# Primitive types

You can make a program for almost anything. There are programs that read books, rank movies, look for interesting numbers, or even play games. In order for programming to be so versatile, it needs to understand a few things — numbers and words, for instance. We call those things primitive types.

## Python's primitive types

Here's the full list of the primitive types in Python.

• int: Integers are whole numbers. You can do math stuff with them. We'll talk about more details later.
>>> 1 + 2 * 3
7
• float: Floats are just numbers that have decimal points. Notice in the example below that dividing two integers produces a float. We'll revisit this point later.
>>> 8 / 2
4.0
>>> 3.14
3.14
• str: Strings represent words or sentences. They're called strings because they make up a sequence, or string, of characters. There is no difference between using single quotes or double quotes, as long as you're consistent. Looking at the last example below, note it's possible to include any character, even quote marks, within a string.
>>> 'robots'
'robots'
>>> "tyrannosaurs"
'tyrannosaurs'
>>> "problem'
Error
>>> "'quote'"
"'quote'"
• bool: Booleans represent whether something is True or False. Those are the only two booleans in Python. We'll talk about them in a separate chapter.
>>> True
True
>>> 1 < 0
False
• None: This is a special value in Python that literally represents nothing. Take a look at the first example below. Notice how when you evaluate None, the result doesn't get displayed on the screen. This is unlike all the examples above, where evaluating 8 / 2 displayed the result 4.0, evaluating 1 < 0 returned False, and so on. If you try to do things with None, you'll usually encounter an error.
>>> None
>>> 0 > None
Error

Make sure you understand these primitives before moving on to the next section.

## Converting between types

You can also convert between primitive types. You probably won't do this very often, but sometimes it can be helpful. For example, you might have a float and want an integer, or have a string and want a boolean. Here's how to change between them.

• int: You can convert to an integer using the function int. Note that converting a float to an integer always rounds down. Also, int(True) gives you 1 while int(False) gives you 0.
>>> int(4.9)
4
>>> int('1')
1
• float: You can convert to a float using the function float. This works pretty much the same as int, except you get a decimal number.
>>> float(4)
4.0
• str: You can convert to a string using the function str.
>>> str(10)
'10'
>>> str(True)
'True'
>>> str(None)
'None'
• bool: You can convert to a boolean using the function bool. Everything in Python evaluates to True, except for 0, 0.0, False, None, and the empty string ('' or ""). Empty lists, tuples, dictionaries, and sets also evaluate to False, but we won't learn about those for a while.
>>> bool(4)
True
>>> bool(None)
False

I've only gone over the not-too-obvious conversions above. The rest are pretty intuitive, but don't worry because I'll make sure to go over all the weird edge cases in the practice. For now, just check that the conversions above make sense to you. Also, in case you're wondering, there's no way to convert to None because that wouldn't be very useful. (If you ever wanted to get None, you could just write None.)

# Variable Assignment

Now that we have a handle on the different types available to us, let's talk about how we can use them.

## Fundamentals of variable assignment

Lots of the time there's a particular value we want to keep track of, by giving it a name. That's where variables come in. You've probably encountered variables in math class, named obscure things like $x$, $y$, or $z$. In computer science we prefer more meaningful names, like this:

>>> magic_level = 10

Now, the variable magic_level is assigned to the value 10. I can ask Python to evaluate an expression involving magic_level, and it will use 10 where it should.

>>> magic_level
10
>>> 2 * magic_level + 7
27

We could even assign another variable, using the one we just defined.

>>> twice_magic_level = 2 * magic_level
>>> magic_level
10
>>> twice_magic_level
20

What happens if magic_level increases to 11? We might expect twice_magic_level to increase to 22, but that's not actually the case.

>>> magic_level = 11
>>> twice_magic_level
20

Why? This is very important. Once twice_magic_level has been assigned to 20, it stays that way until we explicitly change it by writing something like twice_magic_level = 22. We could also say twice_magic_level = 2 * magic_level, and this would have the same effect since we just reassigned magic_level to be 11.

Variables are pretty useful, so make use of them. They can make your code more efficient, and easier to read. If you ever want Python to remember a value, you should make a variable for it.

## How variable assignment works

In the examples we've seen so far, the thing on the left side of the equals sign has always been a variable name. This is for good reason.

You actually can't write 11 = magic_level. This is because = doesn't represent a statement about the relationship between two values, like it does in math. Instead, = is our way of telling Python to change the left side to be whatever's on the right side. So if magic_level was 10, then saying 11 = magic_level is like telling Python to change 11 to be equal to 10. That doesn't make sense.

You also couldn't write twice_magic_level / 2 = magic_level. That's because twice_magic_level / 2 is a mathematical expression, not a variable. It involves a variable, but Python isn't smart enough to do the algebra and rearrange this into a legal expression like twice_magic_level = 2 * magic_level.

To summarize, you need the left side of the equals sign to be a variable name. It can't be a value, like 11. It can't be an expression that involves a variable name, like twice_magic_level / 2. The left side of the equals sign has to be a variable name, and that's it.

