Suppose we minimize the average time to store $n$ files of lengths $l_1,l_2,$dots,$l_n$ on a

tape. If the probability of requesting file $k$ is given by $p_k,$ the expected access

time to load these $n$ files in the order $k_1,k_2,$dots,$k_n$ is given by the formula

$T_{\text{a}\text{v}\text{e}\text{r}\text{a}\text{g}\text{e}}=C{\displaystyle \underset{f=1}{\overset{n}{}}}(p_{k_f}{\displaystyle \underset{i=1}{\overset{f}{}}}{l}_{k_i}).$

The constant $C$ represents parameters such as the speed of the drive and the

recording density.

$($a$)$ In what order should a greedy approach store these files to guarantee

minimum average access time?

$($b$)$ Write the algorithm that stores the files, analyze your algorithm, and show the