用python实现平衡二叉树的增删查改

在Python中，可以使用内置的数据结构如`list`或自定义`Node`和`BinaryTree`类来模拟一个简单的平衡二叉搜索树（Balanced Binary Search Tree，BBST），比如AVL树。这里简述如何实现基本操作：

1. **创建节点** (插入):

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

class BinaryTree:
    def insert(self, root, value):
        if not root:
            return Node(value)
        elif value < root.value:
            root.left = self.insert(root.left, value)
        else:
            root.right = self.insert(root.right, value)

        root.height = 1 + max(self.getHeight(root.left), self.getHeight(root.right))
        balance = self.getBalance(root)

        # 旋转调整
        if balance > 1 and value < root.left.value:
            return self.rightRotate(root)
        elif balance < -1 and value > root.right.value:
            return self.leftRotate(root)
        elif balance > 1 and value > root.left.value:
            root.left = self.leftRotate(root.left)
            return self.rightRotate(root)
        elif balance < -1 and value < root.right.value:
            root.right = self.rightRotate(root.right)
            return self.leftRotate(root)

        return root

2. **查找** (查询):

def search(self, root, value):
    if not root or root.value == value:
        return root
    elif value < root.value:
        return self.search(root.left, value)
    else:
        return self.search(root.right, value)

3. **删除** (删除特定值):

def delete(self, root, value):
    if not root:
        return root

    if value < root.value:
        root.left = self.delete(root.left, value)
    elif value > root.value:
        root.right = self.delete(root.right, value)
    else:  # 找到需要删除的节点
        if root.left is None:  # 只有右子树
            temp = root.right
            root = None
            return temp
        elif root.right is None:  # 只有左子树
            temp = root.left
            root = None
            return temp

        # 有两个子节点
        temp = self.getMinValueNode(root.right)  # 获取右子树最小值节点
        root.value = temp.value  # 替换为最小值
        root.right = self.delete(root.right, temp.value)

    if root is None:
        return root

    root.height = 1 + max(self.getHeight(root.left), self.getHeight(root.right))
    balance = self.getBalance(root)

    # 如果不平衡，则应用适当的旋转
    # ...

    return root

4. **其他辅助函数**:

def getHeight(self, root):
    if not root:
        return 0
    return root.height

def getBalance(self, root):
    if not root:
        return 0
    return self.getHeight(root.left) - self.getHeight(root.right)

# 左旋
def leftRotate(self, z):
    y = z.right
    T2 = y.left
    y.left = z
    z.right = T2
    z.height = 1 + max(self.getHeight(z.left), self.getHeight(z.right))
    y.height = 1 + max(self.getHeight(y.left), self.getHeight(y.right))
    return y

# 右旋
def rightRotate(self, y):
    x = y.left
    T2 = x.right
    x.right = y
    y.left = T2
    y.height = 1 + max(self.getHeight(y.left), self.getHeight(y.right))
    x.height = 1 + max(self.getHeight(x.left), self.getHeight(x.right))
    return x

def getMinValueNode(self, root):
    current = root
    while current.left is not None:
        current = current.left
    return current