## Algorithm |

in

andmathematics , ancomputer science **algorithm**( / (əm listen )) is a finite sequence of , computer-implementable instructions, typically to solve a class of problems or to perform a computation.well-defined ^{[1]}^{[2]}algorithms are always and are used as specifications for performingunambiguous ,calculations ,data processing , and other tasks.automated reasoning as an

, an algorithm can be expressed within a finite amount of space and time,effective method ^{[3]}and in a well-defined formal language^{[4]}for calculating a .function ^{[5]}starting from an initial state and initial input (perhaps ),empty ^{[6]}the instructions describe a that, whencomputation , proceeds through a finiteexecuted ^{[7]}number of well-defined successive states, eventually producing "output"^{[8]}and terminating at a final ending state. the transition from one state to the next is not necessarily ; some algorithms, known asdeterministic , incorporate random input.randomized algorithms ^{[9]}the concept of algorithm has existed since antiquity.

algorithms, such as aarithmetic , was used by ancientdivision algorithm c. 2500 bc andbabylonian mathematicians c. 1550 bc.egyptian mathematicians ^{[10]} later used algorithms in thegreek mathematicians for finding prime numbers,sieve of eratosthenes ^{[11]}and the for finding theeuclidean algorithm of two numbers.greatest common divisor ^{[12]} such asarabic mathematicians in the 9th century usedal-kindi algorithms forcryptographic , based oncode-breaking .frequency analysis ^{[13]}the word

*algorithm*itself is derived from the 9th-century mathematicianpersian , latinizedmuḥammad ibn mūsā al-khwārizmī *algoritmi*.^{[14]}a partial formalization of what would become the modern concept of algorithm began with attempts to solve the (decision problem) posed byentscheidungsproblem in 1928. later formalizations were framed as attempts to define "david hilbert "effective calculability ^{[15]}or "effective method".^{[16]}those formalizations included the –gödel –herbrand kleene of 1930, 1934 and 1935,recursive functions 'salonzo church of 1936,lambda calculus 'semil post of 1936, andformulation 1 'salan turing of 1936–37 and 1939.turing machines - etymology
- informal definition
- formalization
- design
- implementation
- computer algorithms
- examples
- algorithmic analysis
- classification
- continuous algorithms
- legal issues
- history: development of the notion of "algorithm"
- see also
- notes
- bibliography
- further reading
- external links

In **algorithm** (^{[1]}^{[2]} Algorithms are always

As an ^{[3]} and in a well-defined formal language^{[4]} for calculating a ^{[5]} Starting from an initial state and initial input (perhaps ^{[6]} the instructions describe a ^{[7]} number of well-defined successive states, eventually producing "output"^{[8]} and terminating at a final ending state. The transition from one state to the next is not necessarily ^{[9]}

The concept of algorithm has existed since antiquity. ^{[10]} ^{[11]} and the ^{[12]} ^{[13]}

The word *algorithm* itself is derived from the 9th-century *Algoritmi*.^{[14]} A partial formalization of what would become the modern concept of algorithm began with attempts to solve the ^{[15]} or "effective method".^{[16]} Those formalizations included the