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btree.py
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btree.py
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# -*- coding: UTF-8 -*-
# Btree的实现代码,详细见:https://www.codedump.info/post/20200609-btree-1/
import random
import unittest
INVALID_KEY = -1
class BTreeNode(object):
def __init__(self, tree, isLeaf):
self.num = 0
self.leaf = isLeaf
self.tree = tree
self.t = tree.t
t = self.t
self.keys = []
self.datas = []
for i in range(2 * t - 1):
self.keys.append(INVALID_KEY)
self.datas.append(INVALID_KEY)
self.children = []
if not isLeaf:
for i in range(2 * t):
self.children.append(None)
def isLeaf(self):
return self.leaf
def getNum(self):
return self.num
def setNum(self, num):
self.num = num
def setKeyAndData(self, index, packed):
key, data = packed
self.keys[index] = key
self.datas[index] = data
def getKeyAndData(self, index):
return self.keys[index],self.datas[index]
def getKey(self, index):
return self.keys[index]
def setChild(self, index, child):
self.children[index] = child
def getChild(self, index):
return self.children[index]
def isFull(self):
return self.num == 2 * self.t - 1
# split the child y of this node,y must be full when called
def splitChild(self, i, y):
assert(y.isFull())
t = self.t
# allocate a new node which is going to store (t-1) keys of y
z = BTreeNode(self.tree, y.isLeaf())
z.setNum(t - 1)
# move y.keys[t:2t-1] to z.keys[0:t-1]
for j in range(0, t - 1):
z.setKeyAndData(j, y.getKeyAndData(j + t))
if not y.isLeaf(): # if y is not a leaf
# move y.children[t:2t] to z.children[0:t]
for j in range(0, t):
z.setChild(j, y.getChild(j + t))
# reset y's moved child
#y.setChild(j + t, None)
# reduce y keys number
y.setNum(t - 1)
# move child to create space for new child
for j in range(self.getNum(), i, -1):
self.setChild(j + 1, self.getChild(j))
# insert z to self.children
self.setChild(i + 1, z)
# move key to create space for new key
for j in range(self.getNum() - 1, i - 1, -1):
self.setKeyAndData(j + 1, self.getKeyAndData(j))
self.setKeyAndData(i,y.getKeyAndData(t - 1))
# increment the number
self.setNum(self.getNum() + 1)
# when called node must be not full
def insertNonFull(self, key, data):
i = self.getNum() - 1
if self.isLeaf(): # if is leaf
# 1.find the location of the new key
# 2.move all greater keys to one place ahead
while i >= 0 and (self.getKey(i) == INVALID_KEY or self.getKey(i) > key):
self.setKeyAndData(i + 1, self.getKeyAndData(i))
i -= 1
# insert new key
self.setKeyAndData(i + 1, (key, data))
self.setNum(self.getNum() + 1)
else: # if is internal node
# find the location of the new key
while i >= 0 and (self.getKey(i) == INVALID_KEY or self.getKey(i) > key):
i -= 1
# if the child is full,split it
y = self.getChild(i + 1)
if y.isFull():
self.splitChild(i + 1, y)
if self.getKey(i + 1) < key:
i += 1
self.getChild(i + 1).insertNonFull(key, data)
# find the location of the key, return index and found
def findKey(self, key):
i = 0
while (i < self.getNum() and self.getKey(i) < key):
i += 1
return i, i < self.getNum() and self.getKey(i) == key
# remove the idx-th key from this node,which is a leaf
def removeFromLeaf(self, idx):
for i in range(idx + 1, self.getNum()):
self.setKeyAndData(i - 1, self.getKeyAndData(i))
self.setNum(self.getNum() - 1)
# remove the idx-th key from this node,which is a internal node
def removeFromNode(self, idx):
key = self.getKey(idx)
if self.getChild(idx).getNum() >= self.t:
# If the child that precedes k (C[idx]) has atleast t keys,
# find the predecessor 'pred' of k in the subtree rooted at
# C[idx]. Replace k by pred. Recursively delete pred
# in C[idx]
pred,data = self.getPred(idx)
self.setKeyAndData(idx, (pred, data))
self.getChild(idx).remove(pred)
elif self.getChild(idx + 1).getNum() >= self.t:
