August 2017
Intermediate to advanced
360 pages
8h 35m
Chinese
Content preview from 算法技术手册（原书第2 版）
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126
｜
第
5
章
多只会做
O
(log
n
)
次旋转。所以我们可以非常肯定地说，插入和删除的性能是
O
(log
n
)
。
额外的旋转操作一般都是非常值得的，尤其是考虑到平衡情况下的搜索性能改进。
AV L
树也需要在每个结点中存储额外的
高度
信息，这样也增加了存储需求。
5.5.5 衍生算法
很自然地，我们可以从二叉树延伸到
n
路树，其每个结点都有
n
> 2
个子
结点。这类树
的一个常见版本叫作
B
树，它在关系数据库中表现出优异的性能。完整的
B
树分析可以
在相关资料（
Cormen
等
, 2009
）中找到，而且网上还有不少关于
B
树的教程，并且有
许多实现的例子。
另外一个常见的自平衡二叉树是
红黑树
。红黑树是近似平衡的，它能够保证没有一个分
支会比树中其他分支长两倍以上。这一宽松的规则能够减少插入和删除所需要的旋转操
作数，从而改善性能。在代码库的
algs.model.tree.BalancedThree
类中可以找到我们
提供的红黑树的实现代码。更多的细节可以在相关资料
(Cormen
等，
2009)
中找到。
5.6 参考文献
Adel
l’
son-Ve
l’
skii, G. M. and E. Landis,
“
An algorithm for the organization of information,
”
Soviet Mathematics Doklady
, 3: 1259-1263, 1962.
Bloom, B.,
“
Space/time trade-offs in hash coding with allowable errors, ...
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