On 12/15/07, Rob B. [email protected] wrote:
should be at the top level. I also created an AVLTree::ExternalNode
to duck-type with AVLTree::Node as a special kind of nil alternative
to clean up a lot of code that would otherwise need to make a special
case of @left or @right being nil.
I had a little time, so I’ve added the other two types of rebalancing,
and
added a test for Tree#find {block}
I hope some people are still interested in ping-pong.
-Adam
==> avl_tree.rb <==
class AVLTree
Need something smarter than nil for external nodes
class ExternalNode
attr_accessor :parent
def initialize(parent)
@parent = parent
end
def include?(); false; end
def <<(); raise RuntimeError; end
def height; 0; end
def balance_factor; 0; end
def left; self; end
def right; self; end
def left=(node)
raise(NotImplementedError,
“external node of #{@parent}”)
end
def right=(node)
raise(NotImplementedError,
“external node of #{@parent}”)
end
def to_s; ‘’; end
def to_a; []; end
end
class Node
attr_accessor :data, :parent
attr_reader :left, :right
def initialize obj
@parent = nil
@data = obj
@left = ExternalNode.new(self)
@right = ExternalNode.new(self)
end
def left=(node)
@left = node
node.parent = self
end
def right=(node)
@right = node
node.parent = self
end
def height
[ @left.height, @right.height ].max + 1
end
def << node
case node.data <=> @data
when -1
if Node === @left
@left << node
else
self.left = node
end
when 0
return self # no dups
when +1
if Node === @right
@right << node
else
self.right = node
end
end
rebalance if balance_factor.abs > 1
end
def include? obj
case obj <=> @data
when -1 : @left.include?(obj)
when 0 : true
when +1 : @right.include?(obj)
end
end
def to_a
result = @left.to_a
result << @data
result.concat @right.to_a
result
end
def to_s
bf = case balance_factor <=> 0
when -1 : '-' * -balance_factor
when 0 : '.'
when 1 : '+' * balance_factor
end
"[#{left} "+
"(#{@data}{#{height}#{bf}}^#{parent.data})"+
" #{right}]"
end
protected
def balance_factor
@right.height - @left.height
end
def rebalance weight=0
if (bf = balance_factor + 0) > 1
puts "balancing: #{self.to_s}"
# right is too high
if @right.balance_factor < 0
# double rotate right-left - first the right subtree
#add some weight to force rotation even if it was nearly
balanced
@right.rebalance -1
end
# single rotate left
my_parent, from, to = @parent, self, @right
temp = @right.left
@right.left = self
self.right = temp
my_parent.send :replace_child, from, to
to.parent = my_parent
#~ else
#~ end
elsif bf < -1
# left must be too high
if @left.balance_factor > 0
#double rotate - first force left subtree,
@left.rebalance 1
end
# single rotate right
my_parent, from, to = @parent, self, @left
temp = @left.right
@left.right = self
self.left = temp
my_parent.send :replace_child, from, to
to.parent = my_parent
end
puts my_parent
end
def replace_child(from, to)
if from.eql? @left
@left = to
elsif from.eql? @right
@right = to
else
raise(ArgumentError,
"#{from} is not a branch of #{self}")
end
end
end
def initialize
@root = nil
end
def empty?
@root.nil?
end
def include?(obj)
empty? ? false : @root.include?(obj)
end
def <<(obj)
raise(ArgumentError,
“Objects added to #{self.class.name} must” +
" respond to <=>"
) unless obj.respond_to?(:<=>)
if empty?
@root = Node.new(obj)
@root.parent = self
else
@root << Node.new(obj)
end
self
end
def height
empty? ? 0 : @root.height
end
naive implementation [not O(lg N)]
def
to_a[idx]
end
def to_a
empty? ? [] : @root.to_a
end
naive implementation [not O(lg N)]
def each
to_a.each {|e| yield e}
end
def to_s
empty? ? “[]” : @root.to_s
end
Indicates that parent is root in to_s
def data; ‘*’; end
protected
def replace_child(from, to)
if @root.eql? from
@root = to
else
raise(ArgumentError,
“#{from} is not a branch of #{self}”)
end
end
end
END
==> package.rb <==
Dir[ARGV[0] || ‘*.rb’].each do |f|
lines = IO.readlines(f)
lines.unshift “==> #{f} <==\n”
lines << “END\n” unless lines.last.chomp == ‘END’
lines << “\n”
puts lines
end
END
==> test_avl_tree.rb <==
#!/usr/bin/env ruby -wKU
require “test/unit”
require “avl_tree”
class TestAVLTree < Test::Unit::TestCase
def setup
@tree = AVLTree.new
end
##################################################
Membership tests
def test_tree_membership
assert_equal(true, @tree.empty?)
