Cloud Array is the new upcoming company that has an innovative business model. They offer services

in secure array accesses. For this they charge their customers per array access. They have different types

of cloud arrays and their pricing for cost per access is as follows:

Red$[$k$]$ Blue$[$k$]$ Green$[$k$]$

log k k log k k

Starc is running the following code on his machine:

Algorithm $1$ Starc$$s Algorithm

$1$: function ProgramToRun$($n: A natural number$)$

$2$: k $1$

$3$: sum $0$

$4$: for i $1$ to n$2$ step $2$ do

$5$: sum $$ sum $+$ Red$[$i$]$

$6$: if i $==$ k then

$7$: sum $$ sum $+$ Blue$[$i$]$

$8$: for j $1$ to k do

$9$: sum $$ sum $+$ Green$[$j$]$

$10$: end for

$11$: k $3\backslash$times k

$12$: end if

$13$: end for

$14$: return sum

$15$: end function

$($a$)$ Analyze the code and give the total asymptotic cost for accessing the Red array.

$($b$)$ Analyze the code and give the total asymptotic cost for accessing the Blue array.

$($c$)$ Analyze the code and give the total asymptotic cost for accessing the Green array.

$($d$)$ Starc feels he is spending too much money on array accesses. He switches to a new plan where

the costs are: Red$[$k$]=$ k$,$ Blue$[$k$]=$ log k and Green$[$k$]=1.$ Is this plan better in terms of total

asymptotic cost?