Question $1$: Please perform step count on the following:

Note to section B: The question is asking you to perform runtime analysis of the following codes using $\backslash$theta notation

a$.$

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

$\{$

for$($j $=1$;j $<=$ i;j$++)$

print $($j$)$;

$\}$

Hint: Please note:

When n $=1,$ internal loop runs once

When n $=2,$ internal loop runs $1+2$ times

When n $=3,$ internal loop runs $1+2$ times

When n $=4,$ internal loop runs $1+2+4$ times

When n $=5,$ internal loop runs $1+2+4$ times

When n $=8,$ internal loop runs $1+2+4+8$ times

When n $=$ n$,$ internal loop runs for $1+2+4+8+...?$ times?

b$.$

sum $=0$;

for$($i $=$ n;i $>0$; i $=$ i$/6)$

sum $=$ sum$+$i;

c$.$

sum $=0$;

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

for$($j $=1$;j $<$ i; j $=$ j$*3)$

sum $=$ sum$+$i;