From: James Koppel <jamesbkoppel@...>
Date: 2007-12-19T12:34:59+09:00
Subject: Re: [QUIZ] Programmer Ping-Pong (#150)

I just realized that it might be a good idea to change my test to make each accept an options hash rather than ordered arguments, since my change and my new test will cause each to accept two keyword arguments. That is, rather than having calls like

@tree.each(:postorder,:node){...}

having something along the lines of

@ree.each(:traversal=>:postorder,:val=>:node)

----- Original Message ----
From: James Koppel <jamesbkoppel@yahoo.com>
To: ruby-talk ML <ruby-talk@ruby-lang.org>
Sent: Tuesday, December 18, 2007 8:23:35 PM
Subject: Re: [QUIZ] Programmer Ping-Pong (#150)


On 12/18/07, Adam Shelly wrote:
>I added test_remove_multiple_nodes - there are definitely a few
>mistakes in the current remove :)

Seems the only mistake was that remove was expecting AVLTree#each to
 return the node traversed, but it was instead returning the node's data.
 I modified each to accept the name of a function to be passed to
 itself, which defaults to data. I made an "identity" method called node, and
 the passed it in when each is called within remove.

For my test, each and to_a must now accept symbols denoting the type of
 traversal to be performed, including inorder (the current traversal),
 preorder, postorder, and level-by-level.

==>avl_tree.rb<==
class AVLTree

  include Enumerable

  # 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 each(*args,&iter)                        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, sortblock
      @parent = nil
      @data  = obj
      @left  = ExternalNode.new(self)
      @right  = ExternalNode.new(self)
      @height = 1
      @compare = sortblock
    end

    def left=(node)
      @height = nil
      @left = node
      node.parent = self
    end

    def right=(node)
      @height = nil
      @right = node
      node.parent = self
    end

    def each(returns=:data,&iter)
      @left.each(&iter)
      iter[self.send(returns)]
      @right.each(&iter)
    end
    
    def node
      self
    end

    def height
      @height || ( [ @left.height, @right.height ].max + 1)
    end

    def << node
      case @compare[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
      @height = nil
    end

    def remove obj
      @height = nil
      case @compare[obj,@data]
      when -1
        if Node === @left
          @left.remove(obj)
        else
          nil
        end
      when 0
        if Node === @left
          largest = nil
          AVLTree.new(@left).each(:node) do |n|
            largest = n if largest.nil? or n.data > largest.data
            largest = n if largest.nil? or n.data > largest.data
          end
          self.data = largest.data
          self.left = largest.left
        elsif Node === @right
          smallest = nil
          AVLTree.new(@right).each(:node) do |n|
            smallest = n if smallest.nil? or n.data < smallest.data
            smallest = n if smallest.nil? or n.data < smallest.data
          end
          self.data  = smallest.data
          self.right = smallest.right
        else
          parent.send :replace_child, self, ExternalNode.new(parent)
        end
        path = self
        while Node === (path = path.parent)
          path.rebalance if path.balance_factor.abs > 1
        end
        self
      when +1
        if Node === @right
          @right.remove(obj)
        else
          nil
        end
      end
    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 [](idx)
        if idx < (leftheight = @left.height)
          @left[idx]
        elsif (idx== leftheight)
          @data
        elsif (idx-=(leftheight+1)) < @right.height
          @right[idx]
        end
    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 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
    end

    def 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

    def rebalance
      if (bf = balance_factor) > 1 # right is too high
        if @right.balance_factor < 0
          # double rotate right-left
          # - first the right subtree
          @right.rotate_right
        end
        rotate_left            # single rotate left
      elsif bf < -1            # left must be too high
        if @left.balance_factor > 0
          # double rotate left-right
          # - first force left subtree
          @left.rotate_left
        end
        rotate_right            # single rotate right
      end
    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, &block)
    @root = root
    if block
      raise(ArgumentError,
        "Block argument for #{self.class.name} must" +
        " take 2 arguments and act as sort function"
        ) unless block.arity == 2
    else
      block = proc{|a,b| a<=>b}
    end
    @compare = block
  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, @compare)
      @root.parent = self
    else
      @root << Node.new(obj, @compare)
    end
    self
  end

  def remove(obj)
    @root.remove(obj) unless empty?
  end

  def height
    empty? ? 0 : @root.height
  end

  def [](idx)
    @root[idx]
  end

  def to_a
    empty? ? [] : @root.to_a
  end

  def each(*args,&iter)
    @root.each(*args,&iter) unless empty?
  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_

==>test_avl_tree.rb<==


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

  def test_non_sequential_insertion__part_2
    items = [ 3, 1, 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_alternate_traversals
    items = [3,2,4,1,5]
    items.each {|el| @tree << el}
    
    preorder_result = [3,2,1,4,5]
    assert_equal(@tree.to_a(:preorder),preorder_result)
    @tree.each(:preorder) {|el| assert_equal(preorder_result.shift,el)}
    
    inorder_result = [1,2,3,4,5]
    assert_equal(@tree.to_a(:inorder),inorder_result)
    @tree.each(:inorder) {|el| assert_equal(inorder_result.shift,el)}
    
    postorder_result = [1,2,5,4,3]
    assert_equal(@tree.to_a(:postorder),postorder_result)
    @tree.each(:postorder) {|el|
 assert_equal(postorder_result.shift,el)}
    
    bylevel_result = [3,2,4,1,5]
    assert_equal(@tree.to_a(:by_level),bylevel_result)
    @tree.each(:by_level) {|el| assert_equal(bylevel_result.shift,el)}
  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

  def test_sequential_access
    items = [ 50, 17, 72 ]
    items.each { |n| @tree << n }
    items.sort.each_with_index do |e,i|
      assert_equal(e, @tree[i],
                    "@tree[#{i}] should be like " +
                    "#{items.inspect}.sort[#{i}]")
    end
  end

  # [Knuth] p.473: "The problem of deletion can be solved
  # in O(log N) steps if we approach it correctly."
  def test_remove_node
    @tree << 314
    @tree.remove(314)
    assert_equal(false, @tree.include?(314),
                  '314 still in the tree')
    end

    def test_remove_multiple_nodes
    items = [ 50, 17, 72, 45, 43, 23 ]
    items.each { |n| @tree << n }
    puts @tree, @tree.height
    @tree.remove(50)
    assert_equal(false, @tree.include?(50),
                  '50 still in the tree')
    @tree.remove(72)
    assert_equal(false, @tree.include?(72),
                  '72 still in the tree')
    @tree.remove(45)
    assert_equal(false, @tree.include?(45),
                  '45 still in the tree')
    assert_equal(2, @tree.height)  #tree should have 3 items, height =
 2
    end



  ##################################################
  # Interface tests

  def test_custom_comparison_code
    rev_tree = AVLTree.new { |a, b| b <=> a }
    values  = [3, 2, 1]
    values.each { |v| rev_tree << v }
    rev_tree.each { |v| assert_equal(values.shift, v) }

    len_tree = AVLTree.new { |a, b| a.length <=> b.length }
    values  = %w[3 22 111]
    values.each { |v| len_tree << v }
    len_tree.each { |v| assert_equal(values.shift, v) }
  end

end
_END_



    
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