My implementation of 2-3 Trees on python
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Python 2-3 Tree implementation
2-3 Tree is a balanced tree each node of which may contain 2 elements
and 3 references on its children.
Element lookup speed is log2(N) < x < log3(N)
Insertion and deletion is about 2 * log2(N)
See http://en.wikipedia.org/wiki/2-3_tree for more info
2011 by Boris Tatarintsev
"""
class Pair(object):
# use this class if associative tree (or map) is needed
# over 2-3 tree
def __init__(self, key, value):
self.key = key
self.value = value
def __lt__(self, other):
if type(other) is Pair:
return self.key < other.key
else:
return self.key < other
def __gt__(self, other):
if type(other) is Pair:
return self.key > other.key
else:
return self.key > other
def __eq__(self, other):
if type(other) is Pair:
return self.key == other.key
else:
return self.key == other
return None
def __str__(self):
return 'key: %s, value: %s' % (str(self.key), str(self.value))
def key(self):
return self.key
def val(self):
return self.value
class Node(object):
def __init__(self, v = None, parent = None):
self.values, self.valcnt = None, 0
self.links, self.refcnt = None, 0
self.parent = parent
self.insertValue(v)
def __str__(self):
out = []
if self.values is not None:
for v in self.values:
if v is not None:
out.append(' %s ' % str(v))
return ''.join(out)
else: return 'empty'
def __iter__(self):
if self.values is not None:
for item in self.values:
yield item
def __getlink(self, a):
for idx in xrange(self.valcnt):
if idx is 0:
if a < self.values[idx]: return idx
else:
if self.values[idx - 1] < a < self.values[idx]: return idx
if idx == self.valcnt - 1: return idx + 1
return -1
def __addLink(self, link):
if self.links is None: self.links = [None] * 4
self.links[self.refcnt] = link
self.refcnt += 1
def __insertLink(self, idx, anotherNode):
if self.links is None: self.links = [None] * 4
if idx == 0:
self.links[0],self.links[1],self.links[2], self.links[3] = anotherNode,self.links[0],self.links[1], self.links[2]
elif idx == 1:
self.links[1], self.links[2], self.links[3] = anotherNode, self.links[1], self.links[2]
elif idx == 2:
self.links[2], self.links[3] = anotherNode, self.links[2]
else:
self.links[3] = anotherNode
self.refcnt += 1
def __removeLink(self, idx):
if idx == 0:
self.links[0], self.links[1], self.links[2], self.links[3] = self.links[1], self.links[2], self.links[3], None
elif idx == 1:
self.links[1], self.links[2], self.links[3] = self.links[2], self.links[3], None
elif idx == 2:
self.links[2], self.links[3] = self.links[3], None
else:
self.links[3] = None
self.refcnt -= 1
def __rearrangeLinks(self, a):
""" Rearrange links when adding a new node """
if self.valcnt != 0:
if a < self.values[0] and not self.isLeafNode() and self.refcnt < 3:
# shift all the links to the right when adding new in element
self.__insertLink(0, None)
elif self.valcnt == 2 and self.refcnt == 3 and self.values[self.valcnt - 1] > a > self.values[0]:
# rearrange middle links when adding med element
self.__insertLink(1, None)
def __sort3(self, arr, l):
""" Sort 2 or 3 arrays (very rubost and fast) """
if l >= 2:
if arr[0] > arr[1]: arr[0], arr[1] = arr[1], arr[0]
if l == 3:
if arr[1] > arr[2]: arr[1], arr[2] = arr[2], arr[1]
if arr[0] > arr[1]: arr[0], arr[1] = arr[1], arr[0]
# interface methods & properties
def insertValue(self, a):
""" Insert a value into node """
if a is not None and self.valcnt < 3:
if self.valcnt is 0: self.values = [None] * 3
self.__rearrangeLinks(a)
self.values[self.valcnt] = a
self.valcnt += 1
self.__sort3(self.values, self.valcnt)
return self
def removeValue(self, val):
""" Remove value from node """
if self.contains(val):
idx = self.values.index(val)
if idx == 0:
self.values[0], self.values[1], self.values[2] = self.values[1], self.values[2], None
elif idx == 1:
self.values[1], self.values[2] = self.values[2], None
else:
self.values[2] = None
self.valcnt -= 1
return self
def removeLink(self, node):
""" Remove link from self to another node """
self.__removeLink(self.getLinkIdx(node))
return self
def isConsistent(self):
""" Check whether the node is consistent, this means it doesn't contain 3 items or 4 links """
return not (self.valcnt > 2 or self.refcnt > 3)
def isLeafNode(self):
""" Check whether this is a leaf node or not """
return self.refcnt == 0
def isEmptyNode(self):
""" Returns true if node doesn't containt any value """
return self.valcnt == 0
def getLink(self, linkIdx):
""" Get link by its index, return None if there is no link with such an index """
if linkIdx < self.refcnt:
return self.links[linkIdx]
def getLinkIdx(self, destNode):
""" Get index of the link which points to the given node """
return self.links.index(destNode)
def addLink(self, anotherNode):
""" Add link to another node """
if anotherNode is not None:
if self.links is None: self.links = [None] * 4
idx = self.__getlink(anotherNode.values[0])
if idx != -1:
if idx < self.refcnt and self.links[idx] is None:
self.links[idx] = anotherNode
else:
self.__insertLink(idx, anotherNode)
anotherNode.parent = self
return self
def contains(self, a):
""" Check if node contains a given value """
if self.valcnt is not 0:
if (self.values[0] > a or self.values[self.valcnt - 1] < a) or a not in self.values:
return None
return self.values[self.values.index(a)]
def chooseChild(self, a):
""" Choose where to go according to the value a """
idx = self.__getlink(a)
if 0 <= idx < self.refcnt:
return self.links[idx]
def getItem(self, a):
if self.contains(a):
return self.values[self.values.index(a)]
return None
class TTTree(object):
def __init__(self):
self.root = Node()
self.lastSearchDepth = 0
def __iter__(self):
stack = [self.root]
while len(stack):
node = stack.pop()
yield node
for j in xrange(node.refcnt - 1, -1, -1):
stack.append(node.getLink(j))
def __str__(self):
""" String representation of a tree (parentheses form) """
out, stack = [], [self.root]
while stack:
node = stack.pop()
if node == ')':
out.append(')')
continue
out.append('%s(' % str(node))
stack.append(')')
for j in xrange(node.refcnt - 1, -1, -1):
stack.append(node.getLink(j))
return ''.join(out)
def __nextSucc(self, node):
self.lastSearchDepth += 1
if not node.isLeafNode():
return self.__nextSucc(node.links[0])
return node
def __find(self, curNode, a):
if curNode is not None:
if curNode.contains(a):
return curNode
nextNode = curNode.chooseChild(a)
if nextNode is None:
return curNode
self.lastSearchDepth += 1
return self.__find(nextNode, a)
def __getLeftSibling(self, node):
""" Returns left sibling of a node """
if (node and node.parent) is not None:
return node.parent.getLink(node.parent.getLinkIdx(node) - 1)
def __getRightSibling(self, node):
""" Returns right sibling of a node """
if (node and node.parent) is not None:
return node.parent.getLink(node.parent.getLinkIdx(node) + 1)
def __getSiblings(self, node):
""" Returns node's siblings """
# check whether one of our siblings has two items
lS, rS, lCnt, rCnt = None, None, 0, 0
if self.__getRightSibling(node) is not None:
rS = self.__getRightSibling(node)
rCnt = rS.valcnt
if self.__getLeftSibling(node) is not None:
lS = self.__getLeftSibling(node)
lCnt = lS.valcnt
return lS, lCnt, rS, rCnt
def __swapValues(self, node1, a1, node2, a2):
""" Swap any two values in nodes """
if node1 is not node2:
idx1, idx2 = node1.values.index(a1), node2.values.index(a2)
node1.values[idx1], node2.values[idx2] = node2.values[idx2], node1.values[idx1]
def __fixNodeRemove(self, node, parent = -1):
""" Fix deletion """
if node.isEmptyNode():
if node is not self.root:
if parent == -1:
parent = node.parent
if node.isEmptyNode() or not node.isConsistent():
lS, lCnt, rS, rCnt = self.__getSiblings(node)
rSS, lSS = self.__getRightSibling(rS), self.__getLeftSibling(lS)
redistribute = True
if (rS or lS) is not None:
if rCnt == 2 or (rCnt == 1 and rSS != None and rSS.valcnt == 2):
sib = rS
elif lCnt == 2 or (lCnt == 1 and lSS != None and lSS.valcnt == 2):
sib = lS
elif lCnt == 1:
sib, redistribute = lS, False
elif rCnt == 1:
sib, redistribute = rS, False
if redistribute:
# case 1: redistribute
# left and right case
if parent.valcnt == 1:
if node == parent.getLink(0):
parent_val, sib_val = parent.values[0], sib.values[0]
child = sib.chooseChild(sib_val - 1)
elif node == parent.getLink(1):
parent_val, sib_val = parent.values[parent.valcnt - 1], sib.values[sib.valcnt - 1]
child = sib.chooseChild(sib_val + 1)
else:
