b$.$ Problem $2.$ Again, create an array of $30$ random numbers that range between $1$ and

And again, write a function that will receive a number from the user and

determine if that number exists in the array or not.

Approach:

This time, implement a method called $f$ indB $(x,A),$ where $x$ is the number we are

looking for and A is an array. In the body of the function, compare $x$ with the MIDDLE

item that is in the array. If this item is equal to $x,$ return true. If not, divide A into

TWO lists as follows:

Call the middle of index of the array mid.

Place items at indices mid$+1$ to A$.$ length$-1$ in one array and call it A$1.$

Place items at indices $0$ to mid $($excluding mid$)$ in an array called A$2.$

Then, recursively call $f$ indB $(x,A1)$ and findB$(x,A2).$ If you call find on an empty

list, you will want to return false.

Writing any explicit loop in your code results a $0$ for this question. Remember to provide

pre$-$ and post$-$conditions. How many recursive calls will you need to search the entire

list? Do you think this implementation will run more quickly than your first

implementation? Why or why not? How might you limit the number of recursive calls in

your implementation?

Now copy the trace table on the next page in your Word file and trace your function

findB$($x$,$A$)$ for when A and x are initially $1,6,10,14,77,82,100$ and $77,$

respectively. As a guideline, we have populated the tables with the values for the

first $2$ calls and the corresponding returned values for each of those calls. Again

remember that, the call numbers will be populated top down $($i$.$e$.$ time elapses from

row $x$ to row $x+1)$ while returned values are populated bottom$-$up $($i$.$e$.$ the value in

row $x$ is returned before the value in row $x-1.$ You may want to use console.log to

observe these values when you write your solution.