Symmetric tree (#9871)

* symmectric tree

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* removed trailing spaces

* escape sequence fix

* added return type

* added class

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* wordings fix

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* added static method

* added type

* added static method

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* testcase added

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* testcase added for mirror function

* testcase added for mirror function

* made the requested changes

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* made the requested changes

* doc test added for symmetric, asymmetric

* Update symmetric_tree.py

---------

Co-authored-by: jeevaramanthan.m <jeevaramanathan.m@infosys.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

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()