The word algorithm is derived from the Latin translation, Algoritmi de numero Indorum, of the 9th-century Persian mathematician Muhammad ibn Musa al-Khwarizmi's arithmetic treatise “Al-Khwarizmi Concerning the Hindu Art of Reckoning”. Arabic mathematicians such as al-Kindi in the 9th century used cryptographic algorithms for code-breaking, based on frequency analysis. Greek mathematicians later used algorithms in 240 BC in the sieve of Eratosthenes for finding prime numbers, and the Euclidean algorithm for finding the greatest common divisor of two numbers. Arithmetic algorithms, such as a division algorithm, were used by ancient Babylonian mathematicians c. The concept of algorithms has existed since antiquity. The transition from one state to the next is not necessarily deterministic some algorithms, known as randomized algorithms, incorporate random input. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. Īs an effective method, an algorithm can be expressed within a finite amount of space and time, and in a well-defined formal language for calculating a function. In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually. Algorithms are used as specifications for performing calculations and data processing. In mathematics and computer science, an algorithm ( / ˈ æ l ɡ ə r ɪ ð əm/ ( listen)) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation.
Ada Lovelace's diagram from "note G", the first published computer algorithm
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