Symmetric tree

data_structures/binary_tree/symmetric_tree.py

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+"""
+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()