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Shunting-yard Algorithm
In computer science, the shunting yard algorithm is a method for parsing arithmetical or logical expressions, or a combination of both, specified in infix notation. It can produce either a postfix notation string, also known as Reverse Polish notation (RPN), or an abstract syntax tree (AST). The algorithm was invented by Edsger Dijkstra and named the "shunting yard" algorithm because its operation resembles that of a railroad shunting yard. Dijkstra first described the shunting yard algorithm in the Mathematisch Centrum reporMR 34/61 Like the evaluation of RPN, the shunting yard algorithm is stack-based. Infix expressions are the form of mathematical notation most people are used to, for instance or . For the conversion there are two text variables ( strings), the input and the output. There is also a stack that holds operators not yet added to the output queue. To convert, the program reads each symbol in order and does something based on that symbol. The result for the a ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Queue (data Structure)
In computer science, a queue is a collection of entities that are maintained in a sequence and can be modified by the addition of entities at one end of the sequence and the removal of entities from the other end of the sequence. By convention, the end of the sequence at which elements are added is called the back, tail, or rear of the queue, and the end at which elements are removed is called the head or front of the queue, analogously to the words used when people line up to wait for goods or services. The operation of adding an element to the rear of the queue is known as ''enqueue'', and the operation of removing an element from the front is known as ''dequeue''. Other operations may also be allowed, often including a ''peek'' or ''front'' operation that returns the value of the next element to be dequeued without dequeuing it. The operations of a queue make it a first-in-first-out (FIFO) data structure. In a FIFO data structure, the first element added to the queue will ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stack-sortable Permutation
In mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a single stack data structure. The stack-sortable permutations are exactly the permutations that do not contain the permutation pattern 231; they are counted by the Catalan numbers, and may be placed in bijection with many other combinatorial objects with the same counting function including Dyck paths and binary trees. Sorting with a stack The problem of sorting an input sequence using a stack was first posed by , who gave the following linear time algorithm (closely related to algorithms for the later all nearest smaller values problem): *Initialize an empty stack *For each input value ''x'': **While the stack is nonempty and ''x'' is larger than the top item on the stack, pop the stack to the output **Push ''x'' onto the stack *While the stack is nonempty, pop it to the output K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reverse Polish Notation
Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators ''follow'' their operands, in contrast to Polish notation (PN), in which operators ''precede'' their operands. It does not need any parentheses as long as each operator has a fixed number of operands. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924. The first computer to use postfix notation, though it long remained essentially unknown outside of Germany, was Konrad Zuse's Z3 in 1941 as well as his Z4 in 1945. The reverse Polish scheme was again proposed in 1954 by Arthur Burks, Don Warren, and Jesse Wright and was independently reinvented by Friedrich L. Bauer and Edsger W. Dijkstra in the early 1960s to reduce computer memory access and use the stack to evaluate expressions. The algorithms and notation for this scheme were extended ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_. The exponent is usually shown as a superscript to the right of the base. In that case, is called "''b'' raised to the ''n''th power", "''b'' (raised) to the power of ''n''", "the ''n''th power of ''b''", "''b'' to the ''n''th power", or most briefly as "''b'' to the ''n''th". Starting from the basic fact stated above that, for any positive integer n, b^n is n occurrences of b all multiplied by each other, several other properties of exponentiation directly follow. In particular: \begin b^ & = \underbrace_ \\ ex& = \underbrace_ \times \underbrace_ \\ ex& = b^n \times b^m \end In other words, when multiplying a base raised to one e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Associativity
In programming language theory, the associativity of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses. If an operand is both preceded and followed by operators (for example, ^ 3 ^), and those operators have equal precedence, then the operand may be used as input to two different operations (i.e. the two operations indicated by the two operators). The choice of which operations to apply the operand to, is determined by the associativity of the operators. Operators may be associative (meaning the operations can be grouped arbitrarily), left-associative (meaning the operations are grouped from the left), right-associative (meaning the operations are grouped from the right) or non-associative (meaning operations cannot be chained, often because the output type is incompatible with the input types). The associativity and precedence of an operator is a part of the definition of the programming language; different p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Notation
Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators ''precede'' their operands, in contrast to the more common infix notation, in which operators are placed ''between'' operands, as well as reverse Polish notation (RPN), in which operators ''follow'' their operands. It does not need any parentheses as long as each operator has a fixed number of operands. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924. The term ''Polish notation'' is sometimes taken (as the opposite of ''infix notation'') to also include reverse Polish notation. When Polish notation is used as a syntax for mathematical expressions by programming language interpreters, it is readily parsed into abstract syntax trees and can, in fact, define a one-to-one representation for the same. Because ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of Operations
In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. Thus, the expression is interpreted to have the value , and not . When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base. Thus and . These conventions exist to eliminate notational ambiguity, while allowing notation to be as brief as possible. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used. For example, forces addition to precede multipl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Token (parser)
In computer science, lexical analysis, lexing or tokenization is the process of converting a sequence of characters (such as in a computer program or web page) into a sequence of ''lexical tokens'' ( strings with an assigned and thus identified meaning). A program that performs lexical analysis may be termed a ''lexer'', ''tokenizer'', or ''scanner'', although ''scanner'' is also a term for the first stage of a lexer. A lexer is generally combined with a parser, which together analyze the syntax of programming languages, web pages, and so forth. Applications A lexer forms the first phase of a compiler frontend in modern processing. Analysis generally occurs in one pass. In older languages such as ALGOL, the initial stage was instead line reconstruction, which performed unstropping and removed whitespace and comments (and had scannerless parsers, with no separate lexer). These steps are now done as part of the lexer. Lexers and parsers are most often used for compilers, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wye Junction
In railroad structures, and rail terminology, a wye (like the'' 'Y' '' glyph) or triangular junction (often shortened to just "triangle") is a triangular joining arrangement of three rail lines with a railroad switch (set of points) at each corner connecting to each incoming line. A turning wye is a specific case. Where two rail lines join, or in a joint between a railroad's mainline and a spur, wyes can be used at a mainline rail junction to allow incoming trains the ability to travel in either direction, or in order to allow trains to pass from one line to the other line. Wyes can also be used for turning railway equipment, and generally cover less area than a balloon loop doing the same job, but at the cost of two additional sets of points to construct, then maintain. These turnings are accomplished by performing the railway equivalent of a three-point turn through successive junctions of the wye, the direction of travel and the relative orientation of a locomotive or ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shunting Yard
Shunting yard may refer to: * Classification yard * Shunting yard algorithm * British term for rail yard A rail yard, railway yard, railroad yard (US) or simply yard, is a series of tracks in a rail network for storing, sorting, or loading and unloading rail vehicles and locomotives. Yards have many tracks in parallel for keeping rolling stock or ... {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
