Question $5(11$ points$)$Question $5(11$ points$)$: Consider the following algorithm

count larr$0$

for ilarr$1$ to $n$

$,$ for jlarrn down to $i$

$,$ for klarri to $j$

$,$ count larr count $+1$

end for

end for

end for

a$)$ How many times step $5$ is executed? $($You must show your steps$)$ and what is the time

complexity of the algorithm in $-$notation?: Consider the following algorithm

$1.$ count $0$

$2.$ for i $1$ to n

$3.$

for j $$ n down to i

$4.$

$5.$

$6.$

$7.$

for k $$ i to j

count $$ count $+1$

end for

end for

$8.$ end for

a$)$ How many times step $5$ is executed? $($You must show your steps$)$ and what is the time

complexity of the algorithm in $\backslash$Theta $-$notation?