Attention: The parts $($a$)$ and $($b$)$ of this question are independent of each other!!!

a$)$ Consider the recursive function below! Find, in terms of m$,$ the recurrence $($i$.$e$.,$ the

difference equation$)$ that represents the execution time f$($m$)$ for recfunc.

void recfunc$($int m$)\{$

if $($m $<9)\{$

return;

$\}$

recfunc$($m$/3)$;

for $($int j $=0$; j $<$ m; j$++)$ printf$(\%$d

$,$ j$)$;

for $($int j $=0$; j $<3$; j$++)$ recfunc$($m$/9)$;

for $($int j $=0$; j $<$ m; j$++)$ printf$(\%$d

$,$ j$)$;

recfunc$($m$/3)$;

for $($int j $=0$; j $<$ m; j$++)$ printf$(\%$d

$,$ j$)$;

$\}$

f$($m$)=$

b$)$ Find the particular solution for the following recurrence with the given initial values!

Also give the asymptotic upper bound $($O$()).$ Show all your work!

t$($n$)=$t$($n$-2)+$n$,$ t$(0)=$t$(1)=0$;