# Asymptotic Notation - O(), o(), Ω(), ω(), and θ()

Data StructureAnalysis of AlgorithmsAlgorithms

## Asymptotic Notations

Asymptotic notations are used to represent the complexities of algorithms for asymptotic analysis. These notations are mathematical tools to represent the complexities. There are three notations that are commonly used.

## Big Oh Notation

Big-Oh (O) notation gives an upper bound for a function f(n) to within a constant factor.

## Little o Notations

There are some other notations present except the Big-Oh, Big-Omega and Big-Theta notations. The little o notation is one of them.

Little o notation is used to describe an upper bound that cannot be tight. In other words, loose upper bound of f(n).

## Big Omega Notation

Big-Omega (Ω) notation gives a lower bound for a function f(n) to within a constant factor.

## Little ω Notations

Another asymptotic notation is little omega notation. it is denoted by (ω).

Little omega (ω) notation is used to describe a loose lower bound of f(n).

## Big Theta Notation

Big-Theta(Θ) notation gives bound for a function f(n) to within a constant factor.