# Asymptotic Notation:

Formal way to speak about function and classify them we will to describe time of algorithm.

1) O (Big-o)

2) Theta

3) Big-omega

1) O (Big -0) (upper Bound):-This is a Worst Case.It is the set of all function a smaller or the same order of growth as f(n).

Little-oh notation :little-oh of g of n as the set

o(g(n))={f(n): for any positive constant c>0 , n0>0 such that 0=<f(n)<cg(n)

or

o(g(n)) is the set of all function with a smaller rate of growth than f(n).

Big Omega:-This is a Average Case.

Let f and g are non-negative function,The function f(n)=Omega(g(n)) if there exit positive constant c and n

1) O (Big-o)

2) Theta

3) Big-omega

1) O (Big -0) (upper Bound):-This is a Worst Case.It is the set of all function a smaller or the same order of growth as f(n).

O(n

^{2})={2n^{2},2n+1 , logn…….}
2n

^{2}=o(n^{2})
2n=o(n

^{2})Little-oh notation :little-oh of g of n as the set

o(g(n))={f(n): for any positive constant c>0 , n0>0 such that 0=<f(n)<cg(n)

or

o(g(n)) is the set of all function with a smaller rate of growth than f(n).

Big Omega:-This is a Average Case.

Let f and g are non-negative function,The function f(n)=Omega(g(n)) if there exit positive constant c and n

_{0.}_{ Big Theta:- This is a Best Case.}_{Let f and g are non-negative function.The function f(n)=theta(g(n))}_{if there exit positive constant }C_{1},C_{2}and n_{0}such that c_{1}g(n)<=f(n)<=C_{2}g(n) for all n, n>=n_{0}._{ }_{ }
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