I have a recurrence of Divide and Conquer in which I can divide input $n$ into $f(n)$ parts and combining their solutions will take $O(f(n))$ time, where $f(n)$ is a function of $n$ and $f(n)\leq n$.
Formally the recurrence is: $T(n)=f(n)T(\frac{n}{f(n)})+O(f(n))$
What can be $T(n)$ in Big-oh notation (tight bound) and for which $f(n)$ ?
My guess is $T(n)=O(n^2)$.