Q$5-14$ pts$)$

Consider the array $($assigned to you$)$ that has a sequence of negative integers $(<0),$ followed by a

sequence of $0$s and then a sequence of positive integers $(>0).$ Run a binary search algorithm in two stages

to determine the number negative integers, number of $0$s and the number of positive integers.

For each stage of the binary search algorithm:

$($a$)$ Show the appropriate initial values for the left index $($LI$)$ and right index $($RI$).$

$($b$)$ State the invariant property that will be maintained for the LI and RI vis$-$a$-$vis the array values for the

entire algorithm.

$($c$)$ Provide a pseudo code of the binary search algorithm, including the scenarios when you will move the

LI and RI

$($d$)$ Show your iterations in detail $($incl$.$ the latest vales for LI and RI; the middle index; the comparison

and the decision to move either the LI or the RI for that iteration$)$

Array$=\{-1,-1,5,0,0,0,0,0,5,2,10,1,1,5\}$