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a pure-python B tree implementation
import bisect
import itertools
import operator
class _BNode(object):
__slots__ = ["tree", "contents", "children"]
def __init__(self, tree, contents=None, children=None):
self.tree = tree
self.contents = contents or []
self.children = children or []
if self.children:
assert len(self.contents) + 1 == len(self.children), \
"one more child than data item required"
def __repr__(self):
name = getattr(self, "children", 0) and "Branch" or "Leaf"
return "<%s %s>" % (name, ", ".join(map(str, self.contents)))
def lateral(self, parent, parent_index, dest, dest_index):
if parent_index > dest_index:
dest.contents.append(parent.contents[dest_index])
parent.contents[dest_index] = self.contents.pop(0)
if self.children:
dest.children.append(self.children.pop(0))
else:
dest.contents.insert(0, parent.contents[parent_index])
parent.contents[parent_index] = self.contents.pop()
if self.children:
dest.children.insert(0, self.children.pop())
def shrink(self, ancestors):
parent = None
if ancestors:
parent, parent_index = ancestors.pop()
# try to lend to the left neighboring sibling
if parent_index:
left_sib = parent.children[parent_index - 1]
if len(left_sib.contents) < self.tree.order:
self.lateral(
parent, parent_index, left_sib, parent_index - 1)
return
# try the right neighbor
if parent_index + 1 < len(parent.children):
right_sib = parent.children[parent_index + 1]
if len(right_sib.contents) < self.tree.order:
self.lateral(
parent, parent_index, right_sib, parent_index + 1)
return
center = len(self.contents) // 2
sibling, push = self.split()
if not parent:
parent, parent_index = self.tree.BRANCH(
self.tree, children=[self]), 0
self.tree._root = parent
# pass the median up to the parent
parent.contents.insert(parent_index, push)
parent.children.insert(parent_index + 1, sibling)
if len(parent.contents) > parent.tree.order:
parent.shrink(ancestors)
def grow(self, ancestors):
parent, parent_index = ancestors.pop()
minimum = self.tree.order // 2
left_sib = right_sib = None
# try to borrow from the right sibling
if parent_index + 1 < len(parent.children):
right_sib = parent.children[parent_index + 1]
if len(right_sib.contents) > minimum:
right_sib.lateral(parent, parent_index + 1, self, parent_index)
return
# try to borrow from the left sibling
if parent_index:
left_sib = parent.children[parent_index - 1]
if len(left_sib.contents) > minimum:
left_sib.lateral(parent, parent_index - 1, self, parent_index)
return
# consolidate with a sibling - try left first
if left_sib:
left_sib.contents.append(parent.contents[parent_index - 1])
left_sib.contents.extend(self.contents)
if self.children:
left_sib.children.extend(self.children)
parent.contents.pop(parent_index - 1)
parent.children.pop(parent_index)
else:
self.contents.append(parent.contents[parent_index])
self.contents.extend(right_sib.contents)
if self.children:
self.children.extend(right_sib.children)
parent.contents.pop(parent_index)
parent.children.pop(parent_index + 1)
if len(parent.contents) < minimum:
if ancestors:
# parent is not the root
parent.grow(ancestors)
elif not parent.contents:
# parent is root, and its now empty
self.tree._root = left_sib or self
def split(self):
center = len(self.contents) // 2
median = self.contents[center]
sibling = type(self)(
self.tree,
self.contents[center + 1:],
self.children[center + 1:])
self.contents = self.contents[:center]
self.children = self.children[:center + 1]
return sibling, median
def insert(self, index, item, ancestors):
self.contents.insert(index, item)
if len(self.contents) > self.tree.order:
self.shrink(ancestors)
def remove(self, index, ancestors):
minimum = self.tree.order // 2
if self.children:
# try promoting from the right subtree first,
# but only if it won't have to resize
additional_ancestors = [(self, index + 1)]
descendent = self.children[index + 1]
while descendent.children:
additional_ancestors.append((descendent, 0))
descendent = descendent.children[0]
if len(descendent.contents) > minimum:
ancestors.extend(additional_ancestors)
self.contents[index] = descendent.contents[0]
descendent.remove(0, ancestors)
return
# fall back to the left child
additional_ancestors = [(self, index)]
descendent = self.children[index]
while descendent.children:
additional_ancestors.append(
(descendent, len(descendent.children) - 1))
descendent = descendent.children[-1]
