quartz/content/notes/aymptotic-notation.md

title	tags
asymptotic-notation	cosc201 analysis-of-algorithms

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

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)