assert_equal(false, @tree.include?(3))
@tree << 3
assert_equal(false, @tree.empty?)
assert_equal(true, @tree.include?(3))
end
def test_tree_should_allow_more_than_one_element
@tree << 3
@tree << 4
assert(@tree.include?(4), "4 not in #{@tree}")
assert(@tree.include?(3), "3 not in #{@tree}")
end
def test_tree_include_many
0.upto(10) do |i|
assert_equal(false, @tree.include?(i),
"Tree should not include #{i} yet.")
@tree << i
0.upto(i) do |j|
assert_equal(true, @tree.include?(j),
"Tree should have 0..#{i},"+
" where's #{j}? ")
end
end
end
This sits at the intersection of membership
and height tests. We know one node has height 1,
and two nodes has height 2, so if we insert one
object twice and the height is 1, there must
only be one node in the tree.
def test_tree_does_not_keep_duplicates
@tree << ‘a’
@tree << ‘a’
assert_equal 1, @tree.height, “one node: #{@tree}”
end
##################################################
Height tests
def test_tree_height_of_one_or_two_nodes_is_N
@tree << 5
assert_equal 1, @tree.height, "one node: #{@tree}"
@tree << 6
assert_equal 2, @tree.height, "two nodes: #{@tree}"
end
def test_tree_height_of_three_nodes_is_two
@tree << 5
@tree << 6
@tree << 7
assert_equal 2, @tree.height, @tree.to_s
end
RobB: The more precise limit given in [Knuth] is
used rather than that from [Wikipedia]
def test_tree_growth_limit_is_1pt44_log_N
(1..10).each do |i|
@tree << i
limit = ((1.4405 *
Math::log(i+2.0)/Math::log(2.0)
) - 0.3277).ceil
assert(@tree.height <= limit,
"Tree of #{i} nodes is too tall by" +
" #{@tree.height - limit}" +
" #{@tree}")
end
end
def test_balances_left
4.downto(1) { |i| @tree << i }
assert(@tree.height < 4,
"expected tree height #{@tree.height} < 4")
end
def test_balances_right
1.upto(4) { |i| @tree << i }
assert(@tree.height < 4,
"expected tree height #{@tree.height} < 4")
end
def test_non_sequential_insertion__part_1
items = [ 1, 3, 2 ]
items.each do |i|
@tree << i
end
items.each do |i|
assert_equal(true, @tree.include?(i),
"where is #{i}? ")
end
end
##################################################
Access tests (getting data back out)
RobB: this tests too much at one time; I sorted ary.
def test_tree_traverse
ary = [ 3, 5, 17, 30, 42, 54, 1, 2 ].sort
ary.each { |n| @tree << n }
traversal = []
@tree.each { |n| traversal << n }
assert_equal(ary.size, traversal.size)
ary.each do |n|
assert_equal(true, traversal.include?(n),
"#{n} was not visited in tree.")
end
end
def test_tree_find
[1,2,3,4].each{|n| @tree<<n}
assert_equal(1, @tree.find{|v|v>0} )
assert_equal(2, @tree.find{|v|v%2==0} )
end
##################################################
Things that aren’t tested anymore…
[Knuth] p.473: "The problem of deletion can be solved
in O(log N) steps if we approach it correctly."
RobB: I’m choosing to skip this capability since
the test was added before an actual tree structure
emerged.
def future__test_remove_node
@tree << 314
@tree.remove(314)
assert_equal(false, @tree.include?(314),
'314 still in the tree')
end
RobB: While I think the spirit of this test is good,
it attempts to expose the implementation too much.
I replaced this with test_sequential_access.
def never__test_has_branches
[50, 17, 72].each {|n| @tree << n}
assert_equal 50, @tree.data
assert_equal 17, @tree.left.data
assert_equal 72, @tree.right.data
end
end
=begin
[Knuth] Knuth, Donald Ervin,
The Art of Computer Programming, 2nd ed.
Volume 3, Sorting and Searching,
section 6.2.3 “Balanced Trees”, pp. 458-478
[Wikipedia]
AVL Tree, AVL tree - Wikipedia
=end
END
Also, I’ve included my package and extract scripts that can pull the
