B+树的删除操作相对比较复杂,需要考虑多种情况。下面是一个简单的示例代码,用于演示B+树的删除操作:
class Node:
def __init__(self, leaf=False):
self.leaf = leaf
self.keys = []
self.child = []
class BPlusTree:
def __init__(self, t):
self.root = Node(True)
self.t = t
def insert(self, k):
root = self.root
if len(root.keys) == (2 * self.t) - 1:
temp = Node()
self.root = temp
temp.child.insert(0, root)
self.split_child(temp, 0)
self.insert_non_full(temp, k)
else:
self.insert_non_full(root, k)
def insert_non_full(self, x, k):
i = len(x.keys) - 1
if x.leaf:
x.keys.append((None, None))
while i >= 0 and k < x.keys[i]:
x.keys[i+1] = x.keys[i]
i -= 1
x.keys[i+1] = k
else:
while i >= 0 and k < x.keys[i]:
i -= 1
i += 1
if len(x.child[i].keys) == (2 * self.t) - 1:
self.split_child(x, i)
if k > x.keys[i]:
i += 1
self.insert_non_full(x.child[i], k)
def split_child(self, x, i):
t = self.t
y = x.child[i]
z = Node(y.leaf)
x.child.insert(i+1, z)
x.keys.insert(i, y.keys[t-1])
z.keys = y.keys[t: (2 * t) - 1]
y.keys = y.keys[0: t-1]
if not y.leaf:
z.child = y.child[t: 2 * t]
y.child = y.child[0: t-1]
def display(self):
self.display_helper(self.root)
def display_helper(self, x):
if x:
for i in range(len(x.keys)):
print(x.keys[i])
if not x.leaf:
for i in range(len(x.child)):
self.display_helper(x.child[i])
def delete(self, k):
x = self.search(self.root, k)
if not x:
return
if k in x.keys:
self.delete_key(x, k)
else:
i = 0
while i < len(x.keys) and k > x.keys[i]:
i += 1
if i < len(x.keys):
self.delete(x.child[i], k)
def delete_key(self, x, k):
t = self.t
if x.leaf:
x.keys.remove(k)
else:
if len(x.keys) >= t:
pred = self.get_predecessor(x.keys, k)
x.keys.remove(k)
x.keys.insert(0, pred)
self.delete(x.child[0], pred)
else:
succ = self.get_successor(x.keys, k)
x.keys.remove(k)
x.keys.append(succ)
self.delete(x.child[-1], succ)
def get_predecessor(self, keys, k):
for i in range(len(keys)-1, -1, -1):
if keys[i] < k:
return keys[i]
def get_successor(self, keys, k):
for i in range(len(keys)):
if keys[i] > k:
return keys[i]
def search(self, x, k):
i = 0
while i < len(x.keys) and k > x.keys[i]:
i += 1
if i < len(x.keys) and k == x.keys[i]:
return x
elif x.leaf:
return None
else:
return self.search(x.child[i], k)
这个示例代码实现了B+树的插入和删除操作。其中,insert()
方法用于插入一个新的键值对,delete()
方法用于删除指定的键值对。
需要注意的是,这只是一个简单的示例代码,可能不够完善和高效。实际应用中,可能需要根据具体需求进行修改和优化。