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Graphs of functions commonly used in the analysis of algorithms, showing the number of operations N as the result of input size n for each function. In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm.
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.
function factorial (n is a non-negative integer) if n is 0 then return 1 [by the convention that 0! = 1] else if n is in lookup-table then return lookup-table-value-for-n else let x = factorial(n – 1) times n [recursively invoke factorial with the parameter 1 less than n] store x in lookup-table in the n th slot [remember the result of n! for ...
The computational complexity of these algorithms may be analyzed using the unit-cost random-access machine model of computation, in which each arithmetic operation takes constant time and each number uses a constant amount of storage space.
To make worstsort truly pessimal, k may be assigned to the value of a computable increasing function such as : (e.g. f(n) = A(n, n), where A is Ackermann's function). Therefore, to sort a list arbitrarily badly, one would execute worstsort( L , f ) = badsort( L , f (length( L ))) , where length( L ) is the number of elements in L .
Since the time taken on different inputs of the same size can be different, the worst-case time complexity () is defined to be the maximum time taken over all inputs of size . If T ( n ) {\displaystyle T(n)} is a polynomial in n {\displaystyle n} , then the algorithm is said to be a polynomial time algorithm.
In computer science (specifically computational complexity theory), the worst-case complexity measures the resources (e.g. running time, memory) that an algorithm requires given an input of arbitrary size (commonly denoted as n in asymptotic notation). It gives an upper bound on the resources required by the algorithm.
In computational complexity theory, the complexity class NTIME(f(n)) is the set of decision problems that can be solved by a non-deterministic Turing machine which runs in time O(f(n)). Here O is the big O notation, f is some function, and n is the size of the input (for which the problem is to be decided).