B+树删除

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。