NAME¶
gg-tree,
GG_SPLAY_PROTOTYPE,
GG_SPLAY_GENERATE,
GG_SPLAY_ENTRY,
GG_SPLAY_HEAD,
GG_SPLAY_INITIALIZER,
GG_SPLAY_ROOT,
GG_SPLAY_EMPTY,
GG_SPLAY_NEXT,
GG_SPLAY_MIN,
GG_SPLAY_MAX,
GG_SPLAY_FIND,
GG_SPLAY_LEFT,
GG_SPLAY_RIGHT,
GG_SPLAY_FOREACH,
GG_SPLAY_INIT,
GG_SPLAY_INSERT,
GG_SPLAY_REMOVE,
GG_RB_PROTOTYPE,
GG_RB_GENERATE,
GG_RB_ENTRY,
GG_RB_HEAD,
GG_RB_INITIALIZER,
GG_RB_ROOT,
GG_RB_EMPTY,
GG_RB_NEXT,
GG_RB_MIN,
GG_RB_MAX,
GG_RB_FIND,
GG_RB_LEFT,
GG_RB_RIGHT,
GG_RB_PARENT,
GG_RB_FOREACH,
GG_RB_INIT,
GG_RB_INSERT,
GG_RB_REMOVE - implementations of splay and red-black trees
SYNOPSIS¶
#include <ggi/gg-tree.h>
GG_SPLAY_PROTOTYPE(NAME, TYPE, FIELD, CMP);
GG_SPLAY_GENERATE(NAME, TYPE, FIELD, CMP);
GG_SPLAY_ENTRY(TYPE);
GG_SPLAY_HEAD(HEADNAME, TYPE);
struct TYPE *
GG_SPLAY_INITIALIZER(GG_SPLAY_HEAD *head);
GG_SPLAY_ROOT(GG_SPLAY_HEAD *head);
bool
GG_SPLAY_EMPTY(GG_SPLAY_HEAD *head);
struct TYPE *
GG_SPLAY_NEXT(NAME, GG_SPLAY_HEAD *head, struct TYPE *elm);
struct TYPE *
GG_SPLAY_MIN(NAME, GG_SPLAY_HEAD *head);
struct TYPE *
GG_SPLAY_MAX(NAME, GG_SPLAY_HEAD *head);
struct TYPE *
GG_SPLAY_FIND(NAME, GG_SPLAY_HEAD *head, struct TYPE *elm);
struct TYPE *
GG_SPLAY_LEFT(struct TYPE *elm, GG_SPLAY_ENTRY NAME);
struct TYPE *
GG_SPLAY_RIGHT(struct TYPE *elm, GG_SPLAY_ENTRY NAME);
GG_SPLAY_FOREACH(VARNAME, NAME, GG_SPLAY_HEAD *head);
void
GG_SPLAY_INIT(GG_SPLAY_HEAD *head);
struct TYPE *
GG_SPLAY_INSERT(NAME, GG_SPLAY_HEAD *head, struct TYPE *elm);
struct TYPE *
GG_SPLAY_REMOVE(NAME, GG_SPLAY_HEAD *head, struct TYPE *elm);
GG_RB_PROTOTYPE(NAME, TYPE, FIELD, CMP);
GG_RB_GENERATE(NAME, TYPE, FIELD, CMP);
GG_RB_ENTRY(TYPE);
GG_RB_HEAD(HEADNAME, TYPE);
GG_RB_INITIALIZER(GG_RB_HEAD *head);
struct TYPE *
GG_RB_ROOT(GG_RB_HEAD *head);
bool
GG_RB_EMPTY(GG_RB_HEAD *head);
struct TYPE *
GG_RB_NEXT(NAME, GG_RB_HEAD *head, struct TYPE *elm);
struct TYPE *
GG_RB_MIN(NAME, GG_RB_HEAD *head);
struct TYPE *
GG_RB_MAX(NAME, GG_RB_HEAD *head);
struct TYPE *
GG_RB_FIND(NAME, GG_RB_HEAD *head, struct TYPE *elm);
struct TYPE *
GG_RB_LEFT(struct TYPE *elm, GG_RB_ENTRY NAME);
struct TYPE *
GG_RB_RIGHT(struct TYPE *elm, GG_RB_ENTRY NAME);
struct TYPE *
GG_RB_PARENT(struct TYPE *elm, GG_RB_ENTRY NAME);
GG_RB_FOREACH(VARNAME, NAME, GG_RB_HEAD *head);
void
GG_RB_INIT(GG_RB_HEAD *head);
struct TYPE *
GG_RB_INSERT(NAME, GG_RB_HEAD *head, struct TYPE *elm);
struct TYPE *
GG_RB_REMOVE(NAME, GG_RB_HEAD *head, struct TYPE *elm);
DESCRIPTION¶
These macros define data structures for different types of trees: splay trees
and red-black trees.
In the macro definitions,
TYPE is the name tag of a user defined
structure that must contain a field of type
GG_SPLAY_ENTRY, or
GG_RB_ENTRY, named
ENTRYNAME. The argument
HEADNAME is
the name tag of a user defined structure that must be declared using the
macros
GG_SPLAY_HEAD or
GG_RB_HEAD. The argument
NAME has
to be a unique name prefix for every tree that is defined.
The function prototypes are declared with either
GG_SPLAY_PROTOTYPE or
GG_RB_PROTOTYPE. The function bodies are generated with either
GG_SPLAY_GENERATE or
GG_RB_GENERATE. See the examples below for
further explanation of how these macros are used.
