algorithm (redirected from algorithmically)

algorithm (ăl`gərĭth'əm) or algorism (–rĭz'əm) [for Al-Khowarizmi], a clearly defined procedure for obtaining the solution to a general type of problem, often numerical. Much of ordinary arithmetic as traditionally taught consists of algorithms involving the fundamental operations of addition, subtraction, multiplication, and division. An example of an algorithm is the common procedure for division, e.g., the division of 1,347 by 8, in which the remainders of partial divisions are carried to the next digit or digits; in this case the remainder of 5 in the division of 13 by 8 is placed in front of the 4, and 8 is then divided into 54. The software that instructs modern computers embodies algorithms, often of great sophistication.

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algorithm

Procedure that produces the answer to a question or the solution to a problem in a finite number of steps. An algorithm that produces a yes or no answer is called a decision procedure; one that leads to a solution is a computation procedure. A mathematical formula and the instructions in a computer program are examples of algorithms. Euclid's Elements (c. 300 BC) contained an algorithm for finding the greatest common divisor of two integers. Manipulation of lists (searching for, inserting, and removing items) can be done efficiently by using algorithms.

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algorithm

A set of ordered steps for solving a problem, such as a mathematical formula or the instructions in a program. The terms algorithm and logic are synonymous. Both refer to a sequence of steps to solve a problem. However, an algorithm implies an expression that solves a complex problem rather than the overall input-process-output logic of typical business programs. See encryption algorithm.

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algorithm

1. a logical arithmetical or computational procedure that if correctly applied ensures the solution of a problem

2. Logic Maths a recursive procedure whereby an infinite sequence of terms can be generated

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Algorithm

A well-defined procedure to solve a problem. The study of algorithms is a fundamental area of computer science. In writing a computer program to solve a problem, a programmer expresses in a computer language an algorithm that solves the problem, thereby turning the algorithm into a computer program. See Computer programming

Operation

An algorithm generally takes some input, carries out a number of effective steps in a finite amount of time, and produces some output. An effective step is an operation so basic that it is possible, at least in principle, to carry it out using pen and paper. In computer science theory, a step is considered effective if it is feasible on a Turing machine or any of its equivalents. A Turing machine is a mathematical model of a computer used in an area of study known as computability, which deals with such questions as what tasks can be algorithmically carried out and what cannot. See Automata theory

Many computer programs deal with a substantial amount of data. In such applications, it is important to organize data in appropriate structures to make it easier or faster to process the data. In computer programming, the development of an algorithm and the choice of appropriate data structures are closely intertwined, and a decision regarding one often depends on knowledge of the other. Thus, the study of data structures in computer science usually goes hand in hand with the study of related algorithms. Commonly used elementary data structures include records, arrays, linked lists, stacks, queues, trees, and graphs.

Applications

Many algorithms are useful in a broad spectrum of computer applications. These elementary algorithms are widely studied and considered an essential component of computer science. They include algorithms for sorting, searching, text processing, solving graph problems, solving basic geometric problems, displaying graphics, and performing common mathematical calculations.

Sorting arranges data objects in a specific order, for example, in numerically ascending or descending orders. Internal sorting arranges data stored internally in the memory of a computer. Simple algorithms for sorting by selection, by exchange, or by insertion are easy to understand and straightforward to code. However, when the number of objects to be sorted is large, the simple algorithms are usually too slow, and a more sophisticated algorithm, such as heap sort or quick sort, can be used to attain acceptable performance. External sorting arranges stored data records.

Searching looks for a desired data object in a collection of data objects. Elementary searching algorithms include linear search and binary search. Linear search examines a sequence of data objects one by one. Binary search adopts a more sophisticated strategy and is faster than linear search when searching a large array. A collection of data objects that are to be frequently searched can also be stored as a tree. If such a tree is appropriately structured, searching the tree will be quite efficient.

A text string is a sequence of characters. Efficient algorithms for manipulating text strings, such as algorithms to organize text data into lines and paragraphs and to search for occurrences of a given pattern in a document, are essential in a word processing system. A source program in a high-level programming language is a text string, and text processing is a necessary task of a compiler. A compiler needs to use efficient algorithms for lexical analysis (grouping individual characters into meaningful words or symbols) and parsing (recognizing the syntactical structure of a source program). See Software engineering

A graph is useful for modeling a group of interconnected objects, such as a set of locations connected by routes for transportation. Graph algorithms are useful for solving those problems that deal with objects and their connections—for example, determining whether all of the locations are connected, visiting all of the locations that can be reached from a given location, or finding the shortest path from one location to another.

Mathematical algorithms are of wide application in science and engineering. Basic algorithms for mathematical computation include those for generating random numbers, performing operations on matrices, solving simultaneous equations, and numerical integration. Modern programming languages usually provide predefined functions for many common computations, such as random number generation, logarithm, exponentiation, and trigonometric functions.

In many applications, a computer program needs to adapt to changes in its environment and continue to perform well. An approach to make a computer program adaptive is to use a self-organizing data structure, such as one that is reorganized regularly so that those components most likely to be accessed are placed where they can be most efficiently accessed. A self-modifying algorithm that adapts itself is also conceivable. For developing adaptive computer programs, biological evolution has been a source of ideas and has inspired evolutionary computation methods such as genetic algorithms. See Genetic algorithms

Certain applications require a tremendous amount of computation to be performed in a timely fashion. An approach to save time is to develop a parallel algorithm that solves a given problem by using a number of processors simultaneously. The basic idea is to divide the given problem into subproblems and use each processor to solve a subproblem. The processors usually need to communicate among themselves so that they may cooperate. The processors may share memory, through which they can communicate, or they may be connected by communication links into some type of network such as a hypercube. See Concurrent processing, Multiprocessing, Supercomputer

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(algorithm, programming)

algorithm - A detailed sequence of actions to perform to accomplish some task. Named after the Iranian mathematician, Mohammed Al-Khawarizmi. Technically, an algorithm must reach a result after a finite number of steps, thus ruling out brute force search methods for certain problems, though some might claim that brute force search was also a valid (generic) algorithm. The term is also used loosely for any sequence of actions (which may or may not terminate). Paul E. Black's Dictionary of Algorithms, Data Structures, and Problems.