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-.\" $Id: tree.mdoc,v 8.3 2001/08/08 07:50:28 marka Exp $
-.\"
-.\"Copyright (c) 1995-1999 by Internet Software Consortium
-.\"
-.\"Permission to use, copy, modify, and distribute this software for any
-.\"purpose with or without fee is hereby granted, provided that the above
-.\"copyright notice and this permission notice appear in all copies.
-.\"
-.\"THE SOFTWARE IS PROVIDED "AS IS" AND INTERNET SOFTWARE CONSORTIUM DISCLAIMS
-.\"ALL WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES
-.\"OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL INTERNET SOFTWARE
-.\"CONSORTIUM BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL
-.\"DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR
-.\"PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS
-.\"ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
-.\"SOFTWARE.
-.\"
-.Dd April 5, 1994
-.Dt TREE 3
-.Os BSD 4
-.Sh NAME
-.Nm tree_init ,
-.Nm tree_mung ,
-.Nm tree_srch ,
-.Nm tree_add ,
-.Nm tree_delete ,
-.Nm tree_trav
-.Nd balanced binary tree routines
-.Sh SYNOPSIS
-.Ft void
-.Fn tree_init "void **tree"
-.Ft void *
-.Fn tree_srch "void **tree" "int (*compare)()" "void *data"
-.Ft void
-.Fn tree_add "void **tree" "int (*compare)()" \
-"void *data" "void (*del_uar)()"
-.Ft int
-.Fn tree_delete "void **tree" "int (*compare)()" \
-"void *data" "void (*del_uar)()"
-.Ft int
-.Fn tree_trav "void **tree" "int (*trav_uar)()"
-.Ft void
-.Fn tree_mung "void **tree" "void (*del_uar)()"
-.Sh DESCRIPTION
-These functions create and manipulate a balanced binary (AVL) tree.  Each node
-of the tree contains the expected left & right subtree pointers, a short int
-balance indicator, and a pointer to the user data.  On a 32 bit system, this
-means an overhead of 4+4+2+4 bytes per node (or, on a RISC or otherwise
-alignment constrained system with implied padding, 4+4+4+4 bytes per node).
-There is no key data type enforced by this package; a caller supplied
-compare routine is used to compare user data blocks.
-.Pp
-Balanced binary trees are very fast on searches and replacements, but have a
-moderately high cost for additions and deletions.  If your application does a
-lot more searches and replacements than it does additions and deletions, the
-balanced (AVL) binary tree is a good choice for a data structure.
-.Pp
-.Fn Tree_init
-creates an empty tree and binds it to
-.Dq Fa tree
-(which for this and all other routines in this package should be declared as
-a pointer to void or int, and passed by reference), which can then be used by
-other routines in this package.  Note that more than one
-.Dq Fa tree
-variable can exist at once; thus multiple trees can be manipulated
-simultaneously.
-.Pp
-.Fn Tree_srch
-searches a tree for a specific node and returns either
-.Fa NULL
-if no node was found, or the value of the user data pointer if the node
-was found.
-.Fn compare
-is the address of a function to compare two user data blocks.  This routine
-should work much the way 
-.Xr strcmp 3
-does; in fact,
-.Xr strcmp
-could be used if the user data was a \s-2NUL\s+2 terminated string.
-.Dq Fa Data
-is the address of a user data block to be used by
-.Fn compare
-as the search criteria.  The tree is searched for a node where
-.Fn compare
-returns 0.
-.Pp
-.Fn Tree_add
-inserts or replaces a node in the specified tree.  The tree specified by
-.Dq Fa tree
-is searched as in
-.Fn tree_srch ,
-and if a node is found to match
-.Dq Fa data ,
-then the
-.Fn del_uar
-function, if non\-\s-2NULL\s+2, is called with the address of the user data
-block for the node (this routine should deallocate any dynamic memory which
-is referenced exclusively by the node); the user data pointer for the node
-is then replaced by the value of
-.Dq Fa data .
-If no node is found to match, a new node is added (which may or may not
-cause a transparent rebalance operation), with a user data pointer equal to
-.Dq Fa data .
-A rebalance may or may not occur, depending on where the node is added
-and what the rest of the tree looks like.
-.Fn Tree_add
-will return the
-.Dq Fa data
-pointer unless catastrophe occurs in which case it will return \s-2NULL\s+2.
-.Pp
-.Fn Tree_delete
-deletes a node from
-.Dq Fa tree .
-A rebalance may or may not occur, depending on where the node is removed from
-and what the rest of the tree looks like.
-.Fn Tree_delete
-returns TRUE if a node was deleted, FALSE otherwise.
-.Pp
-.Fn Tree_trav
-traverses all of
-.Dq Fa tree ,
-calling
-.Fn trav_uar
-with the address of each user data block.  If
-.Fn trav_uar
-returns FALSE at any time,
-.Fn tree_trav
-will immediately return FALSE to its caller.  Otherwise all nodes will be 
-reached and
-.Fn tree_trav
-will return TRUE.
-.Pp
-.Fn Tree_mung
-deletes every node in
-.Dq Fa tree ,
-calling
-.Fn del_uar
-(if it is not \s-2NULL\s+2) with the user data address from each node (see
-.Fn tree_add
-and
-.Fn tree_delete
-above).  The tree is left in the same state that
-.Fn tree_init
-leaves it in \- i.e., empty.
-.Sh BUGS
-Should have a way for the caller to specify application-specific
-.Xr malloc
-and
-.Xr free
-functions to be used internally when allocating meta data.
-.Sh AUTHOR
-Paul Vixie, converted and augumented from Modula\-2 examples in
-.Dq Algorithms & Data Structures ,
-Niklaus Wirth, Prentice\-Hall, ISBN 0\-13\-022005\-1.