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tree (3)
  • tree (1) ( Linux man: Команды и прикладные программы пользовательского уровня )
  • >> tree (3) ( FreeBSD man: Библиотечные вызовы )
  • Ключ tree обнаружен в базе ключевых слов.

  • BSD mandoc
     

    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, Fa 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 Fa ENTRYNAME . The argument Fa HEADNAME is the name tag of a user defined structure that must be declared using the macros SPLAY_HEAD (,);
    or RB_HEAD (.);
    The argument Fa 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 Fa HEADNAME is the name of the structure to be defined, and struct Fa 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 Fa NAME is a unique identifier for this particular tree. The Fa TYPE argument is the type of the structure that is being managed by the tree. The Fa 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 Fa 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 Fa 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 Fa elm into the tree.

    The SPLAY_REMOVE ();
    macro removes the element Fa elm from the tree pointed by Fa 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 Fa HEADNAME is the name of the structure to be defined, and struct Fa 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 Fa NAME is a unique identifier for this particular tree. The Fa TYPE argument is the type of the structure that is being managed by the tree. The Fa 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 Fa CMP argument is the name of a function used to compare tree noded 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 Fa 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 Fa elm into the tree.

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

    AUTHORS

    The author of the tree macros is An Niels Provos .


     

    Index

    NAME
    SYNOPSIS
    DESCRIPTION
    SPLAY TREES
    RED-BLACK TREES
    NOTES
    AUTHORS


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