数据库B+tree ，Python语言实现
#!/usr/bin/env python
from random import randint, choice
from bisect import bisect_right, bisect_left
from collections import deque
class InitError(Exception):
pass
class ParaError(Exception):
pass
#生成键值对
class KeyValue(object):
__slots__=('key', 'value')
def __init__(self, key, value):
self.key=int(key) #一定要保证键值是整型
self.value=value
def __str__(self):
return str((self.key, self.value))
def __cmp__(self, key):
if self.key>key:
return 1
elif self.key < key:
return -1
else:
return 0
def __lt__(self, other):
if (type(self) == type(other)):
return self.key < other.key;
else:
return int(self.key) < int(other);
def __eq__(self, other):
if (type(self) == type(other)):
return self.key == other.key;
else:
return int(self.key) == int(other);
def __gt__(self, other):
return not self < other;
#B+树实现
#实现过程和btree很像，不过有几点显著不同。
#1.内节点不存储key-value，只存放key
#
#2.沿着内节点搜索的时候，查到索引相等的数要向树的右边走。所以二分查找要选择
#bisect_right
#
#3.在叶子节点满的时候，并不是先分裂再插入而是先插入再分裂。因为b+tree无法保证
#分裂的两个节点的大小都是相等的。在奇数大小的数据分裂的时候右边的子节点会比左
#边的大。如果先分裂再插入无法保证插入的节点一定会插在数量更少的子节点上，满足
#节点数量平衡的条件。
#
#4.在删除数据的时候，b+tree的左右子节点借数据的方式比btree更加简单有效，只把子
#节点的子树直接剪切过来，再把索引变一下就行了，而且叶子节点的兄弟指针也不用动。
#
class Bptree(object):
class __InterNode(object):
def __init__(self, M):
if not isinstance(M, int):
raise InitError('M must be int')
if M<=3:
raise InitError('M must be greater then 3')
else:
self.__M=M
self.clist=[] #存放区间
self.ilist=[] #存放索引/序号
self.par=None
def isleaf(self):
return False
def isfull(self):
return len(self.ilist)>=self.M-1
def isempty(self):
return len(self.ilist)<=(self.M+1)/2-1
@property
def M(self):
return self.__M
#叶子
class __Leaf(object):
def __init__(self,L):
if not isinstance(L,int):
raise InitError('L must be int')
else:
self.__L=L
self.vlist=[]
self.bro=None #兄弟结点
self.par=None #父结点
def isleaf(self):
return True
def isfull(self):
return len(self.vlist)>self.L
def isempty(self):
return len(self.vlist)<=(self.L+1)/2
@property
def L(self):
return self.__L
#初始化
def __init__(self,M,L):
if L>M:
raise InitError('L must be less or equal then M')
else:
self.__M=M
self.__L=L
self.__root=Bptree.__Leaf(L)
self.__leaf=self.__root
@property
def M(self):
return self.__M
@property
def L(self):
return self.__L
#插入
def insert(self, key_value):
node=self.__root
def split_node(n1):
mid=self.M//2 #此处注意，可能出错
newnode=Bptree.__InterNode(self.M)
newnode.ilist=n1.ilist[mid:]
newnode.clist=n1.clist[mid:]
newnode.par=n1.par
for c in newnode.clist:
c.par=newnode
if n1.par is None:
newroot=Bptree.__InterNode(self.M)
newroot.ilist=[n1.ilist[mid-1]]
newroot.clist=[n1,newnode]
n1.par=newnode.par=newroot
self.__root=newroot
else:
i=n1.par.clist.index(n1)
n1.par.ilist.insert(i,n1.ilist[mid-1])
n1.par.clist.insert(i+1,newnode)
n1.ilist=n1.ilist[:mid-1]
n1.clist=n1.clist[:mid]
return n1.par
def split_leaf(n2):
mid=(self.L+1)//2
newleaf=Bptree.__Leaf(self.L)
newleaf.vlist=n2.vlist[mid:]
if n2.par==None:
newroot=Bptree.__InterNode(self.M)
newroot.ilist=[n2.vlist[mid].key]
newroot.clist=[n2,newleaf]
n2.par=newleaf.par=newroot
self.__root=newroot
else:
i=n2.par.clist.index(n2)
