Algorithm
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This is an algorithm that tries to figure out why the lamp doesn't turn on and tries to fix it using the steps. Flowcharts are often used to graphically represent algorithms.In mathematics, computer science, and related subjects, an algorithm is an effective method for solving a problem using a finite sequence of instructions. Algorithms are used for calculation, data processing, and many other fields.
Each algorithm is a list of well-defined instructions for completing a task. Starting from an initial state, the instructions describe a computation that proceeds through a well-defined series of successive states, eventually terminating in a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate randomness.
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"[1] or "effective method"[2]; 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.
Contents [hide]
1 Etymology
2 Why algorithms are necessary: an informal definition
3 Formalization
3.1 Termination
3.2 Expressing algorithms
3.3 Computer algorithms
3.4 Implementation
4 Example
5 Algorithmic analysis
5.1 Formal versus empirical
6 Classification
6.1 By implementation
6.2 By design paradigm
6.3 By field of study
6.4 By complexity
6.5 By computing power
7 Legal issues
8 History: Development of the notion of "algorithm"
8.1 Origin of the word
8.2 Discrete and distinguishable symbols
8.3 Manipulation of symbols as "place holders" for numbers: algebra
8.4 Mechanical contrivances with discrete states
8.5 Mathematics during the 1800s up to the mid-1900s
8.6 Emil Post (1936) and Alan Turing (1936-7, 1939)
8.7 J. B. Rosser (1939) and S. C. Kleene (1943)
8.8 History after 1950
9 See also
10 Notes
11 References
11.1 Secondary references
12 Further reading
13 External links
[edit] Etymology
Al-Khwārizmī, Persian astronomer and mathematician, wrote a treatise in 825 AD, On Calculation with Hindu Numerals. (See algorism). It was translated into Latin in the 12th century as Algoritmi de numero Indorum (al-Daffa 1977), whose title is supposedly likely intended to mean "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's rendition of the author's name; but people misunderstanding the title treated Algoritmi as a Latin plural and this led to the word "algorithm" (Latin algorismus) coming to mean "calculation method". The intrusive "th" is most likely due to a false cognate with the Greek ἀριθμός (arithmos) meaning "numbers".
