# Copyright 2008 the V8 project authors. All rights reserved.
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# * Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above
# copyright notice, this list of conditions and the following
# disclaimer in the documentation and/or other materials provided
# with the distribution.
# * Neither the name of Google Inc. nor the names of its
# contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
# A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
# OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
class Node(object):
"""Nodes in the splay tree."""
def __init__(self, key, value):
self.key = key
self.value = value
self.left = None
self.right = None
class KeyNotFoundError(Exception):
"""KeyNotFoundError is raised when removing a non-existing node."""
def __init__(self, key):
self.key = key
class SplayTree(object):
"""The splay tree itself is just a reference to the root of the tree."""
def __init__(self):
"""Create a new SplayTree."""
self.root = None
def IsEmpty(self):
"""Is the SplayTree empty?"""
return not self.root
def Insert(self, key, value):
"""Insert a new node in the SplayTree."""
# If the tree is empty, insert the new node.
if self.IsEmpty():
self.root = Node(key, value)
return
# Splay on the key to move the last node on the search path for
# the key to the root of the tree.
self.Splay(key)
# Ignore repeated insertions with the same key.
if self.root.key == key:
return
# Insert the new node.
node = Node(key, value)
if key > self.root.key:
node.left = self.root
node.right = self.root.right
self.root.right = None
else:
node.right = self.root
node.left = self.root.left
self.root.left = None
self.root = node
def Remove(self, key):
"""Remove the node with the given key from the SplayTree."""
# Raise exception for key that is not found if the tree is empty.
if self.IsEmpty():
raise KeyNotFoundError(key)
# Splay on the key to move the node with the given key to the top.
self.Splay(key)
# Raise exception for key that is not found.
if self.root.key != key:
raise KeyNotFoundError(key)
removed = self.root
# Link out the root node.
if not self.root.left:
# No left child, so the new tree is just the right child.
self.root = self.root.right
else:
# Left child exists.
right = self.root.right
# Make the original left child the new root.
self.root = self.root.left
# Splay to make sure that the new root has an empty right child.
self.Splay(key)
# Insert the original right child as the right child of the new
# root.
self.root.right = right
return removed
def Find(self, key):
"""Returns the node with the given key or None if no such node exists."""
if self.IsEmpty():
return None
self.Splay(key)
if self.root.key == key:
return self.root
return None
def FindMax(self):
"""Returns the node with the largest key value."""
if self.IsEmpty():
return None
current = self.root
while current.right != None:
current = current.right
return current
# Returns the node with the smallest key value.
def FindMin(self):
if self.IsEmpty():
return None
current = self.root
while current.left != None:
current = current.left
return current
def FindGreatestsLessThan(self, key):
"""Returns node with greatest key less than or equal to the given key."""
if self.IsEmpty():
return None
# Splay on the key to move the node with the given key or the last
# node on the search path to the top of the tree.
self.Splay(key)
# Now the result is either the root node or the greatest node in
# the left subtree.
if self.root.key <= key:
return self.root
else:
tmp = self.root
self.root = self.root.left
result = self.FindMax()
self.root = tmp
return result
def ExportValueList(self):
"""Returns a list containing all the values of the nodes in the tree."""
result = []
nodes_to_visit = [self.root]
while len(nodes_to_visit) > 0:
node = nodes_to_visit.pop()
if not node:
continue
result.append(node.value)
nodes_to_visit.append(node.left)
nodes_to_visit.append(node.right)
return result
def Splay(self, key):
"""Perform splay operation.
Perform the splay operation for the given key. Moves the node with
the given key to the top of the tree. If no node has the given
key, the last node on the search path is moved to the top of the
tree.
This uses the simplified top-down splaying algorithm from:
"Self-adjusting Binary Search Trees" by Sleator and Tarjan
"""
if self.IsEmpty():
return
# Create a dummy node. The use of the dummy node is a bit
# counter-intuitive: The right child of the dummy node will hold
# the L tree of the algorithm. The left child of the dummy node
# will hold the R tree of the algorithm. Using a dummy node, left
# and right will always be nodes and we avoid special cases.
dummy = left = right = Node(None, None)
current = self.root
while True:
if key < current.key:
if not current.left:
break
if key < current.left.key:
# Rotate right.
tmp = current.left
current.left = tmp.right
tmp.right = current
current = tmp
if not current.left:
break
# Link right.
right.left = current
right = current
current = current.left
elif key > current.key:
if not current.right:
break
if key > current.right.key:
# Rotate left.
tmp = current.right
current.right = tmp.left
tmp.left = current
current = tmp
if not current.right:
break
# Link left.
left.right = current
left = current
current = current.right
else:
break
# Assemble.
left.right = current.left
right.left = current.right
current.left = dummy.right
current.right = dummy.left
self.root = current