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tree.h
1 /* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art 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-back 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_ */
678 /* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $ */
679 /*
680 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
681 * All rights reserved.
682 *
683 * Redistribution and use in source and binary forms, with or without
684 * modification, are permitted provided that the following conditions
685 * are met:
686 * 1. Redistributions of source code must retain the above copyright
687 * notice, this list of conditions and the following disclaimer.
688 * 2. Redistributions in binary form must reproduce the above copyright
689 * notice, this list of conditions and the following disclaimer in the
690 * documentation and/or other materials provided with the distribution.
691 *
692 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
693 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
694 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
695 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
696 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
697 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
698 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
699 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
700 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
701 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
702 */
703
704 #ifndef _SYS_TREE_H_
705 #define _SYS_TREE_H_
706
707 /*
708 * This file defines data structures for different types of trees:
709 * splay trees and red-black trees.
710 *
711 * A splay tree is a self-organizing data structure. Every operation
712 * on the tree causes a splay to happen. The splay moves the requested
713 * node to the root of the tree and partly rebalances it.
714 *
715 * This has the benefit that request locality causes faster lookups as
716 * the requested nodes move to the top of the tree. On the other hand,
717 * every lookup causes memory writes.
718 *
719 * The Balance Theorem bounds the total access time for m operations
720 * and n inserts on an initially empty tree as O((m + n)lg n). The
721 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
722 *
723 * A red-black tree is a binary search tree with the node color as an
724 * extra attribute. It fulfills a set of conditions:
725 * - every search path from the root to a leaf consists of the
726 * same number of black nodes,
727 * - each red node (except for the root) has a black parent,
728 * - each leaf node is black.
729 *
730 * Every operation on a red-black tree is bounded as O(lg n).
731 * The maximum height of a red-black tree is 2lg (n+1).
732 */
733
734 #define SPLAY_HEAD(name, type) \
735 struct name { \
736 struct type *sph_root; /* root of the tree */ \
737 }
738
739 #define SPLAY_INITIALIZER(root) \
740 { NULL }
741
742 #define SPLAY_INIT(root) do { \
743 (root)->sph_root = NULL; \
744 } while (0)
745
746 #define SPLAY_ENTRY(type) \
747 struct { \
748 struct type *spe_left; /* left element */ \
749 struct type *spe_right; /* right element */ \
750 }
751
752 #define SPLAY_LEFT(elm, field) (elm)->field.spe_left
753 #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
754 #define SPLAY_ROOT(head) (head)->sph_root
755 #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)
756
757 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
758 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \
759 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
760 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
761 (head)->sph_root = tmp; \
762 } while (0)
763
764 #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \
765 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
766 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
767 (head)->sph_root = tmp; \
768 } while (0)
769
770 #define SPLAY_LINKLEFT(head, tmp, field) do { \
771 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
772 tmp = (head)->sph_root; \
773 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
774 } while (0)
775
776 #define SPLAY_LINKRIGHT(head, tmp, field) do { \
777 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
778 tmp = (head)->sph_root; \
779 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
780 } while (0)
781
782 #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \
783 SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
784 SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
785 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
786 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
787 } while (0)
788
789 /* Generates prototypes and inline functions */
790
791 #define SPLAY_PROTOTYPE(name, type, field, cmp) \
792 void name##_SPLAY(struct name *, struct type *); \
793 void name##_SPLAY_MINMAX(struct name *, int); \
794 struct type *name##_SPLAY_INSERT(struct name *, struct type *); \
795 struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \
796 \
797 /* Finds the node with the same key as elm */ \
798 static __inline struct type * \
799 name##_SPLAY_FIND(struct name *head, struct type *elm) \
800 { \
801 if (SPLAY_EMPTY(head)) \
802 return(NULL); \
803 name##_SPLAY(head, elm); \
804 if ((cmp)(elm, (head)->sph_root) == 0) \
805 return (head->sph_root); \
806 return (NULL); \
807 } \
808 \
809 static __inline struct type * \
810 name##_SPLAY_NEXT(struct name *head, struct type *elm) \
811 { \
812 name##_SPLAY(head, elm); \
813 if (SPLAY_RIGHT(elm, field) != NULL) { \
814 elm = SPLAY_RIGHT(elm, field); \
815 while (SPLAY_LEFT(elm, field) != NULL) { \
816 elm = SPLAY_LEFT(elm, field); \
817 } \
818 } else \
819 elm = NULL; \
820 return (elm); \
821 } \
822 \
823 static __inline struct type * \
824 name##_SPLAY_MIN_MAX(struct name *head, int val) \
825 { \
826 name##_SPLAY_MINMAX(head, val); \
827 return (SPLAY_ROOT(head)); \
828 }
829
830 /* Main splay operation.
