数据结构-非线性结构-树形结构：有序树 -＞二叉树 -＞平衡二叉树（任何节点的左右子树的高度差不大于1）-＞红黑树（O(logn)）【严格来说，不是平衡二叉树；平均来说红黑树比AVL树快一些】

小咪咪 2023-10-04 12:19 4阅读 0赞

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## 一、2-3树 ##

2-3树【不是二叉树，是一颗绝对平衡的树（左右子树的高度一定相等）】【2-3树与红黑树等价】  
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2-3树动画：  
![在这里插入图片描述][20210512183833138.gif_pic_center]

## 二、红黑树 ##

红黑树是保持 “黑节点绝对平衡” 的二叉树；

严格意义上，红黑树不是平衡二叉树；

最大高度为  2 l o g n 2logn 2logn

时间复杂度： O ( l o g n ) O(logn) O(logn)

如果创建后只查询，则AVL树的性能比红黑树高一些（AVL树高度为 l o g n logn logn，红黑树的高度为  2 l o g n 2logn 2logn）；

如果创建后经常添加、删除元素，则红黑树的效率比AVL树高；

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTMyNTA4NjE_size_16_color_FFFFFF_t_70_pic_center 6]  
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## 三、二分搜索树、AVL树、红黑树 性能对比 ##

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