"""
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 represents an element of a binary tree, which contains:
Attributes:
data: The value stored in the node (int).
left: Pointer to the left child node (Node or None).
right: Pointer to the right child node (Node or None).
Example:
>>> node = Node(1, Node(2), Node(3))
>>> node.data
1
>>> node.left.data
2
>>> node.right.data
3
"""
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
Returns:
Node: Root node of a symmetric tree.
Example:
>>> tree = make_symmetric_tree()
>>> tree.data
1
>>> tree.left.data == tree.right.data
True
>>> tree.left.left.data == tree.right.right.data
True
"""
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 an asymmetric tree for testing.
The tree looks like this:
1
/ \
2 2
/ \ / \
3 4 3 4
Returns:
Node: Root node of an asymmetric tree.
Example:
>>> tree = make_asymmetric_tree()
>>> tree.data
1
>>> tree.left.data == tree.right.data
True
>>> tree.left.left.data == tree.right.right.data
False
"""
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:
"""
Check if a binary tree is symmetric (i.e., a mirror of itself).
Parameters:
tree: The root node of the binary tree.
Returns:
bool: True if the tree is symmetric, False otherwise.
Example:
>>> 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
def is_mirror(left: Node | None, right: Node | None) -> bool:
"""
Check if two subtrees are mirror images of each other.
Parameters:
left: The root node of the left subtree.
right: The root node of the right subtree.
Returns:
bool: True if the two subtrees are mirrors of each other, False otherwise.
Example:
>>> tree1 = make_symmetric_tree()
>>> 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:
return True
if left is None or right is None:
return False
if left.data == right.data:
return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
return False
if __name__ == "__main__":
from doctest import testmod
testmod()