Question VII $(15$ points$)$: Given the code segment below and that $n$ and $x$ are the input, where $n$ is a power of

$4,$ answer the following questions:

$//...$

int sum $=0$;

for$($int i $=0$; i $$ n$*$n; i$++)$

sum$++$; $//$ statement$1$

if$($x $>5)\{$

for$($int i $=1$; i n; i$++)$

for$($ int k $=1$; k $$ i; k$++)$

sum$++$; $//$ statement$2$

$\}$

else$\{$

for$($int i $=1$; i n; i $=$ i $*4)$

sum$++$; $//$ statement$3$

$\}$

for$($int i $=1$; i n; i$*=2)$

for$($ int k $=1$; k i; k$++)$

sum$++$; $//$ statement$4$

$(13$ points$)$ Find the number of times statement$1,$ statement$2,$ statement$3$ and statement $4$ get

executed, showing all the details of your solution, if

a$)x=0$

b$)x=10$

$(1$ points$)$ Determine the Big$-()$ complexity of this program fragment in the best case.

$(1$ points$)$ Determine the Big$-()$ complexity of this program fragment in the worst case.