$1.)$

Give the approximate running times of each of the following algo$-$

rithms $($a$.$k$.$a$.$ functions$)$ using $-$notation. Note that you can immediately drop

any floor or ceiling functions and that if you forget the $"+1"$ in something like

${\displaystyle \underset{k=a(n)}{\overset{b(n)}{}}}C=C(b(n)-a(n)+1)$ it won't affect your answers. $($If either summa$-$

tion limit contains a explicit number it is better to include it as it won't complicate

the work.$)$

$($a$)$ FUNCTION $f_1(n)$

slarr$0$

FOR ilarrn $TO{|}_{{?}_{?}}{n}_{{?}_{?}}^{\frac{3}{2}}|DO$

FOR jlarr$5iTO2i^{2}DO$

$,$slarrs$+i-j$

RETURN$(s)$

$($b$)$ FUNCTION $f_2(n)$

slarr$0$

FOR ilarr${|}_{{?}_{?}}\frac{n}{5_{{?}_{?}}}|TOnDO$

FOR jlarri $TOnDO$

slarrs$+i-j$

RETURN $(s)$

$($c$)$ FUNCTION $f_3(n)$

slarr$0$

FOR ilarrn $TO2n^{2}DO$

FOR jlarr$5iTO5i+15DO$

slarrs$+i-j$

RETURN $(s)$

$($d$)$ FUNCTION $f_4(n)$

slarr$0$

FOR ilarr$5nTO6n^{3}DO$

FOR jlarr$5TOiDO$

FOR klarrj $TOiDO$

slarrs$+i-j$

RETURN$(s)$