Class: Tree::RedBlackNode

Inherits:
Object
  • Object
show all
Includes:
Enumerable
Defined in:
lib/tree/red_black/red_black_node.rb

Overview

Tree::RedBlackNode is a pure-Ruby implementation of a Red-Black tree – i.e., a self-balancing binary search tree with O(log n) search, insert and delete operations. It is appropriate for maintaining an ordered collection where insertion and deletion are desired at arbitrary positions.

The implementation differs slightly from the Wikipedia description referenced above. In particular, leaf nodes are nil, which affects the details of node deletion.

While a Red-Black tree can be constructed from nodes alone, the Tree::RedBlack API provides a cleaner way of working with Red-Black trees. Start there if only using the Red-Black tree as a container.

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(value = nil, color = :RED) ⇒ RedBlackNode

Example

require 'tree/red_black'

root = Tree::RedBlackNode.new(10)
p root.key              #=> 10
p root.color            #=> :RED
p root.parent           #=> nil
p root.left             #=> nil
p root.right            #=> nil



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# File 'lib/tree/red_black/red_black_node.rb', line 53

def initialize(value = nil, color = :RED)
  raise "color must be :RED or :BLACK" unless [:RED, :BLACK].include?(color)

  @left = @right = @parent = nil
  @key = value
  @color = color
end

Instance Attribute Details

#color ⇒ Object

Returns the value of attribute color.



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# File 'lib/tree/red_black/red_black_node.rb', line 24

def color
  @color
end

#key ⇒ Object

Returns the value of attribute key.



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# File 'lib/tree/red_black/red_black_node.rb', line 24

def key
  @key
end

#left ⇒ Object

Returns the value of attribute left.



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# File 'lib/tree/red_black/red_black_node.rb', line 24

def left
  @left
end

#parent ⇒ Object

Returns the value of attribute parent.



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# File 'lib/tree/red_black/red_black_node.rb', line 24

def parent
  @parent
end

#right ⇒ Object

Returns the value of attribute right.



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# File 'lib/tree/red_black/red_black_node.rb', line 24

def right
  @right
end

Instance Method Details

#<=>(other) ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 61

def <=>(other) # :nodoc:
  key <=> other.key
end

#bsearch(&block) ⇒ Object

Returns a node satisfying a criterion defined in block by binary search.

If block evaluates to true or false, returns the first node for which the block evaluates to true. In this case, the criterion is expected to return false for nodes preceding the matching node and true for subsequent nodes.

Example

require 'tree/red_black'

shuffled_values = [*1..10].shuffle
root = shuffled_values.reduce(Tree::RedBlackNode.new) do |acc, v|
  acc.insert_red_black(v)
end
root.bsearch { |node| node.key >= 7 }
                      #=> <Tree::RedBlackNode:0x00... @key=7 ...>

If block evaluates to <0, 0 or >0, returns first node for which block evaluates to 0. Otherwise returns nil. In this case, the criterion is expected to return <0 for nodes preceding the matching node, 0 for some subsequent nodes and >0 for nodes beyond that.

Example

require 'tree/red_black'

shuffled_values = [*1..10].shuffle
root = shuffled_values.reduce(Tree::RedBlackNode.new) do |acc, v|
  acc.insert_red_black(v)
end
root.bsearch { |node| 7 <=> node.key }
                      #=> <Tree::RedBlackNode:0x00... @key=7 ...>

If block+ is not given, returns an enumerator.



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# File 'lib/tree/red_black/red_black_node.rb', line 228

def bsearch(&block)
  return enum_for(:bsearch) unless block_given?

  return nil if key.nil?

  result = block.call(self)
  case result
  when Integer
    if result > 0
      right ? right.bsearch(&block) : nil
    elsif result < 0
      left ? left.bsearch(&block) : nil
    else
      self
    end
  when TrueClass, FalseClass
    if result
      left ? (node = left.bsearch(&block); node ? node : self) : self
    else
      right ? right.bsearch(&block) : nil
    end
  else
    nil
  end
end

