Defining a Factorial Function

Computer science

Introduction to Programs Data Types and Variables
Binary Numbers
Python Lists
For Loops in Python
While Loops in Python
Fun with Strings
Writing a Simple Factorial Program. (Python 2)
Stepping Through the Factorial Program
Flowchart for the Factorial Program
Python 3 Not Backwards Compatible with Python 2
Defining a Factorial Function
Diagramming What Happens with a Function Call
Recursive Factorial Function
Comparing Iterative and Recursive Factorial Functions
Exercise - Write a Fibonacci Function
Iterative Fibonacci Function Example
Stepping Through Iterative Fibonacci Function
Recursive Fibonacci Example
Stepping Through Recursive Fibonacci Function
Exercise - Write a Sorting Function
Insertion Sort Algorithm
Insertion Sort in Python
Stepping Through Insertion Sort Function
Simpler Insertion Sort Function

Defining a Factorial Function Defining a function in Python

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Defining a Factorial Function

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In the last few videos we wrote a nice little program here
that asks the user for some type of input
and then computes the factorial of that number
and then prints it out.
And thats nice, but you could imagine a world where
you would want to calculate the factorial in multiple places
or in multiple different programs
or in the same program you want to calculate
the factorial multiple times.
And you don't want to write this code
over and over again every time
you want to calculate the factorial.
So what I'm gonna to in this video,
is define a function that calculates the factorial
and then we could use that function
ever time we want to calculate the factorial.
So essentially what this function is going to do,
is going to put all this code,
all of this code right here,
in one place and then any other
program that i want to calculate the factorial,
i can just recall that code.
I don't have to rewrite it.
So let me just show you what I'm talking about.
So I'm going to define a function
and the keyword in Python,
so it is kind of a special word
that tells the interpret that something
special is about to happen.
The keyword in Python for defining a function is "def".
So I'm going to define a function,
I'm going to call it the factorial function.
And it tends to be a good idea
to name things in indicative of what they actually do.
Sometimes beginning programmers have a habit of
naming things like "x245"
and someone who comes in later
will have no clue what variable
or that function is all about.
So you definitely somehow name it
so it gives an idea what is supposed to do.
My function is called factorial
and the user when they call factorial,
they need to tell factorial
what number I'm going to take the factorial of.
So they gonna pass it in argument called "number".
And if these words look a little confusing
i will explain them in detail in a second
but you can just hopefully the more you see this
the more familiar you will get with these ideas.
And so they gonna pass it number
and I'm just going to have to return back
to the calling program
and I actually shouldn't have said
that the user is going to pass the number,
the calling program is going to pass the number
and I need to return back the factorial of that number
to the calling program.
So let me write this down as a comment actually.
So returns the factorial of the argument "number".
And sometimes you will hear the word parameter
and sometimes you'll hear the word argument.
When you are making a definition of a function,
this is more formally called a parameter.
"Number" is one of the parameters
to the factorial function.
The actual number that someone else passes to it,
so let's say someone calls factorial with a "3" here,
then more formally that 3 would be the argument.
So returns the factorial of the argument "number".
And this is the argument "number" right over here.
I don't mean this just is like arbitrarily the word number
I'm literally talking about this number over here.
Maybe I will say the argument "number".
Maybe I will put it in quotes to make it clear
that this is the argument,
I'm not talking about any general number.
Let's define it.
So we are going to use the same code essentially,
actually let me just copy and paste,
let me just copy and past a lot of what i took over here.
So I'm going to cut that out
and I'm going to re-paste it over here
but i have to be careful about my indentations
cause indentations are how Python knows
whats part of what, it knows how to interpret things.
So everything that is part of this function definition
has to be indented and we do it by four spaces.
One, two, three, four.
And this is another four.
One, two, three, four.
And this is part of the for-loop.
One, two, three, four.
And let's think about what we have so far.
It is going to be passed some number,
we define this variable "product" equals 1.
And we will talk more about scoping of variables
but this variable is only going to be useable
within this factorial definition
because the first time I define it right here
is inside of this right here
so we will go more into scoping of variables in the future.
And then with the same logic we did before,
"for i in range(number)",
now we are not getting the number using the input function
it is just being passed to the function,
then "product" is equal to "product" x ("i"+1).
Same logic as we had before.
So after you go through this for-loop,
after you go through it,
you are essentially going to go through it "number" times.
