|
Backtracking Search
Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of ''k'' queens in the first ''k'' rows of the board, all in different rows and columns. Any partial solution that contains two mutually attacking queens can be abandoned. Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is useless, for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Search
In optimization, line search is a basic iterative approach to find a local minimum \mathbf^* of an objective function f:\mathbb R^n\to\mathbb R. It first finds a descent direction along which the objective function f will be reduced, and then computes a step size that determines how far \mathbf should move along that direction. The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size can be determined either exactly or inexactly. One-dimensional line search Suppose ''f'' is a one-dimensional function, f:\mathbb R\to\mathbb R, and assume that it is unimodal, that is, contains exactly one local minimum ''x''* in a given interval 'a'',''z'' This means that ''f'' is strictly decreasing in ,x*and strictly increasing in *,''z'' There are several ways to find an (approximate) minimum point in this case. Zero-order methods Zero-order methods use only function evaluations (i.e., a value oracle) - not derivatives: * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planner Programming Language
Planner (often seen in publications as "PLANNER" although it is not an acronym) is a programming language designed by Carl Hewitt at MIT, and first published in 1969. First, subsets such as Micro-Planner and Pico-Planner were implemented, and then essentially the whole language was implemented as ''Popler'' by Julian Davies at the University of Edinburgh in the POP-2 programming language. Derivations such as QA4, Conniver, QLISP and Ether (see scientific community metaphor) were important tools in artificial intelligence research in the 1970s, which influenced commercial developments such as Knowledge Engineering Environment (KEE) and Automated Reasoning Tool (ART). Procedural approach versus logical approach The two major paradigms for constructing semantic software systems were procedural and logical. The procedural paradigm was epitomized by Lisp which featured recursive procedures that operated on list structures. The logical paradigm was epitomized by uniform proof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sudoku Solved By Bactracking
Sudoku (; ; originally called Number Place) is a logic-based, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution. French newspapers featured similar puzzles in the 19th century, and the modern form of the puzzle first appeared in 1979 puzzle books by Dell Magazines under the name Number Place. However, the puzzle type only began to gain widespread popularity in 1986 when it was published by the Japanese puzzle company Nikoli under the name Sudoku, meaning "single number". In newspapers outside of Japan, it first appeared in ''The Conway Daily Sun'' (New Hampshire) in September 2004, and then ''The Times'' (London) in Novem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Processing Unit
A central processing unit (CPU), also called a central processor, main processor, or just processor, is the primary Processor (computing), processor in a given computer. Its electronic circuitry executes Instruction (computing), instructions of a computer program, such as arithmetic, logic, controlling, and input/output (I/O) operations. This role contrasts with that of external components, such as main memory and I/O circuitry, and specialized coprocessors such as graphics processing units (GPUs). The form, CPU design, design, and implementation of CPUs have changed over time, but their fundamental operation remains almost unchanged. Principal components of a CPU include the arithmetic–logic unit (ALU) that performs arithmetic operation, arithmetic and Bitwise operation, logic operations, processor registers that supply operands to the ALU and store the results of ALU operations, and a control unit that orchestrates the #Fetch, fetching (from memory), #Decode, decoding and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean-valued Function
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = ), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information. In the formal sciences, mathematics, mathematical logic, statistics, and their applied disciplines, a Boolean-valued function may also be referred to as a characteristic function, indicator function, predicate, or proposition. In all of these uses, it is understood that the various terms refer to a mathematical object and not the corresponding semiotic sign or syntactic expression. In formal semantic theories of truth, a truth predicate is a predicate on the sentences of a formal language, interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Depth-first Search
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking. Extra memory, usually a stack, is needed to keep track of the nodes discovered so far along a specified branch which helps in backtracking of the graph. A version of depth-first search was investigated in the 19th century by French mathematician Charles Pierre Trémaux as a strategy for solving mazes. Properties The time and space analysis of DFS differs according to its application area. In theoretical computer science, DFS is typically used to traverse an entire graph, and takes time where , V, is the number of vertices and , E, the number of edges. This is linear in the size of the graph. In these applications it also uses space O(, V, ) in the worst case to store the stack of vertices on t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursion (computer Science)