831 * Moves node close to the key of elm to top
832 */
833 #define SPLAY_GENERATE(name, type, field, cmp) \
834 struct type * \
835 name##_SPLAY_INSERT(struct name *head, struct type *elm) \
836 { \
837 if (SPLAY_EMPTY(head)) { \
838 SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
839 } else { \
840 int __comp; \
841 name##_SPLAY(head, elm); \
842 __comp = (cmp)(elm, (head)->sph_root); \
843 if(__comp < 0) { \
844 SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
845 SPLAY_RIGHT(elm, field) = (head)->sph_root; \
846 SPLAY_LEFT((head)->sph_root, field) = NULL; \
847 } else if (__comp > 0) { \
848 SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
849 SPLAY_LEFT(elm, field) = (head)->sph_root; \
850 SPLAY_RIGHT((head)->sph_root, field) = NULL; \
851 } else \
852 return ((head)->sph_root); \
853 } \
854 (head)->sph_root = (elm); \
855 return (NULL); \
856 } \
857 \
858 struct type * \
859 name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
860 { \
861 struct type *__tmp; \
862 if (SPLAY_EMPTY(head)) \
863 return (NULL); \
864 name##_SPLAY(head, elm); \
865 if ((cmp)(elm, (head)->sph_root) == 0) { \
866 if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \
867 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
868 } else { \
869 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
870 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
871 name##_SPLAY(head, elm); \
872 SPLAY_RIGHT((head)->sph_root, field) = __tmp; \
873 } \
874 return (elm); \
875 } \
876 return (NULL); \
877 } \
878 \
879 void \
880 name##_SPLAY(struct name *head, struct type *elm) \
881 { \
882 struct type __node, *__left, *__right, *__tmp; \
883 int __comp; \
884 \
885 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
886 __left = __right = &__node; \
887 \
888 while ((__comp = (cmp)(elm, (head)->sph_root))) { \
889 if (__comp < 0) { \
890 __tmp = SPLAY_LEFT((head)->sph_root, field); \
891 if (__tmp == NULL) \
892 break; \
893 if ((cmp)(elm, __tmp) < 0){ \
894 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
895 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
896 break; \
897 } \
898 SPLAY_LINKLEFT(head, __right, field); \
899 } else if (__comp > 0) { \
900 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
901 if (__tmp == NULL) \
902 break; \
903 if ((cmp)(elm, __tmp) > 0){ \
904 SPLAY_ROTATE_LEFT(head, __tmp, field); \
905 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
906 break; \
907 } \
908 SPLAY_LINKRIGHT(head, __left, field); \
909 } \
910 } \
911 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
912 } \
913 \
914 /* Splay with either the minimum or the maximum element \
915 * Used to find minimum or maximum element in tree. \
916 */ \
917 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
918 { \
919 struct type __node, *__left, *__right, *__tmp; \
920 \
921 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
922 __left = __right = &__node; \
923 \
924 while (1) { \
925 if (__comp < 0) { \
926 __tmp = SPLAY_LEFT((head)->sph_root, field); \
927 if (__tmp == NULL) \
928 break; \
929 if (__comp < 0){ \
930 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
931 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
932 break; \
933 } \
934 SPLAY_LINKLEFT(head, __right, field); \
935 } else if (__comp > 0) { \
936 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
937 if (__tmp == NULL) \
938 break; \
939 if (__comp > 0) { \
940 SPLAY_ROTATE_LEFT(head, __tmp, field); \
941 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
942 break; \
943 } \
944 SPLAY_LINKRIGHT(head, __left, field); \
945 } \
946 } \
947 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
948 }
949
950 #define SPLAY_NEGINF -1
951 #define SPLAY_INF 1
952
953 #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
954 #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
955 #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
