Problem $2.[10$ points$]$ Suppose there are three options for dividing a problem of size $n$ into subproblems:

$$ Algorithm A solves the problem by recursituly solving eight instances of size $\frac{n}{2},$ and then combining their solutions in time $(n^3).$

$$ Algorithm $B$ solves the problem by recursively solving twenty instances of size $\frac{n}{3},$ and then combining their solutions in time $(n^2).$

$$ Algorithm $C$ solves the problem by recursively solving two instances of size $2n,$ and then combining their solutions in time $(n).$

Which one is preferable, and why?