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Backtracking
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] |
Algorithmics Of Sudoku
A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box. A Sudoku starts with some cells containing numbers (''clues''), and the goal is to solve the remaining cells. Proper Sudokus have one solution. Players and investigators use a wide range of computer algorithms to solve Sudokus, study their properties, and make new puzzles, including Sudokus with interesting symmetries and other properties. There are several computer algorithms that will solve 9×9 puzzles (=9) in fractions of a second, but combinatorial explosion occurs as increases, creating limits to the properties of Sudokus that can be constructed, analyzed, and solved as increases. Techniques Backtracking Some hobbyists have developed computer programs that will solve Sudoku p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eight Queens Puzzle
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. The problem was first posed in the mid-19th century. In the modern era, it is often used as an example problem for various computer programming techniques. The eight queens puzzle is a special case of the more general ''n'' queens problem of placing ''n'' non-attacking queens on an ''n''×''n'' chessboard. Solutions exist for all natural numbers ''n'' with the exception of ''n'' = 2 and ''n'' = 3. Although the exact number of solutions is only known for ''n'' ≤ 27, the asymptotic growth rate of the number of solutions is (0.143 ''n'')''n''. History Chess composer Max Bezzel published the eight queens puzzle in 1848. Franz Nauck published the first solutions in 1850.W. W. Rouse Ball (1960) "The Eight Queens Problem", in ''Mathemati ... [...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.Carl Hewitt Middle History of Logic Programming: Resolution, Planner, Prolog and the Japanese Fifth Generation Project ArXiv 2009. 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 Lis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Search
In optimization, the line search strategy is one of two basic iterative approaches to find a local minimum \mathbf^* of an objective function f:\mathbb R^n\to\mathbb R. The other approach is trust region. The line search approach 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. Example use Here is an example gradient method that uses a line search in step 4. # Set iteration counter \displaystyle k=0, and make an initial guess \mathbf_0 for the minimum # Repeat: # Compute a descent direction \mathbf_k # Choose \displaystyle \alpha_k to 'loosely' minimize h(\alpha_k)=f(\mathbf_k+\alpha_k\mathbf_k) over \alpha_k\in\mathbb R_+ # &nbs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Satisfaction Problem
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems. Additionally, Boolean satisfiability problem (SAT), the satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parsing
Parsing, syntax analysis, or syntactic analysis is the process of analyzing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar. The term ''parsing'' comes from Latin ''pars'' (''orationis''), meaning part (of speech). The term has slightly different meanings in different branches of linguistics and computer science. Traditional sentence parsing is often performed as a method of understanding the exact meaning of a sentence or word, sometimes with the aid of devices such as sentence diagrams. It usually emphasizes the importance of grammatical divisions such as subject and predicate. Within computational linguistics the term is used to refer to the formal analysis by a computer of a sentence or other string of words into its constituents, resulting in a parse tree showing their syntactic relation to each other, which may also contain semantic and other information ( p-values). Some parsing algo ... [...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'', the ScienceDirect collection of electronic journals, '' Trends'', the '' 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 also include digital tools for 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 2021 Elsevier published more than 600,000 articles annually in over 2,700 journals; as of 2018 its archives contained over 17 million documents and 40,000 e-books, with over one billion annual downloads. Researchers have criticized Elsevier for its high profit ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Procedural Parameter
In computing, a procedural parameter is a parameter of a procedure that is itself a procedure. This concept is an extremely powerful and versatile programming tool, because it allows programmers to modify certain steps of a library procedure in arbitrarily complicated ways, without having to understand or modify the code of that procedure. This tool is particularly effective and convenient in languages that support local function definitions, such as Pascal and the modern GNU dialect of C. It is even more so when function closures are available. The same functionality (and more) is provided by objects in object oriented programming languages, but at a significantly higher cost. Procedural parameters are somewhat related to the concepts of first-class function and anonymous function, but is distinct from them. These two concepts have more to do with how functions are defined, rather than how they are used. Basic concept In most languages that provide this feature, a proc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metaheuristic
In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity. Metaheuristics sample a subset of solutions which is otherwise too large to be completely enumerated or otherwise explored. Metaheuristics may make relatively few assumptions about the optimization problem being solved and so may be usable for a variety of problems. Compared to optimization algorithms and iterative methods, metaheuristics do not guarantee that a globally optimal solution can be found on some class of problems. Many metaheuristics implement some form of stochastic optimization, so that the solution found is dependent on the set of random variables generated. In combinatorial optimization, by searching over a large set of fea ... [...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 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 Markov ... [...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 E. 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. SNOBOL4 stands apart from most programming languages of its era by having patterns as a first-class data type (''i.e.'' 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 interpreted or compiled and executed (as in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amsterdam
Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the Capital of the Netherlands, capital and Municipalities of the Netherlands, most populous city of the Netherlands, with The Hague being the seat of government. It has a population of 907,976 within the city proper, 1,558,755 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 large number of canals, now designated a World Heritage Site, UNESCO World Heritage Site. Amsterdam was founded at the mouth of the Amstel River that was dammed to control flooding; the city's name derives from the Amstel dam. Originally a small fishing village in the late 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 is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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