**Asymptotic Notations**

- Asymptotic Notations are methods to estimate and represent efficiency of the algorithm using simple formula
- To choose the best algorithm we need to check the efficiency of each algorithm.
- The efficiency of the algorithm can be measured by calculating the time complexity of the algorithm
- Asymptotic Notations is a short hand wave to represent time complexity

**Various Asymptotic Notations **

* Big Oh Notation

* Big Omega Notation

*Big Theta Notation

**Big O Notation**

It is Worst case running time of an algorithm and for the large values of n.

The maximum no. Of steps to solve a problem.

Function t(n) is said to be the O[g(n)].If f(n) is bounded by some constant multiples of g(n) for large values of n,then should satisfy

f(n)<=c[g(n)] where n>=n0.

**Big Omega Notation**

It is the best case efficiency of the algorithm and for large values of n.Minimum number of steps required to solve the problem.

Function f(n) is said to be O[g(n)].If f(n) is bounded by some .positive constant multiples of c[g(n)] for large values of n, then there should satisfy

f(n)>=c[g(n)] where n>n0.

**Big Theta Notation **

It is the average case efficiency of the algorithm for the large values of n.Average number of steps required to solve the problem.

Function f(n) is said to be O[g(n)].If f(n) is bounded both above and below by constant multiples of c[g(n)] for large values of n,there should satisfy

c1[g(n)] <= f(n) <= c2[g(n)] where n>n0.

**Little O Notations**

The notations is used to describe the worst case analysis and concerned with the small values of n.

A function t(n) is said to be O[g(n)] if there exists some positive constants C.

**Little Omega Notation**

The notation is used to describe the best case analysis of the algorithm and concerned with the small values of n.A function t(n ) is said to be O[g(n)] if there exists some constants C.