红黑树和b+树一样，是平衡二叉搜索树。红黑树每个节点都是有颜色的，要么是红色，要么黑色，但树的根是黑色，最底部的叶也是黑色的。还需要注意的是，红黑树任何节点到叶的直接路径包含相同数量的黑色节点。

红黑树如何保持自平衡的特性？

红黑树节点颜色的限制确保从根到叶的最长路径不超过最短路径的两倍。

为什么新插入的节点在红黑树中总是红色的？

这是因为插入红色节点不会违反红黑树的黑色节点数量性质。而且即便是新增红色节点插入到原本的红色节点，解决此问题会比违反黑色节点引起的问题更加容易。

立即学习“Python免费学习笔记（深入）”；

红黑树Python代码实现

import sys# 创建节点class Node():    def __init__(self, item):        self.item = item        self.parent = None        self.left = None        self.right = None        self.color = 1class RedBlackTree():    def __init__(self):        self.TNULL = Node(0)        self.TNULL.color = 0        self.TNULL.left = None        self.TNULL.right = None        self.root = self.TNULL    # 前序    def pre_order_helper(self, node):        if node != TNULL:            sys.stdout.write(node.item + " ")            self.pre_order_helper(node.left)            self.pre_order_helper(node.right)    # 中序    def in_order_helper(self, node):        if node != TNULL:            self.in_order_helper(node.left)            sys.stdout.write(node.item + " ")            self.in_order_helper(node.right)# 后根    def post_order_helper(self, node):        if node != TNULL:            self.post_order_helper(node.left)            self.post_order_helper(node.right)            sys.stdout.write(node.item + " ")    # 搜索树    def search_tree_helper(self, node, key):        if node == TNULL or key == node.item:            return node        if key < node.item:            return self.search_tree_helper(node.left, key)        return self.search_tree_helper(node.right, key)    # 删除后平衡树    def delete_fix(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 __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    # 节点删除    def delete_node_helper(self, node, key):        z = self.TNULL        while node != self.TNULL:            if node.item == key:                z = node            if node.item <= key:                node = node.right            else:                node = node.left        if z == self.TNULL:            print("Cannot 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.delete_fix(x)    # 插入后平衡树    def fix_insert(self, k):        while k.parent.color == 1:            if k.parent == k.parent.parent.right:                u = k.parent.parent.left                if u.color == 1:                    u.color = 0                    k.parent.color = 0                    k.parent.parent.color = 1                    k = k.parent.parent                else:                    if k == k.parent.left:                        k = k.parent                        self.right_rotate(k)                    k.parent.color = 0                    k.parent.parent.color = 1                    self.left_rotate(k.parent.parent)            else:                u = k.parent.parent.right                if u.color == 1:                    u.color = 0                    k.parent.color = 0                    k.parent.parent.color = 1                    k = k.parent.parent                else:                    if k == k.parent.right:                        k = k.parent                        self.left_rotate(k)                    k.parent.color = 0                    k.parent.parent.color = 1                    self.right_rotate(k.parent.parent)            if k == self.root:                break        self.root.color = 0    # Printing the tree    def __print_helper(self, node, indent, last):        if node != self.TNULL:            sys.stdout.write(indent)            if last:                sys.stdout.write("R----")                indent += "     "            else:                sys.stdout.write("L----")                indent += "|    "            s_color = "RED" if node.color == 1 else "BLACK"            print(str(node.item) + "(" + s_color + ")")            self.__print_helper(node.left, indent, False)            self.__print_helper(node.right, indent, True)    def preorder(self):        self.pre_order_helper(self.root)    def inorder(self):        self.in_order_helper(self.root)    def postorder(self):        self.post_order_helper(self.root)    def searchTree(self, k):        return self.search_tree_helper(self.root, k)    def minimum(self, node):        while node.left != self.TNULL:            node = node.left        return node    def maximum(self, node):        while node.right != self.TNULL:            node = node.right        return node    def successor(self, x):        if x.right != self.TNULL:            return self.minimum(x.right)        y = x.parent        while y != self.TNULL and x == y.right:            x = y            y = y.parent        return y    def predecessor(self,  x):        if (x.left != self.TNULL):            return self.maximum(x.left)        y = x.parent        while y != self.TNULL and x == y.left:            x = y            y = y.parent        return y    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.item = 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.item < x.item:                x = x.left            else:                x = x.right        node.parent = y        if y == None:            self.root = node        elif node.item < y.item:            y.left = node        else:            y.right = node        if node.parent == None:            node.color = 0            return        if node.parent.parent == None:            return        self.fix_insert(node)    def get_root(self):        return self.root    def delete_node(self, item):        self.delete_node_helper(self.root, item)    def print_tree(self):        self.__print_helper(self.root, "", True)if __name__ == "__main__":    bst = RedBlackTree()    bst.ｉｎｓｅｒｔ(55)    bst.ｉｎｓｅｒｔ(40)    bst.ｉｎｓｅｒｔ(65)    bst.ｉｎｓｅｒｔ(60)    bst.ｉｎｓｅｒｔ(75)    bst.ｉｎｓｅｒｔ(57)    bst.print_tree()    print("\nAfter deleting an element")    bst.delete_node(40)    bst.print_tree()