Derive the closed$-$form

T

$($

n

$)$

T$($n$)$ for the number of times the function

FOO

FOO is called.

Question $2\mathrm{.}1$

Q$2\mathrm{.}13$ Points

Grading comment:

$1.$

algorithm

$1.$ algorithm

EpicCount

$($

n

:

$\{$

n

in

Z

$+$

$$

n

$$

$0$

$($

m

o

d

$2$

$)$

$\}$

$)$

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

$+$

$$n$0($mod$2)\})$

$2.$

for

i

from

$1$

to

n

$2$

do

$2.$ for i from $1$ to n

$2$

do

$3.$

for

j

from

$1$

to

$4$

$\backslash$times

i

do

$3.$ for j from $1$ to $4\backslash$times i do

$4.$

k

$$

$0$

$4.$ k$0$

$5.$

while

k

$<=$

n

do

$5.$ while k$<=$n do

$6.$

FOO

$($

i

$,$

j

$)$

$6.$ FOO$($i$,$j$)$

$7.$

k

$$

k

$+$

$2$

$7.$ k$$k$+2$

$8.$

end

while

$8.$ end while

$9.$

end

for

$9.$ end for

$10.$

end

for

$10.$ end for

$11.$

end

algorithm

$11.$ end algorithm