This is a collection of notes and exercises on the topics covered in COMP 364. The material here is by no means exhaustive and is simply meant as a reference and study aide. I will try my best to keep these notes up to date with the material as we cover it. Please feel free to leave comments at the bottom if anything is unclear.

There is nothing to writing. All you do is sit down at a typewriter and bleed. (Ernest Hemingway)

Data Types, Names, and Objects

reference

Anything you can tell Python to remember in memory is what we call an Object. An object is simply a piece of information that Python stores in a box and gives it a label ID.

Every Object is unique is given a unique identifier id(object)

You can assign names to objects using the = operator.

larry = 5

Assigns the name larry to the object 5. Now if I want to use the value of the object I can just use the name instead of its super complicated id which if i’m crazy I can get using id(5) or id(larry).

The mapping of names to objects is called a namespace. You can give multiple names to the same object.

In Python we have things (objects) and names for things. Think of people (objects) wearing name stickers. The namespace is like the party they’re all attending. We can swap around people’s names (like removing and sticking on nametags) but the people themselves stay the same.

#gives the object '5' the name samantha
>>> samantha = 5
#now the object 5 has 2 names: samantha, tamara
#python puts another sticker that says 'tamara' on 5
>>> tamara = samantha
>>> print(samantha, tamara)
5 5
# now I create the object 500 give it a sticker that says samantha
>>> samantha = 500
# this has no effect on the object '5' samantha used to point to
>>> print(tamara)
5

There are several kinds (eventually we will see this is actually infinite) of data (objects) you can tell Python to remember and to perform operations on. The ones that have been defined out of the box by Python are called the built-in data types.

Here are some of the simplest ones:

  • int e.g. 1, 2, 3, -500, 10000
  • float e.g. 0.1, 1.0, -129.992
  • str e.g "my name is Margaret"
  • bool e.g. True, False
  • NoneType e.g. None empty data.

As we can see, each of these pieces of information is of a different type (aka class) and so each of them behaves differently.

We can always get the type or class of a piece of data with the type(object) function.

>>> print(type("Pizza"))
<type 'str'>

This is how Python is able to know how to manipulate the different types of data. It says, “everything is an Object, and I can perform operations on Objects according to their kind.”

God made the wild animals according to their kinds, the livestock according to their kinds, and all the creatures that move along the ground according to their kinds. And God saw that it was good. (Genesis 1:25)

An operation is an action that the interpreter performs on expressions to yield a new expression.

Depending on the type of Object we are dealing with, we can perform different kinds of operations.

Some examples:

#this is an expression. 
5  
#this is also an expression built using the + and / operators
(5.0 + 4) / 5 
#this is NOT an expression
#no new value is yielded , we are just labeling an object.
#python evaluates the expression on the right
#and assigns a name to the resulting object
matthew = (5.0 + 4) / 5

Operations on numbers

reference

  • + - * / pretty straightforward. Work on float and int
  • % modulo operator, works on int and returns the remainder of dividing the first number by the second.
  • += -= /= *= are are shorthand for x = x + 1, x = x * 4 etc. They evaluate the expression on the right and assign it back to the same name. Example:
#this
>>> x = 5
>>> x += 2 
7
# is equivalent to this
>>> x = 5
>>> x = x + 2
7

Boolean operations

The bool data type can take on one of two values: True or False. Booleans are very useful when we are trying to make decisions with our program.

Operations (given A and B are bool expressions):

  • A and B results in True if and only if A is True and B is True.
  • A or B results in True if one or both of A or B is True
A B or and
True True True True
True False True False
False True True False
False False False False
  • > < >= <= are technically operations on numerical types but they yield a boolean. e.g. 5 <= 6 results in True 6 == 6 is also True.
  • == checks two objects for equality of value.
  • is checks whether two objects are the same. i.e. have the same id.
>>> s = "Juicy J"
>>> y = "Juicy J"
>>> id(s)
4353534928
>>> id(y)
4353535504
>>> s == y
True
>>> s is y
False
>>> y = s
>>> y is s
True

You will probably never use is but == is very useful.

String operations

You can evaluate a slice of a string using indices. An index is like a counter that indicates the position of a character in a string.

This is the syntax for string slicing on some string s: s[start:stop:step]. The stop index is not included in the new string. The first index of a string is 0.

