NAME
Tree::AVL - Perl implemenation of an AVL tree for storing comparable objects.
SYNOPSIS
use Tree::AVL;
####################################################### # # Example 1 # This example shows usage with default constructor. # # With default constructor, the tree works with strings. # # Constructor can also be passed a comparison function, # and accessor methods to use, so that you can store any # type of object in the tree (see Example 2). # #######################################################
# create a tree with default constructor my $avltree = Tree::AVL->new();
# can insert strings by default $avltree->insert("arizona"); $avltree->insert("arkansas"); $avltree->insert("massachusetts"); $avltree->insert("maryland"); $avltree->insert("montana"); $avltree->insert("madagascar");
print $avltree->get_height() . "\n"; # output: 2 (height is zero-based)
$avltree->print("*"); # output: # # *maryland: maryland: height: 2: balance: 0 # **massachusetts: massachusetts: height: 1: balance: 0 # ***montana: montana: height: 0: balance: 0 # **arkansas: arkansas: height: 1: balance: 0 # ***madagascar: madagascar: height: 0: balance: 0 # ***arizona: arizona: height: 0: balance: 0
my $obj = $avltree->remove("maryland"); print "found: $obj\n"; # output: found: maryland my $obj = $avltree->remove("maryland"); if(!$obj){ print "object was not in tree.\n"; }
$avltree->print("*"); # output: # # *madagascar: madagascar: height: 2: balance: 0 # **massachusetts: massachusetts: height: 1: balance: 0 # ***montana: montana: height: 0: balance: 0 # **arkansas: arkansas: height: 1: balance: 1 # ***arizona: arizona: height: 0: balance: 0
# retreive an iterator over the objects in the tree. my $iterator = $avltree->iterator(); while(my $obj = $iterator->()){ print $obj . "\n"; # outputs objects in order low-to-high }
# retreive a reverse-order iterator over the objects in the tree. my $iterator = $avltree->iterator(">"); while(my $obj = $iterator->()){ print $obj . "\n"; # outputs objects in order high-to-low }
# retrieve all objects from tree at once my @list = $avltree->get_list(); foreach my $obj (@list){ print $obj . "\n"; # outputs objects in order low-to-high }
my $obj = $avltree->pop_smallest(); # retrieves arizona print "$obj\n";
my $obj = $avltree->pop_largest(); # retrieves montana print "$obj\n";
undef $avltree;
print "\nExample 2\n"; ####################################################### # # Example 2 # # instantiate tree and specify key, data and # comparison functions. insert any object # you want. Here a basic hash is used, but # any object of your creation will do when you # supply an appropriate comparison function. # #######################################################
my $elt1 = { _name => "Bob", _phone => "444-4444",};
my $elt2 = { _name => "Amy", _phone => "555-5555",};
my $elt3 = { _name => "Sara", _phone => "666-6666",};
$avltree = Tree::AVL->new( fcompare => sub{ my ($o1, $o2) = @_; if($o1->{_name} gt $o2->{_name}){ return -1} elsif($o1->{_name} lt $o2->{_name}){ return -1} return 0;}, fget_key => sub{ my($obj) = @_; return $obj->{_name};}, fget_data => sub{ my($obj) = @_; return $obj->{_phone};}, );
$avltree->insert($elt1); $avltree->insert($elt2); $avltree->insert($elt3);
$avltree->print("-"); # output: # # -Bob: 444-4444: height: 1: balance: 1 # --Amy: 555-5555: height: 0: balance: 0 #
$avltree->insert($elt4); # output: "Error: inserted uninitialized object.."
exit;
DESCRIPTION
AVL Trees are balanced binary trees, first introduced in "An Algorithm for the Organization of Data" by Adelson-Velskii and Landis in 1962.
Balance is kept in an AVL tree during insertion and deletion by maintaining a 'balance' factor in each node.
If the subtree below any node in the tree is evenly balanced, the balance factor for that node will be 0.
When the right-subtree below a node is taller than the left-subtree, the balance factor will be 1. For the opposite case, the balance factor will be -1.
If the either subtree is heavier (taller by more than 2 levels) than the other, the balance factor within the node will be set to (+-)2, and the subtree below that node will be rebalanced.
Re-balancing is done via 'single' or 'double' rotations, each of which takes constant-time.
Insertion into an AVL tree will require at most 1 rotation.
Deletion from an AVL tree may take as much as log(n) rotations in order to restore balance.
Balanced trees can save huge amounts of time in your programs when used over regular flat data structures. For example, if you are processing as much as 1,125,899,906,842,624 ordered objects on some super-awesome mega workstation, the worst-case time (comparisons) required to access one of those objects will be 1,125,899,906,842,624 if you keep them in a flat data structure. However, using a balanced tree such as a 2-3 tree, a Red-Black tree or an AVL tree, worst-case time (comparisons) required will be just 50.
EXPORT
None by default.
SEE ALSO
"An Algorithm for the Organization of Information", G.M. Adelson-Velsky and E.M. Landis.
AUTHOR
Matthias Beebe, <matthiasbeebe@gmail.com<gt>
COPYRIGHT AND LICENSE
Copyright (C) 2009 by Matthias Beebe
This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.8.8 or, at your option, any later version of Perl 5 you may have available.