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In mathematics and computer science, an algorithm i/ˈælɡərɪðəm/ is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning. In simple words an algorithm is a step-by-step procedure for calculations.
Starting from an initial state and initial input (perhaps empty),] the instructions describe a computation that, when executed, will proceed through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.
The first algorithm ever proposed was a theoretical work by countess Ada Lovelace during her notes translating Luigi Menabrea's paper on the analytical engine of Charles Babbage from Italian in 1842 and 1843, though her work was never compiled or run on a functioning computer in her own time, since Babbage's theoretical computer was never completed. A partial formalization of the concept began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.
Source:
http://en.wikipedia.org/wiki/Algorithm
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