symmetric_tree.py

"""
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 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
    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

    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)
    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 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)
    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:
    """
    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())
    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:
    """
    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()
    >>> 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 subtrees recursively.
        return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
    return False


if __name__ == "__main__":
    from doctest import testmod

    testmod()