Question VII $(15$ points$)$: Given the code segment below and that $$ and $$ are the input, where $$ 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 $<=2*$n; i $=$ i $*4)$

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

$\}$

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

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

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

$1)(13$ 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 $=10$

$2)(1$ points$)$ Determine the Big$-\backslash$Theta $()$ complexity of this program fragment in the best case.

$3)(1$ points$)$ Determine the Big$-\backslash$Theta $()$ complexity of this program fragment in the worst case.