Finger Trees: A Simple General-purpose Data Structure

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原文链接：http://www.cnblogs.com/kcbsbo/p/4777894.html

本文介绍了一种称为2-3 Finger Trees的功能性数据结构，该结构支持序列的高效操作，包括常数时间访问两端元素，以及对较小部分进行拼接和分割的日志时间复杂度。文章详细阐述了其非正则类型定义，并通过内部节点注释来支持高效的分割与搜索。

http://staff.city.ac.uk/~ross/papers/FingerTree.html

Summary

We present 2-3 finger trees, a functional representation of persistent sequences supporting access to the ends in amortized constant time, and concatenation and splitting in time logarithmic in the size of the smaller piece. Representations achieving these bounds have appeared previously, but 2-3 finger trees are much simpler, as are the operations on them. Further, by defining the split operation in a general form, we obtain a general purpose data structure that can serve as a sequence, priority queue, search tree, priority search queue and more.

The basic structure is expressed as a non-regular (or nested) type:

data FingerTree a = Empty
                  | Single a
                  | Deep (Digit a) (FingerTree (Node a)) (Digit a)

data Digit a = One a | Two a a | Three a a a | Four a a a a
data Node a = Node2 a a | Node3 a a a

This produces trees of 2-3 trees, with favoured access (fingers) at the ends, like

(more examples) and also supports efficient concatenation. To support splitting and searching, we annotate the internal nodes of the tree with values drawn from an application-specific monoid.

转载于:https://www.cnblogs.com/kcbsbo/p/4777894.html