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tree-walking.py
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"""
Copyright (c) 2016 Willem Hengeveld <[email protected]>
Experiment in btree walking
*-------->[00]
*------>[02]---+ [01]
root ->[08]---+ [05]-+ |
[17]-+ | | +--->[03]
| | | [04]
| | |
| | +----->[06]
| | [07]
| |
| | *-------->[09]
| +->[11]---+ [10]
| [14]-+ |
| | +--->[12]
| | [13]
| |
| +----->[15]
| [16]
|
| *-------->[18]
+--->[20]---+ [19]
[23]-+ |
| +--->[21]
| [22]
|
+----->[24]
[25]
decrement from 08 : ix-- -> getpage, ix=len-1 -> getpage -> ix=len-1
decrement from 17 : ix-- -> getpage, ix=len-1 -> getpage -> ix=len-1
decrement from 02 : ix-- -> getpage, ix=len-1
decrement from 05 : ix-- -> getpage, ix=len-1
decrement from 01 : ix-- -> ix>=0 -> use key at ix
decrement from 03 : ix-- -> <0 -> pop -> ix>=0 -> use key at ix
decrement from 09 : ix-- -> <0 -> pop -> ix<0 -> pop -> ix>=0 -> use key at ix
increment from 09 : ix++
increment from 10 : ix++ -> ix==len(index) -> pop: ix==-1 -> ix++ -> ix==0 -> use
increment from 11 : recurse, ix=0 -> use
increment from 08 : recurse, ix=-1 -> recurse, ix=0 -> use
increment from 07 : ix++ -> ix==len(index) -> pop, ix++ -> ix==len -> pop -> ix++ -> ix==0 -> use
"""
from __future__ import division, print_function, absolute_import, unicode_literals
# shape of the tree
# a <2,2> tree is basically like the tree pictured in the ascii art above.
TREEDEPTH = 2
NODEWIDTH = 2
def binary_search(a, k):
# c++: a.upperbound(k)--
first, last = 0, len(a)
while first < last:
mid = (first + last) >> 1
if k < a[mid].key:
last = mid
else:
first = mid + 1
return first - 1
class Entry(object):
"""
a key/value entry from a b-tree page
"""
def __init__(self, key, val):
self.key = key
self.val = val
def __repr__(self):
return "%s=%d" % (self.key, self.val)
class BasePage(object):
"""
BasePage has methods common to both leaf and index pages
"""
def __init__(self, kv):
self.index = []
for k, v in kv:
self.index.append(Entry(k, v))
def find(self, key):
i = binary_search(self.index, key)
if i < 0:
if self.isindex():
return ('recurse', -1)
return ('gt', 0)
if self.index[i].key == key:
return ('eq', i)
if self.isindex():
return ('recurse', i)
return ('lt', i)
def getkey(self, ix):
return self.index[ix].key
def getval(self, ix):
return self.index[ix].val
def isleaf(self):
return self.preceeding is None
def isindex(self):
return self.preceeding is not None
def __repr__(self):
return ("leaf" if self.isleaf() else ("index<%d>" % self.preceeding)) + repr(self.index)
class LeafPage(BasePage):
""" a leaf page in the b-tree """
def __init__(self, kv):
super(self.__class__, self).__init__(kv)
self.preceeding = None
class IndexPage(BasePage):
"""
An index page in the b-tree.
This page has a preceeding page plus several key+subpage pairs.
For each key+subpage: all keys in the subpage are greater than the key
"""
def __init__(self, preceeding, kv):
super(self.__class__, self).__init__(kv)
self.preceeding = preceeding
def getpage(self, ix):
return self.preceeding if ix < 0 else self.index[ix].val
class Cursor:
"""
A Cursor object represents a position in the b-tree.
It has methods for moving to the next or previous item.
