python/avl.py

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

import logging
from typing import TypeVar, Optional

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


def _balance_factor(node: Optional[Node[T]]) -> int:
    if not node:
        return 0

    left, right = Node.get_rank(node.left), Node.get_rank(node.right)
    return right - left


def _update_rank(node: Node[T]) -> None:
    left, right = Node.get_rank(node.left), Node.get_rank(node.right)
    node.rank = 1 + max(left, right)


class AVLTree(RankedTree[T]):
    def is_correct_node(
        self, node: Optional[Node[T]], recursive: bool = True
    ) -> bool:
        if not node:
            return True

        if not (
            -1 <= _balance_factor(node) <= 1
            and node.rank
            == 1 + max(Node.get_rank(node.left), Node.get_rank(node.right))
        ):
            return False

        return not recursive or (
            self.is_correct_node(node.left)
            and self.is_correct_node(node.right)
        )

    # region InsertRebalance

    def __fix_0_child(
        self,
        x: Node[T],
        y: Optional[Node[T]],
        z: Node[T],
        rotate_left: RotateFunction[T],
        rotate_right: RotateFunction[T],
    ) -> Optional[Node[T]]:
        new_root = x.parent

        if not y or Node.difference(y) == 2:
            new_root = rotate_right(z)
            z.demote()
        elif Node.difference(y) == 1:
            rotate_left(x)
            new_root = rotate_right(z)

            y.promote()
            x.demote()
            z.demote()

        return new_root

    def _insert_rebalance(self, x: Node[T]) -> None:
        diffs = Node.differences(x.parent)
        while x.parent and (diffs == (0, 1) or diffs == (1, 0)):
            x.parent.promote()
            x = x.parent

            diffs = Node.differences(x.parent)

        if not x.parent:
            return

        rotating_around_root = x.parent.parent is None
        new_root: Optional[Node[T]] = x.parent

        rank_difference = Node.difference(x)
        if rank_difference != 0:
            return

        x_parent = x.parent
        assert x_parent is not None
        if rank_difference == 0 and x.parent.left is x:
            new_root = self.__fix_0_child(
                x, x.right, x_parent, Node.rotate_left, Node.rotate_right
            )
        elif rank_difference == 0 and x.parent.right is x:
            new_root = self.__fix_0_child(
                x, x.left, x_parent, Node.rotate_right, Node.rotate_left
            )

        if rotating_around_root:
            self.root = new_root

    # endregion InsertRebalance

    # region DeleteRebalance

    def __delete_rotate(
        self,
        x: Node[T],
        y: Node[T],
        leaning: int,
        rotating_around_root: bool,
        rotate_left: RotateFunction[T],
        rotate_right: RotateFunction[T],
    ) -> bool:
        new_root = x

        factor = _balance_factor(y)
        if factor in (0, leaning):
            new_root = rotate_left(x)
        else:
            rotate_right(y)
            new_root = rotate_left(x)

        for n in filter(None, (new_root.left, new_root.right, new_root)):
            _update_rank(n)

        if rotating_around_root:
            self.root = new_root
        return factor != 0

    def __delete_fixup(
        self, x: Optional[Node[T]], parent: Optional[Node[T]] = None
    ) -> bool:
        factor = _balance_factor(x)
        if factor == 0:
            _update_rank(x)
            return True
        elif factor in (-1, 1):
            return False

        rotating_around_root = x.parent is None
        y, leaning, to_left, to_right = (
            (x.right, 1, Node.rotate_left, Node.rotate_right)
            if factor == 2
            else (x.left, -1, Node.rotate_right, Node.rotate_left)
        )
        assert y
        return self.__delete_rotate(
            x,
            y,
            leaning,
            rotating_around_root,
            to_left,
            to_right,
        )

    def _delete_rebalance(
        self, node: Optional[Node[T]], parent: Optional[Node[T]]
    ) -> None:
        if not node and not parent:
            return

        if not node:
            node, parent = parent, parent.parent

        while node and self.__delete_fixup(node, parent):
            node, parent = parent, parent.parent if parent else None

    # endregion DeleteRebalance