# If the child C[idx] has less that t keys, examine C[idx+1].
# If C[idx+1] has atleast t keys, find the successor 'succ' of k in
# the subtree rooted at C[idx+1]
# Replace k by succ
# Recursively delete succ in C[idx+1]
succ,data = self.getSucc(idx)
self.setKeyAndData(idx, (succ, data))
self.getChild(idx + 1).remove(succ)
else:
# If both C[idx] and C[idx+1] has less that t keys,merge k and all of C[idx+1]
# into C[idx]
# Now C[idx] contains 2t-1 keys
# Free C[idx+1] and recursively delete k from C[idx]
self.merge(idx)
self.getChild(idx).remove(key)
# merge C[idx] with C[idx+1]
# C[idx+1] is freed after merging
def merge(self, idx):
t = self.t
child = self.getChild(idx)
sibling = self.getChild(idx+1)
# Pulling a key from the current node and inserting it into (t-1)th
# position of C[idx]
child.setKeyAndData(t - 1, self.getKeyAndData(idx))
# Copying the keys from C[idx+1] to C[idx] at the end
for i in range(0, sibling.getNum()):
child.setKeyAndData(i + t, sibling.getKeyAndData(i))
# Copying the child pointers from C[idx+1] to C[idx]
if not child.isLeaf():
for i in range(0, sibling.getNum() + 1):
child.setChild(i + t, sibling.getChild(i))
# Moving all keys after idx in the current node one step before -
# to fill the gap created by moving keys[idx] to C[idx]
for i in range(idx + 1, self.getNum()):
self.setKeyAndData(i - 1, self.getKeyAndData(i))
# Moving the child pointers after (idx+1) in the current node one
# step before
for i in range(idx + 2, self.getNum() + 1):
self.setChild(i - 1, self.getChild(i))
# Updating the key count of child and the current node
child.setNum(child.getNum() + sibling.getNum() + 1)
self.setNum(self.getNum() - 1)
# get predecessor of keys[idx]
def getPred(self, idx):
# Keep moving to the right most node until we reach a leaf
cur = self.getChild(idx)
while not cur.isLeaf():
cur = cur.getChild(cur.getNum())
# Return the last key of the leaf
return cur.getKeyAndData(cur.getNum() - 1)
# get successor of keys[idx]
def getSucc(self, idx):
# Keep moving the left most node starting from C[idx+1] until we reach a leaf
cur = self.getChild(idx + 1)
while not cur.isLeaf():
cur = cur.getChild(0)
# Return the first key of the leaf
return cur.getKeyAndData(0)
def rebalance(self, idx):
t = self.t
if idx != 0 and self.getChild(idx - 1).getNum() >= t:
# If the previous child(C[idx-1]) has more than t-1 keys, borrow a key
# from that child
self.borrowFromPrev(idx)
if idx != self.getNum() and self.getChild(idx + 1).getNum() >= t:
# If the next child(C[idx+1]) has more than t-1 keys, borrow a key
# from that child
self.borrowFromNext(idx)
else:
# Merge C[idx] with its sibling
# If C[idx] is the last child, merge it with with its previous sibling
# Otherwise merge it with its next sibling
if idx != self.getNum():
self.merge(idx)
else:
self.merge(idx - 1)
# borrow a key from C[idx-1] and insert it into C[idx]
def borrowFromPrev(self, idx):
child = self.getChild(idx)
sibling = self.getChild(idx - 1)
# The last key from C[idx-1] goes up to the parent and key[idx-1]
# from parent is inserted as the first key in C[idx]. Thus, the loses
# sibling one key and child gains one key
# Moving all key in C[idx] one step ahead
for i in range(child.getNum() - 1, -1, -1):
child.setKeyAndData(i + 1, child.getKeyAndData(i))
# If C[idx] is not a leaf, move all its child pointers one step ahead
if not child.isLeaf():
for i in range(child.getNum(), -1, -1):
child.setChild(i + 1, child.getChild(i))
# Setting child's first key equal to keys[idx-1] from the current node
child.setKeyAndData(0, self.getKeyAndData(idx - 1))
# Moving sibling's last child as C[idx]'s first child
if not child.isLeaf():
child.setChild(0, sibling.getChild(sibling.getNum()))
# Moving the key from the sibling to the parent
# This reduces the number of keys in the sibling
self.setKeyAndData(idx - 1, sibling.getKeyAndData(sibling.getNum() - 1))
child.setNum(child.getNum() + 1)
sibling.setNum(sibling.getNum() - 1)
# borrow a key from the C[idx+1] and place it in C[idx]
def borrowFromNext(self, idx):
child = self.getChild(idx)
sibling = self.getChild(idx + 1)
# keys[idx] is inserted as the last key in C[idx]
child.setKeyAndData(child.getNum(), self.getKeyAndData(idx))
# Sibling's first child is inserted as the last child into C[idx]
if not child.isLeaf():
child.setChild(child.getNum() + 1, sibling.getChild(0))