#color_delete_left ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 565

def color_delete_left # :nodoc:
  child_sibling = right

  if child_sibling.color == :RED
    @color = :RED
    child_sibling.color = :BLACK
    rotate_left
    child_sibling = right
  end

  if (color == :BLACK &&
      child_sibling.color == :BLACK &&
      (child_sibling.left.nil? || child_sibling.left.color   == :BLACK) &&
      (child_sibling.right.nil? || child_sibling.right.color == :BLACK))
    child_sibling.color = :RED
    if self == parent&.left
      parent.color_delete_left
    elsif self == parent&.right
      parent.color_delete_right
    end
  elsif (color == :RED &&
         child_sibling.color == :BLACK &&
         (child_sibling.left.nil? || child_sibling.left.color   == :BLACK) &&
         (child_sibling.right.nil? || child_sibling.right.color == :BLACK))
    child_sibling.color = :RED
    @color = :BLACK
  else
    if child_sibling.color == :BLACK
      if ((child_sibling.right.nil? || child_sibling.right.color == :BLACK) &&
          child_sibling.left&.color  == :RED)
        child_sibling.color = :RED
        child_sibling.left.color = :BLACK
        child_sibling.rotate_right
        child_sibling = right
      end
    end

    child_sibling.color = color
    @color = :BLACK
    child_sibling.right.color = :BLACK # if child_sibling.right
    rotate_left
  end
end

#color_delete_right ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 521

def color_delete_right # :nodoc:
  child_sibling = left

  if child_sibling.color == :RED
    @color = :RED
    child_sibling.color = :BLACK
    rotate_right
    child_sibling = left
  end

  if (color == :BLACK &&
      child_sibling.color == :BLACK &&
      (child_sibling.left.nil? || child_sibling.left.color   == :BLACK) &&
      (child_sibling.right.nil? || child_sibling.right.color == :BLACK))
    child_sibling.color = :RED
    if self == parent&.left
      parent.color_delete_left
    elsif self == parent&.right
      parent.color_delete_right
    end
  elsif (color == :RED &&
         child_sibling.color == :BLACK &&
         (child_sibling.left.nil? || child_sibling.left.color   == :BLACK) &&
         (child_sibling.right.nil? || child_sibling.right.color == :BLACK))
    child_sibling.color = :RED
    @color = :BLACK
  else
    if child_sibling.color == :BLACK
      if (child_sibling.right&.color == :RED &&
          (child_sibling.left.nil? || child_sibling.left&.color == :BLACK))
        child_sibling.color = :RED
        child_sibling.right.color = :BLACK
        child_sibling.rotate_left
        child_sibling = left
      end
    end

    child_sibling.color = color
    @color = :BLACK
    child_sibling.left.color = :BLACK # if child_sibling.left
    rotate_right
  end
end

#color_insert ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 466

def color_insert # :nodoc:
  if parent.nil?
    @color = :BLACK
  elsif parent.color == :BLACK
    return
  elsif parent_sibling&.color == :RED
    parent.color = parent_sibling.color = :BLACK
    grandparent.color = :RED
    grandparent.color_insert
  else
    node = if self == parent.right && parent == grandparent&.left
             parent.rotate_left.left
           elsif self == parent.left && parent == grandparent&.right
             parent.rotate_right.right
           else
             self
           end
    node.parent.color = :BLACK
    if node.grandparent
      node.grandparent.color = :RED
      if node == node.parent.left
        node.grandparent.rotate_right
      else
        node.grandparent.rotate_left
      end
    end
  end
end

#delete_red_black(value) ⇒ Object

Deletes the given value from a tree whose root node is self. If the tree has only one remaining node and its key attribute matches value, then the remaining node’s key attribute is set to nil but the node itself is not removed. Otherwise, the first node found whose key matches value is removed from the tree, and the tree is re-balanced. The root of the balanced tree is returned.

Example

require 'tree/red_black'

root = [*1..10].reduce(Tree::RedBlackNode.new) do |acc, v|
  acc.insert_red_black(v)
end
root = [*4..8].reduce(root) do |acc, v|
  acc.delete_red_black(v)
end
root.map(&:key)                 #=> [1, 2, 3, 9, 10]



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# File 'lib/tree/red_black/red_black_node.rb', line 148

def delete_red_black(value)
  if key.nil?
    nil
  elsif value > key
    right ? right.delete_red_black(value) : nil
  elsif value < key
    left ? left.delete_red_black(value) : nil
  else
    if left && right
      node = right.min
      @key = node.key
      node.substitute_with_child
    else
      substitute_with_child
    end
  end
end

#dup ⇒ Object

Returns a deep copy of the tree with root self, provided that the dup method for the key attribute of a node is also a deep copy.