And methods for retrieving the key and value of the current position
"""
def __init__(self, db, stack):
self.db = db
self.stack = stack
def next(self):
page, ix = self.stack.pop()
if page.isleaf():
# from leaf move towards root
ix += 1
while self.stack and ix == len(page.index):
page, ix = self.stack.pop()
ix += 1
if ix < len(page.index):
self.stack.append((page, ix))
else:
# from node move towards leaf
self.stack.append((page, ix))
page = self.db.readpage(page.getpage(ix))
while page.isindex():
ix = -1
self.stack.append((page, ix))
page = self.db.readpage(page.getpage(ix))
ix = 0
self.stack.append((page, ix))
self.verify()
def prev(self):
page, ix = self.stack.pop()
ix -= 1
if page.isleaf():
# move towards root, until non 'prec' item found
while self.stack and ix < 0:
page, ix = self.stack.pop()
if ix >= 0:
self.stack.append((page, ix))
else:
# move towards leaf
self.stack.append((page, ix))
while page.isindex():
page = self.db.readpage(page.getpage(ix))
ix = len(page.index) - 1
self.stack.append((page, ix))
self.verify()
def verify(self):
""" verify cursor state consistency """
if len(self.stack) == 3:
if not self.stack[-1][0].isleaf():
print("WARN no leaf")
elif len(self.stack) > 3:
print("WARN: stack too large")
if len(self.stack) >= 2:
if self.stack[0][0] == self.stack[1][0]:
print("WARN: identical index pages on stack")
if not self.stack[0][0].isindex():
print("WARN: expected root=index")
if not self.stack[1][0].isindex():
print("WARN: expected 2nd=index")
def eof(self):
return len(self.stack) == 0
def getkey(self):
page, ix = self.stack[-1]
return page.getkey(ix)
def getval(self):
page, ix = self.stack[-1]
return page.getval(ix)
def __repr__(self):
return "cursor:" + repr(self.stack)
class Btree:
"""
A B-tree implementation
"""
def __init__(self):
self.pages = []
self.generate(TREEDEPTH, NODEWIDTH)
def manual(self):
""" manually construct the ascii art tree """
for i in range(9):
self.pages.append(LeafPage((("%02d" % (3 * i), 0), ("%02d" % (3 * i + 1), 0))))
for i in range(3):
self.pages.append(IndexPage(3 * i, (("%02d" % (9 * i + 2), 3 * i + 1), ("%02d" % (9 * i + 5), 3 * i + 2))))
self.pages.append(IndexPage(9, (("08", 10), ("17", 11))))
self.rootindex = len(self.pages) - 1
def generate(self, depth, nodesize):
""" automatically generate the try in the ascii art above """
def namegen():
i = 0
while True:
yield "%03d" % i
i += 1
self.rootindex = self.construct(namegen(), depth, nodesize)
print("%d pages" % (len(self.pages)))
def construct(self, namegen, depth, nodesize):
if depth:
return self.createindex(namegen, depth, nodesize)
else:
return self.createleaf(namegen, nodesize)
def createindex(self, namegen, depth, nodesize):
page = IndexPage(self.construct(namegen, depth - 1, nodesize),
[(next(namegen), self.construct(namegen, depth - 1, nodesize)) for _ in range(nodesize)])
self.pages.append(page)
return len(self.pages) - 1
def createleaf(self, namegen, nodesize):
page = LeafPage([(next(namegen), 0) for _ in range(nodesize)])
self.pages.append(page)
return len(self.pages) - 1
def readpage(self, pn):
return self.pages[pn]
def find(self, key):
"""
Find a node in the tree, returns the cursor plus the reletion to the wanted key:
'eq' for equal, 'lt' when the found key is less than the wanted key,
or 'gt' when the found key is greater than the wanted key.
"""
page = self.readpage(self.rootindex)
stack = []
while True:
act, ix = page.find(key)
stack.append((page, ix))
if act != 'recurse':
break
page = self.readpage(page.getpage(ix))
return act, Cursor(self, stack)
def dumptree(self, pn, indent=0):
""" dump all nodes of the current b-tree """
page = self.readpage(pn)
print(" " * indent, page)
if page.isindex():
print(" " * indent, end="")
self.dumptree(page.preceeding, indent + 1)
for p in range(len(page.index)):
print(" " * indent, end="")
self.dumptree(page.getpage(p), indent + 1)
db = Btree()
print("<<")
db.dumptree(db.rootindex)
print(">>")
for i in range(NODEWIDTH * len(db.pages)):
print("--------- %03d" % i)
act, cursor = db.find("%03d" % i)
print("found", act, cursor.getkey(), cursor)
cursor.prev()
if not cursor.eof():
print("prev:", "..", cursor.getkey(), cursor)
else:
print("prev: EOF", cursor)
for i in range(NODEWIDTH * len(db.pages)):
print("--------- %03d" % i)
act, cursor = db.find("%03d" % i)
print("found", act, cursor.getkey(), cursor)
cursor.next()
if not cursor.eof():
print("next:", "..", cursor.getkey(), cursor)
else:
print("next: EOF", cursor)
for k in ('', '0', '1', '2', '3', '000', '010', '020', '100'):
print("--------- %s" % k)
act, cursor = db.find(k)
print(cursor)
print(act, cursor.getkey(), end=" next=")
cursor.next()
if cursor.eof():
print("EOF")
else:
print(cursor.getkey())
act, cursor = db.find("000")
print("get000", end=" ")
for i in range(NODEWIDTH * len(db.pages)):
cursor.next()
if cursor.eof():
print("EOF")
else:
print("-> %s" % cursor.getkey(), end=" ")
print()
act, cursor = db.find("025")
print("get025", end=" ")
for i in range(NODEWIDTH * len(db.pages)):
cursor.prev()
if cursor.eof():
print("EOF")
else:
print("-> %s" % cursor.getkey(), end=" ")
print()