Negative numbers for start, stop, step, mean “go from the end of the string towards the start.

Note that slicing the string gives you a new string and leaves the original string unaffected.

>>> s = "Bad and Boujee"
#this will be a new string object
>>> bad = s[0:3] 
>>> print(bad)
"Bad"
#if you don't specify a stop index it goes till the end
>>> boujee = s[8:]
>>> print(boujee)
"Boujee"
#string from start to end skipping every other character
>>> skip = s[::2]
>>> print(skip)
'BdadBue'
>>> s[-1]
'e'
>>> s[-6:]
"Boujee"
# nice way to reverse a string. give a negative step.
# give me whole string and step in a negative direction
>>> s[::-1]
'eejuoB dna daB'
# go backwards stepping by 2 positions
>>> s[::-2]
'ejo n a'
# after all this, the original string is unaffected
# we were just creating new strings each time
>>> print(s)
"Bad and Boujee"
# you can also multiply strings!
>>> s * 2
'Bad and BoujeeBad and Boujee'

You can use len(string) to get the length of the string (i.e. number of characters. This returns an integer.

>>> len(s)
14

You can stick two strings together. This is called concatenation. Concatenating two strings yields a new string. The + operator on strings concatenates.

>>> first_name = "Taylor "
>>> last_name =  "Swift"
>>> full_name = first_name + last_name
>>> print(full_name)
"Taylor Swift"
# a shortcut using +=
# this creates a string by evaluating
# first_name + last+name
# and gives it the name first_name
>>> first_name += last_name
>>> print(first_name)
"Taylor Swift"

Mutability

Some objects in Python you are allowed to modify, and others you are not allowed to modify. This is known as mutability (can modify) and immutability (cannot modify). Strings are immutable. You can give different names to the same string, but you can never modify the contents of the object.

s = "Justin"
s[0] = "j" # ERROR

The same goes for numerical and boolean types. The data types we have seen until now are all immutable. The main advantage of immutability is that it makes objects easier to store and look up because Python can always assume they will take up the same amount of space in memory and have to be accessed in exactly the same way. Having immutable types also makes sense when we don’t want the objects to change how they behave. We wouldn’t want to change the meaning of the integers or boolean objects since it is likely to lead to nonesense.

The cost is that if we want to compute expressions with immutable objects, we have to essentially make copies and create new objects each time. See string example above. We’ll see examples of mutable objects in the upcoming sections.

Accessing object attributes

We saw that objects are pieces of data that behave according to their kind. What this means is that they have a specific set of attributes that are shared among all objects of a certain type. attributes are just other objects that belong to each object. So a specific person (object) of type human (class) can have various attributes which themselves are objects with names. For example, the person can have an attribute called 'height' which is a float with some value. Different people will have different values but they will all have as an attribute the height object.

We can access an object’s attributes using the . operator followed by the name of the attribute we want to access.

The dir(object) function prints out a list of all the attributes of a given object or class.

>>> dir(int)
>>> ['__abs__', '__add__', '__and__', '__class__', '__cmp__', '__coerce__', '__delattr__', '__div__', '__divmod__', '__doc__', '__float__', '__floordiv__', '__format__', '__getattribute__', '__getnewargs__', '__hash__', '__hex__', '__index__', '__init__', '__int__', '__invert__', '__long__', '__lshift__', '__mod__', '__mul__', '__neg__', '__new__', '__nonzero__', '__oct__', '__or__', '__pos__', '__pow__', '__radd__', '__rand__', '__rdiv__', '__rdivmod__', '__reduce__', '__reduce_ex__', '__repr__', '__rfloordiv__', '__rlshift__', '__rmod__', '__rmul__', '__ror__', '__rpow__', '__rrshift__', '__rshift__', '__rsub__', '__rtruediv__', '__rxor__', '__setattr__', '__sizeof__', '__str__', '__sub__', '__subclasshook__', '__truediv__', '__trunc__', '__xor__', 'bit_length', 'conjugate', 'denominator', 'imag', 'numerator', 'real']

All of these are names to objects that can be accessed for any instance of the int class. So if I store a specific int object I should expect the same result from dir()

