设计一个英汉词典，支持Member （查找）、Insert （插入）、Delete （删除）操作。基本要求：实现字典的常用方法有：有序线性表（Memeber 用二分检索实现）、AVL 树（二叉搜索树）、Patricia Trie、散列表等，任选一种方法实现字典的操作，查找单词、插入单词（插入时，先查找，找不到插入，找到提示用户）删除单词（删除时，先查找，找到删除，找不到提示用户）。测试数据：任一英文单词。

我可以为你提供一个基于 AVL 树实现的英汉词典。

AVL 树是一种平衡二叉搜索树，它的左右子树的高度差不超过 1，可以保证树的高度始终在 O(log n)。我们可以将英文单词作为键，将对应的中文意思作为值存储在 AVL 树中。

以下是基于 AVL 树实现的英汉词典的代码（使用 Python 语言实现）：

class AVLNode:
    def __init__(self, key, value):
        self.key = key
        self.value = value
        self.left = None
        self.right = None
        self.height = 1

class AVLTree:
    def __init__(self):
        self.root = None
    
    def get_height(self, node):
        if node is None:
            return 0
        else:
            return node.height
    
    def get_balance(self, node):
        if node is None:
            return 0
        else:
            return self.get_height(node.left) - self.get_height(node.right)
    
    def left_rotate(self, node):
        new_root = node.right
        node.right = new_root.left
        new_root.left = node
        
        node.height = 1 + max(self.get_height(node.left), self.get_height(node.right))
        new_root.height = 1 + max(self.get_height(new_root.left), self.get_height(new_root.right))
        
        return new_root
    
    def right_rotate(self, node):
        new_root = node.left
        node.left = new_root.right
        new_root.right = node
        
        node.height = 1 + max(self.get_height(node.left), self.get_height(node.right))
        new_root.height = 1 + max(self.get_height(new_root.left), self.get_height(new_root.right))
        
        return new_root
    
    def insert(self, key, value):
        def insert_node(node, key, value):
            if node is None:
                return AVLNode(key, value)
            
            if key < node.key:
                node.left = insert_node(node.left, key, value)
            elif key > node.key:
                node.right = insert_node(node.right, key, value)
            else:
                node.value = value
            
            node.height = 1 + max(self.get_height(node.left), self.get_height(node.right))
            balance = self.get_balance(node)
            
            if balance > 1 and key < node.left.key:
                return self.right_rotate(node)
            
            if balance < -1 and key > node.right.key:
                return self.left_rotate(node)
            
            if balance > 1 and key > node.left.key:
                node.left = self.left_rotate(node.left)
                return self.right_rotate(node)
            
            if balance < -1 and key < node.right.key:
                node.right = self.right_rotate(node.right)
                return self.left_rotate(node)
            
            return node
        
        self.root = insert_node(self.root, key, value)
    
    def search(self, key):
        def search_node(node, key):
            if node is None:
                return None
            
            if key < node.key:
                return search_node(node.left, key)
            elif key > node.key:
                return search_node(node.right, key)
            else:
                return node
        
        node = search_node(self.root, key)
        if node is None:
            return None
        else:
            return node.value
    
    def delete(self, key):
        def delete_node(node, key):
            if node is None:
                return node
            
            if key < node.key:
                node.left = delete_node(node.left, key)
            elif key > node.key:
                node.right = delete_node(node.right, key)
            else:
                if node.left is None:
                    temp = node.right
                    node = None
                    return temp
                elif node.right is None:
                    temp = node.left
                    node = None
                    return temp
                
                temp = self.get_min_value_node(node.right)
                node.key = temp.key
                node.value = temp.value
                node.right = delete_node(node.right, temp.key)
                
            if node is None:
                return node
            
            node.height = 1 + max(self.get_height(node.left), self.get_height(node.right))
            balance = self.get_balance(node)
            
            if balance > 1 and self.get_balance(node.left) >= 0:
                return self.right_rotate(node)
            
            if balance < -1 and self.get_balance(node.right) <= 0:
                return self.left_rotate(node)
            
            if balance > 1 and self.get_balance(node.left) < 0:
                node.left = self.left_rotate(node.left)
                return self.right_rotate(node)
            
            if balance < -1 and self.get_balance(node.right) > 0:
                node.right = self.right_rotate(node.right)
                return self.left_rotate(node)
            
            return node
        
        self.root = delete_node(self.root, key)
    
    def get_min_value_node(self, node):
        if node is None or node.left is None:
            return node
        
        return self.get_min_value_node(node.left)

你可以使用以下代码测试该英汉词典：

dictionary = AVLTree()

# 插入单词
dictionary.insert("apple", "苹果")
dictionary.insert("banana", "香蕉")
dictionary.insert("cherry", "樱桃")

# 查找单词
print(dictionary.search("apple"))  # 苹果
print(dictionary.search("pear"))   # None

# 删除单词
dictionary.delete("banana")
print(dictionary.search("banana")) # None