a$)$ Purely by looking at the code, and NOT running it$,$ what will the return value be when nums is $\{1,2,3,4,5,4,2\}$ and n is $7?$ Explain how you figured out the answer. difference in outcomes, based on the how the recursive calls are are placed in the code, and how they end up being called.c$)$ Consider the case in which the duplicated value is in the last two elements. Derive a recurrence for the number of item comparisons $($red code$).$ Then solve your recurrence in the usual way.d$)$ Same as part c$,$ but the duplicated value occurs in the first two elements.e$)$ Optimize the code in the obvious way $($factor out unnecessary recursive call using a temp$).$ Now repeat Part d$.$