A moment's reflection shows that the above algorithm and presentation work equally well in this case.

note that the above online algorithm III is a special case of an algorithm that works for any partition of the sample into sets,:

Bennett, Bernstein, Brassard, and Vazirani proved in 1996 that a brute-force key search on a quantum computer cannot be faster than roughly 2 < sup > n / 2 </ sup > invocations of the underlying cryptographic algorithm, compared with roughly 2 < sup > n </ sup > in the classical case.

The condition number may also be infinite, in which case the algorithm will not reliably find a solution to the problem, not even a weak approximation of it ( and not even its order of magnitude ) with any reasonable and provable accuracy.

Using to denote the size of the original grammar, the size blow-up in the worst case may range from to, depending on the transformation algorithm used.

For the case of power-of-two, Papadimitriou ( 1979 ) argued that the number of complex-number additions achieved by Cooley – Tukey algorithms is optimal under certain assumptions on the graph of the algorithm ( his assumptions imply, among other things, that no additive identities in the roots of unity are exploited ).

For case # 1, the painter paints ( fills ) the pixel the painter is standing upon and stops the algorithm.

If R is a Euclidean domain in which euclidean division is given algorithmically ( as is the case for instance when R = F where F is a field, or when R is the ring of Gaussian integers ), then greatest common divisors can be computed using a form of the Euclidean algorithm based on the division procedure.

However, this is not the case with a special-purpose factorization algorithm, since it may not apply to the smaller factors that occur during decomposition, or may execute very slowly on these values.

This might come in the form of a proof that the number in question is in fact irrational ( or rational, as the case may be ); or a finite algorithm that could determine whether the number is rational or not.

Linear search is the simplest search algorithm ; it is a special case of brute-force search.

That algorithm enforces two constraints: children precede their parents and if a class inherits from multiple classes, they are kept in the order specified in the tuple of base classes ( however in this case, some classes high in the inheritance graph may precede classes lower in the graph ).

This algorithm performs well when combined with a fast sequential merge as a base case for merging of small arrays.

For the special case where is a joint probability distribution and the loss function is the negative log likelihood a risk minimization algorithm is said to perform generative training, because can be regarded as a generative model that explains how the data were generated.

These algorithms are not practicable for hand written computation, but are available in any Computer algebra system ( see Berlekamp's algorithm for the case in which the coefficients belong to a finite field or the Berlekamp – Zassenhaus algorithm when working over the rational numbers ).

It has been proven that applying Grover's algorithm to break a symmetric ( secret key ) algorithm by brute force requires roughly 2 < sup > n / 2 </ sup > invocations of the underlying cryptographic algorithm, compared with roughly 2 < sup > n </ sup > in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 would have the same security against an attack using Grover's algorithm that AES-128 has against classical brute-force search ( see Key size ).

In the case of computer networking, the metric is computed by a routing algorithm, and can cover such information as bandwidth, network delay, hop count, path cost, load, MTU, reliability, and communication cost ( see e. g. this survey for a list of proposed routing metrics ).

State Street Bank v. Signature Financial Group is the landmark case in which the Court of Appeals for the Federal Circuit ruled ( July 23, 1998 ) that a computer algorithm can be patented to the extent that it produces " a useful, concrete and tangible result ".

While the patent was initially rejected by the patent office as being a purely mathematical invention, following 12 years of appeals, Pardo and Landau won a landmark court case at the CCPA ( Predecessor Court of the Federal Circuit ) overturning the Patent Office in 1983 — establishing that " something does not cease to become patentable merely because the point of novelty is in an algorithm.

Many detractors have not considered the collection and processing of data, the first order of business, and the refining of those data streams, in the case of SETI through algorithm optimization.

The adversarial system ( or adversary system ) is a legal system where two advocates represent their parties ' positions before an impartial person or group of people, usually a jury or judge, who attempt to determine the truth of the case.

Justice is done when the most effective adversary is able to convince the judge or jury that his or her perspective on the case is the correct one.

In law, interrogatories ( also known as requests for further information ) are a formal set of written questions propounded by one litigant and required to be answered by an adversary, in order to clarify matters of fact and help to determine in advance what facts will be presented at any trial in the case.

Stressed environment: In radio communications, an environment that is under the influence of extrinsic factors that degrade communications integrity, such as when ( a ) the benign communications medium is disturbed by natural or man-made events ( such as an intentional nuclear burst ), ( b ) the received signal is degraded by natural or man-made interference ( such as jamming signals or co-channel interference ), ( c ) an interfering signal can reconfigure the network, and / or ( d ) an adversary threatens successful communications, in which case radio signals may be encrypted in order to deny the adversary an intelligible message, traffic flow information, network information, or automatic link establishment ( ALE ) control information.

