$(24$ points$)$ Construct a minimal DFA for regular expression $(01|)$ following the steps below:

a$.$ construct an equivalent NFA using Thompson's construction,

b$.$ convert the NFA to an equivalent DFA $($show your work$),$

c$.$ minimize the DFA in step b $($show your work$).$

$(20$ points$)$ Problem $2\mathrm{.}5$ in Section $2\mathrm{.}6$ at page $104.$

$(8$ points$)$ Minimize the following DFA. Show your work.