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TREE(3)                FreeBSD Library Functions Manual                TREE(3)

NAME
     SPLAY_PROTOTYPE, SPLAY_GENERATE, SPLAY_ENTRY, SPLAY_HEAD,
     SPLAY_INITIALIZER, SPLAY_ROOT, SPLAY_EMPTY, SPLAY_NEXT, SPLAY_MIN,
     SPLAY_MAX, SPLAY_FIND, SPLAY_LEFT, SPLAY_RIGHT, SPLAY_FOREACH,
     SPLAY_INIT, SPLAY_INSERT, SPLAY_REMOVE, RB_PROTOTYPE,
     RB_PROTOTYPE_STATIC, RB_GENERATE, RB_GENERATE_STATIC, RB_ENTRY, RB_HEAD,
     RB_INITIALIZER, RB_ROOT, RB_EMPTY, RB_NEXT, RB_PREV, RB_MIN, RB_MAX,
     RB_FIND, RB_NFIND, RB_LEFT, RB_RIGHT, RB_PARENT, RB_FOREACH,
     RB_FOREACH_REVERSE, RB_INIT, RB_INSERT, RB_REMOVE - implementations of
     splay and red-black trees

SYNOPSIS
     #include <sys/tree.h>

     SPLAY_PROTOTYPE(NAME, TYPE, FIELD, CMP);

     SPLAY_GENERATE(NAME, TYPE, FIELD, CMP);

     SPLAY_ENTRY(TYPE);

     SPLAY_HEAD(HEADNAME, TYPE);

     struct TYPE *
     SPLAY_INITIALIZER(SPLAY_HEAD *head);

     SPLAY_ROOT(SPLAY_HEAD *head);

     bool
     SPLAY_EMPTY(SPLAY_HEAD *head);

     struct TYPE *
     SPLAY_NEXT(NAME, SPLAY_HEAD *head, struct TYPE *elm);

     struct TYPE *
     SPLAY_MIN(NAME, SPLAY_HEAD *head);

     struct TYPE *
     SPLAY_MAX(NAME, SPLAY_HEAD *head);

     struct TYPE *
     SPLAY_FIND(NAME, SPLAY_HEAD *head, struct TYPE *elm);

     struct TYPE *
     SPLAY_LEFT(struct TYPE *elm, SPLAY_ENTRY NAME);

     struct TYPE *
     SPLAY_RIGHT(struct TYPE *elm, SPLAY_ENTRY NAME);

     SPLAY_FOREACH(VARNAME, NAME, SPLAY_HEAD *head);

     void
     SPLAY_INIT(SPLAY_HEAD *head);

     struct TYPE *
     SPLAY_INSERT(NAME, SPLAY_HEAD *head, struct TYPE *elm);

     struct TYPE *
     SPLAY_REMOVE(NAME, SPLAY_HEAD *head, struct TYPE *elm);

     RB_PROTOTYPE(NAME, TYPE, FIELD, CMP);

     RB_PROTOTYPE_STATIC(NAME, TYPE, FIELD, CMP);

     RB_GENERATE(NAME, TYPE, FIELD, CMP);

     RB_GENERATE_STATIC(NAME, TYPE, FIELD, CMP);

     RB_ENTRY(TYPE);

     RB_HEAD(HEADNAME, TYPE);

     RB_INITIALIZER(RB_HEAD *head);

     struct TYPE *
     RB_ROOT(RB_HEAD *head);

     bool
     RB_EMPTY(RB_HEAD *head);

     struct TYPE *
     RB_NEXT(NAME, RB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     RB_PREV(NAME, RB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     RB_MIN(NAME, RB_HEAD *head);

     struct TYPE *
     RB_MAX(NAME, RB_HEAD *head);

     struct TYPE *
     RB_FIND(NAME, RB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     RB_NFIND(NAME, RB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     RB_LEFT(struct TYPE *elm, RB_ENTRY NAME);

     struct TYPE *
     RB_RIGHT(struct TYPE *elm, RB_ENTRY NAME);

     struct TYPE *
     RB_PARENT(struct TYPE *elm, RB_ENTRY NAME);

     RB_FOREACH(VARNAME, NAME, RB_HEAD *head);

     RB_FOREACH_REVERSE(VARNAME, NAME, RB_HEAD *head);

     void
     RB_INIT(RB_HEAD *head);

     struct TYPE *
     RB_INSERT(NAME, RB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     RB_REMOVE(NAME, 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 SPLAY_ENTRY, or RB_ENTRY,
     named ENTRYNAME.  The argument HEADNAME is the name tag of a user defined
     structure that must be declared using the macros SPLAY_HEAD(), or
     RB_HEAD().  The argument NAME has to be a unique name prefix for every
     tree that is defined.