At the novel's end, Preston's MI5 superior and adversary is denied a senior leadership role due to his misjudgment in the case and subsequently resigns from MI5 altogether.

Sharp immediately became involved in the court case, facing his old adversary over slave trade matters, the Solicitor General for England and Wales, Mr. John Lee.

In the desert-like terrain that ensues, it is impossible for an adversary to travel without being seen, and there is little cover in case of an attack, especially from the air.

Detective Harry Hole is assigned to the case with his long-time adversary Tom Waaler and initially wants no part in it.

Because the adversary possesses the public encryption key in the above game, a semantically secure encryption scheme must by definition be probabilistic, possessing a component of randomness ; if this were not the case, the adversary could simply compute the deterministic encryption of and and compare these encryptions with the returned ciphertext to successfully guess the oracle's choice.

In this case, the adversary can build a large " dictionary " of useful plaintext / ciphertext pairs, then observe the encrypted channel for matching ciphertexts.

A bankruptcy " case " may contain one or more adversary proceedings ( or none at all ).

United States v. Gouveia, 467 U. S. 180 ( 1984 ), was a case in which the United States Supreme Court held that prisoners in administrative segregation pending the investigation of crimes committed within the prison had no Sixth Amendment entitlement to counsel prior to the initiation of adversary judicial proceedings against them.

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

Just as in the case of every prodigy child, we must watch for the efficacy of my teaching to show up in the future -- if he should master all the strenuous exercises I inflicted on him.

And while every writer must be dealt with as a special case, the interested student will want to ask himself a number of questions about each.

Statistically this has represented a loss to the nation, although one must admit that in an individual case the decision in retrospect may have been a wise one.

In the specific case of time diffusion, we must emphasize the significance of the earlier development of mistrust when it is combined with the inevitable time crisis experienced by most ( if not all ) adolescents in our society, and with the failure of the adolescent period to provide opportunities for developing trust.

Presumably, if the reverse is the case and the good effect is more certain than the evil result that may be forthcoming, not only must the good and the evil be prudentially weighed and found proportionate, but also calculation of the probabilities and of the degree of certainty or uncertainty in the good or evil effect must be taken into account.

In the case of new evidence, there must be a high probability that its presence or absence would have made a material difference in the trial.

That is, any conditional steps must be systematically dealt with, case-by-case ; the criteria for each case must be clear ( and computable ).

If the Labours precede the events in Roger Ackroyd, then the Roger Ackroyd case must have taken place around twenty years later than it was published, and so must any of the cases that refer to it.

The Act overturns a 1999 U. S. Supreme Court case that held that an employee was not disabled if the impairment could be corrected by mitigating measures ; it specifically provides that such impairment must be determined without considering such ameliorative measures.

Pierre-Simon Laplace and Antoine Lavoisier, in their 1780 treatise on heat, arrived at values ranging from 1, 500 to 3, 000 below the freezing-point of water, and thought that in any case it must be at least 600 below.

In addition to the balancing described above for insertions, if the balance factor for the tree is 2 and that of the left subtree is 0, a right rotation must be performed on P. The mirror of this case is also necessary.

The Supreme Court held that for the plea to be accepted, the defendant must have been advised by a competent lawyer who was able to inform the individual that his best decision in the case would be to enter a guilty plea.

In an adversarial system, there is no more controversy and the case proceeds to sentencing ; though in many jurisdictions the defendant must have allocution of her or his crime, a false confession will not be accepted even in common law courts.

In any case the population of the region must belong to Ptolemy's Tarabeni or Titiani people, neither of which are ever heard about again.

The Mahabharata permits hunting by warriors ( Kshatriyas ), but opposes it in the case of hermits who must be strictly non-violent.

These test cases must each be accompanied by test case input data or a formal description of the operational activities ( or both ) to be performed — intended to thoroughly exercise the specific case — and a formal description of the expected results.

For larger quantities one must go to a beverage distributor which sells beer only by the case or keg.

In this case the relation from X to Y is the subset G of X × Y, and " from X to Y " must always be either specified or implied by the context when referring to the relation.

In that case they must choose which hand to play behind before the second cards are drawn.

The Celtic tribe of central Europe must in that case be a final daughter population of a linguistically diversifying ancestor tribe.