In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves such recursion, recursive problems by using function (computer science), functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science. Most computer programming languages support recursion by allowing a function to call itself from within its own code. Some functional programming languages (for instance, Clojure) do not define any looping constructs but rely solely on recursion to repeatedly call code. It is proved in computability theory that these recursive-only languages are Turing complete; this means that they are as powerful (they can be used to solve the same problems) as imperative languages based on control structures such as and . Repeatedly calling a function from within itse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree Structure
A tree structure, tree diagram, or tree model is a way of representing the hierarchical nature of a structure in a graphical form. It is named a "tree structure" because the classic representation resembles a tree, although the chart is generally upside down compared to a biological tree, with the "stem" at the top and the "leaves" at the bottom. A tree structure is conceptual, and appears in several forms. For a discussion of tree structures in specific fields, see Tree (data structure) for computer science; insofar as it relates to graph theory, see tree (graph theory) or tree (set theory). Other related articles are listed below. Terminology and properties The tree elements are called "nodes". The lines connecting elements are called "branches". Nodes without children are called leaf nodes, "end-nodes", or "leaves". Every finite tree structure has a member that has no superior. This member is called the "root" or root node. The root is the starting node. But the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SNOBOL
SNOBOL ("StriNg Oriented and symBOlic Language") is a series of programming languages developed between 1962 and 1967 at AT&T Bell Laboratories by David J. Farber, Ralph Griswold and Ivan P. Polonsky, culminating in SNOBOL4. It was one of a number of text-string-oriented languages developed during the 1950s and 1960s; others included COMIT and TRAC. Despite the similar name, it is entirely unlike COBOL. SNOBOL4 stands apart from most programming languages of its era by having patterns as a first-class data type, a data type whose values can be manipulated in all ways permitted to any other data type in the programming language, and by providing operators for pattern concatenation and alternation. SNOBOL4 patterns are a type of object and admit various manipulations, much like later object-oriented languages such as JavaScript whose patterns are known as regular expressions. In addition SNOBOL4 strings generated during execution can be treated as programs and either inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amsterdam
Amsterdam ( , ; ; ) is the capital of the Netherlands, capital and Municipalities of the Netherlands, largest city of the Kingdom of the Netherlands. It has a population of 933,680 in June 2024 within the city proper, 1,457,018 in the City Region of Amsterdam, urban area and 2,480,394 in the Amsterdam metropolitan area, metropolitan area. Located in the Provinces of the Netherlands, Dutch province of North Holland, Amsterdam is colloquially referred to as the "Venice of the North", for its canals of Amsterdam, large number of canals, now a World Heritage Site, UNESCO World Heritage Site. Amsterdam was founded at the mouth of the Amstel River, which was dammed to control flooding. Originally a small fishing village in the 12th century, Amsterdam became a major world port during the Dutch Golden Age of the 17th century, when the Netherlands was an economic powerhouse. Amsterdam was the leading centre for finance and trade, as well as a hub of secular art production. In the 19th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elsevier
Elsevier ( ) is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell (journal), Cell'', the ScienceDirect collection of electronic journals, ''Trends (journals), Trends'', the ''Current Opinion (Elsevier), Current Opinion'' series, the online citation database Scopus, the SciVal tool for measuring research performance, the ClinicalKey search engine for clinicians, and the ClinicalPath evidence-based cancer care service. Elsevier's products and services include digital tools for Data management platform, data management, instruction, research analytics, and assessment. Elsevier is part of the RELX Group, known until 2015 as Reed Elsevier, a publicly traded company. According to RELX reports, in 2022 Elsevier published more than 600,000 articles annually in over 2,800 journals. As of 2018, its archives contained over 17 million documents and 40,000 Ebook, e-books, with over one b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derrick Henry Lehmer
Derrick Henry "Dick" Lehmer (February 23, 1905 – May 22, 1991), almost always cited as D.H. Lehmer, was an American mathematician significant to the development of computational number theory. Lehmer refined Édouard Lucas' work in the 1930s and devised the Lucas–Lehmer test for Mersenne primes. His peripatetic career as a number theorist, with him and his wife taking numerous types of work in the United States and abroad to support themselves during the Great Depression, fortuitously brought him into the center of research into early electronic computing. Early life Lehmer was born in Berkeley, California, to Derrick Norman Lehmer, a professor of mathematics at the University of California, Berkeley, and Clara Eunice Mitchell. He studied physics and earned a bachelor's degree from UC Berkeley, and continued with graduate studies at the University of Chicago. He and his father worked together on Lehmer sieves. Marriage During his studies at Berkeley, Lehmer met Emma Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