     The function prototypes are declared with SPLAY_PROTOTYPE(),
     RB_PROTOTYPE(), or RB_PROTOTYPE_STATIC().  The function bodies are
     generated with SPLAY_GENERATE(), RB_GENERATE(), or RB_GENERATE_STATIC().
     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 structure is declared as follows:

           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 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 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 SPLAY_ENTRY().

     The function bodies are generated with the SPLAY_GENERATE() macro.  It
     takes the same arguments as the SPLAY_PROTOTYPE() macro, but should be
     used only once.

     Finally, the CMP argument is the name of a function used to compare tree
     nodes 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 SPLAY_INIT() macro initializes the tree referenced by head.

     The splay tree can also be initialized statically by using the
     SPLAY_INITIALIZER() macro like this:

           SPLAY_HEAD(HEADNAME, TYPE) head = SPLAY_INITIALIZER(_head);

     The SPLAY_INSERT() macro inserts the new element elm into the tree.

     The SPLAY_REMOVE() macro removes the element elm from the tree pointed by
     head.

     The SPLAY_FIND() macro can be used to find a particular element in the
     tree.

           struct TYPE find, *res;
           find.key = 30;
           res = SPLAY_FIND(NAME, head, &find);

     The SPLAY_ROOT(), SPLAY_MIN(), SPLAY_MAX(), and SPLAY_NEXT() macros can
     be used to traverse the tree:

           for (np = SPLAY_MIN(NAME, &head); np != NULL; np = SPLAY_NEXT(NAME, &head, np))

     Or, for simplicity, one can use the SPLAY_FOREACH() macro:

           SPLAY_FOREACH(np, NAME, head)

     The 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 RB_HEAD() macro.
     A structure is declared as follows:

           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 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 RB_PROTOTYPE() or
     RB_PROTOTYPE_STATIC() 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 RB_ENTRY().

     The function bodies are generated with the RB_GENERATE() or
     RB_GENERATE_STATIC() macro.  These macros take the same arguments as the
     RB_PROTOTYPE() and RB_PROTOTYPE_STATIC() macros, but should be used only
     once.

     Finally, the CMP argument is the name of a function used to compare tree
     nodes 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 RB_INIT() macro initializes the tree referenced by head.

     The red-black tree can also be initialized statically by using the
     RB_INITIALIZER() macro like this:

           RB_HEAD(HEADNAME, TYPE) head = RB_INITIALIZER(_head);

     The RB_INSERT() macro inserts the new element elm into the tree.

     The RB_REMOVE() macro removes the element elm from the tree pointed by
     head.

     The RB_FIND() and RB_NFIND() macros can be used to find a particular
     element in the tree.

           struct TYPE find, *res;
           find.key = 30;
           res = RB_FIND(NAME, head, &find);

     The RB_ROOT(), RB_MIN(), RB_MAX(), RB_NEXT(), and RB_PREV() 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() or RB_FOREACH_REVERSE()
     macro:

           RB_FOREACH(np, NAME, head)

     The 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:

           SPLAY_FOREACH(var, NAME, head) {
                   SPLAY_REMOVE(NAME, head, var);
                   free(var);
           }
           free(head);

     Since var is freed, the FOREACH() macro refers to a pointer that may have
     been reallocated already.  Proper code needs a second variable.

           for (var = SPLAY_MIN(NAME, head); var != NULL; var = nxt) {
                   nxt = SPLAY_NEXT(NAME, head, var);
                   SPLAY_REMOVE(NAME, head, var);
                   free(var);
           }

     Both RB_INSERT() and 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, RB_REMOVE() and SPLAY_REMOVE() return the pointer to the
     removed element otherwise they return NULL to indicate an error.

SEE ALSO
     queue(3)

AUTHORS
     The author of the tree macros is Niels Provos.

FreeBSD 11.0-PRERELEASE        December 27, 2007       FreeBSD 11.0-PRERELEASE

NAME | SYNOPSIS | DESCRIPTION | SPLAY TREES | RED-BLACK TREES | NOTES | SEE ALSO | AUTHORS

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