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/* $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $ */ /* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $ */ /* $FreeBSD: release/9.0.0/sys/sys/tree.h 189204 2009-03-01 04:57:23Z bms $ */ /*- * Copyright 2002 Niels Provos <provos@citi.umich.edu> * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #ifndef _VTREE_H_ #define _VTREE_H_ /* * This file defines data structures for different types of trees: * splay trees and red-black trees. * * A splay tree is a self-organizing data structure. Every operation * on the tree causes a splay to happen. The splay moves the requested * node to the root of the tree and partly rebalances it. * * This has the benefit that request locality causes faster lookups as * the requested nodes move to the top of the tree. On the other hand, * every lookup causes memory writes. * * The Balance Theorem bounds the total access time for m operations * and n inserts on an initially empty tree as O((m + n)lg n). The * amortized cost for a sequence of m accesses to a splay tree is O(lg n); * * A red-black tree is a binary search tree with the node color as an * extra attribute. It fulfills a set of conditions: * - every search path from the root to a leaf consists of the * same number of black nodes, * - each red node (except for the root) has a black parent, * - each leaf node is black. * * Every operation on a red-black tree is bounded as O(lg n). * The maximum height of a red-black tree is 2lg (n+1). */ #define VSPLAY_HEAD(name, type) \ struct name { \ struct type *sph_root; /* root of the tree */ \ } #define VSPLAY_INITIALIZER(root) \ { NULL } #define VSPLAY_INIT(root) do { \ (root)->sph_root = NULL; \ } while (/*CONSTCOND*/ 0) #define VSPLAY_ENTRY(type) \ struct { \ struct type *spe_left; /* left element */ \ struct type *spe_right; /* right element */ \ } #define VSPLAY_LEFT(elm, field) (elm)->field.spe_left #define VSPLAY_RIGHT(elm, field) (elm)->field.spe_right #define VSPLAY_ROOT(head) (head)->sph_root #define VSPLAY_EMPTY(head) (VSPLAY_ROOT(head) == NULL) /* VSPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold VSPLAY_{RIGHT,LEFT} */ #define VSPLAY_ROTATE_RIGHT(head, tmp, field) do { \ VSPLAY_LEFT((head)->sph_root, field) = VSPLAY_RIGHT(tmp, field);\ VSPLAY_RIGHT(tmp, field) = (head)->sph_root; \ (head)->sph_root = tmp; \ } while (/*CONSTCOND*/ 0) #define VSPLAY_ROTATE_LEFT(head, tmp, field) do { \ VSPLAY_RIGHT((head)->sph_root, field) = VSPLAY_LEFT(tmp, field);\ VSPLAY_LEFT(tmp, field) = (head)->sph_root; \ (head)->sph_root = tmp; \ } while (/*CONSTCOND*/ 0) #define VSPLAY_LINKLEFT(head, tmp, field) do { \ VSPLAY_LEFT(tmp, field) = (head)->sph_root; \ tmp = (head)->sph_root; \ (head)->sph_root = VSPLAY_LEFT((head)->sph_root, field); \ } while (/*CONSTCOND*/ 0) #define VSPLAY_LINKRIGHT(head, tmp, field) do { \ VSPLAY_RIGHT(tmp, field) = (head)->sph_root; \ tmp = (head)->sph_root; \ (head)->sph_root = VSPLAY_RIGHT((head)->sph_root, field); \ } while (/*CONSTCOND*/ 0) #define VSPLAY_ASSEMBLE(head, node, left, right, field) do { \ VSPLAY_RIGHT(left, field) = VSPLAY_LEFT((head)->sph_root, field);\ VSPLAY_LEFT(right, field) = VSPLAY_RIGHT((head)->sph_root, field);\ VSPLAY_LEFT((head)->sph_root, field) = VSPLAY_RIGHT(node, field);\ VSPLAY_RIGHT((head)->sph_root, field) = VSPLAY_LEFT(node, field);\ } while (/*CONSTCOND*/ 0) /* Generates prototypes and inline functions */ #define VSPLAY_PROTOTYPE(name, type, field, cmp) \ void name##_VSPLAY(struct name *, struct type *); \ void name##_VSPLAY_MINMAX(struct name *, int); \ struct type *name##_VSPLAY_INSERT(struct name *, struct type *); \ struct type *name##_VSPLAY_REMOVE(struct name *, struct type *); \ \ /* Finds the node with the same key as elm */ \ static __inline struct type * \ name##_VSPLAY_FIND(struct name *head, struct type *elm) \ { \ if (VSPLAY_EMPTY(head)) \ return(NULL); \ name##_VSPLAY(head, elm); \ if ((cmp)(elm, (head)->sph_root) == 0) \ return (head->sph_root); \ return (NULL); \ } \ \ static __inline struct type * \ name##_VSPLAY_NEXT(struct name *head, struct type *elm) \ { \ name##_VSPLAY(head, elm); \ if (VSPLAY_RIGHT(elm, field) != NULL) { \ elm = VSPLAY_RIGHT(elm, field); \ while (VSPLAY_LEFT(elm, field) != NULL) { \ elm = VSPLAY_LEFT(elm, field); \ } \ } else \ elm = NULL; \ return (elm); \ } \ \ static __inline struct type * \ name##_VSPLAY_MIN_MAX(struct name *head, int val) \ { \ name##_VSPLAY_MINMAX(head, val); \ return (VSPLAY_ROOT(head)); \ } /* Main splay operation. * Moves node close to the key of elm to top */ #define VSPLAY_GENERATE(name, type, field, cmp) \ struct type * \ name##_VSPLAY_INSERT(struct name *head, struct type *elm) \ { \ if (VSPLAY_EMPTY(head)) { \ VSPLAY_LEFT(elm, field) = VSPLAY_RIGHT(elm, field) = NULL; \ } else { \ int __comp; \ name##_VSPLAY(head, elm); \ __comp = (cmp)(elm, (head)->sph_root); \ if (__comp < 0) { \ VSPLAY_LEFT(elm, field) = VSPLAY_LEFT((head)->sph_root, field);\ VSPLAY_RIGHT(elm, field) = (head)->sph_root; \ VSPLAY_LEFT((head)->sph_root, field) = NULL; \ } else if (__comp > 0) { \ VSPLAY_RIGHT(elm, field) = VSPLAY_RIGHT((head)->sph_root, field);\ VSPLAY_LEFT(elm, field) = (head)->sph_root; \ VSPLAY_RIGHT((head)->sph_root, field) = NULL; \ } else \ return ((head)->sph_root); \ } \ (head)->sph_root = (elm); \ return (NULL); \ } \ \ struct type * \ name##_VSPLAY_REMOVE(struct name *head, struct type *elm) \ { \ struct type *__tmp; \ if (VSPLAY_EMPTY(head)) \ return (NULL); \ name##_VSPLAY(head, elm); \ if ((cmp)(elm, (head)->sph_root) == 0) { \ if (VSPLAY_LEFT((head)->sph_root, field) == NULL) { \ (head)->sph_root = VSPLAY_RIGHT((head)->sph_root, field);\ } else { \ __tmp = VSPLAY_RIGHT((head)->sph_root, field); \ (head)->sph_root = VSPLAY_LEFT((head)->sph_root, field);\ name##_VSPLAY(head, elm); \ VSPLAY_RIGHT((head)->sph_root, field) = __tmp; \ } \ return (elm); \ } \ return (NULL); \ } \ \ void \ name##_VSPLAY(struct name *head, struct type *elm) \ { \ struct type __node, *__left, *__right, *__tmp; \ int __comp; \ \ VSPLAY_LEFT(&__node, field) = VSPLAY_RIGHT(&__node, field) = NULL;\ __left = __right = &__node; \ \ while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \ if (__comp < 0) { \ __tmp = VSPLAY_LEFT((head)->sph_root, field); \ if (__tmp == NULL) \ break; \ if ((cmp)(elm, __tmp) < 0){ \ VSPLAY_ROTATE_RIGHT(head, __tmp, field);\ if (VSPLAY_LEFT((head)->sph_root, field) == NULL)\ break; \ } \ VSPLAY_LINKLEFT(head, __right, field); \ } else if (__comp > 0) { \ __tmp = VSPLAY_RIGHT((head)->sph_root, field); \ if (__tmp == NULL) \ break; \ if ((cmp)(elm, __tmp) > 0){ \ VSPLAY_ROTATE_LEFT(head, __tmp, field); \ if (VSPLAY_RIGHT((head)->sph_root, field) == NULL)\ break; \ } \ VSPLAY_LINKRIGHT(head, __left, field); \ } \ } \ VSPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ } \ \ /* Splay with either the minimum or the maximum element \ * Used to find minimum or maximum element in tree. \ */ \ void name##_VSPLAY_MINMAX(struct name *head, int __comp) \ { \ struct type __node, *__left, *__right, *__tmp; \ \ VSPLAY_LEFT(&__node, field) = VSPLAY_RIGHT(&__node, field) = NULL;\ __left = __right = &__node; \ \ while (1) { \ if (__comp < 0) { \ __tmp = VSPLAY_LEFT((head)->sph_root, field); \ if (__tmp == NULL) \ break; \ if (__comp < 0){ \ VSPLAY_ROTATE_RIGHT(head, __tmp, field);\ if (VSPLAY_LEFT((head)->sph_root, field) == NULL)\ break; \ } \ VSPLAY_LINKLEFT(head, __right, field); \ } else if (__comp > 0) { \ __tmp = VSPLAY_RIGHT((head)->sph_root, field); \ if (__tmp == NULL) \ break; \ if (__comp > 0) { \ VSPLAY_ROTATE_LEFT(head, __tmp, field); \ if (VSPLAY_RIGHT((head)->sph_root, field) == NULL)\ break; \ } \ VSPLAY_LINKRIGHT(head, __left, field); \ } \ } \ VSPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ } #define VSPLAY_NEGINF -1 #define VSPLAY_INF 1 #define VSPLAY_INSERT(name, x, y) name##_VSPLAY_INSERT(x, y) #define VSPLAY_REMOVE(name, x, y) name##_VSPLAY_REMOVE(x, y) #define VSPLAY_FIND(name, x, y) name##_VSPLAY_FIND(x, y) #define VSPLAY_NEXT(name, x, y) name##_VSPLAY_NEXT(x, y) #define VSPLAY_MIN(name, x) (VSPLAY_EMPTY(x) ? NULL \ : name##_VSPLAY_MIN_MAX(x, VSPLAY_NEGINF)) #define VSPLAY_MAX(name, x) (VSPLAY_EMPTY(x) ? NULL \ : name##_VSPLAY_MIN_MAX(x, VSPLAY_INF)) #define VSPLAY_FOREACH(x, name, head) \ for ((x) = VSPLAY_MIN(name, head); \ (x) != NULL; \ (x) = VSPLAY_NEXT(name, head, x)) /* Macros that define a red-black tree */ #define VRB_HEAD(name, type) \ struct name { \ struct type *rbh_root; /* root of the tree */ \ } #define VRB_INITIALIZER(root) \ { NULL } #define VRB_INIT(root) do { \ (root)->rbh_root = NULL; \ } while (/*CONSTCOND*/ 0) #define VRB_BLACK 0 #define VRB_RED 1 #define VRB_ENTRY(type) \ struct { \ struct type *rbe_left; /* left element */ \ struct type *rbe_right; /* right element */ \ struct type *rbe_parent; /* parent element */ \ int rbe_color; /* node color */ \ } #define VRB_LEFT(elm, field) (elm)->field.rbe_left #define VRB_RIGHT(elm, field) (elm)->field.rbe_right #define VRB_PARENT(elm, field) (elm)->field.rbe_parent #define VRB_COLOR(elm, field) (elm)->field.rbe_color #define VRB_ROOT(head) (head)->rbh_root #define VRB_EMPTY(head) (VRB_ROOT(head) == NULL) #define VRB_SET(elm, parent, field) do { \ VRB_PARENT(elm, field) = parent; \ VRB_LEFT(elm, field) = VRB_RIGHT(elm, field) = NULL; \ VRB_COLOR(elm, field) = VRB_RED; \ } while (/*CONSTCOND*/ 0) #define VRB_SET_BLACKRED(black, red, field) do { \ VRB_COLOR(black, field) = VRB_BLACK; \ VRB_COLOR(red, field) = VRB_RED; \ } while (/*CONSTCOND*/ 0) #ifndef VRB_AUGMENT #define VRB_AUGMENT(x) do {} while (0) #endif #define VRB_ROTATE_LEFT(head, elm, tmp, field) do { \ (tmp) = VRB_RIGHT(elm, field); \ if ((VRB_RIGHT(elm, field) = VRB_LEFT(tmp, field)) != NULL) { \ VRB_PARENT(VRB_LEFT(tmp, field), field) = (elm); \ } \ VRB_AUGMENT(elm); \ if ((VRB_PARENT(tmp, field) = VRB_PARENT(elm, field)) != NULL) {\ if ((elm) == VRB_LEFT(VRB_PARENT(elm, field), field)) \ VRB_LEFT(VRB_PARENT(elm, field), field) = (tmp);\ else \ VRB_RIGHT(VRB_PARENT(elm, field), field) = (tmp);\ } else \ (head)->rbh_root = (tmp); \ VRB_LEFT(tmp, field) = (elm); \ VRB_PARENT(elm, field) = (tmp); \ VRB_AUGMENT(tmp); \ if ((VRB_PARENT(tmp, field))) \ VRB_AUGMENT(VRB_PARENT(tmp, field)); \ } while (/*CONSTCOND*/ 0) #define VRB_ROTATE_RIGHT(head, elm, tmp, field) do { \ (tmp) = VRB_LEFT(elm, field); \ if ((VRB_LEFT(elm, field) = VRB_RIGHT(tmp, field)) != NULL) { \ VRB_PARENT(VRB_RIGHT(tmp, field), field) = (elm); \ } \ VRB_AUGMENT(elm); \ if ((VRB_PARENT(tmp, field) = VRB_PARENT(elm, field)) != NULL) {\ if ((elm) == VRB_LEFT(VRB_PARENT(elm, field), field)) \ VRB_LEFT(VRB_PARENT(elm, field), field) = (tmp);\ else \ VRB_RIGHT(VRB_PARENT(elm, field), field) = (tmp);\ } else \ (head)->rbh_root = (tmp); \ VRB_RIGHT(tmp, field) = (elm); \ VRB_PARENT(elm, field) = (tmp); \ VRB_AUGMENT(tmp); \ if ((VRB_PARENT(tmp, field))) \ VRB_AUGMENT(VRB_PARENT(tmp, field)); \ } while (/*CONSTCOND*/ 0) /* Generates prototypes and inline functions */ #define VRB_PROTOTYPE(name, type, field, cmp) \ VRB_PROTOTYPE_INTERNAL(name, type, field, cmp,) #define VRB_PROTOTYPE_STATIC(name, type, field, cmp) \ VRB_PROTOTYPE_INTERNAL(name, type, field, cmp, v_unused_ static) #define VRB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \ /*lint -esym(528, name##_VRB_*) */ \ attr void name##_VRB_INSERT_COLOR(struct name *, struct type *); \ attr void name##_VRB_REMOVE_COLOR(struct name *, struct type *, struct type *);\ attr struct type *name##_VRB_REMOVE(struct name *, struct type *); \ attr struct type *name##_VRB_INSERT(struct name *, struct type *); \ attr struct type *name##_VRB_FIND(const struct name *, const struct type *); \ attr struct type *name##_VRB_NFIND(const struct name *, const struct type *); \ attr struct type *name##_VRB_NEXT(struct type *); \ attr struct type *name##_VRB_PREV(struct type *); \ attr struct type *name##_VRB_MINMAX(const struct name *, int); \ \ /* Main rb operation. * Moves node close to the key of elm to top */ #define VRB_GENERATE(name, type, field, cmp) \ VRB_GENERATE_INTERNAL(name, type, field, cmp,) #define VRB_GENERATE_STATIC(name, type, field, cmp) \ VRB_GENERATE_INTERNAL(name, type, field, cmp, v_unused_ static) #define VRB_GENERATE_INTERNAL(name, type, field, cmp, attr) \ attr void \ name##_VRB_INSERT_COLOR(struct name *head, struct type *elm) \ { \ struct type *parent, *gparent, *tmp; \ while ((parent = VRB_PARENT(elm, field)) != NULL && \ VRB_COLOR(parent, field) == VRB_RED) { \ gparent = VRB_PARENT(parent, field); \ if (parent == VRB_LEFT(gparent, field)) { \ tmp = VRB_RIGHT(gparent, field); \ if (tmp && VRB_COLOR(tmp, field) == VRB_RED) { \ VRB_COLOR(tmp, field) = VRB_BLACK; \ VRB_SET_BLACKRED(parent, gparent, field);\ elm = gparent; \ continue; \ } \ if (VRB_RIGHT(parent, field) == elm) { \ VRB_ROTATE_LEFT(head, parent, tmp, field);\ tmp = parent; \ parent = elm; \ elm = tmp; \ } \ VRB_SET_BLACKRED(parent, gparent, field); \ VRB_ROTATE_RIGHT(head, gparent, tmp, field); \ } else { \ tmp = VRB_LEFT(gparent, field); \ if (tmp && VRB_COLOR(tmp, field) == VRB_RED) { \ VRB_COLOR(tmp, field) = VRB_BLACK; \ VRB_SET_BLACKRED(parent, gparent, field);\ elm = gparent; \ continue; \ } \ if (VRB_LEFT(parent, field) == elm) { \ VRB_ROTATE_RIGHT(head, parent, tmp, field);\ tmp = parent; \ parent = elm; \ elm = tmp; \ } \ VRB_SET_BLACKRED(parent, gparent, field); \ VRB_ROTATE_LEFT(head, gparent, tmp, field); \ } \ } \ VRB_COLOR(head->rbh_root, field) = VRB_BLACK; \ } \ \ attr void \ name##_VRB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \ { \ struct type *tmp; \ while ((elm == NULL || VRB_COLOR(elm, field) == VRB_BLACK) && \ elm != VRB_ROOT(head)) { \ AN(parent); \ if (VRB_LEFT(parent, field) == elm) { \ tmp = VRB_RIGHT(parent, field); \ if (VRB_COLOR(tmp, field) == VRB_RED) { \ VRB_SET_BLACKRED(tmp, parent, field); \ VRB_ROTATE_LEFT(head, parent, tmp, field);\ tmp = VRB_RIGHT(parent, field); \ } \ if ((VRB_LEFT(tmp, field) == NULL || \ VRB_COLOR(VRB_LEFT(tmp, field), field) == VRB_BLACK) &&\ (VRB_RIGHT(tmp, field) == NULL || \ VRB_COLOR(VRB_RIGHT(tmp, field), field) == VRB_BLACK)) {\ VRB_COLOR(tmp, field) = VRB_RED; \ elm = parent; \ parent = VRB_PARENT(elm, field); \ } else { \ if (VRB_RIGHT(tmp, field) == NULL || \ VRB_COLOR(VRB_RIGHT(tmp, field), field) == VRB_BLACK) {\ struct type *oleft; \ if ((oleft = VRB_LEFT(tmp, field)) \ != NULL) \ VRB_COLOR(oleft, field) = VRB_BLACK;\ VRB_COLOR(tmp, field) = VRB_RED;\ VRB_ROTATE_RIGHT(head, tmp, oleft, field);\ tmp = VRB_RIGHT(parent, field); \ } \ VRB_COLOR(tmp, field) = VRB_COLOR(parent, field);\ VRB_COLOR(parent, field) = VRB_BLACK; \ if (VRB_RIGHT(tmp, field)) \ VRB_COLOR(VRB_RIGHT(tmp, field), field) = VRB_BLACK;\ VRB_ROTATE_LEFT(head, parent, tmp, field);\ elm = VRB_ROOT(head); \ break; \ } \ } else { \ tmp = VRB_LEFT(parent, field); \ if (VRB_COLOR(tmp, field) == VRB_RED) { \ VRB_SET_BLACKRED(tmp, parent, field); \ VRB_ROTATE_RIGHT(head, parent, tmp, field);\ tmp = VRB_LEFT(parent, field); \ } \ if ((VRB_LEFT(tmp, field) == NULL || \ VRB_COLOR(VRB_LEFT(tmp, field), field) == VRB_BLACK) &&\ (VRB_RIGHT(tmp, field) == NULL || \ VRB_COLOR(VRB_RIGHT(tmp, field), field) == VRB_BLACK)) {\ VRB_COLOR(tmp, field) = VRB_RED; \ elm = parent; \ parent = VRB_PARENT(elm, field); \ } else { \ if (VRB_LEFT(tmp, field) == NULL || \ VRB_COLOR(VRB_LEFT(tmp, field), field) == VRB_BLACK) {\ struct type *oright; \ if ((oright = VRB_RIGHT(tmp, field)) \ != NULL) \ VRB_COLOR(oright, field) = VRB_BLACK;\ VRB_COLOR(tmp, field) = VRB_RED;\ VRB_ROTATE_LEFT(head, tmp, oright, field);\ tmp = VRB_LEFT(parent, field); \ } \ VRB_COLOR(tmp, field) = VRB_COLOR(parent, field);\ VRB_COLOR(parent, field) = VRB_BLACK; \ if (VRB_LEFT(tmp, field)) \ VRB_COLOR(VRB_LEFT(tmp, field), field) = VRB_BLACK;\ VRB_ROTATE_RIGHT(head, parent, tmp, field);\ elm = VRB_ROOT(head); \ break; \ } \ } \ } \ if (elm) \ VRB_COLOR(elm, field) = VRB_BLACK; \ } \ \ attr struct type * \ name##_VRB_REMOVE(struct name *head, struct type *elm) \ { \ struct type *child, *parent, *old = elm; \ int color; \ if (VRB_LEFT(elm, field) == NULL) \ child = VRB_RIGHT(elm, field); \ else if (VRB_RIGHT(elm, field) == NULL) \ child = VRB_LEFT(elm, field); \ else { \ struct type *left; \ elm = VRB_RIGHT(elm, field); \ while ((left = VRB_LEFT(elm, field)) != NULL) \ elm = left; \ child = VRB_RIGHT(elm, field); \ parent = VRB_PARENT(elm, field); \ color = VRB_COLOR(elm, field); \ if (child) \ VRB_PARENT(child, field) = parent; \ if (parent) { \ if (VRB_LEFT(parent, field) == elm) \ VRB_LEFT(parent, field) = child; \ else \ VRB_RIGHT(parent, field) = child; \ VRB_AUGMENT(parent); \ } else \ VRB_ROOT(head) = child; \ if (VRB_PARENT(elm, field) == old) \ parent = elm; \ (elm)->field = (old)->field; \ if (VRB_PARENT(old, field)) { \ if (VRB_LEFT(VRB_PARENT(old, field), field) == old)\ VRB_LEFT(VRB_PARENT(old, field), field) = elm;\ else \ VRB_RIGHT(VRB_PARENT(old, field), field) = elm;\ VRB_AUGMENT(VRB_PARENT(old, field)); \ } else \ VRB_ROOT(head) = elm; \ VRB_PARENT(VRB_LEFT(old, field), field) = elm; \ if (VRB_RIGHT(old, field)) \ VRB_PARENT(VRB_RIGHT(old, field), field) = elm; \ if (parent) { \ left = parent; \ do { \ VRB_AUGMENT(left); \ } while ((left = VRB_PARENT(left, field)) != NULL); \ } \ goto color; \ } \ parent = VRB_PARENT(elm, field); \ color = VRB_COLOR(elm, field); \ if (child) \ VRB_PARENT(child, field) = parent; \ if (parent) { \ if (VRB_LEFT(parent, field) == elm) \ VRB_LEFT(parent, field) = child; \ else \ VRB_RIGHT(parent, field) = child; \ VRB_AUGMENT(parent); \ } else \ VRB_ROOT(head) = child; \ color: \ if (color == VRB_BLACK) { \ name##_VRB_REMOVE_COLOR(head, parent, child); \ } \ return (old); \ } \ \ /* Inserts a node into the RB tree */ \ attr struct type * \ name##_VRB_INSERT(struct name *head, struct type *elm) \ { \ struct type *tmp; \ struct type *parent = NULL; \ int comp = 0; \ tmp = VRB_ROOT(head); \ while (tmp) { \ parent = tmp; \ comp = (cmp)(elm, parent); \ if (comp < 0) \ tmp = VRB_LEFT(tmp, field); \ else if (comp > 0) \ tmp = VRB_RIGHT(tmp, field); \ else \ return (tmp); \ } \ VRB_SET(elm, parent, field); \ if (parent != NULL) { \ if (comp < 0) \ VRB_LEFT(parent, field) = elm; \ else \ VRB_RIGHT(parent, field) = elm; \ VRB_AUGMENT(parent); \ } else \ VRB_ROOT(head) = elm; \ name##_VRB_INSERT_COLOR(head, elm); \ return (NULL); \ } \ \ /* Finds the node with the same key as elm */ \ attr struct type * \ name##_VRB_FIND(const struct name *head, const struct type *elm) \ { \ struct type *tmp = VRB_ROOT(head); \ int comp; \ while (tmp) { \ comp = cmp(elm, tmp); \ if (comp < 0) \ tmp = VRB_LEFT(tmp, field); \ else if (comp > 0) \ tmp = VRB_RIGHT(tmp, field); \ else \ return (tmp); \ } \ return (NULL); \ } \ \ /* Finds the first node greater than or equal to the search key */ \ attr struct type * \ name##_VRB_NFIND(const struct name *head, const struct type *elm) \ { \ struct type *tmp = VRB_ROOT(head); \ struct type *res = NULL; \ int comp; \ while (tmp) { \ comp = cmp(elm, tmp); \ if (comp < 0) { \ res = tmp; \ tmp = VRB_LEFT(tmp, field); \ } \ else if (comp > 0) \ tmp = VRB_RIGHT(tmp, field); \ else \ return (tmp); \ } \ return (res); \ } \ \ /* ARGSUSED */ \ attr struct type * \ name##_VRB_NEXT(struct type *elm) \ { \ if (VRB_RIGHT(elm, field)) { \ elm = VRB_RIGHT(elm, field); \ while (VRB_LEFT(elm, field)) \ elm = VRB_LEFT(elm, field); \ } else { \ if (VRB_PARENT(elm, field) && \ (elm == VRB_LEFT(VRB_PARENT(elm, field), field))) \ elm = VRB_PARENT(elm, field); \ else { \ while (VRB_PARENT(elm, field) && \ (elm == VRB_RIGHT(VRB_PARENT(elm, field), field)))\ elm = VRB_PARENT(elm, field); \ elm = VRB_PARENT(elm, field); \ } \ } \ return (elm); \ } \ \ /* ARGSUSED */ \ attr struct type * \ name##_VRB_PREV(struct type *elm) \ { \ if (VRB_LEFT(elm, field)) { \ elm = VRB_LEFT(elm, field); \ while (VRB_RIGHT(elm, field)) \ elm = VRB_RIGHT(elm, field); \ } else { \ if (VRB_PARENT(elm, field) && \ (elm == VRB_RIGHT(VRB_PARENT(elm, field), field))) \ elm = VRB_PARENT(elm, field); \ else { \ while (VRB_PARENT(elm, field) && \ (elm == VRB_LEFT(VRB_PARENT(elm, field), field)))\ elm = VRB_PARENT(elm, field); \ elm = VRB_PARENT(elm, field); \ } \ } \ return (elm); \ } \ \ attr struct type * \ name##_VRB_MINMAX(const struct name *head, int val) \ { \ struct type *tmp = VRB_ROOT(head); \ struct type *parent = NULL; \ while (tmp) { \ parent = tmp; \ if (val < 0) \ tmp = VRB_LEFT(tmp, field); \ else \ tmp = VRB_RIGHT(tmp, field); \ } \ return (parent); \ } #define VRB_NEGINF -1 #define VRB_INF 1 #define VRB_INSERT(name, x, y) name##_VRB_INSERT(x, y) #define VRB_REMOVE(name, x, y) name##_VRB_REMOVE(x, y) #define VRB_FIND(name, x, y) name##_VRB_FIND(x, y) #define VRB_NFIND(name, x, y) name##_VRB_NFIND(x, y) #define VRB_NEXT(name, x, y) name##_VRB_NEXT(y) #define VRB_PREV(name, x, y) name##_VRB_PREV(y) #define VRB_MIN(name, x) name##_VRB_MINMAX(x, VRB_NEGINF) #define VRB_MAX(name, x) name##_VRB_MINMAX(x, VRB_INF) #define VRB_FOREACH(x, name, head) \ for ((x) = VRB_MIN(name, head); \ (x) != NULL; \ (x) = name##_VRB_NEXT(x)) #define VRB_FOREACH_FROM(x, name, y) \ for ((x) = (y); \ ((x) != NULL) && ((y) = name##_VRB_NEXT(x), (x) != NULL); \ (x) = (y)) #define VRB_FOREACH_SAFE(x, name, head, y) \ for ((x) = VRB_MIN(name, head); \ ((x) != NULL) && ((y) = name##_VRB_NEXT(x), (x) != NULL); \ (x) = (y)) #define VRB_FOREACH_REVERSE(x, name, head) \ for ((x) = VRB_MAX(name, head); \ (x) != NULL; \ (x) = name##_VRB_PREV(x)) #define VRB_FOREACH_REVERSE_FROM(x, name, y) \ for ((x) = (y); \ ((x) != NULL) && ((y) = name##_VRB_PREV(x), (x) != NULL); \ (x) = (y)) #define VRB_FOREACH_REVERSE_SAFE(x, name, head, y) \ for ((x) = VRB_MAX(name, head); \ ((x) != NULL) && ((y) = name##_VRB_PREV(x), (x) != NULL); \ (x) = (y)) #endif /* _VTREE_H_ */