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

http://greenteapress.com/complexity

This code is based on the description of the red-black tree at
http://en.wikipedia.org/wiki/Red-black_tree.

Some code and ideas were taken from code by Darren Hart at
http://dvhart.com/darren/files/rbtree.py

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(2)

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. The optional value is useful for using the
    red-black tree to implement a map datastructure.

    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

    def __str__(self):
        c = 'B' if self.color == BLACK else 'R'
        if self.value:
            return '({}: {} => {})'.format(c, self.key, self.value)
        else:
            return '({}: {})'.format(c, self.key)


class Tree(object):
    """A red-black Tree class.

    A red-black tree is a binary search tree with the following properties:

        1. A node is either red or black.
        2. The root is black.
        3. All leaves are black.
        4. Both children of every red node are black.
        5. Every simple path from a given node to any descendant leaf contains
           the same number of black nodes.

    These rules ensure that the path from the root to the furthest leaf is no
    more than twice as long as the path from the root to the nearest leaf. Thus
    the tree is roughly height-balanced.

    """

    def __init__(self):
        self.root = None

    def __iter__(self):
        return self._inorder(self.root)

    def _inorder(self, node):
        """A generator to perform an inorder traversal of the nodes in the
        tree starting at the given node.

        """
        if node.left:
            for n in self._inorder(node.left):
                yield n

        yield node

        if node.right:
            for n in self._inorder(node.right):
                yield n

    def insert(self, key, value=None):
        node = Node(key=key, value=value, color=RED)

        # trivial case of inserting into an empty tree:
        if self.root is None:
            self.root = node
            self.root.color = BLACK
            return

        # Find a spot to insert the new red node:

        x = self.root
        while x is not None:
            p = x
            if key < x.key:
                x = x.left
            else:
                x = x.right

        node.parent = p     # p is the new node's parent

        # p now has 1 child; decide if the new node goes on the left or right

        if key < p.key:
            p.left = node
        else:
            p.right = node

        # ensure the new tree follows the red-black rules:

        while True:
            p = node.parent

            # Case 1: root node
            if p is None:
                node.color = BLACK
                break

            # Case 2: parent is black
            if p.color == BLACK:
                break

            # Case 3: parent and uncle are red
            u = node.uncle
            if u and u.color == RED:
                # repaint parent & uncle black; grandparent becomes red:
                p.color = BLACK
                u.color = BLACK
                gp = node.grandparent
                gp.color = RED

                # enforce the rules at the grandparent level
                node = gp
                continue

            # gp is the grandparent; it can't be None because we know the parent
            # is red at this point
            gp = p.parent

            # Case 4: At this point we know the parent is red and the uncle is
            # black. 
            # If the new node is a right child of the parent, and the
            # parent is on the left of the grandparent => left rotation on the
            # parent.
            # If the new node is a left child of the parent, and the parent is
            # on the right of the grandparent => right rotation on the parent.

            if node is p.right and p is gp.left:
                self._rotate_left(p)
                node = node.left
            elif node is p.left and p is gp.right:
                self._rotate_right(p)
                node = node.right

            # Note that case 4 must fall through to case 5 to fix up the former parent
            # node, which is now the child of the new red node.

            # Case 5: The parent is red and the uncle is black.
            # If the new node is the left child of the parent and the parent is
            # the left child of the grandparent => rotate right on the
            # grandparent.
            # If the new node is the right child of the parent and the parent 
            # is the right child of the grandparent => rotate left on the
            # grandparent.

            p = node.parent
            gp = p.parent

            p.color = BLACK
            gp.color = RED

            if node is p.left and p is gp.left:
                self._rotate_right(gp)
            elif node is p.right and p is gp.right: #TODO: can this be an else?
                self._rotate_left(gp)
            break

    def _rotate_right(self, node):
        """Rotate the tree right on the given node."""

        p = node.parent
        left = node.left

        if p:
            if node is p.right:
                p.right = left
            else:
                p.left = left

        left.parent = p
        node.left = left.right

        if node.left:
            node.left.parent = node

        left.right = node
        node.parent = left

        # fix up the root if necessary
        if self.root is node:
            self.root = left

    def _rotate_left(self, node):
        """Rotate the tree left on the given node."""

        p = node.parent
        right = node.right

        if p:
            if node is p.right:
                p.right = right
            else:
                p.left = right

        right.parent = p
        node.right = right.left

        if node.right:
            node.right.parent = node

        right.left = node
        node.parent = right

        # fix up the root if necessary
        if self.root is node:
            self.root = right


if __name__ == '__main__':
    import random

    tree = Tree()

    for i in range(20):
        val = random.randint(0, 100)
        tree.insert(val)

    for n in tree:
        print n.key,