n2.par.ilist.insert(i,n2.vlist[mid].key)
n2.par.clist.insert(i+1,newleaf)
newleaf.par=n2.par
n2.vlist=n2.vlist[:mid]
n2.bro=newleaf
def insert_node(n):
if not n.isleaf():
if n.isfull():
insert_node(split_node(n))
else:
p=bisect_right(n.ilist,key_value)
insert_node(n.clist[p])
else:
p=bisect_right(n.vlist,key_value)
n.vlist.insert(p,key_value)
if n.isfull():
split_leaf(n)
else:
return
insert_node(node)
#搜索
def search(self,mi=None,ma=None):
result=[]
node=self.__root
leaf=self.__leaf
if mi is None or ma is None:
raise ParaError('you need to setup searching range')
elif mi > ma:
raise ParaError('upper bound must be greater or equal than lower bound')
def search_key(n,k):
if n.isleaf():
p=bisect_left(n.vlist,k)
return (p,n)
else:
p=bisect_right(n.ilist,k)
return search_key(n.clist[p],k)
if mi is None:
while True:
for kv in leaf.vlist:
if kv<=ma:
result.append(kv)
else:
return result
if leaf.bro==None:
return result
else:
leaf=leaf.bro
elif ma is None:
index,leaf=search_key(node,mi)
result.extend(leaf.vlist[index:])
while True:
if leaf.bro==None:
return result
else:
leaf=leaf.bro
result.extend(leaf.vlist)
else:
if mi==ma:
i,l=search_key(node,mi)
try:
if l.vlist[i]==mi:
result.append(l.vlist[i])
return result
else:
return result
except IndexError:
return result
else:
i1,l1=search_key(node,mi)
i2,l2=search_key(node,ma)
if l1 is l2:
if i1==i2:
return result
else:
result.extend(l2.vlist[i1:i2])
return result
else:
result.extend(l1.vlist[i1:])
l=l1
while True:
if l.bro==l2:
result.extend(l2.vlist[:i2])
return result
elif l.bro != None:
result.extend(l.bro.vlist)
l=l.bro
else:
return result;
def traversal(self):
result=[]
l=self.__leaf
while True:
result.extend(l.vlist)
if l.bro==None:
return result
else:
l=l.bro
def show(self):
print('this b+tree is:\n')
q=deque()
h=0
q.append([self.__root,h])
while True:
try:
w,hei=q.popleft()
except IndexError:
return
else:
if not w.isleaf():
print(w.ilist,'the height is',hei)
if hei==h:
h+=1
q.extend([[i,h] for i in w.clist])
else:
print([(v.key,v.value) for v in w.vlist],'the leaf is,',hei)
#删除
def delete(self,key_value):
def merge(n,i):
if n.clist[i].isleaf():
n.clist[i].vlist=n.clist[i].vlist+n.clist[i+1].vlist
n.clist[i].bro=n.clist[i+1].bro
else:
n.clist[i].ilist=n.clist[i].ilist+[n.ilist[i]]+n.clist[i+1].ilist
n.clist[i].clist=n.clist[i].clist+n.clist[i+1].clist
n.clist.remove(n.clist[i+1])
n.ilist.remove(n.ilist[i])
if n.ilist==[]:
n.clist[0].par=None
self.__root=n.clist[0]
del n
return self.__root
else:
return n
def tran_l2r(n,i):
if not n.clist[i].isleaf():
n.clist[i+1].clist.insert(0,n.clist[i].clist[-1])
n.clist[i].clist[-1].par=n.clist[i+1]
n.clist[i+1].ilist.insert(0,n.ilist[i])
n.ilist[i]=n.clist[i].ilist[-1]
n.clist[i].clist.pop()
n.clist[i].ilist.pop()
else:
n.clist[i+1].vlist.insert(0,n.clist[i].vlist[-1])
n.clist[i].vlist.pop()
n.ilist[i]=n.clist[i+1].vlist[0].key
def tran_r2l(n,i):
if not n.clist[i].isleaf():
n.clist[i].clist.append(n.clist[i+1].clist[0])
n.clist[i+1].clist[0].par=n.clist[i]
n.clist[i].ilist.append(n.ilist[i])