Example

require 'tree/red_black'

root = Tree::RedBlackNode.new({a: 1, b: 2})
root_copy = root.dup
p root.key                       #=> {:a=>1, :b=>2}
p root.key.delete(:a)            #=> 1
p root.key                       #=> {:b=>2}
p root_copy.key                  #=> {:a=>1, :b=>2}



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# File 'lib/tree/red_black/red_black_node.rb', line 405

def dup
  copy = RedBlackNode.new(key.dup, color)
  if left
    copy.left = left.dup
    copy.left.parent = copy
  end
  if right
    copy.right = right.dup
    copy.right.parent = copy
  end
  copy
end

#grandparent ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 69

def grandparent # :nodoc:
  parent&.parent
end

#in_order {|_self| ... } ⇒ Object Also known as: each

Returns an enumerator for nodes in the tree with root self by in-order traversal.

Example

require 'tree/red_black'

shuffled_values = [*1..10].shuffle
root = shuffled_values.reduce(Tree::RedBlackNode.new) do |acc, v|
  acc.insert_red_black(v)
end
root.in_order.map(&:key)        #=> [1, 2, ..., 10]

Yields:

  • (_self)

Yield Parameters:



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# File 'lib/tree/red_black/red_black_node.rb', line 381

def in_order(&block)
  return enum_for(:in_order) unless block_given?

  left.in_order(&block) if left
  yield self
  right.in_order(&block) if right
end

#insert_key(value) ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 418

def insert_key(value) # :nodoc:
  if key.nil?
    @key = value
    self
  elsif value >= key
    if right
      right.insert_key(value)
    else
      @right = RedBlackNode.new(value)
      @right.parent = self
      right
    end
  else
    if left
      left.insert_key(value)
    else
      @left = RedBlackNode.new(value)
      @left.parent = self
      left
    end
  end
end

#insert_red_black(value, allow_duplicates = true) ⇒ Object

Since a Red-Black tree maintains an ordered, Enumerable collection, every value inserted must be Comparable with every other value. Methods each, map, select, find, sort, etc., can be applied to a Red-Black tree’s root node to iterate over all nodes in the tree.

Each node yielded by enumeration has a key attribute to retrieve the value stored in that node. Method each, in particular, is aliased to in_order, so that nodes are sorted in ascending order by key value. Nodes can also be traversed by method pre_order, e.g., to generate paths in the tree.

Example

require 'tree/red_black'

root = Tree::RedBlackNode.new
p root.key                      #=> nil
root = root.insert_red_black(0)
p root.key                      #=> 0
root = root.insert_red_black(1)
p root.key                      #=> 0
p root.left                     #=> nil
p root.right.key                #=> 1
root = root.insert_red_black(2)
p root.key                      #=> 1
p root.left.key                 #=> 0
p root.right.key                #=> 2



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# File 'lib/tree/red_black/red_black_node.rb', line 114

def insert_red_black(value, allow_duplicates = true)
  node = allow_duplicates ? insert_key(value) : insert_unique_key(value)

  return nil if node.nil?

  node.color_insert

  while node.parent
    node = node.parent
  end
  node
end

#insert_unique_key(value) ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 441

def insert_unique_key(value) # :nodoc:
  if key.nil?
    @key = value
    self
  elsif value > key
    if right
      right.insert_unique_key(value)
    else
      @right = RedBlackNode.new(value)
      @right.parent = self
      right
    end
  elsif value < key
    if left
      left.insert_unique_key(value)
    else
      @left = RedBlackNode.new(value)
      @left.parent = self
      left
    end
  else
    nil
  end
end

#max ⇒ Object

Returns the node whose key is a maximum in the sub-tree with root self.

Example

require 'tree/red_black'

root = [*0..10].reduce(Tree::RedBlackNode.new) do |acc, v|
  acc.insert_red_black(v)
end
root                  #=> <Tree::RedBlackNode:0x00..., @key=4, ...>
root.max              #=> <Tree::RedBlackNode:0x00..., @key=10, ...>
root.left             #=> <Tree::RedBlackNode:0x00..., @key=2, ...>
root.left.max         #=> <Tree::RedBlackNode:0x00..., @key=3, ...>



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# File 'lib/tree/red_black/red_black_node.rb', line 292

def max
  node = self
  while node.right
    node = node.right
  end
  node
end

#min ⇒ Object

Returns the node whose key is a minimum in the sub-tree with root self.

