { \
171 SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
172 SPLAY_LEFT(elm, field) = (head)->sph_root; \
173 SPLAY_RIGHT((head)->sph_root, field) = NULL; \
174 } else \
175 return ((head)->sph_root); \
176 } \
177 (head)->sph_root = (elm); \
178 return (NULL); \
179 } \
180 \
181 struct type * \
182 name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
183 { \
184 struct type *__tmp; \
185 if (SPLAY_EMPTY(head)) \
186 return (NULL); \
187 name##_SPLAY(head, elm); \
188 if ((cmp)(elm, (head)->sph_root) == 0) { \
189 if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \
190 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
191 } else { \
192 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
193 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
194 name##_SPLAY(head, elm); \
195 SPLAY_RIGHT((head)->sph_root, field) = __tmp; \
196 } \
197 return (elm); \
198 } \
199 return (NULL); \
200 } \
201 \
202 void \
203 name##_SPLAY(struct name *head, struct type *elm) \
204 { \
205 struct type __node, *__left, *__right, *__tmp; \
206 int __comp; \
207 \
208 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
209 __left = __right = &__node; \
210 \
211 while ((__comp = (cmp)(elm, (head)->sph_root))) { \
212 if (__comp < 0) { \
213 __tmp = SPLAY_LEFT((head)->sph_root, field); \
214 if (__tmp == NULL) \
215 break; \
216 if ((cmp)(elm, __tmp) < 0){ \
217 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
218 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
219 break; \
220 } \
221 SPLAY_LINKLEFT(head, __right, field); \
222 } else if (__comp > 0) { \
223 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
224 if (__tmp == NULL) \
225 break; \
226 if ((cmp)(elm, __tmp) > 0){ \
227 SPLAY_ROTATE_LEFT(head, __tmp, field); \
228 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
229 break; \
230 } \
231 SPLAY_LINKRIGHT(head, __left, field); \
232 } \
233 } \
234 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
235 } \
236 \
237 /* Splay with either the minimum or the maximum element \
238 * Used to find minimum or maximum element in tree. \
239 */ \
240 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
241 { \
242 struct type __node, *__left, *__right, *__tmp; \
243 \
244 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
245 __left = __right = &__node; \
246 \
247 while (1) { \
248 if (__comp < 0) { \
249 __tmp = SPLAY_LEFT((head)->sph_root, field); \
250 if (__tmp == NULL) \
251 break; \
252 if (__comp < 0){ \
253 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
254 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
255 break; \
256 } \
257 SPLAY_LINKLEFT(head, __right, field); \
258 } else if (__comp > 0) { \
259 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
260 if (__tmp == NULL) \
261 break; \
262 if (__comp > 0) { \
263 SPLAY_ROTATE_LEFT(head, __tmp, field); \
264 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
265 break; \
266 } \
267 SPLAY_LINKRIGHT(head, __left, field); \
268 } \
269 } \
270 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
271 }
272
273 #define SPLAY_NEGINF -1
274 #define SPLAY_INF 1
275
276 #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
277 #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
278 #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
279 #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
280 #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \
281 : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
282 #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \
283 : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
284
285 #define SPLAY_FOREACH(x, name, head) \
286 for ((x) = SPLAY_MIN(name, head); \
287 (x) != NULL; \
288 (x) = SPLAY_NEXT(name, head, x))
289
290 /* Macros that define a red-black tree */
291 #define RB_HEAD(name, type) \
292 struct name { \
293 struct type *rbh_root; /* root of the tree */ \
294 }
295
296 #define RB_INITIALIZER(root) \
297 { NULL }
