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Algorithms are often studied abstractly, without referencing any specific programming language or implementation. Algorithm analysis resembles other mathematical disciplines as it focuses on the algorithm's properties, not implementation. Pseudocode is typical for analysis as it is a simple and general representation.
Algorithms have become synonymous with something highly technical and difficult to understand, that is either an arbiter of objective truth, or, on the other end of the spectrum, something wholly ...
The word algorithm also derives from algorism, a generalization of the meaning to any set of rules specifying a computational procedure. Occasionally algorism is also used in this generalized meaning, especially in older texts.
Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the most practical, since they can be run on real machines efficiently. Formally, a deterministic algorithm computes a mathematical function ; a function has a unique value for any input in its domain , and the algorithm is a process that ...
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
The competitive ratio of an online problem is the best competitive ratio achieved by an online algorithm. Intuitively, the competitive ratio of an algorithm gives a measure on the quality of solutions produced by this algorithm, while the competitive ratio of a problem shows the importance of knowing the future for this problem.
Algorithm characterizations are attempts to formalize the word algorithm. Algorithm does not have a generally accepted formal definition. Researchers [1] are actively working on this problem. This article will present some of the "characterizations" of the notion of "algorithm" in more detail.
In elementary arithmetic, a standard algorithm or method is a specific method of computation which is conventionally taught for solving particular mathematical problems. . These methods vary somewhat by nation and time, but generally include exchanging, regrouping, long division, and long multiplication using a standard notation, and standard formulas for average, area, and vol