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|
/* $OpenBSD: tree.h,v 1.14 2015/05/25 03:07:49 deraadt Exp $ */
/*
* 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 _SYS_TREE_H_
#define _SYS_TREE_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 SPLAY_HEAD(name, type) \
struct name { \
struct type *sph_root; /* root of the tree */ \
}
#define SPLAY_INITIALIZER(root) \
{ \
NULL \
}
#define SPLAY_INIT(root) \
do { \
(root)->sph_root = NULL; \
} while (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) == NULL)
/* 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 (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 (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 (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 (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 (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 (NULL); \
name##_SPLAY(head, elm); \
if ((cmp)(elm, (head)->sph_root) == 0) \
return (head->sph_root); \
return (NULL); \
} \
\
static __inline struct type *name##_SPLAY_NEXT(struct name *head, \
struct type *elm) \
{ \
name##_SPLAY(head, elm); \
if (SPLAY_RIGHT(elm, field) != NULL) { \
elm = SPLAY_RIGHT(elm, field); \
while (SPLAY_LEFT(elm, field) != NULL) { \
elm = SPLAY_LEFT(elm, field); \
} \
} else \
elm = NULL; \
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) = \
NULL; \
} 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) = NULL; \
} 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) = NULL; \
} else \
return ((head)->sph_root); \
} \
(head)->sph_root = (elm); \
return (NULL); \
} \
\
struct type *name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
{ \
struct type *__tmp; \
if (SPLAY_EMPTY(head)) \
return (NULL); \
name##_SPLAY(head, elm); \
if ((cmp)(elm, (head)->sph_root) == 0) { \
if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \
(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 (NULL); \
} \
\
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) = \
NULL; \
__left = __right = &__node; \
\
while ((__comp = (cmp)(elm, (head)->sph_root))) { \
if (__comp < 0) { \
__tmp = SPLAY_LEFT((head)->sph_root, field); \
if (__tmp == NULL) \
break; \
if ((cmp)(elm, __tmp) < 0) { \
SPLAY_ROTATE_RIGHT(head, __tmp, \
field); \
if (SPLAY_LEFT((head)->sph_root, \
field) \
== NULL) \
break; \
} \
SPLAY_LINKLEFT(head, __right, field); \
} else if (__comp > 0) { \
__tmp = SPLAY_RIGHT((head)->sph_root, field); \
if (__tmp == NULL) \
break; \
if ((cmp)(elm, __tmp) > 0) { \
SPLAY_ROTATE_LEFT(head, __tmp, field); \
if (SPLAY_RIGHT((head)->sph_root, \
field) \
== NULL) \
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) = \
NULL; \
__left = __right = &__node; \
\
while (1) { \
if (__comp < 0) { \
__tmp = SPLAY_LEFT((head)->sph_root, field); \
if (__tmp == NULL) \
break; \
if (__comp < 0) { \
SPLAY_ROTATE_RIGHT(head, __tmp, \
field); \
if (SPLAY_LEFT((head)->sph_root, \
field) \
== NULL) \
break; \
} \
SPLAY_LINKLEFT(head, __right, field); \
} else if (__comp > 0) { \
__tmp = SPLAY_RIGHT((head)->sph_root, field); \
if (__tmp == NULL) \
break; \
if (__comp > 0) { \
SPLAY_ROTATE_LEFT(head, __tmp, field); \
if (SPLAY_RIGHT((head)->sph_root, \
field) \
== NULL) \
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) ? NULL : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
#define SPLAY_MAX(name, x) \
(SPLAY_EMPTY(x) ? NULL : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
#define SPLAY_FOREACH(x, name, head) \
for ((x) = SPLAY_MIN(name, head); (x) != NULL; \
(x) = SPLAY_NEXT(name, head, x))
/*