956 #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
957 #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \
958 : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
959 #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \
960 : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
961
962 #define SPLAY_FOREACH(x, name, head) \
963 for ((x) = SPLAY_MIN(name, head); \
964 (x) != NULL; \
965 (x) = SPLAY_NEXT(name, head, x))
966
967 /* Macros that define a red-back tree */
968 #define RB_HEAD(name, type) \
969 struct name { \
970 struct type *rbh_root; /* root of the tree */ \
971 }
972
973 #define RB_INITIALIZER(root) \
974 { NULL }
975
976 #define RB_INIT(root) do { \
977 (root)->rbh_root = NULL; \
978 } while (0)
979
980 #define RB_BLACK 0
981 #define RB_RED 1
982 #define RB_ENTRY(type) \
983 struct { \
984 struct type *rbe_left; /* left element */ \
985 struct type *rbe_right; /* right element */ \
986 struct type *rbe_parent; /* parent element */ \
987 int rbe_color; /* node color */ \
988 }
989
990 #define RB_LEFT(elm, field) (elm)->field.rbe_left
991 #define RB_RIGHT(elm, field) (elm)->field.rbe_right
992 #define RB_PARENT(elm, field) (elm)->field.rbe_parent
993 #define RB_COLOR(elm, field) (elm)->field.rbe_color
994 #define RB_ROOT(head) (head)->rbh_root
995 #define RB_EMPTY(head) (RB_ROOT(head) == NULL)
996
997 #define RB_SET(elm, parent, field) do { \
998 RB_PARENT(elm, field) = parent; \
999 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
1000 RB_COLOR(elm, field) = RB_RED; \
1001 } while (0)
1002
1003 #define RB_SET_BLACKRED(black, red, field) do { \
1004 RB_COLOR(black, field) = RB_BLACK; \
1005 RB_COLOR(red, field) = RB_RED; \
1006 } while (0)
1007
1008 #ifndef RB_AUGMENT
1009 #define RB_AUGMENT(x)
1010 #endif
1011
1012 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
1013 (tmp) = RB_RIGHT(elm, field); \
1014 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) { \
1015 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
1016 } \
1017 RB_AUGMENT(elm); \
1018 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) { \
1019 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
1020 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
1021 else \
1022 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
1023 } else \
1024 (head)->rbh_root = (tmp); \
1025 RB_LEFT(tmp, field) = (elm); \
1026 RB_PARENT(elm, field) = (tmp); \
1027 RB_AUGMENT(tmp); \
1028 if ((RB_PARENT(tmp, field))) \
1029 RB_AUGMENT(RB_PARENT(tmp, field)); \
1030 } while (0)
1031
1032 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
1033 (tmp) = RB_LEFT(elm, field); \
1034 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) { \
1035 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
1036 } \
1037 RB_AUGMENT(elm); \
1038 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) { \
1039 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
1040 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
1041 else \
1042 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
1043 } else \
1044 (head)->rbh_root = (tmp); \
1045 RB_RIGHT(tmp, field) = (elm); \
1046 RB_PARENT(elm, field) = (tmp); \
1047 RB_AUGMENT(tmp); \
1048 if ((RB_PARENT(tmp, field))) \
1049 RB_AUGMENT(RB_PARENT(tmp, field)); \
1050 } while (0)
1051
1052 /* Generates prototypes and inline functions */
1053 #define RB_PROTOTYPE(name, type, field, cmp) \
1054 void name##_RB_INSERT_COLOR(struct name *, struct type *); \
1055 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
1056 struct type *name##_RB_REMOVE(struct name *, struct type *); \
1057 struct type *name##_RB_INSERT(struct name *, struct type *); \
1058 struct type *name##_RB_FIND(struct name *, struct type *); \
1059 struct type *name##_RB_NEXT(struct type *); \
1060 struct type *name##_RB_MINMAX(struct name *, int); \
1061 \
1062
1063 /* Main rb operation.
