Merge pull request #200 from aparibocci/feature/avl_tree

Adding `AVL Tree` implementation

data_structures/binary_trees/avl_tree.rb

@@ -0,0 +1,281 @@
+class AvlTreeNode
+
+  attr_reader :key
+  attr_accessor :parent
+  attr_accessor :left
+  attr_accessor :right
+  attr_accessor :height
+
+  def initialize(key, parent=nil)
+    @key = key
+    @parent = parent
+    @height = 1
+  end
+end
+
+##
+# This class represents an AVL tree (a self-balancing binary search tree) with distinct node keys.
+# Starting from the root, every node has up to two children (one left and one right child node).
+#
+# For the BST property:
+# - the keys of nodes in the left subtree of a node are strictly less than the key of the node;
+# - the keys of nodes in the right subtree of a node are strictly greater than the key of the node.
+#
+# Due to self-balancing upon key insertion and deletion, the main operations of this data structure
+# (insertion, deletion, membership) run - in worst case - in O(log(n)), where n is the number of nodes in the tree.
+
+class AvlTree
+
+  attr_reader :size
+  attr_accessor :root
+
+  def initialize(keys=[])
+    @size = 0
+    keys.each {|key| insert_key(key) }
+  end
+
+  def empty?
+    size == 0
+  end
+
+  def insert_key(key)
+    @size += 1
+    if root.nil?
+      @root = AvlTreeNode.new(key)
+      return
+    end
+    parent = root
+    while (key < parent.key && !parent.left.nil? && parent.left.key != key) ||
+        (key > parent.key && !parent.right.nil? && parent.right.key != key)
+      parent = key < parent.key ? parent.left : parent.right
+    end
+    if key < parent.key
+      raise ArgumentError.new("Key #{key} is already present in the AvlTree") unless parent.left.nil?
+      parent.left = AvlTreeNode.new(key, parent)
+    else
+      raise ArgumentError.new("Key #{key} is already present in the AvlTree") unless parent.right.nil?
+      parent.right = AvlTreeNode.new(key, parent)
+    end
+    balance(parent)
+  end
+
+  def min_key(node=root)
+    return nil if node.nil?
+    min_key_node(node).key
+  end
+
+  def max_key(node=root)
+    return nil if node.nil?
+    max_key_node(node).key
+  end
+
+  def contains_key?(key)
+    !find_node_with_key(key).nil?
+  end
+
+  def delete_key(key)
+    parent = find_parent_of_node_with_key(key)
+    if parent.nil?
+      return if root.nil? || root.key != key
+      @size -= 1
+      @root = adjusted_subtree_after_deletion(root.left, root.right)
+      root.parent = nil
+      balance(root.right.nil? ? root : root.right)
+      return
+    end
+    if key < parent.key
+      node = parent.left
+      parent.left = adjusted_subtree_after_deletion(node.left, node.right)
+      unless parent.left.nil?
+        parent.left.parent = parent
+        balance(parent.left.right.nil? ? parent.left : parent.left.right)
+      end
+    else
+      node = parent.right
+      parent.right = adjusted_subtree_after_deletion(node.left, node.right)
+      unless parent.right.nil?
+        parent.right.parent = parent
+        balance(parent.right.right.nil? ? parent.right : parent.right.right)
+      end
+    end
+    @size -= 1
+  end
+
+  def traverse_preorder(key_consumer, node=root)
+    return if node.nil?
+    key_consumer.call(node.key)
+    traverse_preorder(key_consumer, node.left) unless node.left.nil?
+    traverse_preorder(key_consumer, node.right) unless node.right.nil?
+  end
+
+  def traverse_inorder(key_consumer, node=root)
+    return if node.nil?
+    traverse_inorder(key_consumer, node.left) unless node.left.nil?
+    key_consumer.call(node.key)
+    traverse_inorder(key_consumer, node.right) unless node.right.nil?
+  end
+
+  def traverse_postorder(key_consumer, node=root)
+    return if node.nil?
+    traverse_postorder(key_consumer, node.left) unless node.left.nil?
+    traverse_postorder(key_consumer, node.right) unless node.right.nil?
+    key_consumer.call(node.key)
+  end
+
