algorithm

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

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

For some alternate conceptions of what constitutes an algorithm see functional programming and logic programming.

:: "... prose to describe an algorithm, ignoring the implementation details.

: For an example of the simple algorithm " Add m + n " described in all three levels see Algorithm examples.

In computer systems, an algorithm is basically an instance of logic written in software by software developers to be effective for the intended " target " computer ( s ), in order for the target machines to produce output from given input ( perhaps null ).

is the length of time taken to perform the algorithm.

.. Other criteria are adaptability of the algorithm to computers, its simplicity and elegance, etc "

Algorithm versus function computable by an algorithm: For a given function multiple algorithms may exist.

important to distinguish between the notion of algorithm, i. e. procedure and the notion of function computable by algorithm, i. e. mapping yielded by procedure.

An example of using Euclid's algorithm will be shown below.

Simulation of an algorithm: computer ( computor ) language: Knuth advises the reader that " the best way to learn an algorithm is to try it.

The programmer must translate the algorithm into a language that the simulator / computer / computor can effectively execute.

If they don't then for the algorithm to be effective it must provide a set of rules for extracting a square root.

For example, the subprogram in Euclid's algorithm to compute the remainder would execute much faster if the programmer had a " modulus " ( division ) instruction available rather than just subtraction ( or worse: just Minsky's " decrement ").

Structured programming, canonical structures: Per the Church-Turing thesis any algorithm can be computed by a model known to be Turing complete, and per Minsky's demonstrations Turing completeness requires only four instruction types — conditional GOTO, unconditional GOTO, assignment, HALT.

Canonical flowchart symbols: The graphical aide called a flowchart offers a way to describe and document an algorithm ( and a computer program of one ).

An animation of the quicksort | quicksort algorithm sorting an array of randomized values.

From this follows a simple algorithm, which can be stated in a high-level description English prose, as:

Written in prose but much closer to the high-level language of a computer program, the following is the more formal coding of the algorithm in pseudocode or pidgin code:

The example-diagram of Euclid's algorithm from T. L.

Euclid ’ s algorithm appears as Proposition II in Book VII (" Elementary Number Theory ") of his Elements.

While Nicomachus ' algorithm is the same as Euclid's, when the numbers are prime to one another it yields the number " 1 " for their common measure.