p

```
"""
Given the root of a binary tree, check whether it is a mirror of itself
(i.e., symmetric around its center).
Leetcode reference: https://leetcode.com/problems/symmetric-tree/
"""
from __future__ import annotations
from dataclasses import dataclass
@dataclass
class Node:
"""
A Node has data variable and pointers to Nodes to its left and right.
"""
data: int
left: Node | None = None
right: Node | None = None
def make_symmetric_tree() -> Node:
r"""
Create a symmetric tree for testing.
The tree looks like this:
1
/ \
2 2
/ \ / \
3 4 4 3
"""
root = Node(1)
root.left = Node(2)
root.right = Node(2)
root.left.left = Node(3)
root.left.right = Node(4)
root.right.left = Node(4)
root.right.right = Node(3)
return root
def make_asymmetric_tree() -> Node:
r"""
Create a asymmetric tree for testing.
The tree looks like this:
1
/ \
2 2
/ \ / \
3 4 3 4
"""
root = Node(1)
root.left = Node(2)
root.right = Node(2)
root.left.left = Node(3)
root.left.right = Node(4)
root.right.left = Node(3)
root.right.right = Node(4)
return root
def is_symmetric_tree(tree: Node) -> bool:
"""
Test cases for is_symmetric_tree function
>>> is_symmetric_tree(make_symmetric_tree())
True
>>> is_symmetric_tree(make_asymmetric_tree())
False
"""
if tree:
return is_mirror(tree.left, tree.right)
return True # An empty tree is considered symmetric.
def is_mirror(left: Node | None, right: Node | None) -> bool:
"""
>>> tree1 = make_symmetric_tree()
>>> tree1.right.right = Node(3)
>>> is_mirror(tree1.left, tree1.right)
True
>>> tree2 = make_asymmetric_tree()
>>> is_mirror(tree2.left, tree2.right)
False
"""
if left is None and right is None:
# Both sides are empty, which is symmetric.
return True
if left is None or right is None:
# One side is empty while the other is not, which is not symmetric.
return False
if left.data == right.data:
# The values match, so check the subtree
return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
return False
if __name__ == "__main__":
from doctest import testmod
testmod()
```