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Big-O is upper limit; names for typical complexity classes; some other minor modifications

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Revision as of 15:02, 18 July 2008 (view source) rosettacode>Mwn3d (Added ordered list of notations) ← Older edit		Revision as of 16:34, 18 July 2008 (view source) rosettacode>Dirkt (Big-O is upper limit; names for typical complexity classes; some other minor modifications) Newer edit →
Line 1: [[Category:Encyclopedia]]'''Complexity'''. In computer science the notation O(Pf(n)) is used to denote an upper limit of the asymptotic behavior of an algorithm, usually its complexity in terms of execution time or memory consumption (space). Here ''Pf'' is ~~an algebraic~~a function of ''n'', ~~usually~~often a ~~polynomial~~power or ~~logarithmic~~logarithm. ''n'' describes the size of the problem. The meaning of O(Pf(n)) is that the complexity grows with n at most as Pf(n) does. The notation can also be used to describe a computational problem. In that case it characterizes the problem's complexity through the best known algorithm that solves it. Line 5: Examples: searching in an unordered container of ''n'' elements has the complexity of O(''n''). Binary search in an ordered container with random element access is O(log ''n''). The term random access actually means that the complexity of access is constant, i.e. O(1). Here are some typical ~~Big-O's~~complexity classes listed from 'slowest' to 'fastest' (that is, slower algorithms have Big-O's near the top): O(ne<sup>n</sup>) ('exponential') O(n<sup>k</sup>) for some fixed ''k'' ('polynomial') O(n!) O(kn<sup>n3</sup>) ('cubic') O(n<sup>32</sup>) ('quadratic') O(n<sup>2</sup>) O(nlog(n)) (fastest possible time for a comparison sort) O(n) ('linear') O(log(n)) ('logarithmic') *O(1) ('constant') See also [http://en.wikipedia.org/wiki/Big_O_notation Big O notation]