$($Based on Exercise C$-4\mathrm{.}11$ from the book$)($a$)$ Describe an efficient recursive algorithm for solving the element uniqueness $($determine if every element in a list is unique$)$ problem that runs in time at most $O(n^2)$ in the worst case. Do not use sorting. $($b$)$ Implement your algorithm in Python. $($c$)$ Is your function tail$-$recursive? Why or why not?

$($Based on exercise C$-4\mathrm{.}16$ from the book$)($a$)$ Write a short recursive Python function that takes a character string $s$ and outputs its reverse. E$.$g$.,$ calling it on 'pots&pans' would return 'snap&stop'. $($b$)$ What is your function's running time? Show how you arrived at the answer. $($c$)$ Is your function tail$-$recursive? Why or why not?