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"""

Is a binary tree a sum tree where the value of every non-leaf node is equal to the sum

of the values of its left and right subtrees?

https://www.geeksforgeeks.org/check-if-a-given-binary-tree-is-sumtree

"""

from __future__ import annotations

from collections.abc import Iterator

from dataclasses import dataclass

@dataclass

class Node:

data: int

left: Node | None = None

right: Node | None = None

def __iter__(self) -> Iterator[int]:

"""

>>> root = Node(2)

>>> list(root)

[2]

>>> root.left = Node(1)

>>> tuple(root)

(1, 2)

"""

if self.left:

yield from self.left

yield self.data

if self.right:

yield from self.right

def __len__(self) -> int:

"""

>>> root = Node(2)

>>> len(root)

>>> root.left = Node(1)

>>> len(root)

"""

return sum(1 for _ in self)

@property

def is_sum_node(self) -> bool:

"""

>>> root = Node(3)

>>> root.is_sum_node

True

>>> root.left = Node(1)

>>> root.is_sum_node

False

>>> root.right = Node(2)

>>> root.is_sum_node

True

"""

if not self.left and not self.right:

return True # leaf nodes are considered sum nodes

left_sum = sum(self.left) if self.left else 0

right_sum = sum(self.right) if self.right else 0

return all(

(

self.data == left_sum + right_sum,

self.left.is_sum_node if self.left else True,

self.right.is_sum_node if self.right else True,

)

@dataclass

class BinaryTree:

root: Node

def __iter__(self) -> Iterator[int]:

"""

>>> list(BinaryTree.build_a_tree())

[1, 2, 7, 11, 15, 29, 35, 40]

"""

return iter(self.root)

def __len__(self) -> int:

"""

>>> len(BinaryTree.build_a_tree())

"""

return len(self.root)

def __str__(self) -> str:

"""

Returns a string representation of the inorder traversal of the binary tree.

>>> str(list(BinaryTree.build_a_tree()))

'[1, 2, 7, 11, 15, 29, 35, 40]'

"""

return str(list(self))

@property

def is_sum_tree(self) -> bool:

"""

>>> BinaryTree.build_a_tree().is_sum_tree

False

>>> BinaryTree.build_a_sum_tree().is_sum_tree

True

"""

return self.root.is_sum_node

@classmethod

def build_a_tree(cls) -> BinaryTree:

r"""

Create a binary tree with the specified structure:

/ \

2 29

/ \ / \

1 7 15 40

>>> list(BinaryTree.build_a_tree())

[1, 2, 7, 11, 15, 29, 35, 40]

"""

tree = BinaryTree(Node(11))

root = tree.root

root.left = Node(2)

root.right = Node(29)

root.left.left = Node(1)

root.left.right = Node(7)

root.right.left = Node(15)

root.right.right = Node(40)

root.right.right.left = Node(35)

return tree

@classmethod

def build_a_sum_tree(cls) -> BinaryTree:

r"""

Create a binary tree with the specified structure:

/ \

10 3

/ \ \

4 6 3

>>> list(BinaryTree.build_a_sum_tree())

[4, 10, 6, 26, 3, 3]

"""

tree = BinaryTree(Node(26))

root = tree.root

root.left = Node(10)

root.right = Node(3)

root.left.left = Node(4)

root.left.right = Node(6)

root.right.right = Node(3)

return tree

if __name__ == "__main__":

from doctest import testmod

testmod()

tree = BinaryTree.build_a_tree()

print(f"{tree} has {len(tree)} nodes and {tree.is_sum_tree = }.")

tree = BinaryTree.build_a_sum_tree()

print(f"{tree} has {len(tree)} nodes and {tree.is_sum_tree = }.")

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