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]