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tree.h
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/* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art 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))
/* Macros that define a red-back tree */
#define RB_HEAD(name, type) \
struct name { \
struct type *rbh_root; /* root of the tree */ \
}
#define RB_INITIALIZER(root) \
{ NULL }
#define RB_INIT(root) do { \
(root)->rbh_root = NULL; \
} while (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) == NULL)
#define RB_SET(elm, parent, field) do { \
RB_PARENT(elm, field) = parent; \
RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
RB_COLOR(elm, field) = RB_RED; \
} while (0)
#define RB_SET_BLACKRED(black, red, field) do { \
RB_COLOR(black, field) = RB_BLACK; \
RB_COLOR(red, field) = RB_RED; \
} while (0)
#ifndef RB_AUGMENT
#define RB_AUGMENT(x)
#endif
#define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
(tmp) = RB_RIGHT(elm, field); \
if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) { \
RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
} \
RB_AUGMENT(elm); \
if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) { \
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 (0)
#define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
(tmp) = RB_LEFT(elm, field); \
if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) { \
RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
} \
RB_AUGMENT(elm); \
if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) { \
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 (0)
/* Generates prototypes and inline functions */
#define RB_PROTOTYPE(name, type, field, cmp) \
void name##_RB_INSERT_COLOR(struct name *, struct type *); \
void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
struct type *name##_RB_REMOVE(struct name *, struct type *); \
struct type *name##_RB_INSERT(struct name *, struct type *); \
struct type *name##_RB_FIND(struct name *, struct type *); \
struct type *name##_RB_NEXT(struct type *); \
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) \
void \
name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
{ \
struct type *parent, *gparent, *tmp; \
while ((parent = RB_PARENT(elm, field)) && \
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; \
} \
\
void \
name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
{ \
struct type *tmp; \
while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
elm != RB_ROOT(head)) { \
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) == NULL || \
RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
(RB_RIGHT(tmp, field) == NULL || \
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) == NULL || \
RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
struct type *oleft; \
if ((oleft = RB_LEFT(tmp, field)))\
RB_COLOR(oleft, field) = RB_BLACK;\
RB_COLOR(tmp, field) = RB_RED; \
RB_ROTATE_RIGHT(head, tmp, oleft, field);\
tmp = RB_RIGHT(parent, field); \
} \
RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
RB_COLOR(parent, field) = RB_BLACK; \
if (RB_RIGHT(tmp, field)) \
RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
RB_ROTATE_LEFT(head, parent, tmp, field);\
elm = RB_ROOT(head); \
break; \
} \
} else { \
tmp = RB_LEFT(parent, field); \
if (RB_COLOR(tmp, field) == RB_RED) { \
RB_SET_BLACKRED(tmp, parent, field); \
RB_ROTATE_RIGHT(head, parent, tmp, field);\
tmp = RB_LEFT(parent, field); \
} \
if ((RB_LEFT(tmp, field) == NULL || \
RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
(RB_RIGHT(tmp, field) == NULL || \
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_LEFT(tmp, field) == NULL || \
RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
struct type *oright; \
if ((oright = RB_RIGHT(tmp, field)))\
RB_COLOR(oright, field) = RB_BLACK;\
RB_COLOR(tmp, field) = RB_RED; \
RB_ROTATE_LEFT(head, tmp, oright, field);\
tmp = RB_LEFT(parent, field); \
} \
RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
RB_COLOR(parent, field) = RB_BLACK; \
if (RB_LEFT(tmp, field)) \
RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
RB_ROTATE_RIGHT(head, parent, tmp, field);\
elm = RB_ROOT(head); \
break; \
} \
} \
} \
if (elm) \
RB_COLOR(elm, field) = RB_BLACK; \
} \
\
struct type * \
name##_RB_REMOVE(struct name *head, struct type *elm) \
{ \
struct type *child, *parent, *old = elm; \
int color; \
if (RB_LEFT(elm, field) == NULL) \
