#### Floor and Ceiling

p
```"""
In a binary search tree (BST):
* The floor of key 'k' is the maximum value that is smaller than or equal to 'k'.
* The ceiling of key 'k' is the minimum value that is greater than or equal to 'k'.

Reference:
https://bit.ly/46uB0a2

Author : Arunkumar
Date : 14th October 2023
"""

from __future__ import annotations

from collections.abc import Iterator
from dataclasses import dataclass

@dataclass
class Node:
key: int
left: Node | None = None
right: Node | None = None

def __iter__(self) -> Iterator[int]:
if self.left:
yield from self.left
yield self.key
if self.right:
yield from self.right

def __len__(self) -> int:
return sum(1 for _ in self)

def floor_ceiling(root: Node | None, key: int) -> tuple[int | None, int | None]:
"""
Find the floor and ceiling values for a given key in a Binary Search Tree (BST).

Args:
root: The root of the binary search tree.
key: The key for which to find the floor and ceiling.

Returns:
A tuple containing the floor and ceiling values, respectively.

Examples:
>>> root = Node(10)
>>> root.left = Node(5)
>>> root.right = Node(20)
>>> root.left.left = Node(3)
>>> root.left.right = Node(7)
>>> root.right.left = Node(15)
>>> root.right.right = Node(25)
>>> tuple(root)
(3, 5, 7, 10, 15, 20, 25)
>>> floor_ceiling(root, 8)
(7, 10)
>>> floor_ceiling(root, 14)
(10, 15)
>>> floor_ceiling(root, -1)
(None, 3)
>>> floor_ceiling(root, 30)
(25, None)
"""
floor_val = None
ceiling_val = None

while root:
if root.key == key:
floor_val = root.key
ceiling_val = root.key
break

if key < root.key:
ceiling_val = root.key
root = root.left
else:
floor_val = root.key
root = root.right

return floor_val, ceiling_val

if __name__ == "__main__":
import doctest

doctest.testmod()
```