1 /* $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $ */ 2 /* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $ */ 3 /* $FreeBSD: head/sys/sys/tree.h 189204 2009-03-01 04:57:23Z bms $ */ 4 5 /*- 6 * Copyright 2002 Niels Provos <provos@citi.umich.edu> 7 * All rights reserved. 8 * 9 * Redistribution and use in source and binary forms, with or without 10 * modification, are permitted provided that the following conditions 11 * are met: 12 * 1. Redistributions of source code must retain the above copyright 13 * notice, this list of conditions and the following disclaimer. 14 * 2. Redistributions in binary form must reproduce the above copyright 15 * notice, this list of conditions and the following disclaimer in the 16 * documentation and/or other materials provided with the distribution. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 19 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 20 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 21 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 22 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 23 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 24 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 25 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 26 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 27 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 28 */ 29 30 #ifndef _SYS_TREE_H_ 31 #define _SYS_TREE_H_ 32 33 #include <sys/cdefs.h> 34 35 /* 36 * This file defines data structures for different types of trees: 37 * splay trees and red-black trees. 38 * 39 * A splay tree is a self-organizing data structure. Every operation 40 * on the tree causes a splay to happen. The splay moves the requested 41 * node to the root of the tree and partly rebalances it. 42 * 43 * This has the benefit that request locality causes faster lookups as 44 * the requested nodes move to the top of the tree. On the other hand, 45 * every lookup causes memory writes. 46 * 47 * The Balance Theorem bounds the total access time for m operations 48 * and n inserts on an initially empty tree as O((m + n)lg n). The 49 * amortized cost for a sequence of m accesses to a splay tree is O(lg n); 50 * 51 * A red-black tree is a binary search tree with the node color as an 52 * extra attribute. It fulfills a set of conditions: 53 * - every search path from the root to a leaf consists of the 54 * same number of black nodes, 55 * - each red node (except for the root) has a black parent, 56 * - each leaf node is black. 57 * 58 * Every operation on a red-black tree is bounded as O(lg n). 59 * The maximum height of a red-black tree is 2lg (n+1). 60 */ 61 62 #define SPLAY_HEAD(name, type) \ 63 struct name { \ 64 struct type *sph_root; /* root of the tree */ \ 65 } 66 67 #define SPLAY_INITIALIZER(root) \ 68 { NULL } 69 70 #define SPLAY_INIT(root) do { \ 71 (root)->sph_root = NULL; \ 72 } while (/*CONSTCOND*/ 0) 73 74 #define SPLAY_ENTRY(type) \ 75 struct { \ 76 struct type *spe_left; /* left element */ \ 77 struct type *spe_right; /* right element */ \ 78 } 79 80 #define SPLAY_LEFT(elm, field) (elm)->field.spe_left 81 #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right 82 #define SPLAY_ROOT(head) (head)->sph_root 83 #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL) 84 85 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */ 86 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \ 87 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \ 88 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ 89 (head)->sph_root = tmp; \ 90 } while (/*CONSTCOND*/ 