A divide and conquer algorithm takes an array of n elements and divides into three sub arrays of size n$4$ each taking $\backslash$Theta $($n$)$ time to do the subdivision. The time taken to combine outputs of each subproblem is $\backslash$Theta $(1)$

$.$

Which of the recurrences below will describe the running time T$($n$)$

on an input of size n

$?$ We ignore the base case for this discussion.

Select one:

a$.$

T$($n$)=3$T$($n$4)+\backslash$Theta $($n$)$

b$.$

T$($n$)=4$T$($n$3)+\backslash$Theta $($n$)$

c$.$

T$($n$)=4$T$($n$)+\backslash$Theta $($n$34)$

d$.$

T$($n$)=4$T$($n$3)+\backslash$Theta $(1)$

e$.$

T$($n$)=3$T$($n$4)+\backslash$Theta $(1)$