Symmetric tree

data_structures/binary_tree/symmetric_tree.py

@@ -0,0 +1,107 @@
+"""
+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
+        """
+    tree = Node(1)
+    tree.left = Node(2)
+    tree.right = Node(2)
+    tree.left.left = Node(3)
+    tree.left.right = Node(4)
+    tree.right.left = Node(4)
+    tree.right.right = Node(3)
+    return tree
+
+
+def make_asymmetric_tree() -> Node:
+    r"""
+        Create a asymmetric tree for testing.
+        The tree looks like this:
+               1
+             /   \
+            2     2
+          / \    / \
+         3   4   3  4
+        """
+    tree = Node(1)
+    tree.left = Node(2)
+    tree.right = Node(2)
+    tree.left.left = Node(3)
+    tree.left.right = Node(4)
+    tree.right.left = Node(3)
+    tree.right.right = Node(4)
+    return tree
+
+
+class SymmetricTree:
+    def is_symmetric_tree(self, tree: Node) -> bool:
+        r"""
+        Test cases for is_symmetric_tree function
+
+        >>> SymmetricTree().is_symmetric_tree(make_symmetric_tree())
+        True
+
+        >>> SymmetricTree().is_symmetric_tree(make_asymmetric_tree())
+        False
+        """
+        if tree is None:
+            # An empty tree is considered symmetric.
+            return True
+        return self.is_mirror(tree.left, tree.right)
+
+    def is_mirror(self, left: Node | None, right: Node | None) -> bool:
+        """
+        >>> tree1 = make_symmetric_tree()
+        >>> tree1.right.right = Node(3)
+        >>> SymmetricTree().is_mirror(tree1.left, tree1.right)
+        True
+
+        >>> tree2 = make_asymmetric_tree()
+        >>> SymmetricTree().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 self.is_mirror(left.left, right.right) and self.is_mirror(
+                left.right, right.left
+            )
+        return False
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()