# Aufgabe 6: Rekursion
from dataclasses import dataclass
from typing import Optional


@dataclass
class Node[T]:
    mark: T
    left: Optional["Node[T]"] = None
    right: Optional["Node[T]"] = None


type BTree[T] = Optional[Node[T]]


# a)
def sum_of_subtree(tree: BTree[int]) -> int:
    match tree:
        case None:
            return 0
        case Node(_, left, right):
            tree.mark += sum_of_subtree(left) + sum_of_subtree(right)
            return tree.mark


# b)
def cut_at[T](tree: BTree[T], at: T) -> BTree[T]:
    match tree:
        case None:
            return None
        case Node(mark, _, _) if mark == at:
            return None
        case Node(mark, left, right):  # f(mark)
            return Node(mark, cut_at(left, at), cut_at(right, at))


if __name__ == "__main__":
    t1 = None
    assert sum_of_subtree(t1) == 0
    assert t1 is None

    t3 = Node(1, Node(2, Node(3), Node(4)), Node(5, Node(6)))
    assert sum_of_subtree(t3) == 21
    assert t3 == Node(21, Node(9, Node(3), Node(4)), Node(11, Node(6)))

    assert cut_at(None, 42) is None
    t = Node(1, Node(2, Node(3), Node(4)), Node(3, Node(3), Node(6)))
    assert cut_at(t, 1) is None
    assert cut_at(t, 3) == Node(1, Node(2, None, Node(4)))