Algorithm Analysis. In this question, you will need to analyze three algorithms ana prove the required correctness and$/$or running time properties.

$($a$)$ You are given the following algorithm which accepts as input a list of positive integers $A=(a_1,$dots,$a_n)$ and we need to determine whether all elements are unique $($that is$,$ there are no repeated elements in the list$).$ If all elements are unique, the algorithm outputs True, otherwise it will output False.

procedure CheckUnique $(A,n)$

for $i=1$ to $n-1$ do

for $j=i+1$ to $n$ do

if $a_i==a_j$ then

return FALSE

end if

end for

end for

return TRUE

end procedure

$($i$)(3$ points$)$ State the primitive operations and the data structure$($s$)$ to be used in this algorithm.

$($ii$)(2$ points$)$ Compute the worst$-$case running time $T(n)$ to output the final result using $-$notation.

To get the worst case running time please use this method in this example