* Copyright (c) 2016 David Gwynne <dlg@openbsd.org>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
#define RB_BLACK 0
#define RB_RED 1
struct rb_type {
int (*t_compare)(const void *, const void *);
void (*t_augment)(void *);
unsigned int t_offset; /* offset of rb_entry in type */
};
struct rbt_tree {
struct rb_entry *rbt_root;
};
struct rb_entry {
struct rb_entry *rbt_parent;
struct rb_entry *rbt_left;
struct rb_entry *rbt_right;
unsigned int rbt_color;
};
#define RB_HEAD(_name, _type) \
struct _name { \
struct rbt_tree rbh_root; \
}
#define RB_ENTRY(_type) struct rb_entry
static inline void _rb_init(struct rbt_tree *rbt)
{
rbt->rbt_root = NULL;
}
static inline int _rb_empty(struct rbt_tree *rbt)
{
return (rbt->rbt_root == NULL);
}
void *_rb_insert(const struct rb_type *, struct rbt_tree *, void *);
void *_rb_remove(const struct rb_type *, struct rbt_tree *, void *);
void *_rb_find(const struct rb_type *, struct rbt_tree *, const void *);
void *_rb_nfind(const struct rb_type *, struct rbt_tree *, const void *);
void *_rb_root(const struct rb_type *, struct rbt_tree *);
void *_rb_min(const struct rb_type *, struct rbt_tree *);
void *_rb_max(const struct rb_type *, struct rbt_tree *);
void *_rb_next(const struct rb_type *, void *);
void *_rb_prev(const struct rb_type *, void *);
void *_rb_left(const struct rb_type *, void *);
void *_rb_right(const struct rb_type *, void *);
void *_rb_parent(const struct rb_type *, void *);
void _rb_set_left(const struct rb_type *, void *, void *);
void _rb_set_right(const struct rb_type *, void *, void *);
void _rb_set_parent(const struct rb_type *, void *, void *);
void _rb_poison(const struct rb_type *, void *, unsigned long);
int _rb_check(const struct rb_type *, void *, unsigned long);
#define RB_INITIALIZER(_head) { { NULL } }
#define RB_PROTOTYPE(_name, _type, _field, _cmp) \
extern const struct rb_type *const _name##_RB_TYPE; \
\
__attribute__((__unused__)) static inline void _name##_RB_INIT( \
struct _name *head) \
{ \
_rb_init(&head->rbh_root); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_INSERT(struct _name *head, struct _type *elm) \
{ \
return _rb_insert(_name##_RB_TYPE, &head->rbh_root, elm); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_REMOVE(struct _name *head, struct _type *elm) \
{ \
return _rb_remove(_name##_RB_TYPE, &head->rbh_root, elm); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_FIND(struct _name *head, const struct _type *key) \
{ \
return _rb_find(_name##_RB_TYPE, &head->rbh_root, key); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_NFIND(struct _name *head, const struct _type *key) \
{ \
return _rb_nfind(_name##_RB_TYPE, &head->rbh_root, key); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_ROOT(struct _name *head) \
{ \
return _rb_root(_name##_RB_TYPE, &head->rbh_root); \
} \
\
__attribute__((__unused__)) static inline int _name##_RB_EMPTY( \
struct _name *head) \
{ \
return _rb_empty(&head->rbh_root); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_MIN(struct _name *head) \
{ \
return _rb_min(_name##_RB_TYPE, &head->rbh_root); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_MAX(struct _name *head) \
{ \
return _rb_max(_name##_RB_TYPE, &head->rbh_root); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_NEXT(struct _type *elm) \
{ \
return _rb_next(_name##_RB_TYPE, elm); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_PREV(struct _type *elm) \
{ \
return _rb_prev(_name##_RB_TYPE, elm); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_LEFT(struct _type *elm) \
{ \
return _rb_left(_name##_RB_TYPE, elm); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_RIGHT(struct _type *elm) \
