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Hash Tree (persistent Data Structure)
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 computer science, purely functional programming usually designates a programming paradigm—a style of building the structure and elements of computer programs—that treats all computation as the evaluation of function (mathematics), mathematic .... 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. Hash array mapped tries and Ctries are refined versions of this data structure, using particular type of trie implementations. References Functional data structures Hashing {{compu-prog-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trie
In computer science, a trie (, ), also known as a digital tree or prefix tree, is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key. Instead, each node's ''position'' within the trie determines its associated key, with the connections between nodes defined by individual Character (computing), characters rather than the entire key. Tries are particularly effective for tasks such as autocomplete, spell checking, and IP routing, offering advantages over hash tables due to their prefix-based organization and lack of hash collisions. Every child node shares a common prefix (computer science), prefix with its parent node, and the root node represents the empty string. While basic trie implementations can be memory-intensive, various optimization techniques such as compression and bitwise representations have been developed to improve their efficiency. A n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Persistent Data Structure
In computing, a persistent data structure or not ephemeral data structure is a data structure that always preserves the previous version of itself when it is modified. Such data structures are effectively immutable, as their operations do not (visibly) update the structure in-place, but instead always yield a new updated structure. The term was introduced in Driscoll, Sarnak, Sleator, and Tarjan's 1986 article. A data structure is partially persistent if all versions can be accessed but only the newest version can be modified. The data structure is fully persistent if every version can be both accessed and modified. If there is also a meld or merge operation that can create a new version from two previous versions, the data structure is called confluently persistent. Structures that are not persistent are called ''ephemeral''. These types of data structures are particularly common in logical and functional programming, as languages in those paradigms discourage (or fully forbid) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set (abstract Data Type)
In computer science, a set is an abstract data type that can store unique values, without any particular sequence, order. It is a computer implementation of the mathematics, mathematical concept of a finite set. Unlike most other collection (abstract data type), collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set. Some set data structures are designed for static or frozen sets that do not change after they are constructed. Static sets allow only query operations on their elements — such as checking whether a given value is in the set, or enumerating the values in some arbitrary order. Other variants, called dynamic or mutable sets, allow also the insertion and deletion of elements from the set. A multiset is a special kind of set in which an element can appear multiple times in the set. Type theory In type theory, sets are generally identified with their indicator function (characteristic function): accord ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Associative Array
In computer science, an associative array, key-value store, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with ''finite'' domain. It supports 'lookup', 'remove', and 'insert' operations. The dictionary problem is the classic problem of designing efficient data structures that implement associative arrays. The two major solutions to the dictionary problem are hash tables and search trees..Dietzfelbinger, M., Karlin, A., Mehlhorn, K., Meyer auf der Heide, F., Rohnert, H., and Tarjan, R. E. 1994"Dynamic Perfect Hashing: Upper and Lower Bounds". SIAM J. Comput. 23, 4 (Aug. 1994), 738-761. http://portal.acm.org/citation.cfm?id=182370 It is sometimes also possible to solve the problem using directly addressed arrays, binary search trees, or other more specialized structures. Many programmin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Table
In computer science, a hash table is a data structure that implements an associative array, also called a dictionary or simply map; an associative array is an abstract data type that maps Unique key, keys to Value (computer science), values. A hash table uses a hash function to compute an ''index'', also called a ''hash code'', into an array of ''buckets'' or ''slots'', from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored. A map implemented by a hash table is called a hash map. Most hash table designs employ an Perfect hash function, imperfect hash function. Hash collision, Hash collisions, where the hash function generates the same index for more than one key, therefore typically must be accommodated in some way. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the table. Many hash table designs also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Purely Functional Programming
