Project 2 - Factorial

This project won't be much difficult than the last one, but it's still a fun one.

My source code.

So, factorial of a number, some of you might be wondering what that is. The factorial is written like this 3!, 5!, 1234! and it multiplies a series of descending natural numbers from the given number.

For example:

• 4! = 1 x 2 x 3 x 4 = 24 
• 7! = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 5040 
• 0! = 1

As you can see the factorial function rises very quickly.

There are two possible approaches to writing a factorial function, iterative and recursive. Iterative generally means a loop of some kind, and recursion which is a powerful tool in programming, but somewhat tricky to understand, happens when a function calls itself.

Iterative version:
The iterative part will consist of a simple for loop and a variable in which we will save the result. The only tricky part is the declaration of both. The first thing we must realize that we're operating with multiplying so that means that we have to be careful with zeros. So we set our sum = 1 and the for loop to for(int i = 1; i <= factorial; i++). The only thing that is left if the body of the for loop. In there we will multiply the sum with the current i.

Written out for factorial of 4 this looks like:

• sum = 1; i = 1; sum becomes 1
• sum = 1; i = 2; sum becomes 2
• sum = 2; i = 3; sum becomes 6
• sum = 6; i = 4; sum becomes 24 
• The loop ends and 24 is the correct result

Recursive version:
Here be dragons. Just kidding, recursion is not that scary (in this case). Well because recursion is when a function calls itself, we'll obviously need a function. We know that we have two cases in which 1 is the result - 0! and 1!. And we can write the an if statement that handles this. Now comes the else part, where the good stuff happens. Here I'd like to bring up an analogy for recursion that our teacher mentioned. Imagine you're being called by your buddy. You're talking, having fun, and then suddenly your mother calls you and you put your buddy on hold. Then your mom talks to you, asks you showered, eaten anything etc. A minute later your boss calls and you put your mom on hold, because you don't want to lose your job. Then you talk to your boss for a while about some reports and then finally he hangs up. Then you're back at your mom, and you say goodbye to her, and you're back at the start with your buddy. This is when recursion clicked for me (of course it helps to do some exercises). So if our number isn't 1 or 0, we should do the following: multiply the number, and let's call the function again with the number subtracted by 1 (this is your buddy calling), and then we do this until we subtracted the number to 1 (this is when the boss hangs up and you go back the chain).

Let's write this out with the same example of 4!:

• we call the function; factorial(4)
• we check is it 1 or 0; No; now we do 4 * factorial(3)
• 3 is not 1 or 0, we do 3 * factorial(2)
• 2 is not 1 or 0, we do 2 * factorial(1)
• 1 IS 1 or 0; we return 1
• now we go back up the chain
• 2 * factorial(1) returns 2
• 3 * factorial(2) returns 6
• 4 * factorial(3) returns 24 and this is the result

I hope you liked it and please feel free to leave any comments. Thanks for reading.