Improve comments, add doctests in symmetric_tree.py

data_structures/binary_tree/symmetric_tree.py

@@ -13,7 +13,21 @@
 @dataclass
 class Node:
  """
- A Node has data variable and pointers to Nodes to its left and right.
+ 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
@@ -24,12 +38,25 @@ class Node:
 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)
@@ -43,13 +70,26 @@ def make_symmetric_tree() -> Node:
 
 def make_asymmetric_tree() -> Node:
  r"""
- Create a asymmetric tree for testing.
+ 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)
@@ -63,7 +103,15 @@ def make_asymmetric_tree() -> Node:
 
 def is_symmetric_tree(tree: Node) -> bool:
  """
- Test cases for is_symmetric_tree function
+ 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())
@@ -76,8 +124,17 @@ def is_symmetric_tree(tree: Node) -> bool:
 
 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()
- >>> tree1.right.right = Node(3)
  >>> is_mirror(tree1.left, tree1.right)
  True
  >>> tree2 = make_asymmetric_tree()
@@ -91,7 +148,7 @@ def is_mirror(left: Node | None, right: Node | None) -> bool:
  # 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
+ # The values match, so check the subtrees recursively.
  return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
  return False
 

data_structures/binary_tree/symmetric_tree.py

@@ -13,7 +13,21 @@
 @dataclass
 class Node:
  """
- A Node has data variable and pointers to Nodes to its left and right.
+ 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
@@ -24,12 +38,25 @@ class Node:
 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)
@@ -43,13 +70,26 @@ def make_symmetric_tree() -> Node:
 
 def make_asymmetric_tree() -> Node:
  r"""
- Create a asymmetric tree for testing.
+ 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)
@@ -63,7 +103,15 @@ def make_asymmetric_tree() -> Node:
 
 def is_symmetric_tree(tree: Node) -> bool:
  """
- Test cases for is_symmetric_tree function
+ 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())
@@ -76,8 +124,17 @@ def is_symmetric_tree(tree: Node) -> bool:
 
 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()
- >>> tree1.right.right = Node(3)
  >>> is_mirror(tree1.left, tree1.right)
  True
  >>> tree2 = make_asymmetric_tree()
@@ -91,7 +148,7 @@ def is_mirror(left: Node | None, right: Node | None) -> bool:
  # 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
+ # The values match, so check the subtrees recursively.
  return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
  return False
 

data_structures/binary_tree/symmetric_tree.py

@@ -13,7 +13,21 @@
 @dataclass
 class Node:
  """
- A Node has data variable and pointers to Nodes to its left and right.
+ 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
@@ -24,12 +38,25 @@ class Node:
 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)
@@ -43,13 +70,26 @@ def make_symmetric_tree() -> Node:
 
 def make_asymmetric_tree() -> Node:
  r"""
- Create a asymmetric tree for testing.
+ 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)
@@ -63,7 +103,15 @@ def make_asymmetric_tree() -> Node:
 
 def is_symmetric_tree(tree: Node) -> bool:
  """
- Test cases for is_symmetric_tree function
+ 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())
@@ -76,8 +124,17 @@ def is_symmetric_tree(tree: Node) -> bool:
 
 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()
- >>> tree1.right.right = Node(3)
  >>> is_mirror(tree1.left, tree1.right)
  True
  >>> tree2 = make_asymmetric_tree()
@@ -91,7 +148,7 @@ def is_mirror(left: Node | None, right: Node | None) -> bool:
  # 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
+ # The values match, so check the subtrees recursively.
  return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
  return False
 

data_structures/binary_tree/symmetric_tree.py

@@ -13,7 +13,21 @@
 @dataclass
 class Node:
  """
- A Node has data variable and pointers to Nodes to its left and right.
+ 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
@@ -24,12 +38,25 @@ class Node:
 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)
@@ -43,13 +70,26 @@ def make_symmetric_tree() -> Node:
 
 def make_asymmetric_tree() -> Node:
  r"""
- Create a asymmetric tree for testing.
+ 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)
@@ -63,7 +103,15 @@ def make_asymmetric_tree() -> Node:
 
 def is_symmetric_tree(tree: Node) -> bool:
  """
- Test cases for is_symmetric_tree function
+ 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())
@@ -76,8 +124,17 @@ def is_symmetric_tree(tree: Node) -> bool:
 