In order to avoid these mistakes, let's talk about how it works when Python assigns variables. Whenever you encounter an equals sign, this is what you have to do:

1. Do not look at the left side of the equals sign. It doesn't matter yet.
2. Evaluate the right side of the equals sign. Write the result somewhere with enough space.
3. Now look at the left side of the equals sign, and assign that variable to the value you just wrote down.

So for example, when you see magic_level = 10:

1. Cover the left side. For now, we just care about the = 10 part.
2. Evaluate the right side. 10 evaluates to the integer 10.
3. Now look at the left side. We see the name magic_level, so we assign magic_level to 10.

Python always follows this 3-step procedure, whenever you want to give a new value to a variable. Don't forget it. We'll see some pretty complicated stuff in later chapters, so it will serve you well to remember this little procedure. Even when you're writing code, just keep in mind that the thing on the right gets evaluated before we bind it to the thing on the left.

## Updating variables

In our earlier example we wanted to increase magic_level from 10 to 11. This was pretty straightforward, because we just had to write magic_level = 11. But what if we didn't know the current value of magic_level, and we wanted to increase it anyways? Referring back to the 3-step procedure we just covered, would need something like this to change magic_level:

magic_level = _______________

We just have to fill in the blank with an expression that evaluates to 1 more than the current value of magic_level. So, what evaluates to 1 more than the current value of magic_level? Let's try magic_level + 1.

magic_level = magic_level + 1

It looks a bit weird. In math class you would never see something like this. But in computer science, it's okay. Why? Recall from earlier, = is different in math than it is in computer science. The expression above is not a statement claiming that magic_level is the same as magic_level + 1. It's a command, telling Python to change magic_level so that it equals the current value of magic_level + 1. To see how it works, we'll apply the 3-step procedure that we just learned:

1. Cover the left side. For now, we just care about the = magic_level + 1 part.
2. Evaluate the right side. magic_level + 1 evaluates to 11, if the current value of magic_level is 10.
3. Now we look at the left side. We see the name magic_level, so we assign magic_level to 11. We successfully increased it!

Make sure you understand why this works, before you keep reading.

## Shorthand for updating variables

It's actually really common to do stuff like magic_level = magic_level + 1. In fact, it's so common that there's a special shorthand for it in Python: magic_level += 1. You can do this with any of the four arithmetic operators. Here are some examples:

>>> x = 8
>>> x += 2
>>> x
10
>>> x = 8
>>> x -= 2
>>> x
6
>>> x = 8
>>> x *= 2
>>> x
16
>>> x = 8
>>> x /= 2
>>> x
4.0

## Multiple assignment

It's even possible to assign multiple variables on one line. These next two expressions are exactly the same:

>>> x = 10
>>> y = 'dragon'
>>> z = True
>>> x, y, z = 10, 'dragon', True

But assigning multiple variables on one line is not always the same as assigning each variable on a separate line. For instance, consider this code:

>>> x = 5
>>> x = x + 5
>>> y = x + 10

In the end, x is 10 and y is 20. It's different if we combine the second and third line:

>>> x = 5
>>> x, y = x + 5, x + 10

Now x ends up 10 and y ends up 15. To understand why, we'll have to walk through it more carefully. The first line is pretty simple, we just bind x to 5. The next line is less simple, so let's use the 3-step procedure for variable assignment that we learned earlier.

1. Cover the left side. For now, we just care about the = x + 5, x + 10 part.
2. Evaluate the right side. x is 5, so x + 5 evaluates to 10 and x + 10 evaluates to 15.
3. Now we look at the left side. We see the names x and y, so we assign x to 10 and we assign y to 15.

Pay close attention the second step. We use the old value of x to calculate both x + 5 and x + 10. That's because everything on the right gets evaluated before we update x or y. Whenever you come across a complicated expression, you should refer back to the 3-step procedure for variable assignment.

This syntax is also particularly convenient for swapping the values of two variables. Pretend we want to swap the values of the variables width and height. Here's how we might attempt it, without using multiple assignment:

>>> height = width
>>> width = height

But this won't work, since both variables end up with the original value of width. Instead, we would need to bring in a third, temporary variable:

>>> old_height = height
>>> height = width
>>> width = old_height

It's a lot simpler using multiple assignment, since both values on the right get evaluated before updating them on the left:

>>> height, width = width, height

Review everything above, and check that it all makes sense up to this point, before you go to the next section.

# Tracking state

Up until now, we've been keeping track of all our variables mentally. But as we write more and more complicated programs, it's going to get much harder to do that. Like, literally impossible. It's time to meet your most useful tool for learning computer science. (Yes, even more useful than computers. Actually.) A pyagram, short for "Python diagram", is a way of tracing how your code runs. You use pyagrams to work your way through confusing bugs, or edge cases you don't understand. How do they work? Basically, we pretend we're the computer, and we go through a piece of code one line at a time to see what it does.

Here's an empty pyagram. The box is called a frame, which just means it's a place where code gets executed. The word "global" tells you this particular frame is the global frame. It's always the first thing you draw in a pyagram, and for this chapter we'll constrain ourselves to the global frame only.