{ \
return _rb_right(_name##_RB_TYPE, elm); \
} \
\
__attribute__((__unused__)) static inline struct _type \
*_name##_RB_PARENT(struct _type *elm) \
{ \
return _rb_parent(_name##_RB_TYPE, elm); \
} \
\
__attribute__((__unused__)) static inline void _name##_RB_SET_LEFT( \
struct _type *elm, struct _type *left) \
{ \
return _rb_set_left(_name##_RB_TYPE, elm, left); \
} \
\
__attribute__((__unused__)) static inline void _name##_RB_SET_RIGHT( \
struct _type *elm, struct _type *right) \
{ \
return _rb_set_right(_name##_RB_TYPE, elm, right); \
} \
\
__attribute__((__unused__)) static inline void _name##_RB_SET_PARENT( \
struct _type *elm, struct _type *parent) \
{ \
return _rb_set_parent(_name##_RB_TYPE, elm, parent); \
} \
\
__attribute__((__unused__)) static inline void _name##_RB_POISON( \
struct _type *elm, unsigned long poison) \
{ \
return _rb_poison(_name##_RB_TYPE, elm, poison); \
} \
\
__attribute__((__unused__)) static inline int _name##_RB_CHECK( \
struct _type *elm, unsigned long poison) \
{ \
return _rb_check(_name##_RB_TYPE, elm, poison); \
}
#define RB_GENERATE_INTERNAL(_name, _type, _field, _cmp, _aug) \
static int _name##_RB_COMPARE(const void *lptr, const void *rptr) \
{ \
const struct _type *l = lptr, *r = rptr; \
return _cmp(l, r); \
} \
static const struct rb_type _name##_RB_INFO = { \
_name##_RB_COMPARE, _aug, offsetof(struct _type, _field), \
}; \
const struct rb_type *const _name##_RB_TYPE = &_name##_RB_INFO;
#define RB_GENERATE_AUGMENT(_name, _type, _field, _cmp, _aug) \
static void _name##_RB_AUGMENT(void *ptr) \
{ \
struct _type *p = ptr; \
return _aug(p); \
} \
RB_GENERATE_INTERNAL(_name, _type, _field, _cmp, _name##_RB_AUGMENT)
#define RB_GENERATE(_name, _type, _field, _cmp) \
RB_GENERATE_INTERNAL(_name, _type, _field, _cmp, NULL)
#define RB_INIT(_name, _head) _name##_RB_INIT(_head)
#define RB_INSERT(_name, _head, _elm) _name##_RB_INSERT(_head, _elm)
#define RB_REMOVE(_name, _head, _elm) _name##_RB_REMOVE(_head, _elm)
#define RB_FIND(_name, _head, _key) _name##_RB_FIND(_head, _key)
#define RB_NFIND(_name, _head, _key) _name##_RB_NFIND(_head, _key)
#define RB_ROOT(_name, _head) _name##_RB_ROOT(_head)
#define RB_EMPTY(_name, _head) _name##_RB_EMPTY(_head)
#define RB_MIN(_name, _head) _name##_RB_MIN(_head)
#define RB_MAX(_name, _head) _name##_RB_MAX(_head)
#define RB_NEXT(_name, _elm) _name##_RB_NEXT(_elm)
#define RB_PREV(_name, _elm) _name##_RB_PREV(_elm)
#define RB_LEFT(_name, _elm) _name##_RB_LEFT(_elm)
#define RB_RIGHT(_name, _elm) _name##_RB_RIGHT(_elm)
#define RB_PARENT(_name, _elm) _name##_RB_PARENT(_elm)
#define RB_SET_LEFT(_name, _elm, _l) _name##_RB_SET_LEFT(_elm, _l)
#define RB_SET_RIGHT(_name, _elm, _r) _name##_RB_SET_RIGHT(_elm, _r)
#define RB_SET_PARENT(_name, _elm, _p) _name##_RB_SET_PARENT(_elm, _p)
#define RB_POISON(_name, _elm, _p) _name##_RB_POISON(_elm, _p)
#define RB_CHECK(_name, _elm, _p) _name##_RB_CHECK(_elm, _p)
#define RB_FOREACH(_e, _name, _head) \
for ((_e) = RB_MIN(_name, (_head)); (_e) != NULL; \
(_e) = RB_NEXT(_name, (_e)))
#define RB_FOREACH_SAFE(_e, _name, _head, _n) \
for ((_e) = RB_MIN(_name, (_head)); \
(_e) != NULL && ((_n) = RB_NEXT(_name, (_e)), 1); (_e) = (_n))
#define RB_FOREACH_REVERSE(_e, _name, _head) \
for ((_e) = RB_MAX(_name, (_head)); (_e) != NULL; \
(_e) = RB_PREV(_name, (_e)))
#define RB_FOREACH_REVERSE_SAFE(_e, _name, _head, _n) \
for ((_e) = RB_MAX(_name, (_head)); \
(_e) != NULL && ((_n) = RB_PREV(_name, (_e)), 1); (_e) = (_n))
#endif /* _SYS_TREE_H_ */
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