Tree-AVL version 1.077 ===================== An implementation of an AVL tree for storing comparable objects. AVL Trees are balanced binary trees, first introduced in "An Algorithm for the Organization of Information" 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 time in your programs when used instead of regular flat data-structures. For example, if you are processing as much as 1,125,899,906,842,624 (a quadrillion) ordered objects, the time (number of comparisons) required to access one of those objects will be on the order of 1,125,899,906,842,624 in the worst case 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, the worst-case time (comparisons) required will be 50. Example usage ===================== 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"); # just seeing if you're paying attention.. 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. # # Note: whereas in this example, anonymous subroutines are # passed in to the constructor, you can just as well supply # your own object's comparison methods- i.e., # # $avltree = Tree::AVL->new( # fcompare => \&MyObj::compare, # # . . . # # etc... # ####################################################### 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 # --Sara: 666-6666: height: 0: balance: 0 $avltree->insert($elt4); # output: "Error: inserted uninitialized object.." exit; INSTALLATION To install this module type the following: perl Makefile.PL make make test make install DEPENDENCIES This module requires these other modules and libraries: no dependencies. COPYRIGHT AND LICENSE Put the correct copyright and licence information here. Copyright (C) 2009,2010 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.