Algorithm From Wikipedia, the free encyclopedia "Algorithms" redirects here. For the journal, see Algorithms (journal). "Rule set" redirects here. For other uses, see Rule. Flow chart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbersa and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields "yes" (or true) (more accurately the number b in location B is greater than or equal to the number ain location A) THEN, the algorithm specifies B ← B − A (meaning the number b − a replaces the old b). Similarly, IF A > B, THEN A ← A − B. The process terminates when (the contents of) B is 0, yielding the g.c.d. in A. (Algorithm derived from Scott 2009:13; symbols and drawing style from Tausworthe 1977). In mathematics and computer science, an algorithm ( i / ˈ æ l ɡ ə r ɪ ð əm / AL-gə- ri-dhəm) is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning. An algorithm is an effective method that can be expressed within a finite amount of space and time [1] and in a well-defined formal language [2] for calculating a function. [3] Starting from an initial state and initial input (perhaps empty), [4] the instructions describe acomputation that, when executed, proceeds through a finite [5] number of well-defined successive states, eventually producing "output" [6] 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. [7] The concept of algorithm has existed for centuries, however a partial formalization of what would become the modern algorithm 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" [8] or "effective method"; [9] those formalizations included the Gödel–Herbrand– Kleenerecursive 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. [10]
AlgorithmFrom Wikipedia, the free encyclopedia"Algorithms"
redirects here. For the journal, seeAlgorithms (journal)."Rule set"
redirects here. For other uses, seeRule.
Flow chartof an algorithm (Euclid's algorithm) for calculating
the greatest common divisor (g.c.d.) of two numbersaandbin
locations named A and B. The algorithm proceeds by successive
subtractions in two loops: IF the test B A yields "yes" (or true)
(more accurately thenumberbin location B is greater than or equal
to thenumberain location A) THEN, the algorithm specifies B B A
(meaning the numberbareplaces the oldb). Similarly, IF A > B,
THEN A A B. The process terminates when (the contents of) B is 0,
yielding the g.c.d. in A. (Algorithm derived from Scott 2009:13;
symbols and drawing style from Tausworthe 1977).In mathematics
andcomputer science, analgorithm(i/lrm/al-g-ri-dhm) is a
self-contained step-by-step set of operations to be performed.
Algorithms exist that performcalculation,data processing,
andautomated reasoning.An algorithm is aneffective methodthat can
be expressed within a finite amount of space and time[1]and in a
well-defined formal language[2]for calculating
afunction.[3]Starting from an initial state and initial input
(perhapsempty),[4]the instructions describe acomputationthat,
whenexecuted, proceeds through a finite[5]number of well-defined
successive states, eventually producing "output"[6]and terminating
at a final ending state. The transition from one state to the next
is not necessarilydeterministic; some algorithms, known
asrandomized algorithms, incorporate random input.[7]The concept
ofalgorithmhas existed for centuries, however a partial
formalization of what would become the modernalgorithmbegan with
attempts to solve theEntscheidungsproblem(the "decision problem")
posed byDavid Hilbertin 1928. Subsequent formalizations were framed
as attempts to define "effective calculability"[8]or "effective
method";[9]those formalizations included
theGdelHerbrandKleenerecursive functionsof 1930, 1934 and
1935,Alonzo Church'slambda calculusof 1936,Emil Post's "Formulation
1" of 1936, andAlan Turing'sTuring machinesof 19367 and 1939.
Giving a formal definition of algorithms, corresponding to the
intuitive notion, remains a challenging problem.[10]
