What is the recurrence relation for the given code below?

private static void function$\_$foo$($int $[]$ a$,$ int i$,$ int j$)$

$\{$

if $($i $>=$ j$)$ return;

int mid $=($i $+$ j$)/2$;

int k$=$ rand$()$; $//$ this is a constant time operation that can be considered as $1.$

function$\_$foo $($a$,$ i$,$ mid$)$; $//$ inputs the left half of the original array a$[]$

function$\_$foo $($a$,$ mid$+1,$ j$)$; $//$ inputs the right half of the original array a$[]$

$\}$

a$)$ Tn$=2$ Tn $+2$n;

b$)$ Tn $=$ Tn$-1+1$;

c$)$ Tn $=2$ Tn$/2+1$;

d$)$ Tn $=$ n log n $+1$;

e$)$ Tn$=2$ T$2$n $+$ n;