File: gb_trees.html

package info (click to toggle)
erlang-doc-html 1%3A8.0-1
links: PTS
area: main
in suites: woody
size: 18,028 kB
ctags: 7,419
sloc: perl: 1,841; ansic: 323; erlang: 155
file content (169 lines) | stat: -rw-r--r-- 6,193 bytes
<HTML>
<HEAD>
<!-- refpage -->
<TITLE>gb_trees</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFFFF">
<CENTER>


<A HREF="http://www.erlang.se"><IMG BORDER=0 ALT="[Erlang Systems]" SRC="min_head.gif"></A>
<H1>gb_trees</H1>
</CENTER>
<H3>MODULE</H3>
<UL>
gb_trees</UL>
<H3>MODULE SUMMARY</H3>
<UL>
General Balanced Trees</UL>
<H3>DESCRIPTION</H3>
<UL>
<P> An efficient implementation of Prof. Arne Andersson's General
Balanced Trees. These have no storage overhead compared to
unbalaced binary trees, and their performance is in general
better than AVL trees.
</UL>
<H3>Data structure</H3>
<UL>
<P> Data structure:
<PRE>      
- {Size, Tree}, where `Tree' is composed of nodes of the form:
  - {Key, Value, Smaller, Bigger}, and the &#34;empty tree&#34; node:
  - nil.
    </PRE><P>There is no attempt to balance trees after deletions. Since
deletions don't increase the height of a tree, this should be
OK.
<P> Original balance condition <STRONG>h(T) &#60;= ceil(c * log(|T|))</STRONG>
has been changed to the similar (but not quite equivalent)
condition <STRONG>2 ^ h(T) &#60;= |T| ^ c</STRONG>. This should also be OK.
<P> Performance is comparable to the AVL trees in the Erlang book
(and faster in general due to less overhead); the difference is
that deletion works for these trees, but not for the book's
trees. Behaviour is logaritmic (as it should be).
</UL>
<H3>EXPORTS</H3>
<P><A NAME="empty%0"><STRONG><CODE>empty()</CODE></STRONG></A><BR>
<UL>
<P>      Returns a new, empty tree.
</UL>
<P><A NAME="is_empty%1"><STRONG><CODE>is_empty(T)</CODE></STRONG></A><BR>
<UL>
<P>      Returns 'true' if T is an empty tree, and 'false' otherwise.
</UL>
<P><A NAME="size%1"><STRONG><CODE>size(T)</CODE></STRONG></A><BR>
<UL>
<P>      Returns the number of nodes in the tree as an
         integer. Returns 0 (zero) if the tree is empty.
</UL>
<P><A NAME="lookup%2"><STRONG><CODE>lookup(X, T)</CODE></STRONG></A><BR>
<UL>
<P>      Looks up key X in tree T; returns {value, V}, or `none' if
         the key is not present.
</UL>
<P><A NAME="get%2"><STRONG><CODE>get(X, T)</CODE></STRONG></A><BR>
<UL>
<P>      Retreives the value stored with key X in tree T. Assumes
         that the key is present in the tree, crashes otherwise.
</UL>
<P><A NAME="insert%3"><STRONG><CODE>insert(X, V, T)</CODE></STRONG></A><BR>
<UL>
<P>      Inserts key X with value V into tree T; returns the new
         tree. Assumes that the key is *not* present in the tree,
         crashes otherwise.
</UL>
<P><A NAME="update%3"><STRONG><CODE>update(X, V, T)</CODE></STRONG></A><BR>
<UL>
<P>      Updates key X to value V in tree T; returns the new
         tree. Assumes that the key is present in the tree.
