Problem $1.$ Consider the following algorithm:

Input: $a_1{a}_2,$dots,$a_n,n$ length of sequence, $p$ a real number

Output: True only if the product of two numbers in the sequence equals $p$

For $i=1$ to $n-1$

For $j=i+1$ to $n$

If $a_i{a}_j=p$ return True

End$-$for

End$-$for

return False

A$.$ What are best and worst case scenarios for time complexity?

B$.$ Determine the worst$-$case time complexity $($operation count$)$ as a function of $n.$

C$.$ What is the exponent $c$ for the asymptotic behavior of the time complexity $(n^c)?$