$2.$ Count the exact number of $$sum$++$ operations $($as a function of N$)$ of each of following

code fragments.

$($a$)$ int sum $=0$;

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

for$($int j $=0$; j $<$ i; j$++)$

sum$++$;

$($b$)$ int sum $=0$;

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

for $($int j $=0$; j $<$ N; j$++)$

sum$++$;

$3.$ Indicate the class $\backslash$Theta $($g$($n$))$ the following function belongs to$.$ Us the simplest and the

strongest g$($n$)$ possible in your answer. Prove your assertion.

$2$n log

$($

n$2)$

$+($n $+1)2$ log

$($ n

$2$

$)$

$1$