n.ilist[i]=n.clist[i+1].ilist[0]
n.clist[i+1].clist.remove(n.clist[i+1].clist[0])
n.clist[i+1].ilist.remove(n.clist[i+1].ilist[0])
else:
n.clist[i].vlist.append(n.clist[i+1].vlist[0])
n.clist[i+1].vlist.remove(n.clist[i+1].vlist[0])
n.ilist[i]=n.clist[i+1].vlist[0].key
def del_node(n,kv):
if not n.isleaf():
p=bisect_right(n.ilist,kv)
if p==len(n.ilist):
if not n.clist[p].isempty():
return del_node(n.clist[p],kv)
elif not n.clist[p-1].isempty():
tran_l2r(n,p-1)
return del_node(n.clist[p],kv)
else:
return del_node(merge(n,p),kv)
else:
if not n.clist[p].isempty():
return del_node(n.clist[p],kv)
elif not n.clist[p+1].isempty():
tran_r2l(n,p)
return del_node(n.clist[p],kv)
else:
return del_node(merge(n,p),kv)
else:
p=bisect_left(n.vlist,kv)
try:
pp=n.vlist[p]
except IndexError:
return -1
else:
if pp!=kv:
return -1
else:
n.vlist.remove(kv)
return 0
del_node(self.__root,key_value)
def test():
#初始化数据源
mini=50
maxi=200
testlist=[]
for i in range(20):
key=randint(1,1000)
#key=i
value=choice(['Do', 'Re', 'Mi', 'Fa', 'So', 'La', 'Si'])
testlist.append(KeyValue(key,value))
#初始化B树
mybptree=Bptree(4, 4)
#插入操作
for x in testlist:
mybptree.insert(x)
mybptree.show()
#查找操作
print('\nnow we are searching item between %d and %d\n==>'%(mini,maxi))
print([v.key for v in mybptree.search(mini,maxi)])
#删除操作
mybptree.delete(testlist[0])
print('\n删除 {0}后， the newtree is:\n'.format(testlist[0]));
mybptree.show()
#深度遍历操作
print('\nkey of this b+tree is \n')
print([kv.key for kv in mybptree.traversal()])
if __name__ == '__main__':
test();
#!/usr/bin/env python
from random import randint, choice
from bisect import bisect_right, bisect_left
from collections import deque
class InitError(Exception):
pass
class ParaError(Exception):
pass
#生成键值对
class KeyValue(object):
__slots__=('key', 'value')
def __init__(self, key, value):
self.key=int(key) #一定要保证键值是整型
self.value=value
def __str__(self):
return str((self.key, self.value))
def __cmp__(self, key):
if self.key>key:
return 1
elif self.key < key:
return -1
else:
return 0
def __lt__(self, other):
if (type(self) == type(other)):
return self.key < other.key;
else:
return int(self.key) < int(other);
def __eq__(self, other):
if (type(self) == type(other)):
return self.key == other.key;
else:
return int(self.key) == int(other);
def __gt__(self, other):
return not self < other;
#B+树实现
#实现过程和btree很像，不过有几点显著不同。
#1.内节点不存储key-value，只存放key
#
#2.沿着内节点搜索的时候，查到索引相等的数要向树的右边走。所以二分查找要选择
#bisect_right
#
#3.在叶子节点满的时候，并不是先分裂再插入而是先插入再分裂。因为b+tree无法保证
#分裂的两个节点的大小都是相等的。在奇数大小的数据分裂的时候右边的子节点会比左
#边的大。如果先分裂再插入无法保证插入的节点一定会插在数量更少的子节点上，满足
#节点数量平衡的条件。
#
#4.在删除数据的时候，b+tree的左右子节点借数据的方式比btree更加简单有效，只把子
#节点的子树直接剪切过来，再把索引变一下就行了，而且叶子节点的兄弟指针也不用动。
#
class Bptree(object):
class __InterNode(object):
def __init__(self, M):
if not isinstance(M, int):
raise InitError('M must be int')
if M<=3:
raise InitError('M must be greater then 3')
else:
self.__M=M
self.clist=[] #存放区间
self.ilist=[] #存放索引/序号
self.par=None
def isleaf(self):
return False
def isfull(self):
return len(self.ilist)>=self.M-1
def isempty(self):
