$3\mathrm{.}2$ N Days $(20$ pt$.)$

Now, suppose you are given prices over n days. Using your solution to part $($a$)$ as a guide, design an O$($nkQ$)$ time algorithm that determines whether you can reach your goal, and if not, reports the maximum profit achievable. Prove your algorithm$$s runtime and correctness.

Hint: It$$s helpful to reframe each day as $1)$ selling all the shares you own and $2)$ then buying a set of shares that you can afford.