 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()
- >>> tree1.right.right = Node(3)
  >>> is_mirror(tree1.left, tree1.right)
  True
  >>> tree2 = make_asymmetric_tree()
@@ -91,7 +148,7 @@ def is_mirror(left: Node | None, right: Node | None) -> bool:
  # 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
+ # The values match, so check the subtrees recursively.
  return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
  return False
 

data_structures/binary_tree/symmetric_tree.py

@@ -13,7 +13,21 @@
 @dataclass
 class Node:
  """
- A Node has data variable and pointers to Nodes to its left and right.
+ 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
@@ -24,12 +38,25 @@ class Node:
 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)
@@ -43,13 +70,26 @@ def make_symmetric_tree() -> Node:
 
 def make_asymmetric_tree() -> Node:
  r"""
- Create a asymmetric tree for testing.
+ 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)
@@ -63,7 +103,15 @@ def make_asymmetric_tree() -> Node:
 
 def is_symmetric_tree(tree: Node) -> bool:
  """
- Test cases for is_symmetric_tree function
+ 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())
@@ -76,8 +124,17 @@ def is_symmetric_tree(tree: Node) -> bool:
 
 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()
- >>> tree1.right.right = Node(3)
  >>> is_mirror(tree1.left, tree1.right)
  True
  >>> tree2 = make_asymmetric_tree()
@@ -91,7 +148,7 @@ def is_mirror(left: Node | None, right: Node | None) -> bool:
  # 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
+ # The values match, so check the subtrees recursively.
  return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
  return False
 

data_structures/binary_tree/symmetric_tree.py

@@ -13,7 +13,21 @@
 @dataclass
 class Node:
  """
- A Node has data variable and pointers to Nodes to its left and right.
+ 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
@@ -24,12 +38,25 @@ class Node:
 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)
@@ -43,13 +70,26 @@ def make_symmetric_tree() -> Node:
 
 def make_asymmetric_tree() -> Node:
  r"""
- Create a asymmetric tree for testing.
+ 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)
@@ -63,7 +103,15 @@ def make_asymmetric_tree() -> Node:
 
 def is_symmetric_tree(tree: Node) -> bool:
  """
- Test cases for is_symmetric_tree function
+ 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())
@@ -76,8 +124,17 @@ def is_symmetric_tree(tree: Node) -> bool:
 
 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()
- >>> tree1.right.right = Node(3)
  >>> is_mirror(tree1.left, tree1.right)
  True
  >>> tree2 = make_asymmetric_tree()
@@ -91,7 +148,7 @@ def is_mirror(left: Node | None, right: Node | None) -> bool:
  # 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
+ # The values match, so check the subtrees recursively.
  return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
  return False
 

data_structures/binary_tree/symmetric_tree.py

@@ -13,7 +13,21 @@
 @dataclass
 class Node:
  """
- A Node has data variable and pointers to Nodes to its left and right.
+ 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
@@ -24,12 +38,25 @@ class Node:
 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)
@@ -43,13 +70,26 @@ def make_symmetric_tree() -> Node:
 
 def make_asymmetric_tree() -> Node:
  r"""
- Create a asymmetric tree for testing.
+ 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)
@@ -63,7 +103,15 @@ def make_asymmetric_tree() -> Node:
 
 def is_symmetric_tree(tree: Node) -> bool:
  """
- Test cases for is_symmetric_tree function
+ 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())
@@ -76,8 +124,17 @@ def is_symmetric_tree(tree: Node) -> bool:
 
 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()
- >>> tree1.right.right = Node(3)
  >>> is_mirror(tree1.left, tree1.right)
  True
  >>> tree2 = make_asymmetric_tree()
@@ -91,7 +148,7 @@ def is_mirror(left: Node | None, right: Node | None) -> bool:
  # 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
+ # The values match, so check the subtrees recursively.
  return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
  return False
 

data_structures/binary_tree/symmetric_tree.py

@@ -13,7 +13,21 @@
 @dataclass
 class Node:
  """
- A Node has data variable and pointers to Nodes to its left and right.
+ 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
@@ -24,12 +38,25 @@ class Node:
 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)
@@ -43,13 +70,26 @@ def make_symmetric_tree() -> Node:
 
 def make_asymmetric_tree() -> Node:
  r"""
- Create a asymmetric tree for testing.
+ 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)
@@ -63,7 +103,15 @@ def make_asymmetric_tree() -> Node:
 
 def is_symmetric_tree(tree: Node) -> bool:
  """
- Test cases for is_symmetric_tree function
+ 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())
@@ -76,8 +124,17 @@ def is_symmetric_tree(tree: Node) -> bool:
 
 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()
- >>> tree1.right.right = Node(3)
  >>> is_mirror(tree1.left, tree1.right)
  True
  >>> tree2 = make_asymmetric_tree()
@@ -91,7 +148,7 @@ def is_mirror(left: Node | None, right: Node | None) -> bool:
  # 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
+ # The values match, so check the subtrees recursively.
  return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
  return False