298
299 #define RB_INIT(root) do { \
300 (root)->rbh_root = NULL; \
301 } while (0)
302
303 #define RB_BLACK 0
304 #define RB_RED 1
305 #define RB_ENTRY(type) \
306 struct { \
307 struct type *rbe_left; /* left element */ \
308 struct type *rbe_right; /* right element */ \
309 struct type *rbe_parent; /* parent element */ \
310 int rbe_color; /* node color */ \
311 }
312
313 #define RB_LEFT(elm, field) (elm)->field.rbe_left
314 #define RB_RIGHT(elm, field) (elm)->field.rbe_right
315 #define RB_PARENT(elm, field) (elm)->field.rbe_parent
316 #define RB_COLOR(elm, field) (elm)->field.rbe_color
317 #define RB_ROOT(head) (head)->rbh_root
318 #define RB_EMPTY(head) (RB_ROOT(head) == NULL)
319
320 #define RB_SET(elm, parent, field) do { \
321 RB_PARENT(elm, field) = parent; \
322 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
323 RB_COLOR(elm, field) = RB_RED; \
324 } while (0)
325
326 #define RB_SET_BLACKRED(black, red, field) do { \
327 RB_COLOR(black, field) = RB_BLACK; \
328 RB_COLOR(red, field) = RB_RED; \
329 } while (0)
330
331 #ifndef RB_AUGMENT
332 #define RB_AUGMENT(x)
333 #endif
334
335 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
336 (tmp) = RB_RIGHT(elm, field); \
337 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) { \
338 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
339 } \
340 RB_AUGMENT(elm); \
341 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) { \
342 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
343 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
344 else \
345 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
346 } else \
347 (head)->rbh_root = (tmp); \
348 RB_LEFT(tmp, field) = (elm); \
349 RB_PARENT(elm, field) = (tmp); \
350 RB_AUGMENT(tmp); \
351 if ((RB_PARENT(tmp, field))) \
352 RB_AUGMENT(RB_PARENT(tmp, field)); \
353 } while (0)
354
355 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
356 (tmp) = RB_LEFT(elm, field); \
357 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) { \
358 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
359 } \
360 RB_AUGMENT(elm); \
361 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) { \
362 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
363 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
364 else \
365 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
366 } else \
367 (head)->rbh_root = (tmp); \
368 RB_RIGHT(tmp, field) = (elm); \
369 RB_PARENT(elm, field) = (tmp); \
370 RB_AUGMENT(tmp); \
371 if ((RB_PARENT(tmp, field))) \
372 RB_AUGMENT(RB_PARENT(tmp, field)); \
373 } while (0)
374
375 /* Generates prototypes and inline functions */
376 #define RB_PROTOTYPE(name, type, field, cmp) \
377 void name##_RB_INSERT_COLOR(struct name *, struct type *); \
378 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
379 struct type *name##_RB_REMOVE(struct name *, struct type *); \
380 struct type *name##_RB_INSERT(struct name *, struct type *); \
381 struct type *name##_RB_FIND(struct name *, struct type *); \
382 struct type *name##_RB_NEXT(struct type *); \
383 struct type *name##_RB_MINMAX(struct name *, int); \
384 \
385
386 /* Main rb operation.
387 * Moves node close to the key of elm to top
388 */
389 #define RB_GENERATE(name, type, field, cmp) \
390 void \
391 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
392 { \
393 struct type *parent, *gparent, *tmp; \
394 while ((parent = RB_PARENT(elm, field)) && \
395 RB_COLOR(parent, field) == RB_RED) { \
396 gparent = RB_PARENT(parent, field); \
397 if (parent == RB_LEFT(gparent, field)) { \
398 tmp = RB_RIGHT(gparent, field); \
399 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
400 RB_COLOR(tmp, field) = RB_BLACK; \
401 RB_SET_BLACKRED(parent, gparent, field);\
402 elm = gparent; \
403 continue; \
404 } \
405 if (RB_RIGHT(parent, field) == elm) { \
406 RB_ROTATE_LEFT(head, parent, tmp, field);\
407 tmp = parent; \
408 parent = elm; \
409 elm = tmp; \
410 } \
411 RB_SET_BLACKRED(parent, gparent, field); \
