PART $1-$ Observing the loops $(3+3$ pts$)$

Find the Big$-$ notations for the following pseudocode snippets with regard to n $($the size of data$).$ Please note, you must show us how to find both the upper bound and the lower bound, or you will get zero points. You may also use the l'Hopital's trick for your convenience.

A$.$

$//$ Assuming n is always larger than $10$

for $($k $=0$; k $<$ n; k $++)\{$

for $($j $=10$; j $<$ n; j $++)\{$

$//$ code block that takes a constant amount of runtime

$\}$

$\}$

B$.$

k $=1$;

do $\{$

j $=1$;

do $\{$

$//$ code block that takes a constant amount of runtime

j $=$ j $*3$;

$\}$ until $($j $>=0\mathrm{.}5*$n$)$; $//$ if j $<0\mathrm{.}5*$n$,$ continue the loop

k $=$ k $+1$;

$\}$ until $($k $>=$ n$)$;