In mathematics, computer science and related disciplines, an algorithm (Latin dixit Algorithmus and this in turn from Persian mathematician al-Khwarizmi) is a well-defined list, ordered and finite operations able to find a solution to a problem. Given an initial state and an input, through well-defined successive steps leads to a final state, obtaining a solution. The algorithms are studied in the algorithms, and its definition is formalized by the computational model of the Turing machine.
Its importance lies in showing how to implement processes and solve mathematical problems mechanically or otherwise. As mathematical functions, algorithms receive an input and transform it into an outlet, behaving like a black box. However, for an algorithm can be considered as such, must be deterministic, efficient, have a number Instruction finite and must end. By deterministic means that if you follow the same process more than once, always comes to the same result, for efficient, time-consuming and memory should be near or be the minimum.
The concept of algorithm, although similar and obviously related, not to be confused with the concept of program. While the first is the specification of a set of steps (operations, instructions, orders ,...) oriented problem solving, the second is the set of operations specified in a particular programming language and for a specific computer, capable of being executed (or compiled or interpreted). An algorithm, strictly speaking, can not run until it is implemented, either in a programming language in an electrical circuit, a mechanical device, using paper and pencil, or some other model of computation.
In everyday life algorithms are used many times to solve different problems. Some examples are found in the instructions (user manuals), which show the algorithms to use the device in question or even in a worker receives instructions from his employer. There are also examples of mathematics such as the division algorithm to calculate the ratio of two numbers, the Euclidean algorithm to compute the maximum common divisor of two positive integers, or the Gauss method for solving a linear system of equations.
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