0) 91 92 #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \ 93 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \ 94 SPLAY_LEFT(tmp, field) = (head)->sph_root; \ 95 (head)->sph_root = tmp; \ 96 } while (/*CONSTCOND*/ 0) 97 98 #define SPLAY_LINKLEFT(head, tmp, field) do { \ 99 SPLAY_LEFT(tmp, field) = (head)->sph_root; \ 100 tmp = (head)->sph_root; \ 101 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \ 102 } while (/*CONSTCOND*/ 0) 103 104 #define SPLAY_LINKRIGHT(head, tmp, field) do { \ 105 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ 106 tmp = (head)->sph_root; \ 107 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \ 108 } while (/*CONSTCOND*/ 0) 109 110 #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \ 111 SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \ 112 SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\ 113 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \ 114 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \ 115 } while (/*CONSTCOND*/ 0) 116 117 /* Generates prototypes and inline functions */ 118 119 #define SPLAY_PROTOTYPE(name, type, field, cmp) \ 120 void name##_SPLAY(struct name *, struct type *); \ 121 void name##_SPLAY_MINMAX(struct name *, int); \ 122 struct type *name##_SPLAY_INSERT(struct name *, struct type *); \ 123 struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \ 124 \ 125 /* Finds the node with the same key as elm */ \ 126 static __inline struct type * \ 127 name##_SPLAY_FIND(struct name *head, struct type *elm) \ 128 { \ 129 if (SPLAY_EMPTY(head)) \ 130 return(NULL); \ 131 name##_SPLAY(head, elm); \ 132 if ((cmp)(elm, (head)->sph_root) == 0) \ 133 return (head->sph_root); \ 134 return (NULL); \ 135 } \ 136 \ 137 static __inline struct type * \ 138 name##_SPLAY_NEXT(struct name *head, struct type *elm) \ 139 { \ 140 name##_SPLAY(head, elm); \ 141 if (SPLAY_RIGHT(elm, field) != NULL) { \ 142 elm = SPLAY_RIGHT(elm, field); \ 143 while (SPLAY_LEFT(elm, field) != NULL) { \ 144 elm = SPLAY_LEFT(elm, field); \ 145 } \ 146 } else \ 147 elm = NULL; \ 148 return (elm); \ 149 } \ 150 \ 151 static __inline struct type * \ 152 name##_SPLAY_MIN_MAX(struct name *head, int val) \ 153 { \ 154 name##_SPLAY_MINMAX(head, val); \ 155 return (SPLAY_ROOT(head)); \ 156 } 157 158 /* Main splay operation. 159 * Moves node close to the key of elm to top 160 */ 161 #define SPLAY_GENERATE(name, type, field, cmp) \ 162 struct type * \ 163 name##_SPLAY_INSERT(struct name *head, struct type *elm) \ 164 { \ 165 if (SPLAY_EMPTY(head)) { \ 166 SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \ 167 } else { \ 168 int __comp; \ 169 name##_SPLAY(head, elm); \ 170 __comp = (cmp)(elm, (head)->sph_root); \ 171 if(__comp < 0) { \ 172 SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\ 173 SPLAY_RIGHT(elm, field) = (head)->sph_root; \ 174 SPLAY_LEFT((head)->sph_root, field) = NULL; \ 175 } else if (__comp > 0) { \ 176 SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\ 177 SPLAY_LEFT(elm, field) = (head)->sph_root; \ 178 SPLAY_RIGHT((head)->sph_root, field) = NULL; \ 179 } else \ 180 return ((head)->sph_root); \ 181 } \ 182 (head)->sph_root = (elm); \ 183 return (NULL); \ 184 } \ 185 \ 186 struct type * \ 187 name##_SPLAY_REMOVE(struct name *head, struct type *elm) \ 188 { \ 189 struct type *__tmp; \ 190 if (SPLAY_EMPTY(head)) \ 191 return (NULL); \ 192 name##_SPLAY(head, elm); \ 193 if ((cmp)(elm, (head)->sph_root) == 0) { \ 194 if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \ 195 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\ 196 } else { \ 197 __tmp = SPLAY_RIGHT((head)->sph_root, field); \ 198 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\ 199 name##_SPLAY(head, elm); \ 200 SPLAY_RIGHT((head)->sph_root, field) = __tmp; \ 201 } \ 202 return (elm); \ 203 } \ 204 return (NULL); \ 205 } \ 206 \ 207 void \ 208 name##_SPLAY(struct name *head, struct type *elm) \ 209 { \ 210 struct type __node, *__left, *__right, *__tmp; \ 211 int __comp; \ 212 \ 213 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\ 214 __left = __right = &__node; \ 215 \ 216 while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \ 217 if (__comp < 0) { \ 218 __tmp = SPLAY_LEFT((head)->sph_root, field); \ 219 if (__tmp == NULL) \ 220 break; \ 221 if ((cmp)(elm, __tmp) < 0){ \ 222 SPLAY_ROTATE_RIGHT(head, __tmp, field); \ 223 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\ 224 break; \ 225 } \ 226 SPLAY_LINKLEFT(head, __right, field); \ 227 } else if (__comp > 0) { \ 228 __tmp = SPLAY_RIGHT((head)->sph_root, field); \ 229 if (__tmp == NULL) \ 230 break; \ 231 if ((cmp)(elm, __tmp) > 0){ \ 232 SPLAY_ROTATE_LEFT(head, __tmp, field); \ 233 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\ 234 break; \ 235 } \ 236 SPLAY_LINKRIGHT(head, __left, field); \ 237 } \ 238 } \ 239 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ 240 } \ 241 \ 242 /* Splay with either the minimum or the maximum element \ 243 * Used to find minimum or maximum element in tree. \ 244 */ \ 245 void name##_SPLAY_MINMAX(struct name *head, int __comp) \ 246 { \ 247 struct type __node, *__left, *__right, *__tmp; \ 248 \ 249 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\ 250 __left = __right = &__node; \ 251 \ 252 while (1) { \ 253 if (__comp < 0) { \ 254 __tmp = SPLAY_LEFT((head)->sph_root, field); \ 255 if (__tmp == NULL) \ 256 break; \ 257 if (__comp < 0){ \ 258 SPLAY_ROTATE_RIGHT(head, __tmp, field); \ 259 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\ 260 break; \ 261 } \ 262 SPLAY_LINKLEFT(head, __right, field); \ 263 } else if (__comp > 0) { \ 264 __tmp = SPLAY_RIGHT((head)->sph_root, field); \ 265 if (__tmp == NULL) \ 266 break; \ 267 if (__comp > 0) { \ 268 SPLAY_ROTATE_LEFT(head, __tmp, field); \ 269 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\ 270 break; \ 271 } \ 272 SPLAY_LINKRIGHT(head, __left, field); \ 273 } \ 274 } \ 275 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ 276 } 277 278 #define SPLAY_NEGINF -1 279 #define SPLAY_INF 1 280 281 #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y) 282 #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y) 283 #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y) 284 #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y) 285 #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \ 286 : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF)) 287 #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \ 288 : name##_SPLAY_MIN_MAX(x, SPLAY_INF)) 289 290 #define SPLAY_FOREACH(x, name, head) \ 291 for ((x) = SPLAY_MIN(name, head); \ 292 (x) != NULL; \ 293 (x) = SPLAY_NEXT(name, head, x)) 294 295 /* Macros that define a red-black tree */ 296 #define RB_HEAD(name, type) \ 297 struct name { \ 298 struct type *rbh_root; /* root of the tree */ \ 299 } 300 301 #define RB_INITIALIZER(root) \ 302 { NULL } 303 304 #define RB_INIT(root) do { \ 305 (root)->rbh_root = NULL; \ 306 } while (/*CONSTCOND*/ 0) 307 308 #define RB_BLACK 0 309 #define RB_RED 1 310 #define RB_ENTRY(type) \ 311 struct { \ 312 struct type *rbe_left; /* left element */ \ 313 struct type *rbe_right; /* right element */ \ 314 struct type *rbe_parent; /* parent