rbt.py

@@ -0,0 +1,192 @@
+from node import Node, Comparable, RotateFunction
+from ranked_tree import RankedTree
+
+import enum
+import logging
+from typing import Callable, Tuple, TypeVar, Optional
+
+logger = logging.getLogger(__name__)
+T = TypeVar("T", bound=Comparable)
+
+
+class Colour(enum.IntEnum):
+    Red = 0
+    Black = 1
+
+
+def colour(x: Optional[Node[T]]) -> Colour:
+    if not x or not x.parent:
+        return Colour.Black
+
+    diff = Node.difference(x)
+    assert diff in (0, 1)
+
+    return Colour(diff)
+
+
+class RBTree(RankedTree[T]):
+    def is_correct_node(
+        self, node: Optional[Node[T]], recursive: bool = True
+    ) -> bool:
+        if not node:
+            return True
+
+        left, right = Node.differences(node)
+        if left not in (Colour.Red, Colour.Black):
+            # left subtree has invalid difference
+            return False
+        elif right not in (Colour.Red, Colour.Black):
+            # right subtree has invalid difference
+            return False
+
+        if Node.difference(node) == Colour.Red and (
+            left == Colour.Red or right == Colour.Red
+        ):
+            # two consecutive red nodes
+            return False
+
+        return not recursive or (
+            self.is_correct_node(node.left)
+            and self.is_correct_node(node.right)
+        )
+
+    # region InsertRebalance
+
+    def _insert_rebalance_step(
+        self,
+        x: Node[T],
+        d: Optional[Node[T]],
+        y: Node[T],
+        rotate_left: RotateFunction,
+        rotate_right: RotateFunction,
+    ) -> Node[T]:
+        p = x.parent
+        pp = p.parent
+
+        if d is not None and colour(d) == Colour.Red:
+            pp.rank += 1
+            x = pp
+        elif x == y:
+            x = p
+            rotate_left(tree=self, x=p)
+        else:
+            rotate_right(tree=self, x=pp)
+
+        return x
+
+    def _insert_rebalance(self, x: Node[T]) -> None:
+        while x.parent is not None and colour(x.parent) == Colour.Red:
+            p = x.parent
+            pp = x.parent.parent
+
+            assert pp
+            if p == pp.left:
+                x = self._insert_rebalance_step(
+                    x, pp.right, p.right, Node.rotate_left, Node.rotate_right
+                )
+            else:
+                x = self._insert_rebalance_step(
+                    x, pp.left, p.left, Node.rotate_right, Node.rotate_left
+                )
+
+    # endregion InsertRebalance
+
+    # region DeleteRebalance
+
+    def _delete_rebalance_step(
+        self,
+        x: Node[T],
+        w: Node[T],
+        parent: Node[T],
+        left: Callable[[Node[T]], Node[T]],
+        right: Callable[[Node[T]], Node[T]],
+        rotate_left: RotateFunction,
+        rotate_right: RotateFunction,
+    ) -> Tuple[Optional[Node[T]], Optional[Node[T]]]:
+        if colour(w) == Colour.Red:
+            logger.debug("RB-Delete: Case 1 -- x's sibling w is red")
+            # w.colour = Colour.Black
+            # x.parent.colour = Colour.Red
+            rotate_left(tree=self, x=parent)
+            w = right(parent)
+
+        if colour(w.left) == Colour.Black and colour(w.right) == Colour.Black:
+            logger.debug(
+                "RB-Delete: Case 2 -- x's sibling w is black, and both of w's children are black"
+            )
+            # w.colour = Colour.Red
+            parent.rank -= 1
+            x = parent
+        else:
+            if colour(right(w)) == Colour.Black:
+                logger.debug(
+                    "RB-Delete: Case 3 -- x's sibling w is black, w's left child is red, and w's right child is black"
+                )
+                # left(w).colour = Colour.Black
+                # w.colour = Colour.Red
+                rotate_right(tree=self, x=w)
+                w = right(parent)
+            logger.debug(
+                "RB-Delete: Case 4 -- x's sibling w is black, and w's right child is red"
+            )
+            # w.colour = colour(x.parent)
+            # x.parent.colour = Colour.Black
+            # right(w).colour = Colour.Black
+            rotate_left(tree=self, x=parent)
+            x = self.root
+
+        return x, (x.parent if x else None)
+
+    def _delete_rebalance(
+        self, node: Optional[Node[T]], parent: Optional[Node[T]]
+    ) -> None:
+        if not node and not parent:
+            return
+
+        logger.debug(
+            "RB-Delete: Called with node=‹%s› parent=‹%s›", node, parent
+        )
+        logger.debug("RB-Delete: Colour of node: %s", colour(node))
+        if (node and 2 not in Node.differences(node)) or (
+            2 not in Node.differences(parent)
+        ):
+            # we haven't deleted a black node
+            logger.debug(
+                "RB-Delete: No black node has been deleted; node: %s; diffs: %s",
+                node,
+                Node.differences(node),
+            )
+            return
+
+        logger.debug("RB-Delete: Tree before rebalancing:\n%s", str(self))
+
+        while node != self.root and colour(node) == Colour.Black:
+            logger.debug(
+                "RB-Delete: Rebalancing node=‹%s› (%s-node) parent=‹%s› (%s-node)",
+                node,
+                Node.differences(node),
+                parent,
+                Node.differences(parent),
+            )
+            if node == parent.left:
+                node, parent = self._delete_rebalance_step(
+                    node,
+                    parent.right,
+                    parent,
+                    lambda x: x.left,
+                    lambda x: x.right,
+                    Node.rotate_left,
+                    Node.rotate_right,
+                )
+            else:
+                node, parent = self._delete_rebalance_step(
+                    node,
+                    parent.left,
+                    parent,
+                    lambda x: x.right,
+                    lambda x: x.left,
+                    Node.rotate_right,
+                    Node.rotate_left,
+                )
+
+    # endregion DeleteRebalance

test_properties.py

@@ -1,6 +1,7 @@
 from avl import AVLTree
 from wavl import WAVLTree
 from ravl import RAVLTree
+from rbt import RBTree
 
 import logging
 import random
@@ -13,8 +14,7 @@ logger = logging.getLogger(__name__)
 
 
 @pytest.mark.parametrize(
-    ("RankBalancedTree"),
+    ("RankBalancedTree"), [RBTree, AVLTree, WAVLTree, RAVLTree]
-    [AVLTree, WAVLTree, RAVLTree]
 )
 @hypothesis.settings(max_examples=10000)
 @hypothesis.given(values=st.sets(st.integers()))
@@ -44,8 +44,7 @@ def _report(t_before: str, t_after: str) -> None:
 
 
 @pytest.mark.parametrize(
-    ("RankBalancedTree"),
+    ("RankBalancedTree"), [RBTree, AVLTree, WAVLTree, RAVLTree]
-    [AVLTree, WAVLTree, RAVLTree]
 )
 @hypothesis.settings(max_examples=10000)
 @hypothesis.given(config=delete_strategy())