Problem $3$: $(8$ pts$)$ For each piece of pseudocode below, give its $\backslash$Theta estimate. Include a brief informal explanation.

a$)$ AlgorithmA$($n$)$

for i $1$ to n do

for j $1$ to n$^2+1$ do

for k $1$ to $$n do

Print$($A$)$

b$)$ AlgorithmB$($n$)$

if n $<2$ do

Print$($B$)$

else do

for i $1$ to $4$ do

AlgorithmB$($n$/2)$

Print$($B$)$

c$)$ AlgorithmC$($n$)$

j $1$

for i $1$ to n do

while j $<=8$i do

Print$($C$)$

j $$ j $+1$

d$)$ AlgorithmD$($n$)$

for i $1$ to n$/2$ do

j $$ n

while j $>=1$ do

Print$($D$)$

j $$ j$/4$