In mathematics and computer science, an algorithm ) is a set of instructions, typically to solve a class of problems or perform a computation. Algorithms are unambiguous specifications for performing calculation, data processing, automated reasoning, and other tasks.
As an effective method, an algorithm can be expressed within a finite amount of space and time Starting from an initial state and initial input , 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.
Greek mathematicians used algorithms in the sieve of Eratosthenes for finding prime numbers, and the Euclidean algorithm for finding the greatest common divisor of two numbers.
A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem posed by David Hilbert in 1928.Later formalizations were framed as attempts to define “effective calculability” Those formalizations included the GdelHerbrandKleene 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 193637 and 1939.
