Find the asymptotic cost using Big$-$

$\backslash$Theta

$\backslash$Theta notation for each cloud provider configuration and explain your reasoning. Assume logarithms are base $2.$

$1.$

algorithm

$1.$ algorithm

ProgramToRun

$($

n

:

$\{$

n

in

Z

$+$

$$

n

$=$

$2$

k

$,$

k

in

N

$\}$

$)$

ProgramToRun$($n:$\{$n in Z

$+$

$$n$=2$

k

$,$ k in N$\})$

$2.$

c

$$

$2$

$2.$ c$2$

$3.$

t

o

t

a

l

$$

$0$

$3.$ total$0$

$4.$

for

i

from

$2$

to

n

$2$

by

$2$

do

$4.$ for i from $2$ to n

$2$

by $2$ do

$5.$

t

o

t

a

l

$$

t

o

t

a

l

$+$

Alpha

$($

i

$)$

$5.$ total$$total$+$Alpha$($i$)$

$6.$

if

i

$=$

c

then

$6.$ if i$=$c then

$7.$

t

o

t

a

l

$$

t

o

t

a

l

$+$

Beta

$($

i

$)$

$7.$ total$$total$+$Beta$($i$)$

$8.$

for

j

from

$1$

to

c

by

j

do

$8.$ for j from $1$ to c by j do

$9.$

t

o

t

a

l

$$

t

o

t

a

l

$+$

Gamma

$($

j

$)$

$9.$ total$$total$+$Gamma$($j$)$

$10.$

end

for

$10.$ end for

$11.$

c

$$

c

$\backslash$times

$2$

$11.$ c$$c$\backslash$times $2$

$12.$

end

if

$12.$ end if

$13.$

end

for

$13.$ end for

$14.$

return

t

o

t

a

l

$14.$ return total

$15.$

end

algorithm

$15.$ end algorithm