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As the amount of resources required to run an algorithm generally varies with the size of the input, the complexity is typically expressed as a function n → f(n), where n is the size of the input and f(n) is either the worst-case complexity (the maximum of the amount of resources that are needed over all inputs of size n) or the average-case ...
The complexity of an algorithm is usually taken to be its worst-case complexity unless specified otherwise. Analyzing a particular algorithm falls under the field of analysis of algorithms . To show an upper bound T ( n ) {\displaystyle T(n)} on the time complexity of a problem, one needs to show only that there is a particular algorithm with ...
Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, () below stands in for the complexity of the chosen multiplication algorithm.
A representation of the relation among complexity classes. This is a list of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics. Many of these classes have a 'co' partner which consists of the complements of all languages in the original class ...
In the theoretical analysis of algorithms, the normal practice is to estimate their complexity in the asymptotic sense. The most commonly used notation to describe resource consumption or "complexity" is Donald Knuth 's Big O notation , representing the complexity of an algorithm as a function of the size of the input n {\textstyle n} .
A high sample complexity means that many calculations are needed for running a Monte Carlo tree search. [10] It is equivalent to a model-free brute force search in the state space. In contrast, a high-efficiency algorithm has a low sample complexity. [11]
A major result of complexity theory is that NP can be characterized as the problems solvable by probabilistically checkable proofs where the verifier uses O(log n) random bits and examines only a constant number of bits of the proof string (the class PCP(log n, 1)). More informally, this means that the NP verifier described above can be ...
In order to give the definition for something that is PAC-learnable, we first have to introduce some terminology. [2] For the following definitions, two examples will be used. The first is the problem of character recognition given an array of bits encoding a binary-valued image. The other example is the problem of finding an interval that will ...