For each pseudo$-$code below, give the asymptotic running time in $\backslash$Theta notation. You

may assume that standard arithmetic operations take $\backslash$Theta $(1)$ time. The $4$th part is a bonus part.

CMPSC $465,$ Fall $2024,$ HW $11$

$1.$

k :$=0$;

for i :$=1$ to n do

for j :$=$ i to n do

k :$=$ k $+1$;

end

end

$2.$

for i :$=1$ to n do

for j :$=1$ to n do

k :$=$ j;

while k $>=1$ do

k :$=$ k $1$;

end

end

end

$3.$

for i :$=1$ to n do

j :$=1$;

while j $<=$ n do

j :$=$ j $\backslash$times $2$;

end

end

$4.$

for i :$=1$ to n do

j :$=$ i;

while j $<=$ n do

j :$=$ j $+$ i;

end

end