Simple Balanced Binary Search Trees

TL;DR

This paper presents a complete, purely-functional implementation of balanced binary search trees based on AA trees, simplifying the understanding of deletion and providing detailed code and analysis.

Contribution

It offers the first comprehensive, pedagogically accessible implementation of AA trees with full code, justification, and analysis for purely-functional data structures.

Findings

Provides a complete implementation of AA trees

Simplifies understanding of deletion in balanced trees

Includes detailed code and theoretical analysis

Abstract

Efficient implementations of sets and maps (dictionaries) are important in computer science, and balanced binary search trees are the basis of the best practical implementations. Pedagogically, however, they are often quite complicated, especially with respect to deletion. I present complete code (with justification and analysis not previously available in the literature) for a purely-functional implementation based on AA trees, which is the simplest treatment of the subject of which I am aware.