asymptotic notations and their running time

Question

I know that for

$f(x) = O(g(x))$ running time $T(n) = O(n^3)$

$f(x) = \Omega(g(x))$ running time $T(n) = \Omega(n^2)$

but what is the $T(n)$ for $f(x) = Θ(g(x))$ ?

Also tell me running time for little-oh (o) & little-omega (\omega)

Also what is big-theta?

Answer 1

$\Theta(g(n))$ means that that $\exists c_1, c_2$ such that $\forall n >N c_1 g(n) < f(n) <c_2 g(n)$. In other words, $f(n)$ is up to a constant both upper-and lower-bounded by $f(n)$. In your case (if I understand your question correctly) $f(x)$ is not $\Theta(g(x))$ because runtime bounds are of different order.