$(30$ points$)$ Brute Force. Given a set of n objects, which are characterized by three

attributes, a$,$ b$,$ and c$,$ determine which two of these objects are the most similar based

on these characteristics. To facilitate comparisons, the range of the attributes has been

assigned to the universe of natural numbers $($i$.$e$.$ positive integers$).$ Therefore, each trio

of characteristics can be mapped to a point in three$-$dimensional space, and the distance

between two of these points could represent the similarity of two objects.

a$.$ Write a brute$-$force, pseudo$-$code algorithm for this problem.

b$.$ What is the run$-$time efficiency of your algorithm?

c$.$ Apply your algorithm to this instance of the problem:

A $=<(6,7,3),(1,9,3),(4,9,5),(3,8,7),(10,2,3)>.$

Be sure to show all of your work.

$6$