In computer science, purely functional programming usually designates a programming paradigm—a style of building the structure and elements of computer programs—that treats all computation as the evaluation of function (mathematics), mathematical functions. Program state and mutable objects are usually modeled with temporal logic, as explicit variables that represent the program state at each step of a program execution: a variable state is passed as an input parameter of a state-transforming function, which returns the updated state as part of its return value. This style handles state changes without losing the referential transparency of the program expressions. Purely functional programming consists of ensuring that functions, inside the functional programming, functional paradigm, will only depend on their arguments, regardless of any global or local state. A pure functional subroutine only has visibility of changes of state represented by state variables included in its s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Function
A hash function is any Function (mathematics), function that can be used to map data (computing), data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. The values returned by a hash function are called ''hash values'', ''hash codes'', (''hash/message'') ''digests'', or simply ''hashes''. The values are usually used to index a fixed-size table called a ''hash table''. Use of a hash function to index a hash table is called ''hashing'' or ''scatter-storage addressing''. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally- and storage-space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
École Polytechnique Fédérale De Lausanne
The École Polytechnique Fédérale de Lausanne (, EPFL) is a public university, public research university in Lausanne, Switzerland, founded in 1969 with the mission to "train talented engineers in Switzerland". Like its sister institution ETH Zurich, EPFL is part of the ETH Domain, Swiss Federal Institutes of Technology Domain which groups several universities and research institutes under the Federal Department of Economic Affairs, Education and Research. As of 2024, EPFL enrolled 14,012 students from over 130 countries. EPFL has an Lausanne campus, urban campus that extends alongside Lake Geneva, and includes the Swiss Innovation Park, EPFL Innovation Park as well as university research centers and affiliated laboratories. History The roots of modern-day EPFL can be traced back to the foundation of a private school under the name ''École spéciale de Lausanne'' in 1853 at the initiative of Louis Rivier, a graduate of the and John Gay, the then professor and rector ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Array Mapped Trie
A hash array mapped trie (HAMT, ) is an implementation of an associative array that combines the characteristics of a hash table and an array mapped trie. It is a refined version of the more general notion of a hash tree. Operation A HAMT is an array mapped trie where the keys are first hashed to ensure an even distribution of keys and a constant key length. In a typical implementation of HAMT's array mapped trie, each node contains a table with some fixed number N of slots with each slot containing either a nil pointer or a pointer to another node. N is commonly 32. As allocating space for N pointers for each node would be expensive, each node instead contains a bitmap which is N bits long where each bit indicates the presence of a non-nil pointer. This is followed by an array of pointers equal in length to the number of ones in the bitmap (its Hamming weight). Advantages of HAMTs The hash array mapped trie achieves almost hash table-like speed while using memory much mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ctrie
A concurrent hash-trie or Ctrie is a concurrent thread-safe lock-free implementation of a hash array mapped trie. It is used to implement the concurrent map abstraction. It has particularly scalable concurrent insert and remove operations and is memory-efficient. It is the first known concurrent data-structure that supports O(1), atomic, lock-free snapshots. Operation The Ctrie data structure is a non-blocking concurrent hash array mapped trie based on single-word compare-and-swap instructions in a shared-memory system. It supports concurrent lookup, insert and remove operations. Just like the hash array mapped trie, it uses the entire 32-bit space for hash values thus having low risk of hashcode collisions. Each node may have up to 32 sub-nodes, but to conserve memory, the list of sub-nodes is represented by a 32-bit bitmap where each bit indicates the presence of a branch, followed by a non-sparse array (of pointers to sub-nodes) whose length equals the Hamming weight of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Data Structures
Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional symptom ** Functional disorder * Functional classification for roads * Functional organization * Functional training In mathematics * Functional (mathematics), a term applied to certain scalar-valued functions in mathematics and computer science ** Minnesota functionals ** Functional analysis, a branch of mathematical analysis ** Linear functional, a type of functional often simply called a functional in the context of functional analysis * Higher-order function, also called a functional, a function that takes other functions as arguments In computer science, software engineering * "Functional" (noun) may be used as a synonym for Higher-order function * (C++), a header file in the C++ Standard Library * Functional design, a paradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