ancestors.extend(additional_ancestors)
self.contents[index] = descendent.contents[-1]
descendent.remove(len(descendent.children) - 1, ancestors)
else:
self.contents.pop(index)
if len(self.contents) < minimum and ancestors:
self.grow(ancestors)
class BTree(object):
BRANCH = LEAF = _BNode
def __init__(self, order):
self.order = order
self._root = self._bottom = self.LEAF(self)
def _path_to(self, item):
current = self._root
ancestry = []
while getattr(current, "children", None):
index = bisect.bisect_left(current.contents, item)
ancestry.append((current, index))
if index < len(current.contents) \
and current.contents[index] == item:
return ancestry
current = current.children[index]
index = bisect.bisect_left(current.contents, item)
ancestry.append((current, index))
present = index < len(current.contents)
present = present and current.contents[index] == item
return ancestry
def _present(self, item, ancestors):
last, index = ancestors[-1]
return index < len(last.contents) and last.contents[index] == item
def insert(self, item):
current = self._root
ancestors = self._path_to(item)
node, index = ancestors[-1]
while getattr(node, "children", None):
node = node.children[index]
index = bisect.bisect_left(node.contents, item)
ancestors.append((node, index))
node, index = ancestors.pop()
node.insert(index, item, ancestors)
def remove(self, item):
current = self._root
ancestors = self._path_to(item)
if self._present(item, ancestors):
node, index = ancestors.pop()
node.remove(index, ancestors)
else:
raise ValueError("%r not in %s" % (item, self.__class__.__name__))
def __contains__(self, item):
return self._present(item, self._path_to(item))
def __iter__(self):
def _recurse(node):
if node.children:
for child, item in zip(node.children, node.contents):
for child_item in _recurse(child):
yield child_item
yield item
for child_item in _recurse(node.children[-1]):
yield child_item
else:
for item in node.contents:
yield item
for item in _recurse(self._root):
yield item
def __repr__(self):
def recurse(node, accum, depth):
accum.append((" " * depth) + repr(node))
for node in getattr(node, "children", []):
recurse(node, accum, depth + 1)
accum = []
recurse(self._root, accum, 0)
return "\n".join(accum)
@classmethod
def bulkload(cls, items, order):
tree = object.__new__(cls)
tree.order = order
leaves = tree._build_bulkloaded_leaves(items)
tree._build_bulkloaded_branches(leaves)
return tree
def _build_bulkloaded_leaves(self, items):
minimum = self.order // 2
leaves, seps = [[]], []
for item in items:
if len(leaves[-1]) < self.order:
leaves[-1].append(item)
else:
seps.append(item)
leaves.append([])
if len(leaves[-1]) < minimum and seps:
last_two = leaves[-2] + [seps.pop()] + leaves[-1]
leaves[-2] = last_two[:minimum]
leaves[-1] = last_two[minimum + 1:]
seps.append(last_two[minimum])
return [self.LEAF(self, contents=node) for node in leaves], seps
def _build_bulkloaded_branches(self, (leaves, seps)):
minimum = self.order // 2
levels = [leaves]
while len(seps) > self.order + 1:
items, nodes, seps = seps, [[]], []
for item in items:
if len(nodes[-1]) < self.order:
nodes[-1].append(item)
else:
seps.append(item)
nodes.append([])
if len(nodes[-1]) < minimum and seps:
last_two = nodes[-2] + [seps.pop()] + nodes[-1]
nodes[-2] = last_two[:minimum]
nodes[-1] = last_two[minimum + 1:]
seps.append(last_two[minimum])
offset = 0
for i, node in enumerate(nodes):
children = levels[-1][offset:offset + len(node) + 1]
nodes[i] = self.BRANCH(self, contents=node, children=children)
offset += len(node) + 1
levels.append(nodes)
self._root = self.BRANCH(self, contents=seps, children=levels[-1])
import random
import unittest
class BTreeTests(unittest.TestCase):
def test_additions(self):
bt = BTree(20)
l = range(2000)
for i, item in enumerate(l):
bt.insert(item)
self.assertEqual(list(bt), l[:i + 1])
def test_bulkloads(self):
bt = BTree.bulkload(range(2000), 20)
self.assertEqual(list(bt), range(2000))
def test_removals(self):
bt = BTree(20)
l = range(2000)
map(bt.insert, l)
rand = l[:]
random.shuffle(rand)
while l:
self.assertEqual(list(bt), l)
rem = rand.pop()
l.remove(rem)
bt.remove(rem)
self.assertEqual(list(bt), l)
def test_insert_regression(self):
bt = BTree.bulkload(range(2000), 50)
for i in xrange(100000):
bt.insert(random.randrange(2000))
if __name__ == '__main__':
#unittest.main()
b = BTree(2)
for i in xrange(0,20):
b.insert(i)
print b
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