1064 * Moves node close to the key of elm to top
1065 */
1066 #define RB_GENERATE(name, type, field, cmp) \
1067 void \
1068 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
1069 { \
1070 struct type *parent, *gparent, *tmp; \
1071 while ((parent = RB_PARENT(elm, field)) && \
1072 RB_COLOR(parent, field) == RB_RED) { \
1073 gparent = RB_PARENT(parent, field); \
1074 if (parent == RB_LEFT(gparent, field)) { \
1075 tmp = RB_RIGHT(gparent, field); \
1076 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
1077 RB_COLOR(tmp, field) = RB_BLACK; \
1078 RB_SET_BLACKRED(parent, gparent, field);\
1079 elm = gparent; \
1080 continue; \
1081 } \
1082 if (RB_RIGHT(parent, field) == elm) { \
1083 RB_ROTATE_LEFT(head, parent, tmp, field);\
1084 tmp = parent; \
1085 parent = elm; \
1086 elm = tmp; \
1087 } \
1088 RB_SET_BLACKRED(parent, gparent, field); \
1089 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
1090 } else { \
1091 tmp = RB_LEFT(gparent, field); \
1092 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
1093 RB_COLOR(tmp, field) = RB_BLACK; \
1094 RB_SET_BLACKRED(parent, gparent, field);\
1095 elm = gparent; \
1096 continue; \
1097 } \
1098 if (RB_LEFT(parent, field) == elm) { \
1099 RB_ROTATE_RIGHT(head, parent, tmp, field);\
1100 tmp = parent; \
1101 parent = elm; \
1102 elm = tmp; \
1103 } \
1104 RB_SET_BLACKRED(parent, gparent, field); \
1105 RB_ROTATE_LEFT(head, gparent, tmp, field); \
1106 } \
1107 } \
1108 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
1109 } \
1110 \
1111 void \
1112 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
1113 { \
1114 struct type *tmp; \
1115 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
1116 elm != RB_ROOT(head)) { \
1117 if (RB_LEFT(parent, field) == elm) { \
1118 tmp = RB_RIGHT(parent, field); \
1119 if (RB_COLOR(tmp, field) == RB_RED) { \
1120 RB_SET_BLACKRED(tmp, parent, field); \
1121 RB_ROTATE_LEFT(head, parent, tmp, field);\
1122 tmp = RB_RIGHT(parent, field); \
1123 } \
1124 if ((RB_LEFT(tmp, field) == NULL || \
1125 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
1126 (RB_RIGHT(tmp, field) == NULL || \
1127 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
1128 RB_COLOR(tmp, field) = RB_RED; \
1129 elm = parent; \
1130 parent = RB_PARENT(elm, field); \
1131 } else { \
1132 if (RB_RIGHT(tmp, field) == NULL || \
1133 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
1134 struct type *oleft; \
1135 if ((oleft = RB_LEFT(tmp, field)))\
1136 RB_COLOR(oleft, field) = RB_BLACK;\
1137 RB_COLOR(tmp, field) = RB_RED; \
1138 RB_ROTATE_RIGHT(head, tmp, oleft, field);\
1139 tmp = RB_RIGHT(parent, field); \
1140 } \
1141 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
1142 RB_COLOR(parent, field) = RB_BLACK; \
1143 if (RB_RIGHT(tmp, field)) \
1144 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
1145 RB_ROTATE_LEFT(head, parent, tmp, field);\
1146 elm = RB_ROOT(head); \
1147 break; \
1148 } \
1149 } else { \
1150 tmp = RB_LEFT(parent, field); \