return len(self.ilist)<=(self.M+1)/2-1
@property
def M(self):
return self.__M
#叶子
class __Leaf(object):
def __init__(self,L):
if not isinstance(L,int):
raise InitError('L must be int')
else:
self.__L=L
self.vlist=[]
self.bro=None #兄弟结点
self.par=None #父结点
def isleaf(self):
return True
def isfull(self):
return len(self.vlist)>self.L
def isempty(self):
return len(self.vlist)<=(self.L+1)/2
@property
def L(self):
return self.__L
#初始化
def __init__(self,M,L):
if L>M:
raise InitError('L must be less or equal then M')
else:
self.__M=M
self.__L=L
self.__root=Bptree.__Leaf(L)
self.__leaf=self.__root
@property
def M(self):
return self.__M
@property
def L(self):
return self.__L
#插入
def insert(self, key_value):
node=self.__root
def split_node(n1):
mid=self.M//2 #此处注意，可能出错
newnode=Bptree.__InterNode(self.M)
newnode.ilist=n1.ilist[mid:]
newnode.clist=n1.clist[mid:]
newnode.par=n1.par
for c in newnode.clist:
c.par=newnode
if n1.par is None:
newroot=Bptree.__InterNode(self.M)
newroot.ilist=[n1.ilist[mid-1]]
newroot.clist=[n1,newnode]
n1.par=newnode.par=newroot
self.__root=newroot
else:
i=n1.par.clist.index(n1)
n1.par.ilist.insert(i,n1.ilist[mid-1])
n1.par.clist.insert(i+1,newnode)
n1.ilist=n1.ilist[:mid-1]
n1.clist=n1.clist[:mid]
return n1.par
def split_leaf(n2):
mid=(self.L+1)//2
newleaf=Bptree.__Leaf(self.L)
newleaf.vlist=n2.vlist[mid:]
if n2.par==None:
newroot=Bptree.__InterNode(self.M)
newroot.ilist=[n2.vlist[mid].key]
newroot.clist=[n2,newleaf]
n2.par=newleaf.par=newroot
self.__root=newroot
else:
i=n2.par.clist.index(n2)
n2.par.ilist.insert(i,n2.vlist[mid].key)
n2.par.clist.insert(i+1,newleaf)
newleaf.par=n2.par
n2.vlist=n2.vlist[:mid]
n2.bro=newleaf
def insert_node(n):
if not n.isleaf():
if n.isfull():
insert_node(split_node(n))
else:
p=bisect_right(n.ilist,key_value)
insert_node(n.clist[p])
else:
p=bisect_right(n.vlist,key_value)
n.vlist.insert(p,key_value)
if n.isfull():
split_leaf(n)
else:
return
insert_node(node)
#搜索
def search(self,mi=None,ma=None):
result=[]
node=self.__root
leaf=self.__leaf
if mi is None or ma is None:
raise ParaError('you need to setup searching range')
elif mi > ma:
raise ParaError('upper bound must be greater or equal than lower bound')
def search_key(n,k):
if n.isleaf():
p=bisect_left(n.vlist,k)
return (p,n)
else:
p=bisect_right(n.ilist,k)
return search_key(n.clist[p],k)
if mi is None:
while True:
for kv in leaf.vlist:
if kv<=ma:
result.append(kv)
else:
return result
if leaf.bro==None:
return result
else:
leaf=leaf.bro
elif ma is None:
index,leaf=search_key(node,mi)
result.extend(leaf.vlist[index:])
while True:
if leaf.bro==None:
return result
else:
leaf=leaf.bro
result.extend(leaf.vlist)
else:
if mi==ma:
i,l=search_key(node,mi)
try:
if l.vlist[i]==mi:
result.append(l.vlist[i])
return result
else:
return result
except IndexError:
return result
else:
i1,l1=search_key(node,mi)
i2,l2=search_key(node,ma)
if l1 is l2:
if i1==i2:
return result
else:
result.extend(l2.vlist[i1:i2])
return result
else:
result.extend(l1.vlist[i1:])
l=l1
while True:
if l.bro==l2:
result.extend(l2.vlist[:i2])
