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Man Pages


Manual Reference Pages  -  RB_MIN (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_PROTOTYPE_INSERT, RB_PROTOTYPE_INSERT_COLOR, RB_PROTOTYPE_REMOVE, RB_PROTOTYPE_REMOVE_COLOR, RB_PROTOTYPE_FIND, RB_PROTOTYPE_NFIND, RB_PROTOTYPE_NEXT, RB_PROTOTYPE_PREV, RB_PROTOTYPE_MINMAX, RB_GENERATE, RB_GENERATE_STATIC, RB_GENERATE_INSERT, RB_GENERATE_INSERT_COLOR, RB_GENERATE_REMOVE, RB_GENERATE_REMOVE_COLOR, RB_GENERATE_FIND, RB_GENERATE_NFIND, RB_GENERATE_NEXT, RB_GENERATE_PREV, RB_GENERATE_MINMAX, 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_SAFE, RB_FOREACH_REVERSE, RB_FOREACH_REVERSE_SAFE, RB_INIT, RB_INSERT, RB_REMOVE - implementations of splay and red-black trees

CONTENTS

Synopsis
Description
Splay Trees
Red-black Trees
Notes
See Also
Authors

SYNOPSIS


.In 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_PROTOTYPE_INSERT NAME TYPE ATTR RB_PROTOTYPE_INSERT_COLOR NAME TYPE ATTR RB_PROTOTYPE_REMOVE NAME TYPE ATTR RB_PROTOTYPE_REMOVE_COLOR NAME TYPE ATTR RB_PROTOTYPE_FIND NAME TYPE ATTR RB_PROTOTYPE_NFIND NAME TYPE ATTR RB_PROTOTYPE_NEXT NAME TYPE ATTR RB_PROTOTYPE_PREV NAME TYPE ATTR RB_PROTOTYPE_MINMAX NAME TYPE ATTR RB_GENERATE NAME TYPE FIELD CMP RB_GENERATE_STATIC NAME TYPE FIELD CMP RB_GENERATE_INSERT NAME TYPE FIELD CMP ATTR RB_GENERATE_INSERT_COLOR NAME TYPE FIELD ATTR RB_GENERATE_REMOVE NAME TYPE FIELD ATTR RB_GENERATE_REMOVE_COLOR NAME TYPE FIELD ATTR RB_GENERATE_FIND NAME TYPE FIELD CMP ATTR RB_GENERATE_NFIND NAME TYPE FIELD CMP ATTR RB_GENERATE_NEXT NAME TYPE FIELD ATTR RB_GENERATE_PREV NAME TYPE FIELD ATTR RB_GENERATE_MINMAX NAME TYPE FIELD ATTR 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_SAFE VARNAME NAME RB_HEAD *head TEMP_VARNAME RB_FOREACH_REVERSE VARNAME NAME RB_HEAD *head RB_FOREACH_REVERSE_SAFE VARNAME NAME RB_HEAD *head TEMP_VARNAME 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
.Vt SPLAY_ENTRY , or
.Vt 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 lp]m + nrp]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
.Vt 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. Individual prototypes can be declared with RB_PROTOTYPE_INSERT, RB_PROTOTYPE_INSERT_COLOR, RB_PROTOTYPE_REMOVE, RB_PROTOTYPE_REMOVE_COLOR, RB_PROTOTYPE_FIND, RB_PROTOTYPE_NFIND, RB_PROTOTYPE_NEXT, RB_PROTOTYPE_PREV, and RB_PROTOTYPE_MINMAX in case not all functions are required. The individual prototype macros expect NAME, TYPE, and ATTR arguments. The ATTR argument must be empty for global functions or static for static functions.

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. As an alternative individual function bodies are generated with the RB_GENERATE_INSERT, RB_GENERATE_INSERT_COLOR, RB_GENERATE_REMOVE, RB_GENERATE_REMOVE_COLOR, RB_GENERATE_FIND, RB_GENERATE_NFIND, RB_GENERATE_NEXT, RB_GENERATE_PREV, and RB_GENERATE_MINMAX macros.

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
.Vt 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 macros RB_FOREACH_SAFE and RB_FOREACH_REVERSE_SAFE traverse the tree referenced by head in a forward or reverse direction respectively, assigning each element in turn to np. However, unlike their unsafe counterparts, they permit both the removal of np as well as freeing it from within the loop safely without interfering with the traversal.

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
.An Niels Provos .
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