# The first key from sibling is inserted into keys[idx]
self.setKeyAndData(idx, sibling.getKeyAndData(0))
# Moving all keys in sibling one step behind
for i in range(1, sibling.getNum()):
sibling.setKeyAndData(i - 1, sibling.getKeyAndData(i))
# Moving the child pointers one step behind
if not sibling.isLeaf():
for i in range(1, sibling.getNum() + 1):
sibling.setChild(i - 1, sibling.getChild(i))
# Increasing and decreasing the key count of C[idx] and C[idx+1] respectively
child.setNum(child.getNum() + 1)
sibling.setNum(sibling.getNum() - 1)
def remove(self, key):
i,found = self.findKey(key)
if found: # if key present in this node
if self.isLeaf():
self.removeFromLeaf(i)
else:
self.removeFromNode(i)
return True
else:
# if node is leaf and key is not present in it,return False
if self.isLeaf():
return False
# The key to be removed is present in the sub-tree rooted with this node
# The flag indicates whether the key is present in the sub-tree rooted
# with the last child of this node
flag = False
if i == self.getNum():
flag = True
# If the child where the key is supposed to exist has less that t keys, rebalance that child
if self.getChild(i).getNum() < self.t:
self.rebalance(i)
# If the last child has been merged, it must have merged with the previous
# child and so we recurse on the (i-1)-th child. Else, we recurse on the
# i-th child which now has at least t keys
if flag and i > self.getNum():
return self.getChild(i - 1).remove(key)
else:
return self.getChild(i).remove(key)
def search(self, key):
i,found = self.findKey(key)
if found: # if key present in this node
return self.datas[i]
if self.isLeaf(): # if key not present in this node and is a leaf
return None
# else search key in child
return self.getChild(i).search(key)
def traverse(self, result):
# iterate over all keys
for i in range(self.getNum()):
if not self.isLeaf():
result = self.getChild(i).traverse(result)
result.append(self.getKey(i))
if not self.isLeaf():
result = self.getChild(self.getNum()).traverse(result)
return result
class BTree(object):
def __init__(self, degree):
self.t = degree
self.root = None
def _isEmpty(self):
return self.root == None
def insert(self, key, data):
if self._isEmpty(): # if tree is empty
root = BTreeNode(self, True)
root.setKeyAndData(0, (key, data))
root.setNum(1)
self.root = root
else: # if tree is not empty
root = self.root
if root.isFull(): # if root is full,then grows in height
# allocate a new internal node
s = BTreeNode(self, False)
# make old root as the first child of new root
s.setChild(0, root)
# split the old root and move 1 key to the new root
s.splitChild(0, root)
# now the new root is not full,insert the key
i = 0
if s.getKey(0) != INVALID_KEY and s.getKey(0) < key:
i = 1
s.getChild(i).insertNonFull(key, data)
# change root
self.root = s
else:
# if root is not full,call insertNonFull for root
root.insertNonFull(key, data)
# remove the key,return True or False
def remove(self, key):
if self._isEmpty():
return False
ret = self.root.remove(key)
# if the root is empty,make the first child as new root
if ret and self.root.getNum() == 0:
if self.root.isLeaf():
self.root = None
else:
self.root = self.root.getChild(0)
return ret
def search(self, key):
if self._isEmpty(): # if btree is empty
return None
return self.root.search(key)
# traverse a btree, return mid-order traverse list
def traverse(self):
if self._isEmpty():
return []
return self.root.traverse([])
# unit tests for BTree
class BTreeTests(unittest.TestCase):
def test_additions(self):
bt = BTree(20)
l = []
for i in range(0,1000):
item = random.randint(1,100000)
l.append(item)
bt.insert(item, item)
result = bt.traverse()
l.sort()
for i in range(len(result)):
self.assertEqual(result[i], l[i])
def test_removals(self):
bt = BTree(20)
l = []
for i in range(0,1000):
item = random.randint(1,100000)
l.append(item)
bt.insert(item, item)
index = random.randint(1,100000) % len(l)
item = l[index]
l.pop(index)
bt.remove(item)
l.sort()
result = bt.traverse()
for i in range(len(result)):
self.assertEqual(result[i], l[i])
def test_search(self):
bt = BTree(20)
l = []
for i in range(0,1000):
item = random.randint(1,100000)
l.append(item)
bt.insert(item, item)
index = random.randint(1,100000) % len(l)
item = l[index]
ret = bt.search(item)
self.assertTrue(ret != None)
self.assertEqual(ret,item)
if __name__ == '__main__':
unittest.main()