"""A red-black tree for Section 3.4, Exercise 4 in Allen Downey's _Think
Complexity_ book.

http://greenteapress.com/complexity

Copyright (C) 2012 Brian G. Neal.

Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
the Software, and to permit persons to whom the Software is furnished to do so,
subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

"""

BLACK, RED = range(1)

class Node(object):
    """A node class for red-black trees.

    A node has an optional parent, and optional left and right children. Each
    node also has a color, either red or black. A node has a key and an optional
    value. The key is used to order the red black tree by calling the "<"
    operator when comparing keys.

    In a red-black tree, nil children are always considered black.

    """

    def __init__(self, key, color=RED, value=None):
        self.key = key
        self.value = value
        self.color = color

        self.parent = None
        self.left = None
        self.right = None

    @property
    def grandparent(self):
        """Return the grandparent of this node, or None if it does not exist."""
        return self.parent.parent if self.parent else None

    @property
    def uncle(self):
        """Return this node's uncle if it exists, or None if not.

        An uncle is a parent's sibling.

        """
        g = self.grandparent
        if g:
            return g.left if g.right is self.parent else g.right
        return None