</UL>
<P><A NAME="enter%3"><STRONG><CODE>enter(X, V, T)</CODE></STRONG></A><BR>
<UL>
<P>      Inserts key X with value V into tree T if the key is not
         present in the tree, otherwise updates key X to value V in
         T. Returns the new tree.
</UL>
<P><A NAME="delete%2"><STRONG><CODE>delete(X, T)</CODE></STRONG></A><BR>
<UL>
<P>      Removes key X from tree T; returns new tree. Assumes that
         the key is present in the tree, crashes otherwise.
</UL>
<P><A NAME="delete_any%2"><STRONG><CODE>delete_any(X, T)</CODE></STRONG></A><BR>
<UL>
<P>      Removes key X from tree T if the key is present in the tree,
         otherwise does nothing; returns new tree.
</UL>
<P><A NAME="balance%1"><STRONG><CODE>balance(T)</CODE></STRONG></A><BR>
<UL>
<P>      Rebalances tree T. Note that this is rarely necessary, but
         may be motivated when a large number of entries have been
         deleted from the tree without further
         insertions. Rebalancing could then be forced in order to
         minimise lookup times, since deletion only does not
         rebalance the tree.
</UL>
<P><A NAME="is_defined%2"><STRONG><CODE>is_defined(X, T)</CODE></STRONG></A><BR>
<UL>
<P>      Returns `true' if key X is present in tree T, and `false'
         otherwise.
</UL>
<P><A NAME="keys%1"><STRONG><CODE>keys(T)</CODE></STRONG></A><BR>
<UL>
<P>      Returns an ordered list of all keys in tree T.
</UL>
<P><A NAME="values%1"><STRONG><CODE>values(T)</CODE></STRONG></A><BR>
<UL>
<P>      Returns a list of all values in tree T.
</UL>
<P><A NAME="to_list%1"><STRONG><CODE>to_list(T)</CODE></STRONG></A><BR>
<UL>
<P>      Returns an ordered list of {Key, Value} pairs for all keys
         in tree T.
</UL>
<P><A NAME="from_orddict%1"><STRONG><CODE>from_orddict(L)</CODE></STRONG></A><BR>
<UL>
<P>      turns an ordered list L of {Key, Value} pairs into a
         tree. The list must not contain duplicate keys.
</UL>
<P><A NAME="take_smallest%1"><STRONG><CODE>take_smallest(T)</CODE></STRONG></A><BR>
<UL>
<P>      Returns {X, V, T1}, where X is the smallest key in tree T, V
         is the value associated with X in T, and T1 is the tree T
         with key X deleted. Assumes that the tree T is nonempty.
</UL>
<P><A NAME="iterator%1"><STRONG><CODE>iterator(T)</CODE></STRONG></A><BR>
<UL>
<P>      Returns an iterator that can be used for traversing the
         entries of tree T; see `next'. The implementation of this is
         very efficient; traversing the whole tree using `next' is
         only slightly slower than getting the list of all elements
         using `to_list' and traversing that. The main advantage of
         the iterator approach is that it does not require the
         complete list of all elements to be built in memory at one
         time.
</UL>
<P><A NAME="next%1"><STRONG><CODE>next(S)</CODE></STRONG></A><BR>
<UL>
<P>      Returns {X, V, S1} where X is the smallest key referred to
         by the iterator S, and S1 is the new iterator to be used for
         traversing the remaining entries, or the atom `none' if no
         entries remain.
</UL>
<H3>SEE ALSO</H3>
<UL>
<P> <A HREF="gb_sets.html">gb_sets(3)</A>, 
<A HREF="dict.html">dict(3)</A>, 
</UL>
<H3>AUTHORS</H3>
<UL>
Sven-Olof Nystrom, Richard Carlsson - support@erlang.ericsson.se<BR>
</UL>
<CENTER>
<HR>
<FONT SIZE=-1>stdlib 1.10<BR>
Copyright &copy; 1991-2001
<A HREF="http://www.erlang.se">Ericsson Utvecklings AB</A><BR>
<!--#include virtual="/ssi/otp_footer.html"-->
</FONT>
</CENTER>
</BODY>
</HTML>