+  def to_array(visit_traversal=:traverse_preorder)
+    visited = []
+    method(visit_traversal).call(->(key) { visited.append(key) })
+    visited
+  end
+
+  private
+  def min_key_node(node=root)
+    return nil if node.nil?
+    until node.left.nil?
+      node = node.left
+    end
+    node
+  end
+
+  def max_key_node(node=root)
+    return nil if node.nil?
+    until node.right.nil?
+      node = node.right
+    end
+    node
+  end
+
+  def find_node_with_key(key)
+    node = root
+    until node.nil? || node.key == key
+      node = key < node.key ? node.left : node.right
+    end
+    node
+  end
+
+  def find_parent_of_node_with_key(key)
+    return nil if root.nil? || root.key == key
+    parent = root
+    until parent.nil?
+      if key < parent.key
+        return nil if parent.left.nil?
+        return parent if parent.left.key == key
+        parent = parent.left
+      else
+        return nil if parent.right.nil?
+        return parent if parent.right.key == key
+        parent = parent.right
+      end
+    end
+    nil
+  end
+
+  def adjusted_subtree_after_deletion(left, right)
+    return right if left.nil?
+    return left if right.nil?
+    if right.left.nil?
+      right.left = left
+      left.parent = right
+      return right
+    end
+    successor_parent = right
+    until successor_parent.left.left.nil?
+      successor_parent = successor_parent.left
+    end
+    successor = successor_parent.left
+    successor_parent.left = successor.right
+    successor.right.parent = successor_parent unless successor.right.nil?
+    successor.right = right
+    right.parent = successor
+    successor.left = left
+    left.parent = successor
+    successor
+  end
+
+  def balance(node)
+    return if node.nil?
+    left_height = node.left&.height || 0
+    right_height = node.right&.height || 0
+    # Assumption: the subtrees rooted at `node.left` and `node.right` are balanced
+    adjust_height(node)
+    if right_height - left_height > 1
+      # `node` is right-heavy
+      if !node.right.left.nil? && (node.right.left.height || 0) > (node.right.right&.height || 0)
+        rotate_right_left(node)
+      else
+        rotate_left(node)
+      end
+    elsif left_height - right_height > 1
+      # `node` is left-heavy
+      if !node.left.right.nil? && (node.left.right.height || 0) > (node.left.left&.height || 0)
+        rotate_left_right(node)
+      else
+        rotate_right(node)
+      end
+    end
+
+    balance(node.parent)
+  end
+
+  def rotate_left(node)
+    new_root = node.right
+    if node == root
+      @root = new_root
+    elsif node.parent.left == node
+      node.parent.left = new_root
+    else
+      node.parent.right = new_root
+    end
+    new_root.parent = node.parent
+    if new_root.left.nil?
+      node.right = nil
+      new_root.left = node
+      node.parent = new_root
+    else
+      node.right = new_root.left
+      new_root.left.parent = node
+      new_root.left = node
+      node.parent = new_root
+    end
+    adjust_height(node)
+    adjust_height(new_root)
+  end
+
+  def rotate_right(node)
+    new_root = node.left
+    if node == root
+      @root = new_root
+    elsif node.parent.left == node
+      node.parent.left = new_root
+    else
+      node.parent.right = new_root
+    end
+    new_root.parent = node.parent
+    if new_root.right.nil?
+      node.left = nil
+      new_root.right = node
+      node.parent = new_root
+    else
+      node.left = new_root.right
+      new_root.right.parent = node
+      new_root.right = node
+      node.parent = new_root
+    end
+    adjust_height(node)
+    adjust_height(new_root)
+  end
+
+  def rotate_right_left(node)
+    rotate_right(node.right)
+    rotate_left(node)
+  end
+
+  def rotate_left_right(node)
+    rotate_left(node.left)
+    rotate_right(node)
+  end
+
+  def adjust_height(node)
+    node.height = 1 + [node.left&.height || 0, node.right&.height || 0].max
+  end
+end

