diff --git a/data_structures/binary_tree/symmetric_tree.py b/data_structures/binary_tree/symmetric_tree.py new file mode 100644 index 000000000..331a25849 --- /dev/null +++ b/data_structures/binary_tree/symmetric_tree.py @@ -0,0 +1,101 @@ +""" +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()