高度平衡树 -- AVL 树
Scheme 的表达, 优雅.
#lang scheme
( define nil '() )
( define ( root tree )( car tree ) )
( define ( left-tree tree )( cadr tree ) )
( define ( right-tree tree )( caddr tree ) )
( define ( height tree )
( cond [ ( null? tree ) 0 ]
[ else ( cadddr tree ) ] ) )
( define ( make-leaf elem )( list elem nil nil 1 ) )
( define ( make-avl-tree root left right )
( list root left right ( + 1 ( max ( height left )
( height right ) ) ) ) )
( define ( contains-elem?
elem tree )
( cond [ ( null? tree ) false ]
[ ( = elem ( root tree ) ) true ]
[ ( < elem ( root tree ) )
( contains-elem?
elem ( left-tree tree ) ) ]
[ ( > elem ( root tree ) )
( contains-elem? elem ( right-tree tree ) ) ] ) )
( define ( rotate-left-left tree )
( cond [ ( null? tree ) tree ]
[ else ( make-avl-tree ( root ( left-tree tree ) )
( left-tree ( left-tree tree ) )
( make-avl-tree ( root tree )
( right-tree ( left-tree tree ) )
( right-tree tree ) ) ) ] ) )
( define ( rotate-right-right tree )
( cond [ ( null? tree ) tree ]
[ else ( make-avl-tree ( root ( right-tree tree ) )
( make-avl-tree ( root tree )
( left-tree tree )
( left-tree ( right-tree tree ) ) )
( right-tree ( right-tree tree ) ) ) ] ) )
( define ( rotate-right-left tree )
( cond [ ( null?
tree ) tree ]
[ else ( make-avl-tree ( left-tree ( right-tree tree ) )
( make-avl-tree ( root tree )
( left-tree tree )
( left-tree ( left-tree ( right-tree tree ) ) ) )
( make-avl-tree ( root ( right-tree tree ) )
( right-tree ( left-tree ( right-tree tree ) ) )
( right-tree ( right-tree tree ) ) ) ) ] ) )
( define ( rotate-left-right tree )
( cond [ ( null?
tree ) tree ]
[ else ( make-avl-tree ( root ( right-tree ( left-tree tree ) ) )
( make-avl-tree ( root ( left-tree tree ) )
( left-tree ( left-tree tree ) )
( left-tree ( right-tree ( left-tree tree ) ) ) )
( make-avl-tree ( root tree )
( right-tree ( right-tree ( left-tree tree ) ) )
( right-tree tree ) ) ) ] ) )
( define ( balance-avl-tree tree )
( define ( factor tree )
( - ( height ( right-tree tree ) )
( height ( left-tree tree ) ) ) )
( let ( [ f ( factor tree ) ] )
( cond [ ( = f 2 )
( cond [ ( < ( factor ( right-tree tree ) ) 0 )
( rotate-right-left tree ) ]
[ else ( rotate-right-right tree ) ] ) ]
[ ( = f -2 )
( cond [ ( > ( factor ( left-tree tree ) ) 0 )
( rotate-left-right tree ) ]
[ else ( rotate-left-left tree ) ] ) ]
[ else tree ] ) ) )
( define ( insert-elem elem tree )
( define ( insert-in-son elem tree )
( cond [ ( null? tree )
( make-leaf elem ) ]
[ ( < elem ( root tree ) )
( let* ( [ newLeftTree ( insert-in-son elem ( left-tree tree ) ) ]
[ newAVLTree ( make-avl-tree ( root tree )
newLeftTree
( right-tree tree ) ) ] )
( balance-avl-tree newAVLTree ) ) ]
[ ( > elem ( root tree ) )
( let* ( [ newRightTree ( insert-in-son elem ( right-tree tree ) ) ]
[ newAVLTree ( make-avl-tree ( root tree )
( left-tree tree )
newRightTree ) ] )
( balance-avl-tree newAVLTree ) ) ]
[ else tree ] ) )
( cond [ ( contains-elem? elem tree ) tree ]
[ else ( insert-in-son elem tree ) ] ) )
( define ( delete-elem elem tree )
( define ( delete-left-most tree )
( cond [ ( left-empty? tree ) tree ]
[ else ( let* ( [ leftMost ( delete-left-most ( left-tree tree ) ) ]
[ newRightTree ( make-avl-tree ( root tree )
( right-tree leftMost )
( right-tree tree ) ) ] )
( make-avl-tree ( root leftMost )
nil
( balance-avl-tree newRightTree ) ) ) ] ) )
( define ( delete-in-son elem tree )
( cond [ ( < elem ( root tree ) )
( let* ( [ newLeftTree ( delete-in-son elem ( left-tree tree ) ) ]
[ newAVLTree ( make-avl-tree ( root tree )
newLeftTree
( right-tree tree ) ) ] )
( balance-avl-tree newAVLTree ) ) ]
[ ( > elem ( root tree ) )
( let* ( [ newRightTree ( delete-in-son elem ( right-tree tree ) ) ]
[ newAVLTree ( make-avl-tree ( root tree )
( left-tree tree )
newRightTree ) ] )
( balance-avl-tree newAVLTree ) ) ]
[ ( = elem ( root tree ) )
( cond [ ( and ( right-empty? tree )
( left-empty? tree ) )
nil ]
[ ( right-empty? tree )
( left-tree tree ) ]
[ ( left-empty? tree )
( right-tree tree ) ]
[ else ( let ( [ leftMost ( delete-left-most ( right-tree tree ) ) ] )
( make-avl-tree ( root leftMost )
( left-tree tree )
( right-tree leftMost ) ) ) ] ) ] ) )
( define ( left-empty? tree )( null?
