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{{distinguish|Quasi-polynomial time}} ...bits required to represent it), which is the case for [[polynomial time]] algorithms.<ref>[[Michael R. Garey]] and [[David S. Johnson]]. [[Computers and Intract ...

...the usual poly-time reduction used for NP-hardness proofs. In special, the pseudo-polynomial reduction cannot output a numerical parameter that is not polinomially boun ...nding version of the Knapsack problem can be solved in [[pseudo-polynomial time]] by [[dynamic programming]]. ...

...it does not need to be random. Because of the nature of number generating algorithms, so long as the original seed is ignored, the rest of the values that the a ...[[secret key]], so two or more systems using matching pseudorandom number algorithms and matching seeds can generate matching sequences of non-repeating numbers ...

{{Short description|Sorting algorithms which exploit existing order in its input}} ...ster. Adaptive sorting is usually performed by modifying existing sorting algorithms. ...

...n operators, and can considerably speed up the calculation when using fast algorithms such as the [[fast Fourier transform]]. ...ordinary differential equation has to be evaluated repeatedly at different time steps. At this point, the spectral method has a major problem with the pote ...

| title = Knapsack Problems: Algorithms and Computer Implementations ...1975}}</ref> Both the bounded and unbounded variants admit an [[Polynomial-time approximation scheme|FPTAS]] (essentially the same as the one used in the 0 ...

...that, as close as possible to ''T''. It is NP-hard, but there are several algorithms that can solve it reasonably quickly in practice. The [[run-time complexity]] of SSP depends on two parameters: ...

...he methods of computation are called [[division algorithm|integer division algorithms]], the best known of which being [[long division]]. ...t-andrews.ac.uk/~john/MT4517/Lectures/L6.html|title=Division and Euclidean algorithms|website=www-groups.mcs.st-andrews.ac.uk|access-date=2019-11-15|archive-date ...

...me=29 |issue=9 |pages=902–908 |title=Tree rebalancing in optimal space and time |doi= 10.1145/6592.6599 |url=http://www.eecs.umich.edu/~qstout/pap/CACM86.p ....<ref name="rolfe">{{cite journal |first=Timothy J. |last=Rolfe |title=One-Time Binary Search Tree Balancing: The Day/Stout/Warren (DSW) Algorithm |url=htt ...

...t3=Näher |first3=Stefan |last4=Schweitzer |first4=Pascal |title=Certifying Algorithms |url=https://people.mpi-inf.mpg.de/~mehlhorn/ftp/CertifyingAlgorithms.pdf | ...inite field]]s of non prime order. It follows that both extended Euclidean algorithms are widely used in [[cryptography]]. In particular, the computation of the ...

...h the partition problem is [[NP-complete]], there is a [[pseudo-polynomial time]] [[dynamic programming]] solution, and there are [[Heuristic|heuristics]] ...s. 3-partition is much harder than partition – it has no pseudo-polynomial time algorithm unless '''[[P = NP]]'''.<ref name="Garey & Johnson">{{cite book|l ...

...e the computation of the determinant of the Sylvester matrix with standard algorithms requires <math>O((d+e)^3)</math> arithmetic operations. ...ing determinants. This needs <math>O(n^3)</math> arithmetic operations. As algorithms are known with a better complexity (see below), this method is not used in ...

...ed by Sims in 1970, based on [[Schreier's subgroup lemma]]. The [[running time]] was subsequently improved by [[Donald Knuth]] in 1991. Later, an even fa ...easy to test membership in the group. Since the SGS is critical for many algorithms in computational group theory, [[computer algebra system]]s typically rely ...

...computational complexity theory]], specifically the theory of [[polynomial time]] problems. This has nothing to do with whether the function is [[One-to-on ...y number of repetitions, see [[Kleene star]].) That is, for all randomized algorithms <math>F</math>, all positive integers ''c'' and all sufficiently large ''n' ...

..., where ''n'' can be any odd integer. The Jacobi symbol can be computed in time [[big O notation|O]]((log&nbsp;''n'')²) using Jacobi's generalization of th ...s prime, or 47 is an Euler liar for 221. We try another random ''a'', this time choosing {{math|1=''a'' = 2}}: ...

...in which something travels through a network of nodes. As such, efficient algorithms for solving network flows can also be applied to solve problems that can be ...low network'''.<ref>A.V. Goldberg, É. Tardos and R.E. Tarjan, Network flow algorithms, Tech. Report STAN-CS-89-1252, Stanford University CS Dept., 1989</ref> ...

...ust complete the game and output a ''guess'' within a polynomial number of time steps. In this definition {{math|''E''(''PK'', ''M'')}} represents the encr ...ishable under chosen-plaintext attack''' if every probabilistic polynomial time adversary has only a negligible "[[advantage (cryptography)|advantage]]" ov ...

This is a constant time operation. ...|WAVL trees]], [[splay tree]]s, and [[treap]]s. They require only constant time because they are ''local'' transformations: they only operate on 5 nodes, a ...

...ing which documents they do and do not select for viewing, the duration of time spent viewing a document, or page browsing or scrolling actions.<ref>{{Cita An example of this is [[dwell time (information retrieval)|dwell time]], which is a measure of how long a user spends viewing the page linked to ...

...h), the maximum clique has bounded size and may be found exactly in linear time;<ref>{{harvtxt|Chiba|Nishizeki|1985}}.</ref> however, for the same classes === Exact algorithms === ...