The complement of a set A with respect to another set S $($aka the uni$-$

verse$)$ is defined as the set of elements in S that are not in A and is

denoted by Ac$.$ Let A be a subset of S $=\{0,1,2,...,$ n $1\}.$

$1.$ Devise an algorithm that takes the universal set S and a subset of

the universe A$,$ both represented using their characteristic arrays,

and returns the characteristic array of Ac$.[1$ point$]$

$2.$ What are the best$-$case, worst$-$case, and average$-$case complexities of

your algorithm? Justify your answer.