Part 3: Factorial function In computer science, and other fields, we frequently need to know how many possible combinations are possible given a specific number of numbers or characters. For example, consider three color cards: red (R), green (G), and blue (B). How many different orders are possible of these three cards? RGB, RBG, GRB, GBR, BRG, BGR = six (6) possible combinations The mathematical term for this calculation is factorial (see Factorial Function !Links to an external site. web page) and is expressed using the exclamation point (!). Surprisingly, the JavaScript Math object does not have a function for factorial, so we will write our own.

Question

Part 3: Factorial function

In computer science, and other fields, we frequently need to know how many possible combinations are possible given a specific number of numbers or characters. For example, consider three color cards: red (R), green (G), and blue (B). How many different orders are possible of these three cards?

RGB, RBG, GRB, GBR, BRG, BGR = six (6) possible combinations

The mathematical term for this calculation is factorial (see Factorial Function !Links to an external site. web page) and is expressed using the exclamation point (!). Surprisingly, the JavaScript Math object does not have a function for factorial, so we will write our own.

So how do we calculate factorial? The steps to accomplish a task are known as an algorithm. An algorithm is a series of steps that given the same input will always produce the same output. Often, many possible algorithms exist to accomplish the same task. To calculate the factorial of a specific number, we need to multiply every number starting at 1 and up to and including the number. The example below is for the factorial of 3, or 3!, also the same number of our color cards, so we would expect the answer to be 6.

3! = 1 * 2 * 3 = 6

Factorials only work on values >= 0, with a special rule for 0! = 1.

Below are the factorial rules you will need to implement.

Input	Result
Input > 0	Calculate and return factorial
Input = 0	Return 1 by rule
Input < 0	Return -1 to indicate error
Non-numeric input	Return -1 to indicate error

To create a factorial function, we will give you the algorithm as comment steps, and you will provide the code.

function factorial (num) { // Step 1: Set -1 as a default result for values < 0 (invalid input) // Step 2: Test if input is > 0, calculate factorial and set result to calculated value // Step 3: Test if input = 0, set result to 1 // Return result }

>> Use the above code outline steps and rules to write the factorial function. Your function must use a for loop and if conditional syntax.

Tip: Yes, you can find solutions to this function online, but please try to solve this problem on your own. Your programming "muscles" will only improve through programming "exercise," and using online solutions is not only against the integrity policy of this course and the University, but will only make solving later problems much more difficult where no online solution exists.