if sib == parent.getLink(1):
# left
if node == parent.getLink(0):
parent_val, sib_val = parent.values[0], sib.values[0]
child = sib.chooseChild(sib_val - 1)
# right
elif node == parent.getLink(2):
parent_val, sib_val = parent.values[parent.valcnt - 1], sib.values[sib.valcnt - 1]
child = sib.chooseChild(sib_val + 1)
# middle
elif sib == parent.getLink(2):
parent_val, sib_val = parent.values[parent.valcnt - 1], sib.values[0]
child = sib.chooseChild(sib_val - 1)
elif sib == parent.getLink(0):
parent_val, sib_val = parent.values[0], sib.values[sib.valcnt - 1]
child = sib.chooseChild(sib_val + 1)
node.insertValue(parent_val)
parent.removeValue(parent_val)
parent.insertValue(sib_val)
sib.removeValue(sib_val)
if not node.isLeafNode():
# if this is not a leaf node, redistribute the links also
node.addLink(child)
sib.removeLink(child)
next_node = sib
else:
# case 2: merge
if parent.valcnt == 1:
parent_val = parent.values[0]
else:
if sib == parent.getLink(0):
parent_val = parent.values[0]
elif sib == parent.getLink(1):
if sib == rS:
parent_val = parent.values[0]
if sib == lS:
parent_val = parent.values[parent.valcnt - 1]
child = node.getLink(0)
sib.insertValue(parent_val)
parent.removeValue(parent_val)
parent.removeLink(node)
if not node.isLeafNode():
sib.addLink(child)
next_node = parent
self.__fixNodeRemove(next_node, next_node.parent)
else:
# root node
self.root = self.root.getLink(0)
def __fixNodeInsert(self, node):
if not node.isConsistent():
# conflict detected, try to resolve it
if node.isLeafNode() and node is not self.root:
# case for leaf node
node.parent.insertValue(node.values[1])
node.parent.removeLink(node)
# split the node
node.parent.addLink(Node(node.values[0], node.parent))
node.parent.addLink(Node(node.values[node.valcnt - 1], node.parent))
self.__fixNodeInsert(node.parent)
else:
# case for internal node or root node
if node is not self.root:
node.parent.insertValue(node.values[1])
node.parent.removeLink(node)
parent = node.parent
else:
self.root = Node(node.values[1])
parent = self.root
# split the node
leftNode, rightNode = Node(node.values[0], parent), Node(node.values[node.valcnt - 1], parent)
parent.addLink(leftNode).addLink(rightNode)
leftNode.addLink(node.getLink(0)).addLink(node.getLink(1))
rightNode.addLink(node.getLink(2)).addLink(node.getLink(3))
if node is not self.root:
self.__fixNodeInsert(parent)
# interface methods
def contains(self, a):
""" See if we have a given value in our tree """
node = self.findNode(a)
return node if node.contains(a) else None
def findNode(self, a):
""" Find the node which contains the given value """
self.lastSearchDepth = 0
return self.__find(self.root, a)
def findInorderSucc(self, node, a):
""" Returns inorder successor of any node """
self.lastSearchDepth = 0
if node.isLeafNode():
return node
new_node = node.chooseChild(a + 1)
return self.__nextSucc(new_node)
def insertValue(self, a):
""" Inserts a new value to tree and keeps it balanced """
if self.root is None:
self.root = Node(a)
elif a is not None:
node = self.findNode(a)
res = node.contains(a)
if res: return res
# try to insert a new value into existing node
node.insertValue(a)
self.__fixNodeInsert(node)
return self
def insertList(self, xs):
""" Insert a list of values into a tree """
if xs is not None and type(xs) is list:
for item in xs: self.insertValue(item)
def removeValue(self, a):
""" Removes a value from the tree and keeps it balanced """
node = self.findNode(a)
if not node or not node.contains(a):
return None
# swap the value we want to delete with its inorder successor (always leaf)
succ = self.findInorderSucc(node, a)
self.__swapValues(node, a, succ, succ.values[0])
# delete leaf node value
succ.removeValue(a)
# fix tree if needed
self.__fixNodeRemove(succ)
return self
def removeList(self, xs):
""" Deletes a list of values from a tree """
if xs is not None and type(xs) is list:
for item in xs: self.removeValue(item)
|
If you're looking for an API similar to that provided by a 2-3 tree, check out the sortedcontainers module. It implements sorted list, sorted dict, and sorted set data types in pure-Python and is fast-as-C implementations (even faster!). Learn more about sortedcontainers, available on PyPI and github.