About 825, he wrote a treatise in the Arabic language, which was translated into Latin in the 12th century under the title Algoritmi de numero Indorum.

So far, this discussion of the formalization of an algorithm has assumed the premises of imperative programming.

This is the most common conception, and it attempts to describe a task in discrete, "mechanical" means.

English adopted the French term, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English.

Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu.

Similarly, IF A -gə-ridh-əm) is an unambiguous specification of how to solve a class of problems.

Algorithms can perform calculation, data processing and automated reasoning tasks.

Flow chart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in 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 the number b in location B is greater than or equal to the number a in location A) THEN, the algorithm specifies B ← B − A (meaning the number b − a replaces the old b).

Because an algorithm is a precise list of precise steps, the order of computation is always crucial to the functioning of the algorithm.

Instructions are usually assumed to be listed explicitly, and are described as starting "from the top" and going "down to the bottom", an idea that is described more formally by flow of control.

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