element */ \ 315 int rbe_color; /* node color */ \ 316 } 317 318 #define RB_LEFT(elm, field) (elm)->field.rbe_left 319 #define RB_RIGHT(elm, field) (elm)->field.rbe_right 320 #define RB_PARENT(elm, field) (elm)->field.rbe_parent 321 #define RB_COLOR(elm, field) (elm)->field.rbe_color 322 #define RB_ROOT(head) (head)->rbh_root 323 #define RB_EMPTY(head) (RB_ROOT(head) == NULL) 324 325 #define RB_SET(elm, parent, field) do { \ 326 RB_PARENT(elm, field) = parent; \ 327 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \ 328 RB_COLOR(elm, field) = RB_RED; \ 329 } while (/*CONSTCOND*/ 0) 330 331 #define RB_SET_BLACKRED(black, red, field) do { \ 332 RB_COLOR(black, field) = RB_BLACK; \ 333 RB_COLOR(red, field) = RB_RED; \ 334 } while (/*CONSTCOND*/ 0) 335 336 #ifndef RB_AUGMENT 337 #define RB_AUGMENT(x) do {} while (0) 338 #endif 339 340 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \ 341 (tmp) = RB_RIGHT(elm, field); \ 342 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \ 343 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \ 344 } \ 345 RB_AUGMENT(elm); \ 346 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \ 347 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \ 348 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ 349 else \ 350 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ 351 } else \ 352 (head)->rbh_root = (tmp); \ 353 RB_LEFT(tmp, field) = (elm); \ 354 RB_PARENT(elm, field) = (tmp); \ 355 RB_AUGMENT(tmp); \ 356 if ((RB_PARENT(tmp, field))) \ 357 RB_AUGMENT(RB_PARENT(tmp, field)); \ 358 } while (/*CONSTCOND*/ 0) 359 360 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \ 361 (tmp) = RB_LEFT(elm, field); \ 362 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \ 363 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \ 364 } \ 365 RB_AUGMENT(elm); \ 366 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \ 367 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \ 368 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ 369 else \ 370 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ 371 } else \ 372 (head)->rbh_root = (tmp); \ 373 RB_RIGHT(tmp, field) = (elm); \ 374 RB_PARENT(elm, field) = (tmp); \ 375 RB_AUGMENT(tmp); \ 376 if ((RB_PARENT(tmp, field))) \ 377 RB_AUGMENT(RB_PARENT(tmp, field)); \ 378 } while (/*CONSTCOND*/ 0) 379 380 /* Generates prototypes and inline functions */ 381 #define RB_PROTOTYPE(name, type, field, cmp) \ 382 RB_PROTOTYPE_INTERNAL(name, type, field, cmp,) 383 #define RB_PROTOTYPE_STATIC(name, type, field, cmp) \ 384 RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static) 385 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \ 386 attr void name##_RB_INSERT_COLOR(struct name *, struct type *); \ 387 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\ 388 attr struct type *name##_RB_REMOVE(struct name *, struct type *); \ 389 attr struct type *name##_RB_INSERT(struct name *, struct type *); \ 390 attr struct type *name##_RB_FIND(struct name *, struct type *); \ 391 attr struct type *name##_RB_NFIND(struct name *, struct type *); \ 392 attr struct type *name##_RB_NEXT(struct type *); \ 393 attr struct type *name##_RB_PREV(struct type *); \ 394 attr struct type *name##_RB_MINMAX(struct name *, int); \ 395 \ 396 397 /* Main rb operation. 