412 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
413 } else { \
414 tmp = RB_LEFT(gparent, field); \
415 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
416 RB_COLOR(tmp, field) = RB_BLACK; \
417 RB_SET_BLACKRED(parent, gparent, field);\
418 elm = gparent; \
419 continue; \
420 } \
421 if (RB_LEFT(parent, field) == elm) { \
422 RB_ROTATE_RIGHT(head, parent, tmp, field);\
423 tmp = parent; \
424 parent = elm; \
425 elm = tmp; \
426 } \
427 RB_SET_BLACKRED(parent, gparent, field); \
428 RB_ROTATE_LEFT(head, gparent, tmp, field); \
429 } \
430 } \
431 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
432 } \
433 \
434 void \
435 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
436 { \
437 struct type *tmp; \
438 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
439 elm != RB_ROOT(head)) { \
440 if (RB_LEFT(parent, field) == elm) { \
441 tmp = RB_RIGHT(parent, field); \
442 if (RB_COLOR(tmp, field) == RB_RED) { \
443 RB_SET_BLACKRED(tmp, parent, field); \
444 RB_ROTATE_LEFT(head, parent, tmp, field);\
445 tmp = RB_RIGHT(parent, field); \
446 } \
447 if ((RB_LEFT(tmp, field) == NULL || \
448 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
449 (RB_RIGHT(tmp, field) == NULL || \
450 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
451 RB_COLOR(tmp, field) = RB_RED; \
452 elm = parent; \
453 parent = RB_PARENT(elm, field); \
454 } else { \
455 if (RB_RIGHT(tmp, field) == NULL || \
456 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
457 struct type *oleft; \
458 if ((oleft = RB_LEFT(tmp, field)))\
459 RB_COLOR(oleft, field) = RB_BLACK;\
460 RB_COLOR(tmp, field) = RB_RED; \
461 RB_ROTATE_RIGHT(head, tmp, oleft, field);\
462 tmp = RB_RIGHT(parent, field); \
463 } \
464 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
465 RB_COLOR(parent, field) = RB_BLACK; \
466 if (RB_RIGHT(tmp, field)) \
467 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
468 RB_ROTATE_LEFT(head, parent, tmp, field);\
469 elm = RB_ROOT(head); \
470 break; \
471 } \
472 } else { \
473 tmp = RB_LEFT(parent, field); \
474 if (RB_COLOR(tmp, field) == RB_RED) { \
475 RB_SET_BLACKRED(tmp, parent, field); \
476 RB_ROTATE_RIGHT(head, parent, tmp, field);\
477 tmp = RB_LEFT(parent, field); \
478 } \
479 if ((RB_LEFT(tmp, field) == NULL || \
480 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
481 (RB_RIGHT(tmp, field) == NULL || \
482 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
483 RB_COLOR(tmp, field) = RB_RED; \
484 elm = parent; \
485 parent = RB_PARENT(elm, field); \
486 } else { \
487 if (RB_LEFT(tmp, field) == NULL || \
488 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
489 struct type *oright; \
490 if ((oright = RB_RIGHT(tmp, field)))\
491 RB_COLOR(oright, field) = RB_BLACK;\
492 RB_COLOR(tmp, field) = RB_RED; \
493 RB_ROTATE_LEFT(head, tmp, oright, field);\
494 tmp = RB_LEFT(parent, field); \
495 } \
496 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
497 RB_COLOR(parent, field) = RB_BLACK; \
498 if (RB_LEFT(tmp, field)) \
499 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
500 RB_ROTATE_RIGHT(head, parent, tmp, field);\
501 elm = RB_ROOT(head); \
502 break; \
503 } \
504 } \
505 } \
506 if (elm) \
507 RB_COLOR(elm, field) = RB_BLACK; \
508 } \
509 \
510 struct type * \
511 name##_RB_REMOVE(struct name *head, struct type *elm) \
512 { \
513 struct type *child, *parent, *old = elm; \
514 int color; \
515 if (RB_LEFT(elm, field) == NULL) \
516 child = RB_RIGHT(elm, field); \
517 else if (RB_RIGHT(elm, field) == NULL) \
518 child = RB_LEFT(elm, field); \
519 else { \
520 struct type *left; \
521 elm = RB_RIGHT(elm, field); \
522 while ((left = RB_LEFT(elm, field))) \
523 elm = left; \
524 child = RB_RIGHT(elm, field); \
525 parent = RB_PARENT(elm, field); \
526 color = RB_COLOR(elm, field); \
527 if (child) \
528 RB_PARENT(child, field) = parent; \
529 if (parent) { \
530 if (RB_LEFT(parent, field) == elm) \
