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red_black_tree.py
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red_black_tree.py
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RED = 'red'
BLACK = 'black'
class Node:
def __init__(self, data, color):
self.data = data
self.color = color
self.parent = None
self.left = None
self.right = None
def __eq__(self, other):
if type(other) is type(self):
return self.__dict__ == other.__dict__
return NotImplemented
class RedBlackTree:
def __init__(self):
self.sentinel = Node(None, BLACK)
self.root = self.sentinel
def search(self, node):
raise NotImplementedError
def left_rotation(self, node):
"""assumption: node.right is not None"""
# set y points to node.right
y = node.right
# turn y's left subtree into x's right subtree
node.right = y.left
if y.left != self.sentinel:
y.left.parent = node
# link node's parent to y
y.parent = node.parent
if node.parent == self.sentinel:
self.root = y
elif node == node.parent.left:
node.parent.left = y
else:
node.parent.right = y
# put node on y's left
y.left = node
node.parent = y
def right_rotation(self, node):
"""assumption: node.right is not None"""
# set x points to node.left
x = node.left
# turn x's right subtree to x's left subtree
node.left = x.right
if x.right != self.sentinel:
x.right.parent = node
# link node's parent to x
x.parent = node.parent
if node.parent == self.sentinel:
self.root = x
elif node == node.parent.left:
node.parent.left = x
else:
node.parent.right = x
# turn node into x's right child
x.right = node
node.parent = x
def rb_insert(self, node):
trailing = self.sentinel
pointer = self.root
while pointer != self.sentinel:
trailing = pointer
if node.data < pointer.data:
pointer = pointer.left
else:
pointer = pointer.right
node.parent = trailing
if trailing == self.sentinel:
self.root = node
elif node.data < trailing.data:
trailing.left = node
else:
trailing.right = node
node.left = self.sentinel
node.right = self.sentinel
node.color = RED # color new inserted node as red
self.rb_insert_fixup(node)
def rb_insert_fixup(self, node):
while node.parent.color == RED:
if node.parent == node.parent.parent.left:
uncle = node.parent.parent.right
if uncle.color == RED:
node.parent.color = BLACK
uncle.color = BLACK
node.parent.parent.color = RED
node = node.parent.parent
else:
if node == node.parent.right:
node = node.parent
self.left_rotation(node)
node.parent.color = BLACK
node.parent.parent.color = RED
self.right_rotation(node.parent.parent)
else:
uncle = node.parent.parent.left
if uncle.color == RED:
node.parent.color = BLACK
uncle.color = BLACK
node.parent.parent.color = RED
node = node.parent.parent
else:
if node == node.parent.left:
node = node.parent
self.right_rotation(node)
node.parent.color = BLACK
node.parent.parent.color = RED
self.left_rotation(node.parent.parent)
self.root.color = BLACK
def minimum(self, node):
while node.left != self.sentinel:
node = node.left
return node
def maximum(self, node):
while node.right != self.sentinel:
node = node.right
return node
def rb_transplant(self, removed, to_plant):
if removed.parent == self.sentinel:
self.root = to_plant
elif removed == removed.parent.left:
removed.parent.left = to_plant
else:
removed.parent.right = to_plant
to_plant.parent = removed.parent
def rb_delete(self, node):
"""
y is the node to be removed or the node that is moved within the tree
x points to the node that moves into y's original position
"""
y = node
y_original_color = y.color
if node.left == self.sentinel:
x = node.right
self.rb_transplant(node, node.right)
elif node.right == self.sentinel:
x = node.left
self.rb_transplant(node, node.left)
else:
y = self.minimum(node.right)
y_original_color = y.color
x = y.right
if y.parent == node:
# setting x.p to y, even if x == self.sentinel
x.parent = y
else:
self.rb_transplant(y, y.right)
y.right = node.right
y.right.parent = y
self.rb_transplant(node, y)
y.left = node.left
y.left.parent = y
y.color = node.color
if y_original_color == BLACK:
self.rb_delete_fixup(x)
def rb_delete_fixup(self, x):
"""
because we remove the black node y from its original position,
now assume that y passes its blackness to its position inheritor node x,
so x is now either 'red-and-black' or 'doubly black'.
re_delete_fixup is to remove this extra blackness on the node x
w is the x's sibling
"""
while x != self.root and x.color == BLACK:
# x is a left child
if x == x.p.left:
w = x.p.right
# case 1
# case 1 will be converted to case 2, 3 or 4
if w.color == RED:
w.color = BLACK
x.p.color = RED
self.left_roatation(x.p)
w = x.p.right
# case 2
if w.right.color == BLACK and w.left.color == BLACK:
w.color = RED
x = x.p
# case 3: w.right is black, w.left is red
# case 3 will be converted into case 4
else:
if w.right.color == BLACK:
w.left.color = BLACK
w.color = RED
self.right_rotation(w)
w = x.p.right
# case 4: w.right is red, w.left.color doesn't matter
w.color = x.p.color
x.p.color = BLACK
w.right.color = BLACK
self.left_rotation(x.p)
x = self.root
# x is a right child
else:
w = x.p.left
# case 5, symmetry to case 1
if w.color == RED:
w.color = BLACK
x.p.color = RED
self.right_rotation(x.p)
w = x.p.left
# case 6, symmetry to case 2
if w.right.color == BLACK and w.left.color == BLACK:
w.color = RED
x = x.p
# case 7, symmetry to case 3
else:
if w.left.color == BLACK:
w.right.color = BLACK
w.color = RED
self.left_rotation(w)
w = x.p.left
# case 8, symmetry to case 4
w.color = x.p.color
x.p.color = BLACK
w.left.color = BLACK
self.right_rotation(x.p)
x = self.root
x.color = BLACK
def pred(self, node):
raise NotImplementedError
def succ(self, node):
raise NotImplementedError