Consider the following algorithm which takes an array $U=u_1,$dots,$u_n$ and determines whether any subset of the elements of $U$ has a sum of $0.$What is the worst$-$case number of comparisons $($i$.$e$.$ number of times the algorithm checks the condition $"$if k$=0")?$

Hint: You found the number of elements in $P(\{1,2,$dots,$n\})$ in exercise $4\mathrm{.}3\mathrm{.}9$ and the answer is in the back of the book, or you can look it up on Wikipedia $.$