Whenever you make a pyagram, you'll have a piece of code that you're analyzing. Let's use this code as an example:

>>> whale = 50 + 50
>>> dolphin = 50
>>> whale * dolphin
5000
>>> fish = int(whale / dolphin)
>>> fish *= 'splash '

Here's how that get's expressed in our pyagram:

As always, we start out with the global frame. It is empty.

In the first line we assign the variable whale to the integer 100.

Then we assign dolphin to 50.

The next line is whale * dolphin, which equals 5000. You might notice this value doesn't get assigned to a variable. Python still calculates the number 5000 and displays it on the screen, but since we don't tell it to keep track of 5000 with a variable, Python will forget about it immediately. Our pyagram looks the same as before.

Now let's move on to the fourth line. It's a bit too complicated to do mentally, so let's use the 3-step procedure for variable assignment that we learned earlier.

1. Cover the left side. For now, we just care about the = int(whale / dolphin) part.
2. Evaluate the right side. int(whale / dolphin) evaluates to the integer 2, since whale / dolphin evaluates to the float 2.0.
3. Now we look at the left side. We see the name fish, so we assign fish to 2.

We just have one more line to go: fish *= 'splash '. It's shorthand for saying fish = fish * 'splash '. Since fish is currently 2, it should get reassigned to the string 'splash splash '. If that's confusing, we could also try applying the 3-step procedure from before.

1. Cover the left side. For now, we just care about the = fish * 'splash ' part.
2. Evaluate the right side. fish * 'splash ' evaluates to 'splash splash ', since fish is 2.
3. Now we look at the left side. We see the name fish, so we assign fish to 'splash splash '.

Now we have finished the pyagram.

We'll be using pyagrams a lot in this class, especially as we get into more complicated material, so make sure you're comfortable with them now.

Now we have a good understanding of variable assignment, and how to keep track of our variables using pyagrams. Let's talk about some of the operators available to us, in more detail. Before we get started, though, here are 2 rules about the math operators in Python:

• If you're doing math and any of the numbers is a float, then your output will also be a float. This is because we never want to lose accuracy by getting rid of the decimal place.
• If you're doing math and you see True or False, pretend True is 1 and False is 0. This is because computers work using binary, a language of all ones and zeros. The boolean values True and False are encoded with these numbers.

Now let's talk about Python's math operators.

1. Add: + We've already seen that addition works with numbers. Guess what? You can also add strings. This works like you would expect. It doesn't matter whether you use single quotes or double quotes.
>>> 1 + 2.0
3.0
>>> "taco" + 'cat'
'tacocat'
2. Times: * Multiplication also works between an integer and a string, like so:
>>> 3 * 'vroom!'
'vroom!vroom!vroom!'
>>> 3.0 * 'vroom!'
Error
3. Divide: / Division always gives you a float, even if both the numbers you're dividing are integers. If you ever try to divide by 0, you will get an error.

4. Exponent: ** You may occasionally want a number to the power of another number. Here are some interchangeable expressions:

• English: 2 to the power of 5.
• Python (the hard way): 2 * 2 * 2 * 2 * 2
• Python (the easy way): 2 ** 5
5. Mod or remainder: % Mod is just another word for remainder. For example, 9 mod 4 is 1, since 9 divided by 4 is 2, with the remainder 1. Mod doesn't care about the 2, the remainder of 1.

>>> 9 % 4
1

6. Floor divide: // Floor divide is kind of like the opposite of mod. Instead of giving you the remainder, it gives you everything except the remainder. You can also think of it like normal division, but rounded down.
>>> 9 // 4
2
>>> 9 / 4
2.25

# Practice: the Fibonacci sequence

Using what we've learned today, we can already do snazzy calculations. The Fibonacci sequence is a good example. It starts with the numbers 0 and 1, and every subsequent number is defined by the following recurrence relation, where $F_n$ denotes the $n$th number in the sequence:

F_n = F_{n-1} + F_{n-2}

That means every Fibonacci number is the sum of the previous two. The Fibonacci sequence also grows pretty quickly. Just the 15th number in the sequence is already in the hundreds, so it's not the kind of thing you want to calculate by hand. Let's see if we can use our cool new programming skills to find it.

We'll start by defining fib_0 and fib_1 properly. Then we'll be able to build up from there.

>>> fib_0 = 0
>>> fib_1 = 1

Now we can proceed to calculate the remaining Fibonacci numbers, according to the formula above. We'll stop at fib_14, since we started counting at fib_0.

>>> fib_2 = fib_1 + fib_0
>>> fib_3 = fib_2 + fib_1
>>> fib_4 = fib_3 + fib_2
>>> fib_5 = fib_4 + fib_3
>>> fib_6 = fib_5 + fib_4
>>> fib_7 = fib_6 + fib_5
>>> fib_8 = fib_7 + fib_6
>>> fib_9 = fib_8 + fib_7
>>> fib_10 = fib_9 + fib_8
>>> fib_11 = fib_10 + fib_9
>>> fib_12 = fib_11 + fib_10
>>> fib_13 = fib_12 + fib_11
>>> fib_14 = fib_13 + fib_13
>>> fib_14
377

For extra practice, think about how we might make a pyagram for the code above.

We'll see very soon how to make this calculation easier and more efficient.