/* $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 $ *//* $FreeBSD$ */ /*- * 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. */ #pragma once /* * 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 SPLAY_HEAD(name, type) \struct name { \ struct type *sph_root; /* root of the tree */ \} #define SPLAY_INITIALIZER(root) \ { nil } #define SPLAY_INIT(root) do { \ (root)->sph_root = nil; \} while (/*CONSTCOND*/ 0) #define SPLAY_ENTRY(type) \struct { \ struct type *spe_left; /* left element */ \ struct type *spe_right; /* right element */ \} #define SPLAY_LEFT(elm, field) (elm)->field.spe_left#define SPLAY_RIGHT(elm, field) (elm)->field.spe_right#define SPLAY_ROOT(head) (head)->sph_root#define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == nil) /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */#define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \ SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \ SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ (head)->sph_root = tmp; \} while (/*CONSTCOND*/ 0) #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \ SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \ SPLAY_LEFT(tmp, field) = (head)->sph_root; \ (head)->sph_root = tmp; \} while (/*CONSTCOND*/ 0) #define SPLAY_LINKLEFT(head, tmp, field) do { \ SPLAY_LEFT(tmp, field) = (head)->sph_root; \ tmp = (head)->sph_root; \ (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \} while (/*CONSTCOND*/ 0) #define SPLAY_LINKRIGHT(head, tmp, field) do { \ SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ tmp = (head)->sph_root; \ (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \} while (/*CONSTCOND*/ 0) #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \ SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \ SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\ SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \ SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \} while (/*CONSTCOND*/ 0) /* Generates prototypes and inline functions */ #define SPLAY_PROTOTYPE(name, type, field, cmp) \void name##_SPLAY(struct name *, struct type *); \void name##_SPLAY_MINMAX(struct name *, int); \struct type *name##_SPLAY_INSERT(struct name *, struct type *); \struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \ \/* Finds the node with the same key as elm */ \static __inline struct type * \name##_SPLAY_FIND(struct name *head, struct type *elm) \{ \ if (SPLAY_EMPTY(head)) \ return(nil); \ name##_SPLAY(head, elm); \ if ((cmp)(elm, (head)->sph_root) == 0) \ return (head->sph_root); \ return (nil); \} \ \static __inline struct type * \name##_SPLAY_NEXT(struct name *head, struct type *elm) \{ \ name##_SPLAY(head, elm); \ if (SPLAY_RIGHT(elm, field) != nil) { \ elm = SPLAY_RIGHT(elm, field); \ while (SPLAY_LEFT(elm, field) != nil) { \ elm = SPLAY_LEFT(elm, field); \ } \ } else \ elm = nil; \ return (elm); \} \ \static __inline struct type * \name##_SPLAY_MIN_MAX(struct name *head, int val) \{ \ name##_SPLAY_MINMAX(head, val); \ return (SPLAY_ROOT(head)); \} /* Main splay operation. * Moves node close to the key of elm to top */#define SPLAY_GENERATE(name, type, field, cmp) \struct type * \name##_SPLAY_INSERT(struct name *head, struct type *elm) \{ \ if (SPLAY_EMPTY(head)) { \ SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = nil; \ } else { \ int __comp; \ name##_SPLAY(head, elm); \ __comp = (cmp)(elm, (head)->sph_root); \ if(__comp < 0) { \ SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\ SPLAY_RIGHT(elm, field) = (head)->sph_root; \ SPLAY_LEFT((head)->sph_root, field) = nil; \ } else if (__comp > 0) { \ SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\ SPLAY_LEFT(elm, field) = (head)->sph_root; \ SPLAY_RIGHT((head)->sph_root, field) = nil; \ } else \ return ((head)->sph_root); \ } \ (head)->sph_root = (elm); \ return (nil); \} \ \struct type * \name##_SPLAY_REMOVE(struct name *head, struct type *elm) \{ \ struct type *__tmp; \ if (SPLAY_EMPTY(head)) \ return (nil); \ name##_SPLAY(head, elm); \ if ((cmp)(elm, (head)->sph_root) == 0) { \ if (SPLAY_LEFT((head)->sph_root, field) == nil) { \ (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\ } else { \ __tmp = SPLAY_RIGHT((head)->sph_root, field); \ (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\ name##_SPLAY(head, elm); \ SPLAY_RIGHT((head)->sph_root, field) = __tmp; \ } \ return (elm); \ } \ return (nil); \} \ \void \name##_SPLAY(struct name *head, struct type *elm) \{ \ struct type __node, *__left, *__right, *__tmp; \ int __comp; \\ SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = nil;\ __left = __right = &__node; \\ while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \ if (__comp < 0) { \ __tmp = SPLAY_LEFT((head)->sph_root, field); \ if (__tmp == nil) \ break; \ if ((cmp)(elm, __tmp) < 0){ \ SPLAY_ROTATE_RIGHT(head, __tmp, field); \ if (SPLAY_LEFT((head)->sph_root, field) == nil)\ break; \ } \ SPLAY_LINKLEFT(head, __right, field); \ } else if (__comp > 0) { \ __tmp = SPLAY_RIGHT((head)->sph_root, field); \ if (__tmp == nil) \ break; \ if ((cmp)(elm, __tmp) > 0){ \ SPLAY_ROTATE_LEFT(head, __tmp, field); \ if (SPLAY_RIGHT((head)->sph_root, field) == nil)\ break; \ } \ SPLAY_LINKRIGHT(head, __left, field); \ } \ } \ SPLAY_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##_SPLAY_MINMAX(struct name *head, int __comp) \{ \ struct type __node, *__left, *__right, *__tmp; \\ SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = nil;\ __left = __right = &__node; \\ while (1) { \ if (__comp < 0) { \ __tmp = SPLAY_LEFT((head)->sph_root, field); \ if (__tmp == nil) \ break; \ if (__comp < 0){ \ SPLAY_ROTATE_RIGHT(head, __tmp, field); \ if (SPLAY_LEFT((head)->sph_root, field) == nil)\ break; \ } \ SPLAY_LINKLEFT(head, __right, field); \ } else if (__comp > 0) { \ __tmp = SPLAY_RIGHT((head)->sph_root, field); \ if (__tmp == nil) \ break; \ if (__comp > 0) { \ SPLAY_ROTATE_LEFT(head, __tmp, field); \ if (SPLAY_RIGHT((head)->sph_root, field) == nil)\ break; \ } \ SPLAY_LINKRIGHT(head, __left, field); \ } \ } \ SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \} #define SPLAY_NEGINF -1#define SPLAY_INF 1 #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)#define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)#define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)#define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)#define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? nil \ : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))#define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? nil \ : name##_SPLAY_MIN_MAX(x, SPLAY_INF)) #define SPLAY_FOREACH(x, name, head) \ for ((x) = SPLAY_MIN(name, head); \ (x) != nil; \ (x) = SPLAY_NEXT(name, head, x)) /* Macros that define a red-black tree */#define RB_HEAD(name, type) \struct name { \ struct type *rbh_root; /* root of the tree */ \} #define RB_INITIALIZER(root) \ { nil } #define RB_INIT(root) do { \ (root)->rbh_root = nil; \} while (/*CONSTCOND*/ 0) #define RB_BLACK 0#define RB_RED 1#define RB_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 RB_LEFT(elm, field) (elm)->field.rbe_left#define RB_RIGHT(elm, field) (elm)->field.rbe_right#define RB_PARENT(elm, field) (elm)->field.rbe_parent#define RB_COLOR(elm, field) (elm)->field.rbe_color#define RB_ROOT(head) (head)->rbh_root#define RB_EMPTY(head) (RB_ROOT(head) == nil) #define RB_SET(elm, parent, field) do { \ RB_PARENT(elm, field) = parent; \ RB_LEFT(elm, field) = RB_RIGHT(elm, field) = nil; \ RB_COLOR(elm, field) = RB_RED; \} while (/*CONSTCOND*/ 0) #define RB_SET_BLACKRED(black, red, field) do { \ RB_COLOR(black, field) = RB_BLACK; \ RB_COLOR(red, field) = RB_RED; \} while (/*CONSTCOND*/ 0) #ifndef RB_AUGMENT#define RB_AUGMENT(x) do {} while (0)#endif #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \ (tmp) = RB_RIGHT(elm, field); \ if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != nil) { \ RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \ } \ RB_AUGMENT(elm); \ if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != nil) { \ if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \ RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ else \ RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ } else \ (head)->rbh_root = (tmp); \ RB_LEFT(tmp, field) = (elm); \ RB_PARENT(elm, field) = (tmp); \ RB_AUGMENT(tmp); \ if ((RB_PARENT(tmp, field))) \ RB_AUGMENT(RB_PARENT(tmp, field)); \} while (/*CONSTCOND*/ 0) #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \ (tmp) = RB_LEFT(elm, field); \ if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != nil) { \ RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \ } \ RB_AUGMENT(elm); \ if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != nil) { \ if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \ RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ else \ RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ } else \ (head)->rbh_root = (tmp); \ RB_RIGHT(tmp, field) = (elm); \ RB_PARENT(elm, field) = (tmp); \ RB_AUGMENT(tmp); \ if ((RB_PARENT(tmp, field))) \ RB_AUGMENT(RB_PARENT(tmp, field)); \} while (/*CONSTCOND*/ 0) /* Generates prototypes and inline functions */#define RB_PROTOTYPE(name, type, field, cmp) \ RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)#define RB_PROTOTYPE_STATIC(name, type, field, cmp) \ RB_PROTOTYPE_INTERNAL(name, type, field, cmp, static)#define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \ RB_PROTOTYPE_INSERT_COLOR(name, type, attr); \ RB_PROTOTYPE_REMOVE_COLOR(name, type, attr); \ RB_PROTOTYPE_INSERT(name, type, attr); \ RB_PROTOTYPE_REMOVE(name, type, attr); \ RB_PROTOTYPE_FIND(name, type, attr); \ RB_PROTOTYPE_NFIND(name, type, attr); \ RB_PROTOTYPE_NEXT(name, type, attr); \ RB_PROTOTYPE_PREV(name, type, attr); \ RB_PROTOTYPE_MINMAX(name, type, attr);#define RB_PROTOTYPE_INSERT_COLOR(name, type, attr) \ attr void name##_RB_INSERT_COLOR(struct name *, struct type *)#define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr) \ attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *)#define RB_PROTOTYPE_REMOVE(name, type, attr) \ attr struct type *name##_RB_REMOVE(struct name *, struct type *)#define RB_PROTOTYPE_INSERT(name, type, attr) \ attr struct type *name##_RB_INSERT(struct name *, struct type *)#define RB_PROTOTYPE_FIND(name, type, attr) \ attr struct type *name##_RB_FIND(struct name *, struct type *)#define RB_PROTOTYPE_NFIND(name, type, attr) \ attr struct type *name##_RB_NFIND(struct name *, struct type *)#define RB_PROTOTYPE_NEXT(name, type, attr) \ attr struct type *name##_RB_NEXT(struct type *)#define RB_PROTOTYPE_PREV(name, type, attr) \ attr struct type *name##_RB_PREV(struct type *)#define RB_PROTOTYPE_MINMAX(name, type, attr) \ attr struct type *name##_RB_MINMAX(struct name *, int) /* Main rb operation. * Moves node close to the key of elm to top */#define RB_GENERATE(name, type, field, cmp) \ RB_GENERATE_INTERNAL(name, type, field, cmp,)#define RB_GENERATE_STATIC(name, type, field, cmp) \ RB_GENERATE_INTERNAL(name, type, field, cmp, static)#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \ RB_GENERATE_INSERT_COLOR(name, type, field, attr) \ RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \ RB_GENERATE_INSERT(name, type, field, cmp, attr) \ RB_GENERATE_REMOVE(name, type, field, attr) \ RB_GENERATE_FIND(name, type, field, cmp, attr) \ RB_GENERATE_NFIND(name, type, field, cmp, attr) \ RB_GENERATE_NEXT(name, type, field, attr) \ RB_GENERATE_PREV(name, type, field, attr) \ RB_GENERATE_MINMAX(name, type, field, attr) #define RB_GENERATE_INSERT_COLOR(name, type, field, attr) \attr void \name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \{ \ struct type *parent, *gparent, *tmp; \ while ((parent = RB_PARENT(elm, field)) != nil && \ RB_COLOR(parent, field) == RB_RED) { \ gparent = RB_PARENT(parent, field); \ if (parent == RB_LEFT(gparent, field)) { \ tmp = RB_RIGHT(gparent, field); \ if (tmp && RB_COLOR(tmp, field) == RB_RED) { \ RB_COLOR(tmp, field) = RB_BLACK; \ RB_SET_BLACKRED(parent, gparent, field);\ elm = gparent; \ continue; \ } \ if (RB_RIGHT(parent, field) == elm) { \ RB_ROTATE_LEFT(head, parent, tmp, field);\ tmp = parent; \ parent = elm; \ elm = tmp; \ } \ RB_SET_BLACKRED(parent, gparent, field); \ RB_ROTATE_RIGHT(head, gparent, tmp, field); \ } else { \ tmp = RB_LEFT(gparent, field); \ if (tmp && RB_COLOR(tmp, field) == RB_RED) { \ RB_COLOR(tmp, field) = RB_BLACK; \ RB_SET_BLACKRED(parent, gparent, field);\ elm = gparent; \ continue; \ } \ if (RB_LEFT(parent, field) == elm) { \ RB_ROTATE_RIGHT(head, parent, tmp, field);\ tmp = parent; \ parent = elm; \ elm = tmp; \ } \ RB_SET_BLACKRED(parent, gparent, field); \ RB_ROTATE_LEFT(head, gparent, tmp, field); \ } \ } \ RB_COLOR(head->rbh_root, field) = RB_BLACK; \} #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \attr void \name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \{ \ struct type *tmp; \ while ((elm == nil || RB_COLOR(elm, field) == RB_BLACK) && \ elm != RB_ROOT(head) && parent != nil) { \ if (RB_LEFT(parent, field) == elm) { \ tmp = RB_RIGHT(parent, field); \ if (RB_COLOR(tmp, field) == RB_RED) { \ RB_SET_BLACKRED(tmp, parent, field); \ RB_ROTATE_LEFT(head, parent, tmp, field);\ tmp = RB_RIGHT(parent, field); \ } \ if ((RB_LEFT(tmp, field) == nil || \ RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\ (RB_RIGHT(tmp, field) == nil || \ RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\ RB_COLOR(tmp, field) = RB_RED; \ elm = parent; \ parent = RB_PARENT(elm, field); \ } else { \ if (RB_RIGHT(tmp, field) == nil || \ RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\ struct type *oleft; \ if ((oleft = RB_LEFT(tmp, field)) \ != nil) \Lines 1–500 of 796. 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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 $ */ /* $FreeBSD$ */ /*- * 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. */ #pragma once /* * 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 SPLAY_HEAD(name, type) \ struct name { \ struct type *sph_root; /* root of the tree */ \ } #define SPLAY_INITIALIZER(root) \ { nil } #define SPLAY_INIT(root) do { \ (root)->sph_root = nil; \ } while (/*CONSTCOND*/ 0) #define SPLAY_ENTRY(type) \ struct { \ struct type *spe_left; /* left element */ \ struct type *spe_right; /* right element */ \ } #define SPLAY_LEFT(elm, field) (elm)->field.spe_left #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right #define SPLAY_ROOT(head) (head)->sph_root #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == nil) /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */ #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \ SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \ SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ (head)->sph_root = tmp; \ } while (/*CONSTCOND*/ 0) #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \ SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \ SPLAY_LEFT(tmp, field) = (head)->sph_root; \ (head)->sph_root = tmp; \ } while (/*CONSTCOND*/ 0) #define SPLAY_LINKLEFT(head, tmp, field) do { \ SPLAY_LEFT(tmp, field) = (head)->sph_root; \ tmp = (head)->sph_root; \ (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \ } while (/*CONSTCOND*/ 0) #define SPLAY_LINKRIGHT(head, tmp, field) do { \ SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ tmp = (head)->sph_root; \ (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \ } while (/*CONSTCOND*/ 0) #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \ SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \ SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\ SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \ SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \ } while (/*CONSTCOND*/ 0) /* Generates prototypes and inline functions */ #define SPLAY_PROTOTYPE(name, type, field, cmp) \ void name##_SPLAY(struct name *, struct type *); \ void name##_SPLAY_MINMAX(struct name *, int); \ struct type *name##_SPLAY_INSERT(struct name *, struct type *); \ struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \ \ /* Finds the node with the same key as elm */ \ static __inline struct type * \ name##_SPLAY_FIND(struct name *head, struct type *elm) \ { \ if (SPLAY_EMPTY(head)) \ return(nil); \ name##_SPLAY(head, elm); \ if ((cmp)(elm, (head)->sph_root) == 0) \ return (head->sph_root); \ return (nil); \ } \ \ static __inline struct type * \ name##_SPLAY_NEXT(struct name *head, struct type *elm) \ { \ name##_SPLAY(head, elm); \ if (SPLAY_RIGHT(elm, field) != nil) { \ elm = SPLAY_RIGHT(elm, field); \ while (SPLAY_LEFT(elm, field) != nil) { \ elm = SPLAY_LEFT(elm, field); \ } \ } else \ elm = nil; \ return (elm); \ } \ \ static __inline struct type * \ name##_SPLAY_MIN_MAX(struct name *head, int val) \ { \ name##_SPLAY_MINMAX(head, val); \ return (SPLAY_ROOT(head)); \ } /* Main splay operation. * Moves node close to the key of elm to top */ #define SPLAY_GENERATE(name, type, field, cmp) \ struct type * \ name##_SPLAY_INSERT(struct name *head, struct type *elm) \ { \ if (SPLAY_EMPTY(head)) { \ SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = nil; \ } else { \ int __comp; \ name##_SPLAY(head, elm); \ __comp = (cmp)(elm, (head)->sph_root); \ if(__comp < 0) { \ SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\ SPLAY_RIGHT(elm, field) = (head)->sph_root; \ SPLAY_LEFT((head)->sph_root, field) = nil; \ } else if (__comp > 0) { \ SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\ SPLAY_LEFT(elm, field) = (head)->sph_root; \ SPLAY_RIGHT((head)->sph_root, field) = nil; \ } else \ return ((head)->sph_root); \ } \ (head)->sph_root = (elm); \ return (nil); \ } \ \ struct type * \ name##_SPLAY_REMOVE(struct name *head, struct type *elm) \ { \ struct type *__tmp; \ if (SPLAY_EMPTY(head)) \ return (nil); \ name##_SPLAY(head, elm); \ if ((cmp)(elm, (head)->sph_root) == 0) { \ if (SPLAY_LEFT((head)->sph_root, field) == nil) { \ (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\ } else { \ __tmp = SPLAY_RIGHT((head)->sph_root, field); \ (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\ name##_SPLAY(head, elm); \ SPLAY_RIGHT((head)->sph_root, field) = __tmp; \ } \ return (elm); \ } \ return (nil); \ } \ \ void \ name##_SPLAY(struct name *head, struct type *elm) \ { \ struct type __node, *__left, *__right, *__tmp; \ int __comp; \ \ SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = nil;\ __left = __right = &__node; \ \ while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \ if (__comp < 0) { \ __tmp = SPLAY_LEFT((head)->sph_root, field); \ if (__tmp == nil) \ break; \ if ((cmp)(elm, __tmp) < 0){ \ SPLAY_ROTATE_RIGHT(head, __tmp, field); \ if (SPLAY_LEFT((head)->sph_root, field) == nil)\ break; \ } \ SPLAY_LINKLEFT(head, __right, field); \ } else if (__comp > 0) { \ __tmp = SPLAY_RIGHT((head)->sph_root, field); \ if (__tmp == nil) \ break; \ if ((cmp)(elm, __tmp) > 0){ \ SPLAY_ROTATE_LEFT(head, __tmp, field); \ if (SPLAY_RIGHT((head)->sph_root, field) == nil)\ break; \ } \ SPLAY_LINKRIGHT(head, __left, field); \ } \ } \ SPLAY_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##_SPLAY_MINMAX(struct name *head, int __comp) \ { \ struct type __node, *__left, *__right, *__tmp; \ \ SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = nil;\ __left = __right = &__node; \ \ while (1) { \ if (__comp < 0) { \ __tmp = SPLAY_LEFT((head)->sph_root, field); \ if (__tmp == nil) \ break; \ if (__comp < 0){ \ SPLAY_ROTATE_RIGHT(head, __tmp, field); \ if (SPLAY_LEFT((head)->sph_root, field) == nil)\ break; \ } \ SPLAY_LINKLEFT(head, __right, field); \ } else if (__comp > 0) { \ __tmp = SPLAY_RIGHT((head)->sph_root, field); \ if (__tmp == nil) \ break; \ if (__comp > 0) { \ SPLAY_ROTATE_LEFT(head, __tmp, field); \ if (SPLAY_RIGHT((head)->sph_root, field) == nil)\ break; \ } \ SPLAY_LINKRIGHT(head, __left, field); \ } \ } \ SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ } #define SPLAY_NEGINF -1 #define SPLAY_INF 1 #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y) #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y) #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y) #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y) #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? nil \ : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF)) #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? nil \ : name##_SPLAY_MIN_MAX(x, SPLAY_INF)) #define SPLAY_FOREACH(x, name, head) \ for ((x) = SPLAY_MIN(name, head); \ (x) != nil; \ (x) = SPLAY_NEXT(name, head, x)) /* Macros that define a red-black tree */ #define RB_HEAD(name, type) \ struct name { \ struct type *rbh_root; /* root of the tree */ \ } #define RB_INITIALIZER(root) \ { nil } #define RB_INIT(root) do { \ (root)->rbh_root = nil; \ } while (/*CONSTCOND*/ 0) #define RB_BLACK 0 #define RB_RED 1 #define RB_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 RB_LEFT(elm, field) (elm)->field.rbe_left #define RB_RIGHT(elm, field) (elm)->field.rbe_right #define RB_PARENT(elm, field) (elm)->field.rbe_parent #define RB_COLOR(elm, field) (elm)->field.rbe_color #define RB_ROOT(head) (head)->rbh_root #define RB_EMPTY(head) (RB_ROOT(head) == nil) #define RB_SET(elm, parent, field) do { \ RB_PARENT(elm, field) = parent; \ RB_LEFT(elm, field) = RB_RIGHT(elm, field) = nil; \ RB_COLOR(elm, field) = RB_RED; \ } while (/*CONSTCOND*/ 0) #define RB_SET_BLACKRED(black, red, field) do { \ RB_COLOR(black, field) = RB_BLACK; \ RB_COLOR(red, field) = RB_RED; \ } while (/*CONSTCOND*/ 0) #ifndef RB_AUGMENT #define RB_AUGMENT(x) do {} while (0) #endif #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \ (tmp) = RB_RIGHT(elm, field); \ if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != nil) { \ RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \ } \ RB_AUGMENT(elm); \ if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != nil) { \ if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \ RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ else \ RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ } else \ (head)->rbh_root = (tmp); \ RB_LEFT(tmp, field) = (elm); \ RB_PARENT(elm, field) = (tmp); \ RB_AUGMENT(tmp); \ if ((RB_PARENT(tmp, field))) \ RB_AUGMENT(RB_PARENT(tmp, field)); \ } while (/*CONSTCOND*/ 0) #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \ (tmp) = RB_LEFT(elm, field); \ if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != nil) { \ RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \ } \ RB_AUGMENT(elm); \ if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != nil) { \ if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \ RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ else \ RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ } else \ (head)->rbh_root = (tmp); \ RB_RIGHT(tmp, field) = (elm); \ RB_PARENT(elm, field) = (tmp); \ RB_AUGMENT(tmp); \ if ((RB_PARENT(tmp, field))) \ RB_AUGMENT(RB_PARENT(tmp, field)); \ } while (/*CONSTCOND*/ 0) /* Generates prototypes and inline functions */ #define RB_PROTOTYPE(name, type, field, cmp) \ RB_PROTOTYPE_INTERNAL(name, type, field, cmp,) #define RB_PROTOTYPE_STATIC(name, type, field, cmp) \ RB_PROTOTYPE_INTERNAL(name, type, field, cmp, static) #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \ RB_PROTOTYPE_INSERT_COLOR(name, type, attr); \ RB_PROTOTYPE_REMOVE_COLOR(name, type, attr); \ RB_PROTOTYPE_INSERT(name, type, attr); \ RB_PROTOTYPE_REMOVE(name, type, attr); \ RB_PROTOTYPE_FIND(name, type, attr); \ RB_PROTOTYPE_NFIND(name, type, attr); \ RB_PROTOTYPE_NEXT(name, type, attr); \ RB_PROTOTYPE_PREV(name, type, attr); \ RB_PROTOTYPE_MINMAX(name, type, attr); #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr) \ attr void name##_RB_INSERT_COLOR(struct name *, struct type *) #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr) \ attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *) #define RB_PROTOTYPE_REMOVE(name, type, attr) \ attr struct type *name##_RB_REMOVE(struct name *, struct type *) #define RB_PROTOTYPE_INSERT(name, type, attr) \ attr struct type *name##_RB_INSERT(struct name *, struct type *) #define RB_PROTOTYPE_FIND(name, type, attr) \ attr struct type *name##_RB_FIND(struct name *, struct type *) #define RB_PROTOTYPE_NFIND(name, type, attr) \ attr struct type *name##_RB_NFIND(struct name *, struct type *) #define RB_PROTOTYPE_NEXT(name, type, attr) \ attr struct type *name##_RB_NEXT(struct type *) #define RB_PROTOTYPE_PREV(name, type, attr) \ attr struct type *name##_RB_PREV(struct type *) #define RB_PROTOTYPE_MINMAX(name, type, attr) \ attr struct type *name##_RB_MINMAX(struct name *, int) /* Main rb operation. * Moves node close to the key of elm to top */ #define RB_GENERATE(name, type, field, cmp) \ RB_GENERATE_INTERNAL(name, type, field, cmp,) #define RB_GENERATE_STATIC(name, type, field, cmp) \ RB_GENERATE_INTERNAL(name, type, field, cmp, static) #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \ RB_GENERATE_INSERT_COLOR(name, type, field, attr) \ RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \ RB_GENERATE_INSERT(name, type, field, cmp, attr) \ RB_GENERATE_REMOVE(name, type, field, attr) \ RB_GENERATE_FIND(name, type, field, cmp, attr) \ RB_GENERATE_NFIND(name, type, field, cmp, attr) \ RB_GENERATE_NEXT(name, type, field, attr) \ RB_GENERATE_PREV(name, type, field, attr) \ RB_GENERATE_MINMAX(name, type, field, attr) #define RB_GENERATE_INSERT_COLOR(name, type, field, attr) \ attr void \ name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \ { \ struct type *parent, *gparent, *tmp; \ while ((parent = RB_PARENT(elm, field)) != nil && \ RB_COLOR(parent, field) == RB_RED) { \ gparent = RB_PARENT(parent, field); \ if (parent == RB_LEFT(gparent, field)) { \ tmp = RB_RIGHT(gparent, field); \ if (tmp && RB_COLOR(tmp, field) == RB_RED) { \ RB_COLOR(tmp, field) = RB_BLACK; \ RB_SET_BLACKRED(parent, gparent, field);\ elm = gparent; \ continue; \ } \ if (RB_RIGHT(parent, field) == elm) { \ RB_ROTATE_LEFT(head, parent, tmp, field);\ tmp = parent; \ parent = elm; \ elm = tmp; \ } \ RB_SET_BLACKRED(parent, gparent, field); \ RB_ROTATE_RIGHT(head, gparent, tmp, field); \ } else { \ tmp = RB_LEFT(gparent, field); \ if (tmp && RB_COLOR(tmp, field) == RB_RED) { \ RB_COLOR(tmp, field) = RB_BLACK; \ RB_SET_BLACKRED(parent, gparent, field);\ elm = gparent; \ continue; \ } \ if (RB_LEFT(parent, field) == elm) { \ RB_ROTATE_RIGHT(head, parent, tmp, field);\ tmp = parent; \ parent = elm; \ elm = tmp; \ } \ RB_SET_BLACKRED(parent, gparent, field); \ RB_ROTATE_LEFT(head, gparent, tmp, field); \ } \ } \ RB_COLOR(head->rbh_root, field) = RB_BLACK; \ } #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \ attr void \ name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \ { \ struct type *tmp; \ while ((elm == nil || RB_COLOR(elm, field) == RB_BLACK) && \ elm != RB_ROOT(head) && parent != nil) { \ if (RB_LEFT(parent, field) == elm) { \ tmp = RB_RIGHT(parent, field); \ if (RB_COLOR(tmp, field) == RB_RED) { \ RB_SET_BLACKRED(tmp, parent, field); \ RB_ROTATE_LEFT(head, parent, tmp, field);\ tmp = RB_RIGHT(parent, field); \ } \ if ((RB_LEFT(tmp, field) == nil || \ RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\ (RB_RIGHT(tmp, field) == nil || \ RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\ RB_COLOR(tmp, field) = RB_RED; \ elm = parent; \ parent = RB_PARENT(elm, field); \ } else { \ if (RB_RIGHT(tmp, field) == nil || \ RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\ struct type *oleft; \ if ((oleft = RB_LEFT(tmp, field)) \ != nil) \