mirror of
https://github.com/TheAlgorithms/Python.git
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160 lines
3.6 KiB
Python
160 lines
3.6 KiB
Python
"""
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Given the root of a binary tree, check whether it is a mirror of itself
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(i.e., symmetric around its center).
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Leetcode reference: https://leetcode.com/problems/symmetric-tree/
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"""
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from __future__ import annotations
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from dataclasses import dataclass
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@dataclass
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class Node:
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"""
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A Node represents an element of a binary tree, which contains:
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Attributes:
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data: The value stored in the node (int).
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left: Pointer to the left child node (Node or None).
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right: Pointer to the right child node (Node or None).
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Example:
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>>> node = Node(1, Node(2), Node(3))
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>>> node.data
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1
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>>> node.left.data
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2
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>>> node.right.data
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3
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"""
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data: int
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left: Node | None = None
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right: Node | None = None
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def make_symmetric_tree() -> Node:
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r"""
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Create a symmetric tree for testing.
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The tree looks like this:
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1
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/ \
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2 2
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/ \ / \
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3 4 4 3
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Returns:
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Node: Root node of a symmetric tree.
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Example:
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>>> tree = make_symmetric_tree()
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>>> tree.data
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1
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>>> tree.left.data == tree.right.data
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True
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>>> tree.left.left.data == tree.right.right.data
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True
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"""
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root = Node(1)
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root.left = Node(2)
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root.right = Node(2)
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root.left.left = Node(3)
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root.left.right = Node(4)
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root.right.left = Node(4)
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root.right.right = Node(3)
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return root
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def make_asymmetric_tree() -> Node:
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r"""
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Create an asymmetric tree for testing.
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The tree looks like this:
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1
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/ \
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2 2
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/ \ / \
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3 4 3 4
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Returns:
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Node: Root node of an asymmetric tree.
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Example:
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>>> tree = make_asymmetric_tree()
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>>> tree.data
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1
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>>> tree.left.data == tree.right.data
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True
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>>> tree.left.left.data == tree.right.right.data
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False
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"""
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root = Node(1)
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root.left = Node(2)
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root.right = Node(2)
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root.left.left = Node(3)
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root.left.right = Node(4)
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root.right.left = Node(3)
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root.right.right = Node(4)
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return root
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def is_symmetric_tree(tree: Node) -> bool:
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"""
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Check if a binary tree is symmetric (i.e., a mirror of itself).
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Parameters:
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tree: The root node of the binary tree.
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Returns:
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bool: True if the tree is symmetric, False otherwise.
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Example:
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>>> is_symmetric_tree(make_symmetric_tree())
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True
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>>> is_symmetric_tree(make_asymmetric_tree())
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False
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"""
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if tree:
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return is_mirror(tree.left, tree.right)
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return True # An empty tree is considered symmetric.
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def is_mirror(left: Node | None, right: Node | None) -> bool:
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"""
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Check if two subtrees are mirror images of each other.
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Parameters:
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left: The root node of the left subtree.
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right: The root node of the right subtree.
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Returns:
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bool: True if the two subtrees are mirrors of each other, False otherwise.
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Example:
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>>> tree1 = make_symmetric_tree()
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>>> is_mirror(tree1.left, tree1.right)
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True
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>>> tree2 = make_asymmetric_tree()
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>>> is_mirror(tree2.left, tree2.right)
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False
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"""
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if left is None and right is None:
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# Both sides are empty, which is symmetric.
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return True
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if left is None or right is None:
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# One side is empty while the other is not, which is not symmetric.
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return False
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if left.data == right.data:
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# The values match, so check the subtrees recursively.
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return is_mirror(left.left, right.right) and is_mirror(left.right, right.left)
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return False
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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