In this task, you will complete four recursive functions and trace them for some sample inputs.

a$.$ Create an HTML file that includes five buttons with the following labels: "recursive find A$",$

"recursive find B$",$ "recursive find C$",$ "recursive palindrome", and "recursive count

asterisks". Create a div in your HTML to hold the results of calls to corresponding javascript

methods. You can style this page as you like. Feel free to use the HTML and CSS from prior

labs as a template, if you like.

b$.$ Create a JavaScript file that responds to clicks of these buttons. All implementations should

be recursive.

a$.$ Problem $1.$ Create an array of $30$ random numbers that range between $1$ and $100.$

Then, write a function that will receive a number from the user and determine if

that number exists in the array or not.

For instance, assume the array is:

$[2,93,14,89,12,3,81,15,14,89,52,96,71,82,5,2,41,23,52,59,44,44,88,39,$

$49,50,97,45,48,36]$

Now, assume the user enters $89,$ the program should output true. But, if the user

enters $77,$ the program should output false.

Approach:

We will be implementing this method in two different ways. Both will be recursive.

First, implement a method called $f$ indA$($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 FIRST item that

is in the array. If this first item is equal to $x,$ return true. If not, remove the first item

from A and call findA$(x,A)$ on the revised list. 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?

Next, copy the following trace table in your word file and trace the input values to

the function fidin$(x,A)$ 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. Note

that in this example, 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.