This is a Data Structures question involving time complexity

This is a Data Structures question involving time complexity analysis...

Explain the meaning of the following expressions:

Explain the meaning of the following expressions: f (n) is O(n^2) f (n) is Ohm(n^2) f (n) is Theta(n^2)

Answer:

a) f(n) = O(n^2)

It means that if we have any function f(n) and g(n) = n^2 then f(n) < = c * g(n) at c > 0 , in other words g(n) is tightest bound of f(n)

b) f(n) is Omega(n^2)

It means that f(n) > = c * g(n) , c > 1 and g(n) = n^2

c) f(n) is theta(n^2)

It means that c1 * g(n) < = f(n) < = c1 * g(n) , where c1 and c2 > 1 and g(n) = n^2.