( left-tree tree ) ) )
( define ( right-empty? tree )( null?
( right-tree tree ) ) )
( cond [ ( contains-elem?
elem tree )
( delete-in-son elem tree ) ]
[ else tree ] ) )
( define ( list->avl elems )
( define ( iter elems tree )
( cond [ ( null?
elems ) tree ]
[ else ( iter ( cdr elems )
( insert-elem ( car elems ) tree ) ) ] ) )
( cond [ ( null? elems ) '() ]
[ else ( let( [ avl ( make-leaf ( car elems ) ) ] )
( iter ( cdr elems ) avl ) ) ] ) )
高度平衡树 -- AVL 树的更多相关文章
- 【数据结构】平衡二叉树—AVL树
(百度百科)在计算机科学中,AVL树是最先发明的自平衡二叉查找树.在AVL树中任何节点的两个子树的高度最大差别为一,所以它也被称为高度平衡树.查找.插入和删除在平均和最坏情况下都是O(log n).增 ...
- AVL树(一)之 图文解析 和 C语言的实现
概要 本章介绍AVL树.和前面介绍"二叉查找树"的流程一样,本章先对AVL树的理论知识进行简单介绍,然后给出C语言的实现.本篇实现的二叉查找树是C语言版的,后面章节再分别给出C++ ...
- AVL树的左旋右旋理解 （转）
AVL树是最先发明的自平衡二叉查找树.在AVL树中任何节点的两个子树的高度最大差别为一,所以它也被称为高度平衡树.查找.插入和删除在平均和最坏情况下都是O(log n).增加和删除可能需要通过一次或多 ...
- 简单数据结构———AVL树
C - 万恶的二叉树 Crawling in process... Crawling failed Time Limit:1000MS Memory Limit:32768KB 64b ...
- 算法二叉搜索树之AVL树
最近学习了二叉搜索树中的AVL树,特在此写一篇博客小结. 1.引言 对于二叉搜索树而言,其插入查找删除等性能直接和树的高度有关,因此我们发明了平衡二叉搜索树.在计算机科学中,AVL树是最先发明的自平衡 ...
- AVL树,红黑树
AVL树 https://baike.baidu.com/item/AVL%E6%A0%91/10986648 在计算机科学中,AVL树是最先发明的自平衡二叉查找树.在AVL树中任何节点的两个子树的高 ...
- AVL树的理解及自写AVL树
AVL树是最先发明的自平衡二叉查找树.在AVL树中任何节点的两个子树的高度最大差别为一,所以它也被称为高度平衡树.查找.插入和删除在平均和最坏情况下都是O(log n).增加和删除可能需要通过一次或多 ...
- 红黑树与AVL树
概述:本文从排序二叉树作为引子,讲解了红黑树,最后把红黑树和AVL树做了一个比较全面的对比. 1 排序二叉树 排序二叉树是一种特殊结构的二叉树,可以非常方便地对树中所有节点进行排序和检索. 排序二叉树 ...
- AVL树的实现——c++
一.概念 AVL树是根据它的发明者G.M. Adelson-Velsky和E.M. Landis命名的.它是最先发明的自平衡二叉查找树,也被称为高度平衡树.相比于"二叉查找树",它 ...
随机推荐
- 三. Java类与对象8.再谈Java包
在Java中,为了组织代码的方便,可以将功能相似的类放到一个文件夹内,这个文件夹,就叫做包. 包不但可以包含类,还可以包含接口和其他的包. 目录以"\"来表示层级关系,例如 E:\ ...
- Redis(二)linux下redis安装
上篇讲解了redis在windows下的安装,接下来看看在linux下如何安装redis(纯菜鸟入门级别)? (1)redis的下载及编译 这里,首先进入存放文件目录(我的云服务器的是:cd /jel ...
- C语言的运算符、位操作
+ - * / (加 减 乘 除) > >= < <= (大于 大于等于 小于 小于等于) == != (测试等于 测试不等于) && || ! (逻辑与 逻辑 ...
- 解决413 Request Entity Too Large
修改nginx配置 这是最简单的一个做法,着报错原因是nginx不允许上传配置过大的文件,那么件把nginx的上传大小配置调高就好. 1.打开nginx主配置文件nginx.conf,一般在/u ...
- apache几种限制ip的方法
参考文档来源: http://jingyan.baidu.com/article/4b07be3c193d1648b380f3a9.html1. 禁止访问某些文件/目录增加Files选项来控制,比 ...
- C#中 protected internal 和 internal 的区别
http://kudick.blog.163.com/blog/static/1666066320091055414453/ DoDo: protected: 爷爷有一张银行卡,爸爸可以用,儿子也可以 ...
- zabbix通过snmp监控windows主机
1.开启Windows的snmp功能 2.配置snmp服务 设置snmp服务社区名称及允许的主机,设置完成后重启snmp服务 3.在zabbix server上测试 测试需要使用命令snmpwalk, ...
- Apache环境下搭建KodExplorer网盘
Apache环境下搭建KodExplorer网盘 环境说明: 系统版本 CentOS 6.9 x86_64 软件版本 yum安装httpd和php kodexplorer4.25 1 ...
- android开发常用地址
一. android市场占用率的url http://developer.android.com/about/dashboards/ 二. ADT下载 下载地址是:http://developer.a ...
- 使用uncompyle2直接反编译python字节码文件pyo/pyc
update:在Mac OS X版的September 10, 2014版(5.0.9-1)中发现安装目录中的src.zip已更换位置至WingIDE.app/Contents/Resources/b ...