531 RB_LEFT(parent, field) = child; \
532 else \
533 RB_RIGHT(parent, field) = child; \
534 RB_AUGMENT(parent); \
535 } else \
536 RB_ROOT(head) = child; \
537 if (RB_PARENT(elm, field) == old) \
538 parent = elm; \
539 (elm)->field = (old)->field; \
540 if (RB_PARENT(old, field)) { \
541 if (RB_LEFT(RB_PARENT(old, field), field) == old)\
542 RB_LEFT(RB_PARENT(old, field), field) = elm;\
543 else \
544 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
545 RB_AUGMENT(RB_PARENT(old, field)); \
546 } else \
547 RB_ROOT(head) = elm; \
548 RB_PARENT(RB_LEFT(old, field), field) = elm; \
549 if (RB_RIGHT(old, field)) \
550 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
551 if (parent) { \
552 left = parent; \
553 do { \
554 RB_AUGMENT(left); \
555 } while ((left = RB_PARENT(left, field))); \
556 } \
557 goto color; \
558 } \
559 parent = RB_PARENT(elm, field); \
560 color = RB_COLOR(elm, field); \
561 if (child) \
562 RB_PARENT(child, field) = parent; \
563 if (parent) { \
564 if (RB_LEFT(parent, field) == elm) \
565 RB_LEFT(parent, field) = child; \
566 else \
567 RB_RIGHT(parent, field) = child; \
568 RB_AUGMENT(parent); \
569 } else \
570 RB_ROOT(head) = child; \
571 color: \
572 if (color == RB_BLACK) \
573 name##_RB_REMOVE_COLOR(head, parent, child); \
574 return (old); \
575 } \
576 \
577 /* Inserts a node into the RB tree */ \
578 struct type * \
579 name##_RB_INSERT(struct name *head, struct type *elm) \
580 { \
581 struct type *tmp; \
582 struct type *parent = NULL; \
583 int comp = 0; \
584 tmp = RB_ROOT(head); \
585 while (tmp) { \
586 parent = tmp; \
587 comp = (cmp)(elm, parent); \
588 if (comp < 0) \
589 tmp = RB_LEFT(tmp, field); \
590 else if (comp > 0) \
591 tmp = RB_RIGHT(tmp, field); \
592 else \
593 return (tmp); \
594 } \
595 RB_SET(elm, parent, field); \
596 if (parent != NULL) { \
597 if (comp < 0) \
598 RB_LEFT(parent, field) = elm; \
599 else \
600 RB_RIGHT(parent, field) = elm; \
601 RB_AUGMENT(parent); \
602 } else \
603 RB_ROOT(head) = elm; \
604 name##_RB_INSERT_COLOR(head, elm); \
605 return (NULL); \
606 } \
607 \
608 /* Finds the node with the same key as elm */ \
609 struct type * \
610 name##_RB_FIND(struct name *head, struct type *elm) \
611 { \
612 struct type *tmp = RB_ROOT(head); \
613 int comp; \
614 while (tmp) { \
615 comp = cmp(elm, tmp); \
616 if (comp < 0) \
617 tmp = RB_LEFT(tmp, field); \
618 else if (comp > 0) \
619 tmp = RB_RIGHT(tmp, field); \
620 else \
621 return (tmp); \
622 } \
623 return (NULL); \
624 } \
625 \
626 struct type * \
627 name##_RB_NEXT(struct type *elm) \
628 { \
629 if (RB_RIGHT(elm, field)) { \
630 elm = RB_RIGHT(elm, field); \
631 while (RB_LEFT(elm, field)) \
632 elm = RB_LEFT(elm, field); \
633 } else { \
634 if (RB_PARENT(elm, field) && \
635 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
636 elm = RB_PARENT(elm, field); \
637 else { \
638 while (RB_PARENT(elm, field) && \
639 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
640 elm = RB_PARENT(elm, field); \
641 elm = RB_PARENT(elm, field); \
642 } \
643 } \
644 return (elm); \
645 } \
646 \
647 struct type * \
648 name##_RB_MINMAX(struct name *head, int val) \
649 { \
650 struct type *tmp = RB_ROOT(head); \
651 struct type *parent = NULL; \
652 while (tmp) { \
653 parent = tmp; \
654 if (val < 0) \
655 tmp = RB_LEFT(tmp, field); \
656 else \
657 tmp = RB_RIGHT(tmp, field); \
658 } \
659 return (parent); \
660 }
661
662 #define RB_NEGINF -1
663 #define RB_INF 1
664
665 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
666 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
667 #define RB_FIND(name, x, y) name##_RB_FIND(x, y)
668 #define RB_NEXT(name, x, y) name##_RB_NEXT(y)
669 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
670 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
671
672 #define RB_FOREACH(x, name, head) \
673 for ((x) = RB_MIN(name, head); \
674 (x) != NULL; \
675 (x) = name##_RB_NEXT(x))
676
677 #endif /* _SYS_TREE_H_ */