$1.(10$ points$)$ Consider the problem of finding the distance between the two closest numbers in an array of n numbers. $($The distance between two numbers x and y is computed as $|$x $$ y$|.)$

a$.(5$ points$)$ Design a presorting$-$based algorithm for solving this problem and determine

its efficiency class. Pseudo code only

b$.(5$ points$)$ Compare the efficiency of this algorithm with that of the brute$-$force algorithm