An algorithm is called optimal for the solution of a problem with respect to a specified operation if there is no algorithm for solving this problem using fewer operations. a$)$ Show that Algorithm $1$ in Section $3\mathrm{.}1$ is an optimal algorithm with respect to the number of comparisons of integers. $[$Note: Comparisons used for bookkeeping in the loop are not of concern here.$]$ b$)$ Is the linear search algorithm optimal with respect to the number of comparisons of integers $($not including comparisons used for bookkeeping in the loop$)?$