Hash tree (persistent data structure)

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In computer science, a hash tree (or hash trie) is a persistent data structure that can be used to implement sets and maps, intended to replace hash tables in purely functional programming. In its basic form, a hash tree stores the hashes of its keys, regarded as strings of bits, in a trie, with the actual keys and (optional) values stored at the trie's "final" nodes.^[1]

Hash array mapped tries and Ctries are refined versions of this data structure, using particular type of trie implementations.^[1]

References

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^ ^a ^b Phil Bagwell (2000). Ideal Hash Trees (PDF) (Report). Infoscience Department, École Polytechnique Fédérale de Lausanne.

v t e Tree data structures
Search trees (dynamic sets/associative arrays)	2–3 2–3–4 AA (a,b) AVL B K-Dimensional B+ B* B^x Binary search Optimal Self-balancing Dancing HTree Interval Order statistic Palindrome (Left-leaning) Red–black Scapegoat Splay T Treap UB Weight-balanced
Heaps	Binary Binomial Brodal d-ary Fibonacci Leftist Pairing Skew binomial Skew van Emde Boas Weak
Tries	Ctrie C-trie (compressed ADT) Hash Radix Suffix Ternary search X-fast Y-fast
Spatial data partitioning trees	Ball BK BSP Cartesian Hilbert R k-d (implicit k-d) M Metric MVP Octree PH Priority R Quad R R+ R* Segment VP X
Other trees	Cover Exponential Fenwick Finger Fractal tree index Fusion Hash calendar iDistance K-ary Left-child right-sibling Link/cut Log-structured merge Merkle PQ Range SPQR Top

v t e Data structures
Types	Collection Container
Abstract	Associative array Multimap Retrieval Data Structure List Stack Queue Double-ended queue Priority queue Double-ended priority queue Set Multiset Disjoint-set
Arrays	Bit array Circular buffer Dynamic array Hash table Hashed array tree Sparse matrix
Linked	Association list Linked list Skip list Unrolled linked list XOR linked list
Trees	B-tree Binary search tree AA tree AVL tree Red–black tree Self-balancing tree Splay tree Heap Binary heap Binomial heap Fibonacci heap R-tree R* tree R+ tree Hilbert R-tree Trie Hash tree
Graphs	Binary decision diagram Directed acyclic graph Directed acyclic word graph
List of data structures

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