398 * Moves node close to the key of elm to top 399 */ 400 #define RB_GENERATE(name, type, field, cmp) \ 401 RB_GENERATE_INTERNAL(name, type, field, cmp,) 402 #define RB_GENERATE_STATIC(name, type, field, cmp) \ 403 RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static) 404 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \ 405 attr void \ 406 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \ 407 { \ 408 struct type *parent, *gparent, *tmp; \ 409 while ((parent = RB_PARENT(elm, field)) != NULL && \ 410 RB_COLOR(parent, field) == RB_RED) { \ 411 gparent = RB_PARENT(parent, field); \ 412 if (parent == RB_LEFT(gparent, field)) { \ 413 tmp = RB_RIGHT(gparent, field); \ 414 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \ 415 RB_COLOR(tmp, field) = RB_BLACK; \ 416 RB_SET_BLACKRED(parent, gparent, field);\ 417 elm = gparent; \ 418 continue; \ 419 } \ 420 if (RB_RIGHT(parent, field) == elm) { \ 421 RB_ROTATE_LEFT(head, parent, tmp, field);\ 422 tmp = parent; \ 423 parent = elm; \ 424 elm = tmp; \ 425 } \ 426 RB_SET_BLACKRED(parent, gparent, field); \ 427 RB_ROTATE_RIGHT(head, gparent, tmp, field); \ 428 } else { \ 429 tmp = RB_LEFT(gparent, field); \ 430 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \ 431 RB_COLOR(tmp, field) = RB_BLACK; \ 432 RB_SET_BLACKRED(parent, gparent, field);\ 433 elm = gparent; \ 434 continue; \ 435 } \ 436 if (RB_LEFT(parent, field) == elm) { \ 437 RB_ROTATE_RIGHT(head, parent, tmp, field);\ 438 tmp = parent; \ 439 parent = elm; \ 440 elm = tmp; \ 441 } \ 442 RB_SET_BLACKRED(parent, gparent, field); \ 443 RB_ROTATE_LEFT(head, gparent, tmp, field); \ 444 } \ 445 } \ 446 RB_COLOR(head->rbh_root, field) = RB_BLACK; \ 447 } \ 448 \ 449 attr void \ 450 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \ 451 { \ 452 struct type *tmp; \ 453 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \ 454 elm != RB_ROOT(head)) { \ 455 if (RB_LEFT(parent, field) == elm) { \ 456 tmp = RB_RIGHT(parent, field); \ 457 if (RB_COLOR(tmp, field) == RB_RED) { \ 458 RB_SET_BLACKRED(tmp, parent, field); \ 459 RB_ROTATE_LEFT(head, parent, tmp, field);\ 460 tmp = RB_RIGHT(parent, field); \ 461 } \ 462 if ((RB_LEFT(tmp, field) == NULL || \ 463 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\ 464 (RB_RIGHT(tmp, field) == NULL || \ 465 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\ 466 RB_COLOR(tmp, field) = RB_RED; \ 467 elm = parent; \ 468 parent = RB_PARENT(elm, field); \ 469 } else { \ 470 if (RB_RIGHT(tmp, field) == NULL || \ 471 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\ 472 struct type *oleft; \ 473 if ((oleft = RB_LEFT(tmp, field)) \ 474 != NULL) \ 475 RB_COLOR(oleft, field) = RB_BLACK;\ 476 RB_COLOR(tmp, field) = RB_RED; \ 477 RB_ROTATE_RIGHT(head, tmp, oleft, field);\ 478 tmp = RB_RIGHT(parent, field); \ 479 } \ 480 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\ 481 RB_COLOR(parent, field) = RB_BLACK; \ 482 if (RB_RIGHT(tmp, field)) \ 483 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\ 484 RB_ROTATE_LEFT(head, parent, tmp, field);\ 485 elm = RB_ROOT(head); \ 486 break; \ 487 } \ 488 } else { \ 489 tmp = RB_LEFT(parent, field); \ 490 if (RB_COLOR(tmp, field) == RB_RED) { \ 491 RB_SET_BLACKRED(tmp, parent, field); \ 492 RB_ROTATE_RIGHT(head, parent, tmp, field);\ 493 tmp = RB_LEFT(parent, field); \ 494 } \ 495 if ((RB_LEFT(tmp, field) == NULL || \ 496 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\ 497 (RB_RIGHT(tmp, field) == NULL || \ 498 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\ 499 RB_COLOR(tmp, field) = RB_RED; \ 500 elm = parent; \ 501 parent = RB_PARENT(elm, field); \ 502 } else { \ 503 if (RB_LEFT(tmp, field) == NULL || \ 504 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\ 505 struct type *oright; \ 506 if ((oright = RB_RIGHT(tmp, field)) \ 507 != NULL) \ 508 RB_COLOR(oright, field) = RB_BLACK;\ 509 