return result
elif l.bro != None:
result.extend(l.bro.vlist)
l=l.bro
else:
return result;
def traversal(self):
result=[]
l=self.__leaf
while True:
result.extend(l.vlist)
if l.bro==None:
return result
else:
l=l.bro
def show(self):
print('this b+tree is:\n')
q=deque()
h=0
q.append([self.__root,h])
while True:
try:
w,hei=q.popleft()
except IndexError:
return
else:
if not w.isleaf():
print(w.ilist,'the height is',hei)
if hei==h:
h+=1
q.extend([[i,h] for i in w.clist])
else:
print([(v.key,v.value) for v in w.vlist],'the leaf is,',hei)
#删除
def delete(self,key_value):
def merge(n,i):
if n.clist[i].isleaf():
n.clist[i].vlist=n.clist[i].vlist+n.clist[i+1].vlist
n.clist[i].bro=n.clist[i+1].bro
else:
n.clist[i].ilist=n.clist[i].ilist+[n.ilist[i]]+n.clist[i+1].ilist
n.clist[i].clist=n.clist[i].clist+n.clist[i+1].clist
n.clist.remove(n.clist[i+1])
n.ilist.remove(n.ilist[i])
if n.ilist==[]:
n.clist[0].par=None
self.__root=n.clist[0]
del n
return self.__root
else:
return n
def tran_l2r(n,i):
if not n.clist[i].isleaf():
n.clist[i+1].clist.insert(0,n.clist[i].clist[-1])
n.clist[i].clist[-1].par=n.clist[i+1]
n.clist[i+1].ilist.insert(0,n.ilist[i])
n.ilist[i]=n.clist[i].ilist[-1]
n.clist[i].clist.pop()
n.clist[i].ilist.pop()
else:
n.clist[i+1].vlist.insert(0,n.clist[i].vlist[-1])
n.clist[i].vlist.pop()
n.ilist[i]=n.clist[i+1].vlist[0].key
def tran_r2l(n,i):
if not n.clist[i].isleaf():
n.clist[i].clist.append(n.clist[i+1].clist[0])
n.clist[i+1].clist[0].par=n.clist[i]
n.clist[i].ilist.append(n.ilist[i])
n.ilist[i]=n.clist[i+1].ilist[0]
n.clist[i+1].clist.remove(n.clist[i+1].clist[0])
n.clist[i+1].ilist.remove(n.clist[i+1].ilist[0])
else:
n.clist[i].vlist.append(n.clist[i+1].vlist[0])
n.clist[i+1].vlist.remove(n.clist[i+1].vlist[0])
n.ilist[i]=n.clist[i+1].vlist[0].key
def del_node(n,kv):
if not n.isleaf():
p=bisect_right(n.ilist,kv)
if p==len(n.ilist):
if not n.clist[p].isempty():
return del_node(n.clist[p],kv)
elif not n.clist[p-1].isempty():
tran_l2r(n,p-1)
return del_node(n.clist[p],kv)
else:
return del_node(merge(n,p),kv)
else:
if not n.clist[p].isempty():
return del_node(n.clist[p],kv)
elif not n.clist[p+1].isempty():
tran_r2l(n,p)
return del_node(n.clist[p],kv)
else:
return del_node(merge(n,p),kv)
else:
p=bisect_left(n.vlist,kv)
try:
pp=n.vlist[p]
except IndexError:
return -1
else:
if pp!=kv:
return -1
else:
n.vlist.remove(kv)
return 0
del_node(self.__root,key_value)
def test():
#初始化数据源
mini=50
maxi=200
testlist=[]
for i in range(20):
key=randint(1,1000)
#key=i
value=choice(['Do', 'Re', 'Mi', 'Fa', 'So', 'La', 'Si'])
testlist.append(KeyValue(key,value))
#初始化B树
mybptree=Bptree(4, 4)
#插入操作
for x in testlist:
mybptree.insert(x)
mybptree.show()
#查找操作
print('\nnow we are searching item between %d and %d\n==>'%(mini,maxi))
print([v.key for v in mybptree.search(mini,maxi)])
#删除操作
mybptree.delete(testlist[0])
print('\n删除 {0}后， the newtree is:\n'.format(testlist[0]));
mybptree.show()
#深度遍历操作
print('\nkey of this b+tree is \n')
print([kv.key for kv in mybptree.traversal()])
if __name__ == '__main__':
test();