实现红黑树

红黑树是一种自平衡二叉搜索树，它的插入、删除和查找操作的时间复杂度都是 O(log n)。其中，n 是树中节点的数量。

红黑树的特点：
1. 每个节点都是红色或黑色。
2. 根节点是黑色的。
3. 每个叶子节点（NIL节点，空节点）是黑色的。
4. 如果一个节点是红色的，则它的两个子节点都是黑色的。
5. 对于每个节点，从该节点到其所有后代叶子节点的简单路径上，均包含相同数目的黑色节点。

下面是红黑树的实现：

class Node:
    def __init__(self, key):
        self.key = key
        self.left = None
        self.right = None
        self.parent = None
        self.color = 1  # 1 for red, 0 for black


class RedBlackTree:
    def __init__(self):
        self.nil = Node(None)
        self.nil.color = 0
        self.root = self.nil

    def insert(self, key):
        node = Node(key)
        node.parent = None
        node.left = self.nil
        node.right = self.nil
        node.color = 1

        y = None
        x = self.root

        while x != self.nil:
            y = x
            if node.key < x.key:
                x = x.left
            else:
                x = x.right

        node.parent = y
        if y is None:
            self.root = node
        elif node.key < y.key:
            y.left = node
        else:
            y.right = node

        if node.parent is None:
            node.color = 0
            return

        if node.parent.parent is None:
            return

        self.fix_insert(node)

    def fix_insert(self, node):
        while node.parent.color == 1:
            if node.parent == node.parent.parent.right:
                u = node.parent.parent.left
                if u.color == 1:
                    u.color = 0
                    node.parent.color = 0
                    node.parent.parent.color = 1
                    node = node.parent.parent
                else:
                    if node == node.parent.left:
                        node = node.parent
                        self.right_rotate(node)
                    node.parent.color = 0
                    node.parent.parent.color = 1
                    self.left_rotate(node.parent.parent)
            else:
                u = node.parent.parent.right

                if u.color == 1:
                    u.color = 0
                    node.parent.color = 0
                    node.parent.parent.color = 1
                    node = node.parent.parent
                else:
                    if node == node.parent.right:
                        node = node.parent
                        self.left_rotate(node)
                    node.parent.color = 0
                    node.parent.parent.color = 1
                    self.right_rotate(node.parent.parent)
            if node == self.root:
                break
        self.root.color = 0

    def left_rotate(self, x):
        y = x.right
        x.right = y.left
        if y.left != self.nil:
            y.left.parent = x
        y.parent = x.parent
        if x.parent is None:
            self.root = y
        elif x == x.parent.left:
            x.parent.left = y
        else:
            x.parent.right = y
        y.left = x
        x.parent = y

    def right_rotate(self, x):
        y = x.left
        x.left = y.right
        if y.right != self.nil:
            y.right.parent = x
        y.parent = x.parent
        if x.parent is None:
            self.root = y
        elif x == x.parent.right:
            x.parent.right = y
        else:
            x.parent.left = y
        y.right = x
        x.parent = y

    def inorder(self, root):
        if root == self.nil:
            return
        self.inorder(root.left)
        print(root.key, end=" ")
        self.inorder(root.right)

    def search(self, key):
        return self.search_helper(self.root, key)

    def search_helper(self, node, key):
        if node == self.nil or key == node.key:
            return node

        if key < node.key:
            return self.search_helper(node.left, key)
        return self.search_helper(node.right, key)

    def delete(self, key):
        self.delete_node_helper(self.root, key)

    def fix_delete(self, x):
        while x != self.root and x.color == 0:
            if x == x.parent.left:
                sib = x.parent.right
                if sib.color == 1:
                    sib.color = 0
                    x.parent.color = 1
                    self.left_rotate(x.parent)
                    sib = x.parent.right

                if sib.left.color == 0 and sib.right.color == 0:
                    sib.color = 1
                    x = x.parent
                else:
                    if sib.right.color == 0:
                        sib.left.color = 0
                        sib.color = 1
                        self.right_rotate(sib)
                        sib = x.parent.right

                    sib.color = x.parent.color
                    x.parent.color = 0
                    sib.right.color = 0
                    self.left_rotate(x.parent)
                    x = self.root
            else:
                sib = x.parent.left
                if sib.color == 1:
                    sib.color = 0
                    x.parent.color = 1
                    self.right_rotate(x.parent)
                    sib = x.parent.left

                if sib.right.color == 0 and sib.right.color == 0:
                    sib.color = 1
                    x = x.parent
                else:
                    if sib.left.color == 0:
                        sib.right.color = 0
                        sib.color = 1
                        self.left_rotate(sib)
                        sib = x.parent.left

                    sib.color = x.parent.color
                    x.parent.color = 0
                    sib.left.color = 0
                    self.right_rotate(x.parent)
                    x = self.root
        x.color = 0

    def minimum(self, node):
        while node.left != self.nil:
            node = node.left
        return node

    def delete_node_helper(self, node, key):
        z = self.nil
        while node != self.nil:
            if node.key == key:
                z = node

            if node.key <= key:
                node = node.right
            else:
                node = node.left

        if z == self.nil:
            print("Couldn't find key in the tree")
            return

        y = z
        y_original_color = y.color
        if z.left == self.nil:
            x = z.right
            self.transplant(z, z.right)
        elif z.right == self.nil:
            x = z.left
            self.transplant(z, z.left)
        else:
            y = self.minimum(z.right)
            y_original_color = y.color
            x = y.right
            if y.parent == z:
                x.parent = y
            else:
                self.transplant(y, y.right)
                y.right = z.right
                y.right.parent = y

            self.transplant(z, y)
            y.left = z.left
            y.left.parent = y
            y.color = z.color

        if y_original_color == 0:
            self.fix_delete(x)

    def transplant(self, u, v):
        if u.parent is None:
            self.root = v
        elif u == u.parent.left:
            u.parent.left = v
        else:
            u.parent.right = v
        v.parent = u.parent

上面的代码实现了红黑树的插入、删除、查找和中序遍历等操作。其中，`Node` 类表示树中的节点，它包含一个键值 `key`、左右子节点 `left` 和 `right`、父节点 `parent`，以及一个颜色 `color`，用 0 表示黑色，1 表示红色。

`RedBlackTree` 类包含了一个 NIL 节点 `nil` 和根节点 `root`。`insert` 方法用于插入节点，`fix_insert` 方法用于修复插入后可能违反红黑树性质的问题。`delete` 方法用于删除节点，`fix_delete` 方法用于修复删除后可能违反红黑树性质的问题。`transplant` 方法用于节点替换操作。

红黑树的查找操作和普通二叉搜索树相同，这里不再赘述。