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 ).

In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.

More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.

While there is no generally accepted formal definition of " algorithm ," an informal definition could be " a set of rules that precisely defines a sequence of operations.

" For some people, a program is only an algorithm if it stops eventually ; for others, a program is only an algorithm if it stops before a given number of calculation steps.

A prototypical example of an algorithm is Euclid's algorithm to determine the maximum common divisor of two integers ; an example ( there are others ) is described by the flow chart above and as an example in a later section.

The concept of algorithm is also used to define the notion of decidability.

In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension.

Gurevich: "... Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ... according to Savage, an algorithm is a computational process defined by a Turing machine ".

Typically, when an algorithm is associated with processing information, data is read from an input source, written to an output device, and / or stored for further processing.

Stored data is regarded as part of the internal state of the entity performing the 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.

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.

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

In 2002, a theoretical attack, termed the " XSL attack ", was announced by Nicolas Courtois and Josef Pieprzyk, purporting to show a weakness in the AES algorithm due to its simple description .< ref >

* Martin Davis, author of the " Handbook of Artificial Reasoning ", co-inventor of the DPLL algorithm, recipient of the Herbrand Award 2005.

Huffman coding is the most known algorithm for deriving prefix codes, so prefix codes are also widely referred to as " Huffman codes ", even when the code was not produced by a Huffman algorithm.

" Difficult ", in this sense, is described in terms of the computational resources needed by the most efficient algorithm for a certain problem.

The ASCII codes for the word " Wikipedia ", given here in Binary numeral system | binary, provide a way of representing the word in information theory, as well as for information-processing algorithm s.

The word distributed in terms such as " distributed system ", " distributed programming ", and " distributed algorithm " originally referred to computer networks where individual computers were physically distributed within some geographical area.

* Unpropagated updates ; e. g. programmer changes " myAdd " but forgets to change " mySubtract ", which uses the same algorithm.

The µ-law algorithm ( sometimes written " mu-law ", or misspelled " u-law ") is a companding algorithm, primarily used in the digital telecommunication systems of North America and Japan.

The algorithm is as follows: take any number, square it, remove the middle digits of the resulting number as the " random number ", then use that number as the seed for the next iteration.

To avoid this, some graphics engine implementations " overrender ", drawing the affected edges of both polygons in the order given by painter's algorithm.

Although the purpose of Grover's algorithm is usually described as " searching a database ", it may be more accurate to describe it as " inverting a function ".

The algorithm that evaluates final board positions is termed the " evaluation function ", and these algorithms are often vastly different between different chess programs.

In Gottschalk v. Benson ( 1972 ), the United States Supreme Court ruled that a patent for a process should not be allowed if it would " wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself ", adding that " it is said that the decision precludes a patent for any program servicing a computer.

( 2007 ), " A superfast algorithm for Toeplitz systems of linear equations ", SIAM Journal on Matrix Analysis and Applications, 29: 1247 – 1266.

Although these pseudo-random sequences pass statistical pattern tests for randomness, by knowing the algorithm and the conditions used to initialize it, called the " seed ", the output can be predicted.

Designating each vertex or set of connected vertices a " component ", pseudocode for Borůvka's algorithm is:

** Chi-Min Liu and Wen-Chieh Lee, " A unified fast algorithm for cosine modulated filterbanks in current audio standards ", J.

* SURF, an acronym for " Speeded Up Robust Features ", a computer vision algorithm

The second method is to use a recording software and sound card, using the so-called " analog hole ", for example, Replay Music which records and also identifies and tags the songs using an audio fingerprinting algorithm.

( While one can " delete " an element from an array in constant time by somehow marking its slot as " vacant ", an algorithm that iterates over the elements may have to skip a large number of vacant slots ).

An example of a " divide and conquer algorithm ", binary search involves each element being found by determining which half of the table a match may be found in and repeating until either success or failure.

The project, entitled " Cryptography-A new algorithm versus the RSA ", also won her the EU Young Scientist of the Year Award for 1999.

It is an adversarial search algorithm used commonly for machine playing of two-player games ( Tic-tac-toe, Chess, Go, etc .).

Thus, it is very unlikely that it will be possible to program a reasonably fast algorithm for playing the Go endgame flawlessly, let alone the whole Go game.

The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the smaller number is subtracted from the larger number.

This change required major changes in the routing algorithm.

* Intelligent Water Drops or the IWD algorithm is a nature-inspired optimization algorithm inspired from natural water drops which change their environment to find the near optimal or optimal path to their destination.

A key is often easier to protect ( it's typically a small piece of information ) than an encryption algorithm, and easier to change if compromised.

The PID controller calculation ( algorithm ) involves three separate constant parameters, and is accordingly sometimes called three-term control: the proportional, the integral and derivative values, denoted P, I, and D. Heuristically, these values can be interpreted in terms of time: P depends on the present error, I on the accumulation of past errors, and D is a prediction of future errors, based on current rate of change.

It's not so hard to believe that this algorithm will work relatively quickly if indeed the configuration of bounding boxes does not change significantly from one time step to the next.

If the algorithm is applied to the above example, the Symbol string will change in the following manner.

In terms of the approximation algorithm in the previous paragraph, this is needed to prove that the change in y will eventually become arbitrarily small.

In general, any mathematically defined change in connection weights over time is referred to as the " learning algorithm ".

For multi-loop integrals that will depend on several variables we can make a change of variables to polar coordinates and then replace the integral over the angles by a sum so we have only a divergent integral, that will depend on the modulus and then we can apply the zeta regularization algorithm, the main idea for multi-loop integrals is to replace the factor after a change to hyperspherical coordinates so the UV overlapping divergences are encoded in variable r. In order to regularize these integrals one needs a regulator, for the case of multi-loop integrals, these regulator can be taken as so the multi-loop integral will converge for big enough's ' using the Zeta regularization we can analytic continue the variable's ' to the physical limit where s = 0 and then regularize any UV integral.

It should be noticed that CCA, as an iterative learning algorithm, actually starts with focus on large distances ( like the Sammon algorithm ), then gradually change focus to small distances.

The relative error bound of every ( backwards stable ) summation method by a fixed algorithm in fixed precision ( i. e. not those that use arbitrary precision arithmetic, nor algorithms whose memory and time requirements change based on the data ), is proportional to this condition number.

The dynamic change idea made it into 802. 11i as part of TKIP, but not for the actual WEP algorithm.

A cryptographic hash function is a hash function, that is, an algorithm that takes an arbitrary block of data and returns a fixed-size bit string, the ( cryptographic ) hash value, such that an ( accidental or intentional ) change to the data will ( with very high probability ) change the hash value.

They have an advantage over simulated annealing and genetic algorithm approaches of similar problems when the graph may change dynamically ; the ant colony algorithm can be run continuously and adapt to changes in real time.

Depending on the algorithm used, it may happen that making small changes to the presentation that do not change the group nevertheless have a large impact on the amount of time or memory needed to complete the enumeration.

A learning algorithm is such that, over time, a change in connection weight is possible, allowing networks to modify their connections.

Bose AudioPilot is a noise compensation technology which analyzes background environmental cabin noise and uses an algorithm based on cabin acoustics to boost certain portions of the musical signal so that it may be heard more clearly above environmental sound " clutter " without any apparent change in volume.

# The ARC algorithm extends LRU by maintaining a history of recently evicted pages and uses this to change preference to recent or frequent access.