Merge pull request #199 from aparibocci/feature/bst

Adding `BinarySearchTree` implementation

data_structures/binary_trees/bst.rb

@@ -0,0 +1,176 @@
+class BinarySearchTreeNode
+
+  attr_reader :key
+  attr_accessor :left
+  attr_accessor :right
+
+  def initialize(key)
+    @key = key
+  end
+end
+
+##
+# This class represents a binary search tree (not implementing self-balancing) 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.
+#
+# The main operations of this data structure (insertion, deletion, membership) run - in worst case - in O(n),
+# where n is the number of nodes in the tree.
+# The average case for those operations is O(log(n)) due to the structure of the tree.
+
+class BinarySearchTree
+
+  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 = BinarySearchTreeNode.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 BinarySearchTree") unless parent.left.nil?
+      parent.left = BinarySearchTreeNode.new(key)
+    else
+      raise ArgumentError.new("Key #{key} is already present in the BinarySearchTree") unless parent.right.nil?
+      parent.right = BinarySearchTreeNode.new(key)
+    end
+  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)
+      return
+    end
+    if key < parent.key
+      node = parent.left
+      parent.left = adjusted_subtree_after_deletion(node.left, node.right)
+    else
+      node = parent.right
+      parent.right = adjusted_subtree_after_deletion(node.left, node.right)
+    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
+      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 = right
+    successor.left = left
+    successor
+  end
+end

data_structures/binary_trees/bst_test.rb

@@ -0,0 +1,112 @@
+require 'minitest/autorun'
+require_relative 'bst'
+
+class TestBinarySearchTree < Minitest::Test
+  def test_default_constructor_creates_empty_tree
+    bst = BinarySearchTree.new
+    assert bst.to_array.empty?
+  end
+
+  def test_default_constructor_creates_tree_with_given_keys
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    assert bst.to_array == [4, 2, 1, 3, 6]
+  end
+
+  def test_exception_when_inserting_key_already_present
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    assert_raises ArgumentError do
+        bst.insert_key(6)
+    end
+  end
+
+  def test_size_returns_zero_given_empty_tree
+    bst = BinarySearchTree.new
+    assert bst.size == 0
+  end
+
+  def test_empty_returns_number_of_nodes_in_tree
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    assert bst.size == 5
+  end
+
+  def test_empty_returns_true_given_empty_tree
+    bst = BinarySearchTree.new
+    assert bst.empty?
+  end
+
+  def test_empty_returns_false_given_non_empty_tree
+    bst = BinarySearchTree.new([1])
+    assert !bst.empty?
+  end
+
+  def test_min_key_returns_minimum_key
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    assert bst.min_key == 1
+  end
+
+  def test_max_key_returns_maximum_key
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    assert bst.max_key == 6
+  end
+
+  def test_contains_key_returns_true_if_key_in_tree
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    assert bst.contains_key?(3)
+  end
+
+  def test_contains_key_returns_false_if_key_not_in_tree
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    assert !bst.contains_key?(7)
+  end
+
+  def test_delete_key_does_nothing_if_key_not_in_tree
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    bst.delete_key(7)
+    assert bst.to_array == [4, 2, 1, 3, 6]
+  end
+
+  def test_delete_key_keeps_bst_property_if_leaf_node
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    bst.delete_key(1)
+    assert bst.to_array == [4, 2, 3, 6]
+  end
+
+  def test_delete_key_keeps_bst_property_if_node_with_left_child
+    bst = BinarySearchTree.new([4, 2, 3, 1])
+    bst.delete_key(4)
+    assert bst.to_array == [2, 1, 3]
+  end
+
+  def test_delete_key_keeps_bst_property_if_node_with_right_child
+    bst = BinarySearchTree.new([4, 2, 6, 3])
+    bst.delete_key(2)
+    assert bst.to_array == [4, 3, 6]
+  end
+
+  def test_delete_key_keeps_bst_property_if_node_with_both_children
+    bst = BinarySearchTree.new([4, 2, 7, 3, 1, 5, 10, 6])
+    bst.delete_key(4)
+    assert bst.to_array == [5, 2, 1, 3, 7, 6, 10]
+  end
+
+  def test_preorder_traversal_uses_expected_order
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    visited = []
+    bst.traverse_preorder(->(key) { visited.append(key) })
+    assert visited == [4, 2, 1, 3, 6]
+  end
+
+  def test_inorder_traversal_uses_expected_order
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    visited = []
+    bst.traverse_inorder(->(key) { visited.append(key) })
+    assert visited == [1, 2, 3, 4, 6]
+  end
+
+  def test_postorder_traversal_uses_expected_order
+    bst = BinarySearchTree.new([4, 2, 6, 3, 1])
+    visited = []
+    bst.traverse_postorder(->(key) { visited.append(key) })
+    assert visited == [1, 3, 2, 6, 4]
+  end
+end