#$5.$ Ex$.6\mathrm{.}6\mathrm{.}17$ Suppose you are working in the information technology department for a large hospital. The

people working at the front office are complaining that the software to discharge patients is taking too long to

run. Indeed, on most days around noon there are long lines of people waiting to leave the hospital because of

this slow software. After you ask if there are similar long lines of people waiting to be admitted to the hospital,

you learn that the admissions process is quite fast in comparison. After studying the software for admissions

and discharges, you notice that the set of patients currently admitted in the hospital is being maintained as a

linked list, with new patients simply being added to the end of this list when they are admitted to the hospital.

Describe a modification to this software that can allow both admissions and discharges to go fast. Characterize

the running times of your solution for both admissions and discharges.