for i $=1$ to n $\{$

k $=1$

while $($k $<=$ n$)\{$

print $$hello$$

k $=$ k $*2$ Careful!

$\}$

$\}$

a$)$ Show the look bracketing and the number of times each loop is executed.

b$)$ Give the expression T$($n$)$ for the number of times $$hello$$ is printed, in terms of n$.$

c$)$ How many times will $$hello$$ be printed if n $=1?$ if n $=2?$ if n $=3?$ Make sure it$$s the correct answer you obtain if you substitute n by each of its $3$ values in the expression you have in b$).$

d$)$ Give T$($n$)$ in $\backslash$Theta notation, in its simplest form.