Let A$=\{$ x$1,$ x$2,...,$ xn $\}$ and B $=\{$ y$1,$ y$2,...,$ yn$\}$ be two lists, each with n unique integer elements. Consider the problem of finding their intersection i$.$e$.$ elements they have in common.

a$)$ Give $($in details$)$ a brute$-$force algorithm for solving this problem and determine its efficiency. May either describe or give pseudo code.

b$)$ What if the two list are sorted? Suggest an algorithm with most improved time complexity to find the intersection of the two list. Give the efficiency of your the algorithm.