If the running time of a divide$-$and$-$conquer algorithm can be expressed as follows:

$T(n)=\{\begin{array}{ccc}1,& \text{f}\text{o}\text{r}& n1\\ 3T(\frac{n}{2})+n,& \text{f}\text{o}\text{r}& n2\end{array}$

how many subproblems does the algorithm divide the original problem into, and what is the size of each subproblem?

$2$ subproblems, each of size $\frac{n}{3}$

$2$ subproblems, each of size $3$

$3$ subproblems, each of size $\frac{n}{2}$

$3$ subproblems, each of size $2$