|
|
|
@ -27,33 +27,10 @@ |
|
|
|
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
|
|
|
*/ |
|
|
|
|
|
|
|
#ifndef _SYS_TREE_H_ |
|
|
|
#define _SYS_TREE_H_ |
|
|
|
|
|
|
|
/* FreeBSD <sys/cdefs.h> has a lot of defines we don't really want. */ |
|
|
|
/* tree.h only actually uses __inline and __unused, so we'll just define those. */ |
|
|
|
|
|
|
|
/* #include <sys/cdefs.h> */ |
|
|
|
|
|
|
|
#ifndef __inline |
|
|
|
#define __inline inline |
|
|
|
#endif |
|
|
|
#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); |
|
|
|
* This file defines data structures for red-black trees. |
|
|
|
* |
|
|
|
* A red-black tree is a binary search tree with the node color as an |
|
|
|
* extra attribute. It fulfills a set of conditions: |
|
|
|
@ -66,228 +43,6 @@ |
|
|
|
* 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 (/*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) == 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 (/*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 (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)) != 0) { \ |
|
|
|
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-black tree */ |
|
|
|
#define RB_HEAD(name, type) \ |
|
|
|
struct name { \ |
|
|
|
@ -818,5 +573,3 @@ |
|
|
|
#define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \ |
|
|
|
for ((x) = RB_MAX(name, head); ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ |
|
|
|
(x) = (y)) |
|
|
|
|
|
|
|
#endif /* _SYS_TREE_H_ */ |