硬核红黑树
Posted 袁厨的算法小屋
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红黑树是工程中最常见的二叉查找树的实现,例如在 Linux 的内存管理和进程管理中就用到了红黑树;Java 语言的集合包、C++语言的标准模板库中均提供了红黑树的实现类。
红黑树本身的设计很复杂,多数情况下我们也不需要自己去实现红黑树,但研究红黑树还是有意义的。一方面可以让学习者领略这种神奇的数据结构的奥妙,另一方面可以作为一种思维训练工具,提升自己的算法设计能力。
本文以漫画形式讲述红黑树,第一话讲解二叉查找树的概念和基本操作,包括节点查找、插入、删除;第二话讲解二叉查找树的缺点和红黑树的概念,以及红黑树的节点旋转操作;第三话讲解红黑树的节点插入操作;第四话讲解红黑树的节点删除操作;第五话和彩蛋部分讲解红黑树在插入修正和删除修正时,对各种 CASE 所进行的调整操作背后的思想。
红黑树的实现中,最难的部分在于实现节点的插入和删除时,要穷举所有可能的 CASE,然后对每种 CASE 进行处理。在理解节点的插入和删除的过程时,读者要把握住一个中心:每种 CASE 所进行的调整步骤都在尽量恢复插入/删除节点后所违反的红黑树特性,如果当前 CASE 解决不了,就转成另一种更接近问题解决状态的 CASE。每种 CASE 的所进行的调整步骤都是为了向解决问题的出口更靠近一步,直至找到出口。
正文
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