child = RB_RIGHT(elm, field); \
else if (RB_RIGHT(elm, field) == NULL) \
child = RB_LEFT(elm, field); \
else { \
struct type *left; \
elm = RB_RIGHT(elm, field); \
while ((left = RB_LEFT(elm, field))) \
elm = left; \
child = RB_RIGHT(elm, field); \
parent = RB_PARENT(elm, field); \
color = RB_COLOR(elm, field); \
if (child) \
RB_PARENT(child, field) = parent; \
if (parent) { \
if (RB_LEFT(parent, field) == elm) \
RB_LEFT(parent, field) = child; \
else \
RB_RIGHT(parent, field) = child; \
RB_AUGMENT(parent); \
} else \
RB_ROOT(head) = child; \
if (RB_PARENT(elm, field) == old) \
parent = elm; \
(elm)->field = (old)->field; \
if (RB_PARENT(old, field)) { \
if (RB_LEFT(RB_PARENT(old, field), field) == old)\
RB_LEFT(RB_PARENT(old, field), field) = elm;\
else \
RB_RIGHT(RB_PARENT(old, field), field) = elm;\
RB_AUGMENT(RB_PARENT(old, field)); \
} else \
RB_ROOT(head) = elm; \
RB_PARENT(RB_LEFT(old, field), field) = elm; \
if (RB_RIGHT(old, field)) \
RB_PARENT(RB_RIGHT(old, field), field) = elm; \
if (parent) { \
left = parent; \
do { \
RB_AUGMENT(left); \
} while ((left = RB_PARENT(left, field))); \
} \
goto color; \
} \
parent = RB_PARENT(elm, field); \
color = RB_COLOR(elm, field); \
if (child) \
RB_PARENT(child, field) = parent; \
if (parent) { \
if (RB_LEFT(parent, field) == elm) \
RB_LEFT(parent, field) = child; \
else \
RB_RIGHT(parent, field) = child; \
RB_AUGMENT(parent); \
} else \
RB_ROOT(head) = child; \
color: \
if (color == RB_BLACK) \
name##_RB_REMOVE_COLOR(head, parent, child); \
return (old); \
} \
\
/* Inserts a node into the RB tree */ \
struct type * \
name##_RB_INSERT(struct name *head, struct type *elm) \
{ \
struct type *tmp; \
struct type *parent = NULL; \
int comp = 0; \
tmp = RB_ROOT(head); \
while (tmp) { \
parent = tmp; \
comp = (cmp)(elm, parent); \
if (comp < 0) \
tmp = RB_LEFT(tmp, field); \
else if (comp > 0) \
tmp = RB_RIGHT(tmp, field); \
else \
return (tmp); \
} \
RB_SET(elm, parent, field); \
if (parent != NULL) { \
if (comp < 0) \
RB_LEFT(parent, field) = elm; \
else \
RB_RIGHT(parent, field) = elm; \
RB_AUGMENT(parent); \
} else \
RB_ROOT(head) = elm; \
name##_RB_INSERT_COLOR(head, elm); \
return (NULL); \
} \
\
/* Finds the node with the same key as elm */ \
struct type * \
name##_RB_FIND(struct name *head, struct type *elm) \
{ \
struct type *tmp = RB_ROOT(head); \
int comp; \
while (tmp) { \
comp = cmp(elm, tmp); \
if (comp < 0) \
tmp = RB_LEFT(tmp, field); \
else if (comp > 0) \
tmp = RB_RIGHT(tmp, field); \
else \
return (tmp); \
} \
return (NULL); \
} \
\
struct type * \
name##_RB_NEXT(struct type *elm) \
{ \
if (RB_RIGHT(elm, field)) { \
elm = RB_RIGHT(elm, field); \
while (RB_LEFT(elm, field)) \
elm = RB_LEFT(elm, field); \
} else { \
if (RB_PARENT(elm, field) && \
(elm == RB_LEFT(RB_PARENT(elm, field), field))) \
elm = RB_PARENT(elm, field); \
else { \
while (RB_PARENT(elm, field) && \
(elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
elm = RB_PARENT(elm, field); \
elm = RB_PARENT(elm, field); \
} \
} \
return (elm); \
} \
\
struct type * \
name##_RB_MINMAX(struct name *head, int val) \
{ \
struct type *tmp = RB_ROOT(head); \
struct type *parent = NULL; \
while (tmp) { \
parent = tmp; \
if (val < 0) \
tmp = RB_LEFT(tmp, field); \
else \
tmp = RB_RIGHT(tmp, field); \
} \
return (parent); \
}
#define RB_NEGINF -1
#define RB_INF 1
#define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
#define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
#define RB_FIND(name, x, y) name##_RB_FIND(x, y)
#define RB_NEXT(name, x, y) name##_RB_NEXT(y)
#define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
#define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
#define RB_FOREACH(x, name, head) \
for ((x) = RB_MIN(name, head); \
(x) != NULL; \
(x) = name##_RB_NEXT(x))
#endif /* _SYS_TREE_H_ */
/* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art 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))
/* Macros that define a red-back tree */
#define RB_HEAD(name, type) \
struct name { \
struct type *rbh_root; /* root of the tree */ \
}
#define RB_INITIALIZER(root) \
{ NULL }
#define RB_INIT(root) do { \
(root)->rbh_root = NULL; \
} while (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) == NULL)
#define RB_SET(elm, parent, field) do { \
RB_PARENT(elm, field) = parent; \
RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
RB_COLOR(elm, field) = RB_RED; \