$3.$ Problem $2\mathrm{.}4.$ Suppose you are choosing between the following three algorithms:

$$ 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.

$$ Algorithm B solves problems of size n by recursively solving two subproblems of size n$1$

and then combining the solutions in constant time.

$$ Algorithm C solves problems of size n by dividing them into nine subproblems of size 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 would

you choose?