$O(...)$ running time $of$ the function $,in$ terms $ofn.$ Show your work, using the subtitutaion method and recoursion tree. Consider the following functions;

int recursive$2($int n$)$

$\{$

if$($n$<=1)$

return n

sum $=0$;

for $($int i $=0$; i $<$ n; i$++)$ sum$++$

return recursive$2($n$/3)+$ recursive$2($n$/3)+$ recursve$2($n$/2)+$ sum;

a$)[5$pts$]$ Give a recurrence relation $($T$($n$)=...)$ for this function. Include both base and recursive cases$)$

b$)[10$pts$]$ Solve the recurrence relation to get the $\backslash$Theta $(...)$ running time of the function, in terms of n$.$ Show

your work, using the substitution method and the recursion tree.