Problem $2$:

$($a$)$ What is the exact number of comparisons needed to find the simultaneously the maximum and the minimum of four elements?

$($b$)$ We want to find simultaneously the maximum and minimum of an array with $\backslash ($ n $\backslash )$ elements. We divide the array in groups of four elements plus possibly a group with one, two, or three elements. We determine the maxima and the minima of all groups. Then we use the naive method to find the maximum of the group maxima and the minimum of the group minima. These are the maximum and minimum of the array respectively. What is the exact number of comparisons needed depending on $\backslash ($ n $\backslash )($mod $4).$

Problem $3$:

Given the following NFA, create an equivalent DFA. Give the transition diagram of the DFA. $($Don$\text{'}$t forget the empty set, should it arise$).$ Use double stroke to indicate an accepting state. The initial state is given by the arrow pointing from nowhere.