SPLAY 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 splay tree is headed by a structure defined by the
SPLAY_HEAD macro. A
GG_SPLAY_HEAD structure is declared as follows:
GG_SPLAY_HEAD(HEADNAME, TYPE) head;
where
HEADNAME is the name of the structure to be defined, and struct
TYPE is the type of the elements to be inserted into the tree.
The
GG_SPLAY_ENTRY macro declares a structure that allows elements to be
connected in the tree.
In order to use the functions that manipulate the tree structure, their
prototypes need to be declared with the
GG_SPLAY_PROTOTYPE macro, where
NAME is a unique identifier for this particular tree. The
TYPE
argument is the type of the structure that is being managed by the tree. The
FIELD argument is the name of the element defined by
GG_SPLAY_ENTRY.
The function bodies are generated with the
GG_SPLAY_GENERATE macro. It
takes the same arguments as the
GG_SPLAY_PROTOTYPE macro, but should be
used only once.
Finally, the
CMP argument is the name of a function used to compare trees
noded with each other. The function takes two arguments of type struct
TYPE
*. If the first argument is smaller than the second, the function returns
a value smaller than zero. If they are equal, the function returns zero.
Otherwise, it should return a value greater than zero. The compare function
defines the order of the tree elements.
The
GG_SPLAY_INIT macro initializes the tree referenced by head.
The splay tree can also be initialized statically by using the
GG_SPLAY_INITIALIZER macro like this:
GG_SPLAY_HEAD(HEADNAME, TYPE) head = GG_SPLAY_INITIALIZER(&head);
The
GG_SPLAY_INSERT macro inserts the new element elm into the tree.
The
GG_SPLAY_REMOVE macro removes the element elm from the tree pointed
by head.
The
GG_SPLAY_FIND macro can be used to find a particular element in the
tree.:
struct TYPE find, *res;
find.key = 30;
res = GG_SPLAY_FIND(NAME, head, &find);
The
GG_SPLAY_ROOT,
GG_SPLAY_MIN,
GG_SPLAY_MAX, and
GG_SPLAY_NEXT macros can be used to traverse the tree:
for (np = GG_SPLAY_MIN(NAME, &head); np != NULL; np = GG_SPLAY_NEXT(NAME, &head, np))
Or, for simplicity, one can use the
GG_SPLAY_FOREACH macro:
GG_SPLAY_FOREACH(np, NAME, head)
The
GG_SPLAY_EMPTY macro should be used to check whether a splay tree is
empty.
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:
- 1
- every search path from the root to a leaf consists of the
same number of black nodes,
- 2
- each red node (except for the root) has a black
parent,
- 3
- 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).
A red-black tree is headed by a structure defined by the
GG_RB_HEAD
macro. A
GG_RB_HEAD structure is declared as follows:
GG_RB_HEAD(HEADNAME, TYPE) head;
where
HEADNAME is the name of the structure to be defined, and struct
TYPE is the type of the elements to be inserted into the tree.
The
GG_RB_ENTRY macro declares a structure that allows elements to be
connected in the tree.
In order to use the functions that manipulate the tree structure, their
prototypes need to be declared with the
GG_RB_PROTOTYPE macro, where
NAME is a unique identifier for this particular tree. The
TYPE
argument is the type of the structure that is being managed by the tree. The
FIELD argument is the name of the element defined by
GG_RB_ENTRY.
The function bodies are generated with the
GG_RB_GENERATE macro. It takes
the same arguments as the
GG_RB_PROTOTYPE macro, but should be used
only once.
Finally, the
CMP argument is the name of a function used to compare trees
noded with each other. The function takes two arguments of type struct
TYPE
*. If the first argument is smaller than the second, the function returns
a value smaller than zero. If they are equal, the function returns zero.
Otherwise, it should return a value greater than zero. The compare function
defines the order of the tree elements.
The
GG_RB_INIT macro initializes the tree referenced by head.
The redblack tree can also be initialized statically by using the
GG_RB_INITIALIZER macro like this:
GG_RB_HEAD(HEADNAME, TYPE) head = GG_RB_INITIALIZER(&head);
The
GG_RB_INSERT macro inserts the new element elm into the tree.
The
GG_RB_REMOVE macro removes the element elm from the tree pointed by
head.
The
GG_RB_FIND macro can be used to find a particular element in the
tree.:
struct TYPE find, *res;
find.key = 30;
res = GG_RB_FIND(NAME, head, &find);
The
GG_RB_ROOT,
GG_RB_MIN,
GG_RB_MAX, and
GG_RB_NEXT
macros can be used to traverse the tree:
for (np = RB_MIN(NAME, &head); np != NULL; np = RB_NEXT(NAME, &head, np))
Or, for simplicity, one can use the
RB_FOREACH macro:
GG_RB_FOREACH(np, NAME, head)
The
GG_RB_EMPTY macro should be used to check whether a red-black tree is
empty.
NOTES¶
Trying to free a tree in the following way is a common error:
GG_SPLAY_FOREACH(var, NAME, head) {
GG_SPLAY_REMOVE(NAME, head, var);
free(var);
}
free(head);
Since var is free'd, the
FOREACH macro refers to a pointer that may have
been reallocated already. Proper code needs a second variable.:
for (var = GG_SPLAY_MIN(NAME, head); var != NULL; var = nxt) {
nxt = GG_SPLAY_NEXT(NAME, head, var);
GG_SPLAY_REMOVE(NAME, head, var);
free(var);
}
Both
GG_RB_INSERT and
GG_SPLAY_INSERT return NULL if the element
was inserted in the tree successfully, otherwise they return a pointer to the
element with the colliding key.
Accordingly,
GG_RB_REMOVE and
GG_SPLAY_REMOVE return the pointer
to the removed element, otherwise they return NULL to indicate an error.
SEE ALSO¶
gg-queue(3)