"Product" will have in it the factorial of "number".
And instead of outputting it directly,
what we wanna do is return,
we are going to return it to the calling program
and in the next video I'm going to diagram this out
a little bit cleaner if this seems a little bit confusing to you.
I'm going to return product.
So it is essentially the exact same code as we had before
but we have packaged it inside of a function,
we have defined a function.
It takes in, it has a parameter called a "number",
if you want a factorial of 3
you try the factorial of 3
and 3 would be the argument the thing
that is being put in the place of the variable "number"
or the thing that "number" is referring to.
You define "product" is equal to 1
and then you go "number" times.
So "for i in range(number)",
we have explained the logic of that in the previous video.
Everytime you start with 1,
then you do 1 x 1 is going to be 1,
then "product" is going to be 1
but then "i" is going to be 1.
"i" starts off at zero,
so it is going to be 1 x (0 + 1) gives you 1,
then "i" is 2, so it's going to be 1 x 1,
sorry, then "i" is 1
it is going to be 1 x (1 + 1), which is 1 x 2,
so it is going to be 2 then
and it will incrementing that way
and we explained it in detail in the last video.
And then finally it is going to return that "product".
So if we want to have the same exact behavior as before
but now we are using this function.
What we could do is, we could say,
we still have the input, so this is our function definition
but then along our main program,
we have defined our function
and now we could just say:
"Look, from the user get a non-negative integer
to take the factorial of"
And let's put that into,
lets call that a variable called "user_input".
And then what I'm going to do
is I'm going to define another variable
to called "factorial_of_user_input"
and now this is going to be interesting.
I'm going to call this function up here,
so this is going to be equal to
factorial of whatever the user had input.
So the factorial of "user_input",
the factorial of this variable right over here.
The factorial of user input.
So now "factorial_of_user_input" will be storing,
I guess we should say,
it would be pointing to the actual answer
and now we just have to print it out.
So now we can print "factorial_of_user_input".
They look like sentences
but these are just variable names
that I'm naming this way
so you really now what's inside of those variables
or what those variables are really pointing to.
So "factorial_of_user_input".
Now, you know the moment of truth
is always saving the program and actually trying to run it.
So lets try to run it right now and see what happens.
Let's see what happens here.
So at least nothing broke so far,
so once again,
so I want to be clear the program started here
but up here all we did is defined this
so it is not creating any interaction with the user,
it is actually not processing anything just yet,
so it just defines this function then it goes down here
and says: "Okay, get some input form the user"
and thats what we are doing right here.
After we input some number here,
then it's gonna actually call this function with that number
that we put, the number that we put,
is gonna go put in the "user_input"
and then it is gonna call factorial
with "user_input" as an argument.
So let's try with the number 3.
And it did not work!
Oh, and I see why it did not work
because I had this leftover from the previous program
which actually makes no sense now.
So let me get rid of that.
It is a good lesson that seldom on the first
try does something work perfectly.
Let me try it again!
That was just nonsense
that i didn't even realize what was down there.
So let me try it again.
So 3 again.
And it gave me a good answer.
It gave me the factorial of 3
and what's cool now is because
now my python interpreter
is assuming that this definition has been made
I can now call the factorial straight from the interpreter,
if I had another program
I could call it multiple ways
and now you should hopefully appreciate
why it is cool that we made this function definition
cause we can calculate,
cause I've defined this function factorial,
I can calculate the factorial of 4.
It is 24.
I can say that the factorial of 5 - the factorial of 3.
114.
I can take the factorial of 12
and you can tell the computer,
even though it is just interpreting all this,
we will talk more interpreted vs compile code,
it's incredibly fast.
Faster then we can really even fathom.
So this is the real power of a function,
is that I don't have to rewrite code every time now,
I can just call it with different arguments.
So factorial of 2, I can do it every time,
I don't have to rerun the program.
And if I write other programs that use factorial,
maybe I do something in combinatorics,
I can just use this as a function,
infact I don't even have to know
what is going on inside the function.
That's one of the other powerful aspects of functions is
that let's say i write a bunch of programs that call,
so i have this program right here that calls factorial.
But let's say you come up with a better way of
writing this right over here.
As long as your program
that does the same thing with different guts,
the end user won't notice.
So maybe you write a faster way
or a simpler way of doing this.
The way that uses less memory or less CPU power.
Then you could just replace this later on
and then any program that calls it,
as long as it still works,
it will work for that program
and it will just work that much better.

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