Example

require 'tree/red_black'

root = [*0..10].reduce(Tree::RedBlackNode.new) do |acc, v|
  acc.insert_red_black(v)
end
root                  #=> <Tree::RedBlackNode:0x00..., @key=4, ...>
root.min              #=> <Tree::RedBlackNode:0x00..., @key=0, ...>
root.right            #=> <Tree::RedBlackNode:0x00..., @key=6, ...>
root.right.min        #=> <Tree::RedBlackNode:0x00..., @key=5, ...>



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# File 'lib/tree/red_black/red_black_node.rb', line 269

def min
  node = self
  while node.left
    node = node.left
  end
  node
end

#parent_sibling ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 73

def parent_sibling # :nodoc:
  parent&.sibling
end

#pre_order {|_self| ... } ⇒ Object

Returns an enumerator for nodes in the tree with root self by pre-order traversal.

Example

require 'tree/red_black'

root = [*1..10].reduce(Tree::RedBlackNode.new) do |acc, v|
  acc.insert_red_black(v)
end
root.pre_order.map(&:key)       #=> [4, 2, 1, 3, 6, 5, 8, 7, 9, 10]

Yields:

  • (_self)

Yield Parameters:



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# File 'lib/tree/red_black/red_black_node.rb', line 360

def pre_order(&block)
  return enum_for(:pre_order) unless block_given?

  yield self
  left.pre_order(&block) if left
  right.pre_order(&block) if right
end

#pred ⇒ Object

Returns the node preceding self, or nil if no predecessor exists. If duplicate keys are allowed, it’s possible that pred.key == key.

Example

require 'tree/red_black'

root = [*1..10].reduce(Tree::RedBlackNode.new) do |acc, v|
  acc.insert_red_black(v)
end
root.right.right.key            #=> 8
root.right.right.pred.key       #=> 7



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# File 'lib/tree/red_black/red_black_node.rb', line 314

def pred
  return left.max if left

  node = parent
  while node && node.key > key
    node = node.parent
  end
  node
end

#rotate_left ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 626

def rotate_left # :nodoc:
  return self if right.nil?

  root = right
  root.left.parent = self unless (@right = root.left).nil?
  if (root.parent = parent)
    if self == parent.left
      @parent.left = root
    else
      @parent.right = root
    end
  end
  root.left = self
  @parent = root
  root
end

#rotate_right ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 609

def rotate_right # :nodoc:
  return self if left.nil?

  root = left
  root.right.parent = self unless (@left = root.right).nil?
  if (root.parent = parent)
    if self == parent.left
      @parent.left = root
    else
      @parent.right = root
    end
  end
  root.right = self
  @parent = root
  root
end

#search(value, ifnone = nil) ⇒ Object

Returns a node whose key matches value by binary search. If no match is found, calls non-nil ifnone, otherwise returns nil.

Example

require 'tree/red_black'

shuffled_values = [*1..10].shuffle
root = shuffled_values.reduce(Tree::RedBlackNode.new) do |acc, v|
  acc.insert_red_black(v)
end
root.search(7)        #=> <Tree::RedBlackNode:0x00..., @key=7, ...>



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# File 'lib/tree/red_black/red_black_node.rb', line 179

def search(value, ifnone = nil)
  if key.nil?
    ifnone && ifnone.call
  elsif value > key
    right ? right.search(value, ifnone) : ifnone && ifnone.call
  elsif value < key
    left ? left.search(value, ifnone) : ifnone && ifnone.call
  else
    self
  end
end

#sibling ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 65

def sibling # :nodoc:
  self == parent&.left ? parent&.right : parent&.left
end

#substitute_with_child ⇒ Object

:nodoc:



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# File 'lib/tree/red_black/red_black_node.rb', line 495

def substitute_with_child # :nodoc:
  if (child = right.nil? ? left : right)
    child.parent = parent
    child.color = :BLACK if color == :BLACK
  end

  if self == parent&.left
    parent.left = child
    parent.color_delete_left if (color == :BLACK && child.nil?)
  elsif self == parent&.right
    parent.right = child
    parent.color_delete_right if (color == :BLACK && child.nil?)
  end

  node = parent ? parent : child
  if node.nil?
    @key = nil
    self
  else
    while node.parent
      node = node.parent
    end
    node
  end
end

#succ ⇒ Object

Returns the node succeeding self, or nil if no successor exists. If duplicate keys are allowed, it’s possible that succ.key == key.

Example

require 'tree/red_black'

root = [*1..10].reduce(Tree::RedBlackNode.new) do |acc, v|
  acc.insert_red_black(v)
end
root.right.right.key            #=> 8
root.right.right.succ.key       #=> 9



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# File 'lib/tree/red_black/red_black_node.rb', line 338

def succ
  return right.min if right

  node = parent
  while node && node.key < key
    node = node.parent
  end
  node
end