1151 if (RB_COLOR(tmp, field) == RB_RED) { \
1152 RB_SET_BLACKRED(tmp, parent, field); \
1153 RB_ROTATE_RIGHT(head, parent, tmp, field);\
1154 tmp = RB_LEFT(parent, field); \
1155 } \
1156 if ((RB_LEFT(tmp, field) == NULL || \
1157 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
1158 (RB_RIGHT(tmp, field) == NULL || \
1159 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
1160 RB_COLOR(tmp, field) = RB_RED; \
1161 elm = parent; \
1162 parent = RB_PARENT(elm, field); \
1163 } else { \
1164 if (RB_LEFT(tmp, field) == NULL || \
1165 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
1166 struct type *oright; \
1167 if ((oright = RB_RIGHT(tmp, field)))\
1168 RB_COLOR(oright, field) = RB_BLACK;\
1169 RB_COLOR(tmp, field) = RB_RED; \
1170 RB_ROTATE_LEFT(head, tmp, oright, field);\
1171 tmp = RB_LEFT(parent, field); \
1172 } \
1173 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
1174 RB_COLOR(parent, field) = RB_BLACK; \
1175 if (RB_LEFT(tmp, field)) \
1176 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
1177 RB_ROTATE_RIGHT(head, parent, tmp, field);\
1178 elm = RB_ROOT(head); \
1179 break; \
1180 } \
1181 } \
1182 } \
1183 if (elm) \
1184 RB_COLOR(elm, field) = RB_BLACK; \
1185 } \
1186 \
1187 struct type * \
1188 name##_RB_REMOVE(struct name *head, struct type *elm) \
1189 { \
1190 struct type *child, *parent, *old = elm; \
1191 int color; \
1192 if (RB_LEFT(elm, field) == NULL) \
1193 child = RB_RIGHT(elm, field); \
1194 else if (RB_RIGHT(elm, field) == NULL) \
1195 child = RB_LEFT(elm, field); \
1196 else { \
1197 struct type *left; \
1198 elm = RB_RIGHT(elm, field); \
1199 while ((left = RB_LEFT(elm, field))) \
1200 elm = left; \
1201 child = RB_RIGHT(elm, field); \
1202 parent = RB_PARENT(elm, field); \
1203 color = RB_COLOR(elm, field); \
1204 if (child) \
1205 RB_PARENT(child, field) = parent; \
1206 if (parent) { \
1207 if (RB_LEFT(parent, field) == elm) \
1208 RB_LEFT(parent, field) = child; \
1209 else \
1210 RB_RIGHT(parent, field) = child; \
1211 RB_AUGMENT(parent); \
1212 } else \
1213 RB_ROOT(head) = child; \
1214 if (RB_PARENT(elm, field) == old) \
1215 parent = elm; \
1216 (elm)->field = (old)->field; \
1217 if (RB_PARENT(old, field)) { \
1218 if (RB_LEFT(RB_PARENT(old, field), field) == old)\
1219 RB_LEFT(RB_PARENT(old, field), field) = elm;\
1220 else \
1221 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
1222 RB_AUGMENT(RB_PARENT(old, field)); \
1223 } else \
1224 RB_ROOT(head) = elm; \
1225 RB_PARENT(RB_LEFT(old, field), field) = elm; \
1226 if (RB_RIGHT(old, field)) \
1227 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
1228 if (parent) { \
1229 left = parent; \
1230 do { \
1231 RB_AUGMENT(left); \
1232 } while ((left = RB_PARENT(left, field))); \
1233 } \
1234 goto color; \
1235 } \
1236 parent = RB_PARENT(elm, field); \
1237 color = RB_COLOR(elm, field); \
1238 if (child) \
1239 RB_PARENT(child, field) = parent; \
1240 if (parent) { \
1241 if (RB_LEFT(parent, field) == elm) \
1242 RB_LEFT(parent, field) = child; \
