#### Is Sorted

d
p
```"""
Given the root of a binary tree, determine if it is a valid binary search tree (BST).

A valid binary search tree is defined as follows:
- The left subtree of a node contains only nodes with keys less than the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- Both the left and right subtrees must also be binary search trees.

In effect, a binary tree is a valid BST if its nodes are sorted in ascending order.
leetcode: https://leetcode.com/problems/validate-binary-search-tree/

If n is the number of nodes in the tree then:
Runtime: O(n)
Space: O(1)
"""

from __future__ import annotations

from collections.abc import Iterator
from dataclasses import dataclass

@dataclass
class Node:
data: float
left: Node | None = None
right: Node | None = None

def __iter__(self) -> Iterator[float]:
"""
>>> root = Node(data=2.1)
>>> list(root)
[2.1]
>>> root.left=Node(data=2.0)
>>> list(root)
[2.0, 2.1]
>>> root.right=Node(data=2.2)
>>> list(root)
[2.0, 2.1, 2.2]
"""
if self.left:
yield from self.left
yield self.data
if self.right:
yield from self.right

@property
def is_sorted(self) -> bool:
"""
>>> Node(data='abc').is_sorted
True
>>> Node(data=2,
...      left=Node(data=1.999),
...      right=Node(data=3)).is_sorted
True
>>> Node(data=0,
...      left=Node(data=0),
...      right=Node(data=0)).is_sorted
True
>>> Node(data=0,
...      left=Node(data=-11),
...      right=Node(data=3)).is_sorted
True
>>> Node(data=5,
...      left=Node(data=1),
...      right=Node(data=4, left=Node(data=3))).is_sorted
False
>>> Node(data='a',
...      left=Node(data=1),
...      right=Node(data=4, left=Node(data=3))).is_sorted
Traceback (most recent call last):
...
TypeError: '<' not supported between instances of 'str' and 'int'
>>> Node(data=2,
...      left=Node([]),
...      right=Node(data=4, left=Node(data=3))).is_sorted
Traceback (most recent call last):
...
TypeError: '<' not supported between instances of 'int' and 'list'
"""
if self.left and (self.data < self.left.data or not self.left.is_sorted):
return False
if self.right and (self.data > self.right.data or not self.right.is_sorted):
return False
return True

if __name__ == "__main__":
import doctest

doctest.testmod()
tree = Node(data=2.1, left=Node(data=2.0), right=Node(data=2.2))
print(f"Tree {list(tree)} is sorted: {tree.is_sorted = }.")
assert tree.right
tree.right.data = 2.0
print(f"Tree {list(tree)} is sorted: {tree.is_sorted = }.")
tree.right.data = 2.1
print(f"Tree {list(tree)} is sorted: {tree.is_sorted = }.")
```