RB_COLOR(tmp, field) = RB_RED; \ 510 RB_ROTATE_LEFT(head, tmp, oright, field);\ 511 tmp = RB_LEFT(parent, field); \ 512 } \ 513 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\ 514 RB_COLOR(parent, field) = RB_BLACK; \ 515 if (RB_LEFT(tmp, field)) \ 516 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\ 517 RB_ROTATE_RIGHT(head, parent, tmp, field);\ 518 elm = RB_ROOT(head); \ 519 break; \ 520 } \ 521 } \ 522 } \ 523 if (elm) \ 524 RB_COLOR(elm, field) = RB_BLACK; \ 525 } \ 526 \ 527 attr struct type * \ 528 name##_RB_REMOVE(struct name *head, struct type *elm) \ 529 { \ 530 struct type *child, *parent, *old = elm; \ 531 int color; \ 532 if (RB_LEFT(elm, field) == NULL) \ 533 child = RB_RIGHT(elm, field); \ 534 else if (RB_RIGHT(elm, field) == NULL) \ 535 child = RB_LEFT(elm, field); \ 536 else { \ 537 struct type *left; \ 538 elm = RB_RIGHT(elm, field); \ 539 while ((left = RB_LEFT(elm, field)) != NULL) \ 540 elm = left; \ 541 child = RB_RIGHT(elm, field); \ 542 parent = RB_PARENT(elm, field); \ 543 color = RB_COLOR(elm, field); \ 544 if (child) \ 545 RB_PARENT(child, field) = parent; \ 546 if (parent) { \ 547 if (RB_LEFT(parent, field) == elm) \ 548 RB_LEFT(parent, field) = child; \ 549 else \ 550 RB_RIGHT(parent, field) = child; \ 551 RB_AUGMENT(parent); \ 552 } else \ 553 RB_ROOT(head) = child; \ 554 if (RB_PARENT(elm, field) == old) \ 555 parent = elm; \ 556 (elm)->field = (old)->field; \ 557 if (RB_PARENT(old, field)) { \ 558 if (RB_LEFT(RB_PARENT(old, field), field) == old)\ 559 RB_LEFT(RB_PARENT(old, field), field) = elm;\ 560 else \ 561 RB_RIGHT(RB_PARENT(old, field), field) = elm;\ 562 RB_AUGMENT(RB_PARENT(old, field)); \ 563 } else \ 564 RB_ROOT(head) = elm; \ 565 RB_PARENT(RB_LEFT(old, field), field) = elm; \ 566 if (RB_RIGHT(old, field)) \ 567 RB_PARENT(RB_RIGHT(old, field), field) = elm; \ 568 if (parent) { \ 569 left = parent; \ 570 do { \ 571 RB_AUGMENT(left); \ 572 } while ((left = RB_PARENT(left, field)) != NULL); \ 573 } \ 574 goto color; \ 575 } \ 576 parent = RB_PARENT(elm, field); \ 577 color = RB_COLOR(elm, field); \ 578 if (child) \ 579 RB_PARENT(child, field) = parent; \ 580 if (parent) { \ 581 if (RB_LEFT(parent, field) == elm) \ 582 RB_LEFT(parent, field) = child; \ 583 else \ 584 RB_RIGHT(parent, field) = child; \ 585 RB_AUGMENT(parent); \ 586 } else \ 587 RB_ROOT(head) = child; \ 588 color: \ 589 if (color == RB_BLACK) \ 590 name##_RB_REMOVE_COLOR(head, parent, child); \ 591 return (old); \ 592 } \ 593 \ 594 /* Inserts a node into the RB tree */ \ 595 attr struct type * \ 596 name##_RB_INSERT(struct name *head, struct type *elm) \ 597 { \ 598 struct type *tmp; \ 599 struct type *parent = NULL; \ 600 int comp = 0; \ 601 tmp = RB_ROOT(head); \ 602 while (tmp) { \ 603 parent = tmp; \ 604 comp = (cmp)(elm, parent); \ 605 if (comp < 0) \ 606 tmp = RB_LEFT(tmp, field); \ 607 else if (comp > 0) \ 608 tmp = RB_RIGHT(tmp, field); \ 609 else \ 610 return (tmp); \ 611 } \ 612 RB_SET(elm, parent, field); \ 613 if (parent != NULL) { \ 614 if (comp < 0) \ 615 RB_LEFT(parent, field) = elm; \ 616 else \ 617 RB_RIGHT(parent, field) = elm; \ 618 RB_AUGMENT(parent); \ 619 } else \ 620 RB_ROOT(head) = elm; \ 621 name##_RB_INSERT_COLOR(head, elm); \ 622 return (NULL); \ 623 } \ 624 \ 625 /* Finds the node with the same key as elm */ \ 626 attr struct type * \ 627 name##_RB_FIND(struct name *head, struct type *elm) \ 628 { \ 629 struct type *tmp = RB_ROOT(head); \ 630 int comp; \ 631 while (tmp) { \ 632 comp = cmp(elm, tmp); \ 633 if (comp < 0) \ 634 tmp = RB_LEFT(tmp, field); \ 635 else if (comp > 0) \ 636 