Given an array a of size n and value v$,$ we wish to find the element a$[$j$]$ that is "closest" to v$.$ Mathematically, the closest element is one that minimizes $|$a$[$j$]$v$|$ the absolute value of the difference between the element and v

$.$

If there are multiple elements in the array that are equally close then any of the elements can be returned.

What is the complexity of the best algorithm to solve this problem? Choose all valid options from those given below.

Select one or more:

a$.$ If the array a

is unsorted, then the worst case complexity is $\backslash$Theta $($n$)$

obtained by scanning the elements of the array one by one.

b$.$ If the array a

is sorted, then the worst case complexity is $\backslash$Theta $($log$($n$))$

obtained by modifying binary search.

c$.$ We can solve the problem in $\backslash$Theta $(1)$

time by simply checking if the middle element of the array equals v

or not.

d$.$ The best approach is to use merge sort to sort the array in ascending order and then perform a modified binary search algorithm.

e$.$ The best approach is to use insertion sort to sort the array in ascending order and then perform a scan of the array a

from left to right.