From: markt@dgp.toronto.edu ("Mark A. Tapia")
Newsgroups: comp.lang.lisp.mcl
Subject: RE: AVL tree code
Date: 24 Jul 92 00:49:53 GMT
Original-To: nathan@akbar.teleos.com
Original-Cc: info-mcl@cambridge.apple.com

Nathan Wilson (nathan@akbar.teleos.com) writes:
> I want to efficiently maintain a fairly large set (>3000 elements) of
> sorted values, allowing for the operations insert, delete, min,
> member, and next-member (i.e. (next-member (min avl)) is the second
> smallest element).  From a quick review of my algorithms text book it
> looks like AVL-Trees are the ticket.  Has anyone out there implemented
> such or have code that provides similar functionality?  (AVL-Trees
> allow all of the listed functions in time proportional to the log of
> the number of elements in the tree)
 
Given your requirements to determine min member, next member etc.,
you'll probably need red-black (2,3) trees which look like the following
  (defstruct (btree (:type list))
    min left key val right max (balance *balanced*))
 
The left and right nodes point where you expect them to, min and max
point to the min and max nodes in the subtree rooted at the node.
Balance gives the balance factor (*balanced*, *right-taller* and *left-taller*).
Key is the key (for retrieval) and val contains the value associated
with the key.
 
I've written a series of routines which allow you to specify an
arbitrary ordering function that returns *before* *after* and *equal*
and that allows addition/deletion and key searches. The complete
source is contained at the end of this message.
 
Here is a dump of a tree with 7 elements (1 -7) ordered by <:
 
   4 = [1 7]
    2 L [1 3]
     1 L [NIL NIL]
     3 R [NIL NIL]
    6 R [5 7]
     5 L [NIL NIL]
     7 R [NIL NIL]

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