tmp = RB_RIGHT(tmp, field); \ 637 else \ 638 return (tmp); \ 639 } \ 640 return (NULL); \ 641 } \ 642 \ 643 /* Finds the first node greater than or equal to the search key */ \ 644 attr struct type * \ 645 name##_RB_NFIND(struct name *head, struct type *elm) \ 646 { \ 647 struct type *tmp = RB_ROOT(head); \ 648 struct type *res = NULL; \ 649 int comp; \ 650 while (tmp) { \ 651 comp = cmp(elm, tmp); \ 652 if (comp < 0) { \ 653 res = tmp; \ 654 tmp = RB_LEFT(tmp, field); \ 655 } \ 656 else if (comp > 0) \ 657 tmp = RB_RIGHT(tmp, field); \ 658 else \ 659 return (tmp); \ 660 } \ 661 return (res); \ 662 } \ 663 \ 664 /* ARGSUSED */ \ 665 attr struct type * \ 666 name##_RB_NEXT(struct type *elm) \ 667 { \ 668 if (RB_RIGHT(elm, field)) { \ 669 elm = RB_RIGHT(elm, field); \ 670 while (RB_LEFT(elm, field)) \ 671 elm = RB_LEFT(elm, field); \ 672 } else { \ 673 if (RB_PARENT(elm, field) && \ 674 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \ 675 elm = RB_PARENT(elm, field); \ 676 else { \ 677 while (RB_PARENT(elm, field) && \ 678 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\ 679 elm = RB_PARENT(elm, field); \ 680 elm = RB_PARENT(elm, field); \ 681 } \ 682 } \ 683 return (elm); \ 684 } \ 685 \ 686 /* ARGSUSED */ \ 687 attr struct type * \ 688 name##_RB_PREV(struct type *elm) \ 689 { \ 690 if (RB_LEFT(elm, field)) { \ 691 elm = RB_LEFT(elm, field); \ 692 while (RB_RIGHT(elm, field)) \ 693 elm = RB_RIGHT(elm, field); \ 694 } else { \ 695 if (RB_PARENT(elm, field) && \ 696 (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \ 697 elm = RB_PARENT(elm, field); \ 698 else { \ 699 while (RB_PARENT(elm, field) && \ 700 (elm == RB_LEFT(RB_PARENT(elm, field), field)))\ 701 elm = RB_PARENT(elm, field); \ 702 elm = RB_PARENT(elm, field); \ 703 } \ 704 } \ 705 return (elm); \ 706 } \ 707 \ 708 attr struct type * \ 709 name##_RB_MINMAX(struct name *head, int val) \ 710 { \ 711 struct type *tmp = RB_ROOT(head); \ 712 struct type *parent = NULL; \ 713 while (tmp) { \ 714 parent = tmp; \ 715 if (val < 0) \ 716 tmp = RB_LEFT(tmp, field); \ 717 else \ 718 tmp = RB_RIGHT(tmp, field); \ 719 } \ 720 return (parent); \ 721 } 722 723 #define RB_NEGINF -1 724 #define RB_INF 1 725 726 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y) 727 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y) 728 #define RB_FIND(name, x, y) name##_RB_FIND(x, y) 729 #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y) 730 #define RB_NEXT(name, x, y) name##_RB_NEXT(y) 731 #define RB_PREV(name, x, y) name##_RB_PREV(y) 732 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF) 733 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF) 734 735 #define RB_FOREACH(x, name, head) \ 736 for ((x) = RB_MIN(name, head); \ 737 (x) != NULL; \ 738 (x) = name##_RB_NEXT(x)) 739 740 #define RB_FOREACH_FROM(x, name, y) \ 741 for ((x) = (y); \ 742 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ 743 (x) = (y)) 744 745 #define RB_FOREACH_SAFE(x, name, head, y) \ 746 for ((x) = RB_MIN(name, head); \ 747 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ 748 (x) = (y)) 749 750 #define RB_FOREACH_REVERSE(x, name, head) \ 751 for ((x) = RB_MAX(name, head); \ 752 (x) != NULL; \ 753 (x) = name##_RB_PREV(x)) 754 755 #define RB_FOREACH_REVERSE_FROM(x, name, y) \ 756 for ((x) = (y); \ 757 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ 758 (x) = (y)) 759 760 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \ 761 for ((x) = RB_MAX(name, head); \ 762 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ 763 (x) = (y)) 764 765 #endif /* _SYS_TREE_H_ */ 766