$4(20$pt$)$ Please find the binary search algorithm below.

a$)(5$pt$)$ Given a short list S$=[3,4,5,7,9,11,12,13],$ please express the every$-$casetime T$($n$)$ by following the similar steps that we did for arrayMax in our lecture. b$)(5$pt$)$ For one list S$,$ what$$s the case that you can get the best$-$case runningtime?$($hint: try to manipulate the order or elements in S to test. You can findtheworst

case and best case for arrayMax$)$

c$)(10$pt$)$ For one list S$,$ under which condition you will get the worst$-$case runningtime? $($hint: try to manipulate the order or elements in S to