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Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the most practical, since they can be run on real machines efficiently. Formally, a deterministic algorithm computes a mathematical function ; a function has a unique value for any input in its domain , and the algorithm is a process that ...
The algorithm, as Deutsch had originally proposed it, was not deterministic. The algorithm was successful with a probability of one half. In 1992, Deutsch and Jozsa produced a deterministic algorithm which was generalized to a function which takes bits for its input. Unlike Deutsch's algorithm, this algorithm required two function evaluations ...
When the cost denotes the running time of an algorithm, Yao's principle states that the best possible running time of a deterministic algorithm, on a hard input distribution, gives a lower bound for the expected time of any Las Vegas algorithm on its worst-case input. Here, a Las Vegas algorithm is a randomized algorithm whose runtime may vary ...
A deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states. There may be non-deterministic algorithms that run on a deterministic machine, for example, an algorithm that relies on random choices.
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
Unlike quickselect, this algorithm is deterministic, not randomized. [2] [4] [5] It was the first linear-time deterministic selection algorithm known, [5] and is commonly taught in undergraduate algorithms classes as an example of a divide and conquer that does not divide into two equal subproblems.
These two definitions are equivalent because the algorithm based on the Turing machine consists of two phases, the first of which consists of a guess about the solution, which is generated in a nondeterministic way, while the second phase consists of a deterministic algorithm that verifies whether the guess is a solution to the problem. [3]
A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), [1] is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers.