Repeat Exercise $1,$ this time determining if the set contains any triplicates.

Is the algorithm as efficient as possible?

here is the question in exercise $1$ below:

Suppose you are given a set of n numbers x$1,$ x$2,...,$ xn and are asked to

determine whether this set contains any duplicates.

$($a$)$ Suggest an algorithm and find an order$-$of$-$magnitude expression

for its time complexity.

$($b$)$ Examine if the implementation of the algorithm on a Turing machine

affects your conclusions.