1243 else \
1244 RB_RIGHT(parent, field) = child; \
1245 RB_AUGMENT(parent); \
1246 } else \
1247 RB_ROOT(head) = child; \
1248 color: \
1249 if (color == RB_BLACK) \
1250 name##_RB_REMOVE_COLOR(head, parent, child); \
1251 return (old); \
1252 } \
1253 \
1254 /* Inserts a node into the RB tree */ \
1255 struct type * \
1256 name##_RB_INSERT(struct name *head, struct type *elm) \
1257 { \
1258 struct type *tmp; \
1259 struct type *parent = NULL; \
1260 int comp = 0; \
1261 tmp = RB_ROOT(head); \
1262 while (tmp) { \
1263 parent = tmp; \
1264 comp = (cmp)(elm, parent); \
1265 if (comp < 0) \
1266 tmp = RB_LEFT(tmp, field); \
1267 else if (comp > 0) \
1268 tmp = RB_RIGHT(tmp, field); \
1269 else \
1270 return (tmp); \
1271 } \
1272 RB_SET(elm, parent, field); \
1273 if (parent != NULL) { \
1274 if (comp < 0) \
1275 RB_LEFT(parent, field) = elm; \
1276 else \
1277 RB_RIGHT(parent, field) = elm; \
1278 RB_AUGMENT(parent); \
1279 } else \
1280 RB_ROOT(head) = elm; \
1281 name##_RB_INSERT_COLOR(head, elm); \
1282 return (NULL); \
1283 } \
1284 \
1285 /* Finds the node with the same key as elm */ \
1286 struct type * \
1287 name##_RB_FIND(struct name *head, struct type *elm) \
1288 { \
1289 struct type *tmp = RB_ROOT(head); \
1290 int comp; \
1291 while (tmp) { \
1292 comp = cmp(elm, tmp); \
1293 if (comp < 0) \
1294 tmp = RB_LEFT(tmp, field); \
1295 else if (comp > 0) \
1296 tmp = RB_RIGHT(tmp, field); \
1297 else \
1298 return (tmp); \
1299 } \
1300 return (NULL); \
1301 } \
1302 \
1303 struct type * \
1304 name##_RB_NEXT(struct type *elm) \
1305 { \
1306 if (RB_RIGHT(elm, field)) { \
1307 elm = RB_RIGHT(elm, field); \
1308 while (RB_LEFT(elm, field)) \
1309 elm = RB_LEFT(elm, field); \
1310 } else { \
1311 if (RB_PARENT(elm, field) && \
1312 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
1313 elm = RB_PARENT(elm, field); \
1314 else { \
1315 while (RB_PARENT(elm, field) && \
1316 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
1317 elm = RB_PARENT(elm, field); \
1318 elm = RB_PARENT(elm, field); \
1319 } \
1320 } \
1321 return (elm); \
1322 } \
1323 \
1324 struct type * \
1325 name##_RB_MINMAX(struct name *head, int val) \
1326 { \
1327 struct type *tmp = RB_ROOT(head); \
1328 struct type *parent = NULL; \
1329 while (tmp) { \
1330 parent = tmp; \
1331 if (val < 0) \
1332 tmp = RB_LEFT(tmp, field); \
1333 else \
1334 tmp = RB_RIGHT(tmp, field); \
1335 } \
1336 return (parent); \
1337 }
1338
1339 #define RB_NEGINF -1
1340 #define RB_INF 1
1341
1342 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
1343 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
1344 #define RB_FIND(name, x, y) name##_RB_FIND(x, y)
1345 #define RB_NEXT(name, x, y) name##_RB_NEXT(y)
1346 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
1347 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
1348
1349 #define RB_FOREACH(x, name, head) \
1350 for ((x) = RB_MIN(name, head); \
1351 (x) != NULL; \
1352 (x) = name##_RB_NEXT(x))
1353
1354 #endif /* _SYS_TREE_H_ */