Add Mirror a Binary Tree solution (#9534)

* Add `Invert a Binary Tree` solution

* Add type

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* Add `doctest`

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* Add `test` to `get_tree_inorder`

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* Add `test` changes

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* Fix lint errors

* Fix precommit errors

* Update and rename invert_binary_tree.py to mirror_binary_tree.py

---------

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/mirror_binary_tree.py

@@ -0,0 +1,153 @@
+"""
+Given the root of a binary tree, mirror the tree, and return its root.
+
+Leetcode problem reference: https://leetcode.com/problems/mirror-binary-tree/
+"""
+from __future__ import annotations
+
+from collections.abc import Iterator
+from dataclasses import dataclass
+
+
+@dataclass
+class Node:
+    """
+    A Node has value variable and pointers to Nodes to its left and right.
+    """
+
+    value: int
+    left: Node | None = None
+    right: Node | None = None
+
+    def __iter__(self) -> Iterator[int]:
+        if self.left:
+            yield from self.left
+        yield self.value
+        if self.right:
+            yield from self.right
+
+    def __len__(self) -> int:
+        return sum(1 for _ in self)
+
+    def mirror(self) -> Node:
+        """
+        Mirror the binary tree rooted at this node by swapping left and right children.
+
+        >>> tree = Node(0)
+        >>> list(tree)
+        [0]
+        >>> list(tree.mirror())
+        [0]
+        >>> tree = Node(1, Node(0), Node(3, Node(2), Node(4, None, Node(5))))
+        >>> tuple(tree)
+        (0, 1, 2, 3, 4, 5)
+        >>> tuple(tree.mirror())
+        (5, 4, 3, 2, 1, 0)
+        """
+        self.left, self.right = self.right, self.left
+        if self.left:
+            self.left.mirror()
+        if self.right:
+            self.right.mirror()
+        return self
+
+
+def make_tree_seven() -> Node:
+    r"""
+    Return a binary tree with 7 nodes that looks like this:
+           1
+         /   \
+        2     3
+       / \   / \
+      4   5 6   7
+
+    >>> tree_seven = make_tree_seven()
+    >>> len(tree_seven)
+    7
+    >>> list(tree_seven)
+    [4, 2, 5, 1, 6, 3, 7]
+    """
+    tree = Node(1)
+    tree.left = Node(2)
+    tree.right = Node(3)
+    tree.left.left = Node(4)
+    tree.left.right = Node(5)
+    tree.right.left = Node(6)
+    tree.right.right = Node(7)
+    return tree
+
+
+def make_tree_nine() -> Node:
+    r"""
+    Return a binary tree with 9 nodes that looks like this:
+          1
+         /  \
+        2    3
+       / \    \
+      4   5    6
+     / \   \
+    7   8   9
+
+    >>> tree_nine = make_tree_nine()
+    >>> len(tree_nine)
+    9
+    >>> list(tree_nine)
+    [7, 4, 8, 2, 5, 9, 1, 3, 6]
+    """
+    tree = Node(1)
+    tree.left = Node(2)
+    tree.right = Node(3)
+    tree.left.left = Node(4)
+    tree.left.right = Node(5)
+    tree.right.right = Node(6)
+    tree.left.left.left = Node(7)
+    tree.left.left.right = Node(8)
+    tree.left.right.right = Node(9)
+    return tree
+
+
+def main() -> None:
+    r"""
+    Mirror binary trees with the given root and returns the root
+
+    >>> tree = make_tree_nine()
+    >>> tuple(tree)
+    (7, 4, 8, 2, 5, 9, 1, 3, 6)
+    >>> tuple(tree.mirror())
+    (6, 3, 1, 9, 5, 2, 8, 4, 7)
+
+    nine_tree:
+          1
+         /  \
+        2    3
+       / \    \
+      4   5    6
+     / \   \
+    7   8   9
+
+    The mirrored tree looks like this:
+          1
+         /  \
+        3    2
+       /    / \
+      6    5   4
+          /   / \
+         9   8   7
+    """
+    trees = {"zero": Node(0), "seven": make_tree_seven(), "nine": make_tree_nine()}
+    for name, tree in trees.items():
+        print(f"      The {name} tree: {tuple(tree)}")
+        # (0,)
+        # (4, 2, 5, 1, 6, 3, 7)
+        # (7, 4, 8, 2, 5, 9, 1, 3, 6)
+        print(f"Mirror of {name} tree: {tuple(tree.mirror())}")
+        # (0,)
+        # (7, 3, 6, 1, 5, 2, 4)
+        # (6, 3, 1, 9, 5, 2, 8, 4, 7)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    main()