quartz/content/notes/aymptotic-notation.md

title	aliases	tags
asymptotic-notation	Big O, Big Theta, Algorithm Analysis	cosc201

Asymptotic notations are used in computer science to classify algorithms based how its space and time requirements grow as the input grows.

big O notation

Big O defines a bound for the upper bound of the running time (or space) of a algorithm. However, it is possible that the actual running time is much less as it does not take into account special cases ^fb2c3f

1 Formal definition

f(n) = O(g(n)) if there is some constant A such that f(n) < A \times g(n)

big theta notation

Big theta defines an upper and a lower bound for a the running time (or space) of an algorithm.

2 Formal definition

f(n) = \theta(g(n)) if there are some constants A and B where 0 < B < A such that for all sufficiently large n, B \times g(n) \geq f(n) \leq A \times g(n)