python/rbt.py

from node import Node, Comparable
from ranked_tree import RankedTree, RotateFunction

import enum
import logging
from typing import Callable, Tuple, TypeVar, Optional

logger = logging.getLogger(__name__)
T = TypeVar("T", bound=Comparable)


class Colour(enum.IntEnum):
    """
    Represents colour of the edge or node.
    """

    Red = 0
    Black = 1


def has_double_black(x: Optional[Node[T]]) -> bool:
    """
    Checks for double black child of x.

    Args:
        x: Node to be checked.

    Returns:
        `true`, if `x` has a double black node, `false` otherwise.
    """
    return x is not None and 2 in Node.differences(x)


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,
        z: Node[T],
        y: Optional[Node[T]],
        right_child: Node[T],
        rotate_left: RotateFunction[T],
        rotate_right: RotateFunction[T],
    ) -> Node[T]:
        p = z.parent
        pp = p.parent

        if y is not None and Node.difference(y) == Colour.Red:
            # Case 1
            # ======
            # z’s uncle y is red
            pp.rank += Colour.Black
            z = pp
        elif z == right_child:
            # Case 2
            # ======
            # z’s uncle y is black and z is a right child
            z = p
            rotate_left(p)
        else:
            # Case 3
            # ======
            # z’s uncle y is black and z is a left child
            rotate_right(pp)

        return z

    def _insert_rebalance(self, z: Node[T]) -> None:
        while z.parent is not None and Node.difference(z.parent) == Colour.Red:
            p = z.parent
            pp = p.parent

            assert pp
            if p == pp.left:
                z = self._insert_rebalance_step(
                    z, pp.right, p.right, self.rotate_left, self.rotate_right
                )
            else:
                z = self._insert_rebalance_step(
                    z, pp.left, p.left, self.rotate_right, self.rotate_left
                )

    # endregion InsertRebalance

    # region DeleteRebalance

    def _delete_rebalance_step(
        self,
        x: Node[T],
        w: Node[T],
        parent: Node[T],
        right: Callable[[Node[T]], Optional[Node[T]]],
        rotate_left: RotateFunction[T],
        rotate_right: RotateFunction[T],
    ) -> Tuple[Optional[Node[T]], Optional[Node[T]]]:
        if Node.difference(w) == Colour.Red:
            # Case 1
            # ======
            # x’s sibling w is red
            rotate_left(parent)
            w = right(parent)

        if Node.differences(w) == (Colour.Black, Colour.Black):
            # Case 2
            # ======
            # x’s sibling w is black, and both of w’s children are black
            parent.rank -= Colour.Black
            x = parent
        else:
            # Case 3
            # ======
            # x’s sibling w is black,
            # w’s left child is red, and w’s right child is black
            if Node.difference(right(w), w) == Colour.Black:
                rotate_right(w)
                w = right(parent)

            # Case 4
            # ======
            # x’s sibling w is black, and w’s right child is red
            parent.rank -= Colour.Black
            w.rank += Colour.Black
            rotate_left(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

        while node != self.root and has_double_black(parent):
            if node == parent.left:
                node, parent = self._delete_rebalance_step(
                    node,
                    parent.right,
                    parent,
                    lambda x: x.right,
                    self.rotate_left,
                    self.rotate_right,
                )
            else:
                node, parent = self._delete_rebalance_step(
                    node,
                    parent.left,
                    parent,
                    lambda x: x.left,
                    self.rotate_right,
                    self.rotate_left,
                )

    # endregion DeleteRebalance