Suppose you are choosing between the following three algorithms:

$($a$)$ Algorithm A solves problems by dividing them into five subproblems of half the size, recursively solving each subproblem, and then combining the solutions in linear time.

$($b$)$ Algorithm $B$ solves problems of size $n$ by recursively solving two subproblems of size $n-1$ and then combining the solutions in constant time.

$($c$)$ Algorithm $C$ solves problems of size $n$ by dividing them into nine subproblems of size $\frac{n}{3},$ recursively solving each subproblem, and then combining the solutions in $O(n^2)$ time.

What are the running times of each of these algorithms $($in big$-O$ notation$),$ and which one would you choose and why?