B+树的python实现
B+树的python实现
本代码来自极客学院网站死里逃生2018年发表的blog关于 B+tree (附 python 模拟代码)。该代码实现了B+树的插入、删除、范围查找，功能完善，但也存在诸多问题。本文在原代码基础上对其错误进行了修正，更便于需要者使用。
主要贡献
- 将python3不支持的语法修改成python3支持的语法，主要是__cmp__修改成__lt__,gt
- 解决查找算法bug：当范围查询上界不存在时，原代码返回的查询结果会多出或者缺少元素。点查询则不受影响。
- 为B+树类添加了Size成员，可以查看B+树已插入的数据个数
- 提供了更多的测试，读者可以利用这些测试检查自己需要的功能是否可以正常实现
- 未修复问题：这个插入和删除算法有大问题，插入和删除算法都不会修改上层的键值，除非触发合并或者分裂。
## 使用须知：1. 查找必须得是范围查询，点查询也得是上下界相等才行；查找的返回值一定是一个由KV组成的数组，哪怕点查询
## 2. 删除必须得输入键-值对而不是只靠键，当然如果和查询配合使用还是挺好的；
## 3. 这个算法不会拒绝同一个键多次插入，哪怕值也是相同的也不会报错，照样按从左到右插入
## 4. 注意B+树叶节点不是一个个键值，而是多个键值组成的节点，节点之间才有指向邻居的指针
from collections import deque
def bisect_right(a, x, lo=0, hi=None):
"""Return the index where to insert item x in list a, assuming a is sorted.
The return value i is such that all e in a[:i] have e <= x, and all e in
a[i:] have e > x. So if x already appears in the list, a.insert(x) will
insert just after the rightmost x already there.
Optional args lo (default 0) and hi (default len(a)) bound the
slice of a to be searched.
"""
if lo < 0:
raise ValueError('lo must be non-negative')
if hi is None:
hi = len(a)
while lo < hi:
mid = (lo + hi) // 2
if x < a[mid]:
hi = mid
else:
lo = mid + 1
return lo
def bisect_left(a, x, lo=0, hi=None):
"""Return the index where to insert item x in list a, assuming a is sorted.
The return value i is such that all e in a[:i] have e < x, and all e in
a[i:] have e >= x. So if x already appears in the list, a.insert(x) will
insert just before the leftmost x already there.
Optional args lo (default 0) and hi (default len(a)) bound the
slice of a to be searched.
"""
if lo < 0:
raise ValueError('lo must be non-negative')
if hi is None:
hi = len(a)
while lo < hi:
mid = (lo + hi) // 2
if a[mid] < x:
lo = mid + 1
else:
hi = mid
return lo
class InitError(Exception):
pass
class ParaError(Exception):
pass
class KeyValue(object):
__slots__ = ('key', 'value')
def __init__(self, key, value):
self.key = key
self.value = value
def __str__(self):
return str((self.key, self.value))
def __eq__(self, other):
if isinstance(other, KeyValue):
if self.key == other.key:
return True
else:
return False
else:
if self.key == other:
return True
else:
return False
def __ne__(self, other):
if isinstance(other, KeyValue):
if self.key != other.key:
return True
else:
return False
else:
if self.key != other:
return True
else:
return False
def __lt__(self, other):
if isinstance(other, KeyValue):
if self.key < other.key:
return True
else:
return False
else:
if self.key < other:
return True
else:
return False
def __gt__(self, other):
if isinstance(other, KeyValue):
if self.key > other.key:
return True
else:
return False
else:
if self.key > other:
return True
else:
return False
class Bptree_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 = [] # 如果是index节点，保存 Bptree_InterNode 节点信息
# leaf节点， 保存 Bptree_Leaf的信息
self.ilist = [] # 保存 索引节点
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
class Bptree_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
self.par = None
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 # 删除的填充因子
@property
def L(self):
return self.__L
class Bptree(object):
def __init__(self, M, L): # M为度， L为填充因子