data_structures/binary_trees/avl_tree_test.rb

@@ -0,0 +1,132 @@
+require 'minitest/autorun'
+require_relative 'avl_tree'
+
+class TestAvlTree < Minitest::Test
+  def test_default_constructor_creates_empty_tree
+    tree = AvlTree.new
+    assert tree.to_array.empty?
+  end
+
+  def test_default_constructor_creates_tree_with_given_keys
+    tree = AvlTree.new([1, 2, 3, 4, 5, 6, 7])
+    assert tree.to_array == [4, 2, 1, 3, 6, 5, 7]
+  end
+
+  def test_exception_when_inserting_key_already_present
+    tree = AvlTree.new([4, 2, 6, 3, 1])
+    assert_raises ArgumentError do
+        tree.insert_key(6)
+    end
+  end
+
+  def test_size_returns_zero_given_empty_tree
+    tree = AvlTree.new
+    assert tree.size == 0
+  end
+
+  def test_empty_returns_number_of_nodes_in_tree
+    tree = AvlTree.new([4, 2, 6, 3, 1])
+    assert tree.size == 5
+  end
+
+  def test_empty_returns_true_given_empty_tree
+    tree = AvlTree.new
+    assert tree.empty?
+  end
+
+  def test_empty_returns_false_given_non_empty_tree
+    tree = AvlTree.new([1])
+    assert !tree.empty?
+  end
+
+  def test_min_key_returns_minimum_key
+    tree = AvlTree.new([4, 2, 6, 3, 1])
+    assert tree.min_key == 1
+  end
+
+  def test_max_key_returns_maximum_key
+    tree = AvlTree.new([4, 2, 6, 3, 1])
+    assert tree.max_key == 6
+  end
+
+  def test_contains_key_returns_true_if_key_in_tree
+    tree = AvlTree.new([4, 2, 6, 3, 1])
+    assert tree.contains_key?(3)
+  end
+
+  def test_contains_key_returns_false_if_key_not_in_tree
+    tree = AvlTree.new([4, 2, 6, 3, 1])
+    assert !tree.contains_key?(7)
+  end
+
+  def test_delete_key_does_nothing_if_key_not_in_tree
+    tree = AvlTree.new([4, 2, 6, 3, 1])
+    tree.delete_key(7)
+    assert tree.to_array == [4, 2, 1, 3, 6]
+  end
+
+  def test_delete_key_keeps_avl_property_if_leaf_node
+    tree = AvlTree.new([1, 2, 3, 4, 5, 6, 7])
+    tree.delete_key(3)
+    assert tree.to_array == [4, 2, 1, 6, 5, 7]
+  end
+
+  def test_delete_key_keeps_avl_property_if_node_with_left_child
+    tree = AvlTree.new([4, 2, 5, 1])
+    tree.delete_key(2)
+    assert tree.to_array == [4, 1, 5]
+  end
+
+  def test_delete_key_keeps_avl_property_if_node_with_right_child
+    tree = AvlTree.new([4, 2, 5, 6])
+    tree.delete_key(5)
+    assert tree.to_array == [4, 2, 6]
+  end
+
+  def test_delete_key_keeps_avl_property_if_node_with_both_children
+    tree = AvlTree.new([1, 2, 3, 4, 5, 6, 7, 8, 9])
+    tree.delete_key(4)
+    assert tree.to_array == [5, 2, 1, 3, 8, 6, 7, 9]
+  end
+
+  def test_preorder_traversal_uses_expected_order
+    tree = AvlTree.new([1, 2, 3, 4, 5, 6, 7])
+    visited = []
+    tree.traverse_preorder(->(key) { visited.append(key) })
+    assert visited == [4, 2, 1, 3, 6, 5, 7]
+  end
+
+  def test_inorder_traversal_uses_expected_order
+    tree = AvlTree.new([1, 2, 3, 4, 5, 6, 7])
+    visited = []
+    tree.traverse_inorder(->(key) { visited.append(key) })
+    assert visited == [1, 2, 3, 4, 5, 6, 7]
+  end
+
+  def test_postorder_traversal_uses_expected_order
+    tree = AvlTree.new([1, 2, 3, 4, 5, 6, 7])
+    visited = []
+    tree.traverse_postorder(->(key) { visited.append(key) })
+    assert visited == [1, 3, 2, 5, 7, 6, 4]
+  end
+
+  def test_left_rotation
+    tree = AvlTree.new([1, 2, 3])
+    assert tree.to_array == [2, 1, 3]
+  end
+
+  def test_right_rotation
+    tree = AvlTree.new([3, 2, 1])
+    assert tree.to_array == [2, 1, 3]
+  end
+
+  def test_right_left_rotation
+    tree = AvlTree.new([1, 3, 2])
+    assert tree.to_array == [2, 1, 3]
+  end
+
+  def test_left_right_rotation
+    tree = AvlTree.new([3, 1, 2])
+    assert tree.to_array == [2, 1, 3]
+  end
+end