红黑树节点删除示例代码

红黑树节点删除的示例代码如下所示[^2]：

class Node:
    def __init__(self, key):
        self.key = key
        self.left = None
        self.right = None
        self.parent = None
        self.color = 1

class RedBlackTree:
    def __init__(self):
        self.TNULL = Node(0)
        self.TNULL.color = 0
        self.TNULL.left = None
        self.TNULL.right = None
        self.root = self.TNULL

    def delete_node(self, key):
        self.delete_helper(self.root, key)

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

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

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

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

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

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

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

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

        y = z
        y_original_color = y.color
        if z.left == self.TNULL:
            x = z.right
            self.rb_transplant(z, z.right)
        elif (z.right == self.TNULL):
            x = z.left
            self.rb_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.rb_transplant(y, y.right)
                y.right = z.right
                y.right.parent = y

            self.rb_transplant(z, y)
            y.left = z.left
            y.left.parent = y
            y.color = z.color
        if y_original_color == 0:
            self.balance(x)

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

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

    def left_rotate(self, x):
        y = x.right
        x.right = y.left
        if y.left != self.TNULL:
            y.left.parent = x

        y.parent = x.parent
        if x.parent == 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.TNULL:
            y.right.parent = x

        y.parent = x.parent
        if x.parent == 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 insert(self, key):
        node = Node(key)
        node.parent = None
        node.key = key
        node.left = self.TNULL
        node.right = self.TNULL
        node.color = 1

        y = None
        x = self.root

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

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

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

        if node.parent.parent == None:
            return

        self.balance(node)

    def inorder_helper(self, node):
        if node != self.TNULL:
            self.inorder_helper(node.left)
            print(node.key, end=" ")
            self.inorder_helper(node.right)

    def preorder_helper(self, node):
        if node != self.TNULL:
            print(node.key, end=" ")
            self.preorder_helper(node.left)
            self.preorder_helper(node.right)

    def postorder_helper(self, node):
        if node != self.TNULL:
            self.postorder_helper(node.left)
            self.postorder_helper(node.right)
            print(node.key, end=" ")

    def search_tree_helper(self, node, key):
        if node == self.TNULL or key == node.key:
            return node

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

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

    def searchTree(self, k):
        return self.search_tree_helper(self.root, k)

    def inorder(self):
        self.inorder_helper(self.root)

    def preorder(self):
        self.preorder_helper(self.root)

    def postorder(self):
        self.postorder_helper(self.root)

    def searchTree(self, k):
        return self.search_tree_helper(self.root, k)

# 示例代码
bst = RedBlackTree()
bst.insert(55)
bst.insert(40)
bst.insert(65)
bst.insert(60)
bst.insert(75)
bst.insert(57)

print("Inorder traversal of the given tree:")
bst.inorder()

print("\nDelete 40")
bst.delete(40)
print("Inorder traversal of the modified tree:")
bst.inorder()

print("\nDelete 65")
bst.delete(65)
print("Inorder traversal of the modified tree:")
bst.inorder()

请注意，这只是一个示例代码，用于演示红黑树节点删除的基本操作。具体的实现可能会根据不同的编程语言和应用场景而有所不同。