if L > M:
raise InitError('L must be less or equal then M')
else:
self.__M = M
self.__L = L
self.__Size = 0
self.__root = Bptree_Leaf(L)
self.__leaf = self.__root
@property
def M(self):
return self.__M
@property
def L(self):
return self.__L
@property
def Size(self):
return self.__Size
def insert(self, key_value):
node = self.__root
def split_node(n1):
mid = self.M // 2
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)
self.__Size += 1
if n.isfull():
split_leaf(n)
else:
return
insert_node(node)
def search(self, mi=None, ma=None):
result = []
node = self.__root
leaf = self.__leaf
if mi is None and ma is None:
raise ParaError('you need to setup searching range')
elif mi is not None and ma is not None and 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:
if l2.vlist[i2] == ma:
## 解决了上界ma不存在于B+树中时出错的问题
result.extend(l1.vlist[i1:i2 + 1])
return result
else:
result.extend(l1.vlist[i1:i2])
else:
result.extend(l1.vlist[i1:])
l = l1
while True:
if l.bro == l2:
if l2.vlist[i2] == ma:
result.extend(l2.vlist[:i2 + 1])
return result
else:
result.extend(l2.vlist[:i2])
return result
else:
result.extend(l.bro.vlist)
l = l.bro
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
for v in w.vlist], 'the leaf is,', hei)
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():
# 将i的最后一个节点追加到i+1的第一个节点
n.clist[i + 1].clist.insert(0, n.clist[i].clist[-1])
n.clist[i].clist[-1].par = n.clist[i + 1]
# 追加 i+1的索引值，以及更新n的i+1索引值
## n.clist[i + 1].ilist.insert(0, n.clist[i].ilist[-1])
## n.ilist[i + 1] = n.clist[i].ilist[-1]
## n.clist[i].clist.pop()
## n.clist[i].ilist.pop()
# edit:
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 - 1), 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)
self.__Size -= 1
return 0
del_node(self.__root, key_value)
@property
def leaf(self):
return self.__leaf
def test():
mini = 2
maxi = 60
testlist = []
for i in range(1, 10):
key = i
value = i
testlist.append(KeyValue(key, value))
mybptree = Bptree(4, 4)
for kv in testlist:
mybptree.insert(kv)
mybptree.delete(testlist[0])
mybptree.show()
print('\nkey of this b+tree is \n')
print([kv.key for kv in mybptree.traversal()])
print([kv.key for kv in mybptree.search(mini, maxi)])
#if __name__ == '__main__':
# test()
## B = Bptree(4,4)
## for i in range(10):
## B.insert(KeyValue(1 + i, i**2))
# kv = B.search(10, 12)
# print(len(kv))
## kvs = B.traversal()
## for k_v in kvs:
## print(k_v)
## print("---------")
## B.insert(KeyValue(0, 0))
## B.insert(KeyValue(1, 10))
## kvs = B.traversal()
## for k_v in kvs:
## print(k_v)
## leaf = B.leaf
## smallest = B.leaf.vlist[0]
## print(smallest.key)
## B.insert(KeyValue(0,-1))
## leaf = B.leaf
## smallest = B.leaf.vlist[0]
## print(smallest.key)
B = Bptree(4,4)
print("---检查插入算法---")
for i in range(10):
B.insert(KeyValue(1 + i, i**2))
B.insert(KeyValue(0, -1))
print(B.Size)
print("---检查Size变量是否准确---")
B.delete(KeyValue(6, 25))
print(B.Size)
print("---检查跨块搜索是否正常---")
result = B.search(3,6)
for kv in result:
print(kv)
print("---检查范围查询在键值不连续时是否正常---")
B.delete(KeyValue(7, 36))
# B.insert(KeyValue(6, 25))
# B.insert(KeyValue(7, 36))
result = B.search(3,8)
for kv in result:
print(kv)