>>> x = 300
>>> dir(x)
['__abs__', '__add__', '__and__', '__class__', '__cmp__', '__coerce__', '__delattr__', '__div__', '__divmod__', '__doc__', '__float__', '__floordiv__', '__format__', '__getattribute__', '__getnewargs__', '__hash__', '__hex__', '__index__', '__init__', '__int__', '__invert__', '__long__', '__lshift__', '__mod__', '__mul__', '__neg__', '__new__', '__nonzero__', '__oct__', '__or__', '__pos__', '__pow__', '__radd__', '__rand__', '__rdiv__', '__rdivmod__', '__reduce__', '__reduce_ex__', '__repr__', '__rfloordiv__', '__rlshift__', '__rmod__', '__rmul__', '__ror__', '__rpow__', '__rrshift__', '__rshift__', '__rsub__', '__rtruediv__', '__rxor__', '__setattr__', '__sizeof__', '__str__', '__sub__', '__subclasshook__', '__truediv__', '__trunc__', '__xor__', 'bit_length', 'conjugate', 'denominator', 'imag', 'numerator', 'real']

Okay so that’s good we get the same list of attributes. Let’s see what happens when we try to access one of them.

>>> x = 300
>>> x.bit_length() #more on the brackets later
9 # number of bits to store this number

This is a good point to introduce functions. We’ll get back to accessing object attributes in a bit.

Quick intro to functions

reference

Python is not very fun without functions so let’s give you a little intro so we can talk about more interesting things. I will go into more detail in a later section.

You can think of a function as a box that performs some task given some input and produces some output.

In Python terms, it is a block of python code that executes when you call it. When you call it you can determine how it will run.

You can write your own functions to do whatever you want. Here’s the syntax for defining a basic function.

def function_name(function_input):
	#some code
	
	return #some value

Essentially, you are storing an object and giving it a name just like when we did x=4 except function objects are more complex so they need more work to define. Functions are objects that contain code that executes when you call them.

Functions are used when you write code that can be re-used and you don’t necessarily want to re-write the code each time you want to accomplish some task. Let’s write a function that squares a number.

def square(x):
	return x*x

What this is saying is, take the value of what is in the round brackets, do some operations to it and return it. Python knows which operations belong to the function by taking everything that is indented once to the right.

def some_function():
	#this indented code will only run if some_function() is called
	s = "hello i am in the function"
	y = "i am also in the function"
	#also in function
	print(s + y)
	
print("i am outside the function definition")
# removing the call below will cause the program to not
# print the code in some_function() when executing
some_function()

The return keyword is what spits out the output of the function (an object or a name). You can choose whatever you want for the return. Obviously whatever makes most sense is preferable. Now we can use our square() function to square any number and we only had to write the code to do it once.

>>> x = 5
>>> x_squared = square(x)
>>> print(x_squared)
25
>>> square(12)
144

As you can see, calling a function is as simple as writing its name and including the arguments (a.k.a) input in round brackets.

Since functions are also objects…

>>> id(square)
4303247792

… they can also be used as class or object attributes.

For example, the __cmp__ attribute is a function tells the == operator how to compare two int objects.

>>> x = 20
>>> y = 25
>>> x.__cmp__(y)
-1 #-1 here means x < y
>>> y = x
>>> x.__cmp(y)
0 #means both values are equal

Functions can accept any number of arguments. Example..

def add_five_numbers(a, b, c, d, e):
	result = a + b + c + d + e
	return result
x = add_five_numbers(1, 2, 3, 4, 5) 
print(x)
#prints 15

The print() function can take many arguments:

>>> a = 4
>>> b = "bob"
>>> c = "steve"
>>> print(a, b, c)
4 bob steve

Note that the order in which you provide the arguments matters.

def subtract(a, b):
	return a - b

print(subtract(1, 4))
#not the same as
print(subtract(4, 1))

Important note: when functions are accessed as attributes of an object (with the . operator) the function also receives the object before the . as input. So in the x.__cmp(y)__ call, both x and y are available to the function.

Very important note: return is NOT the same as print(). Calling the print() function simply displays text to the screen. It does not produce an object that you can store in memory and do operations on. Example..

def square(x):
	return x*x
num = 5
#stores the result of the square() function
sq = square(num)
#you can display the result later
print(sq)
#displays 25 to the screen but you can't do anything with
#the value later.
print(x*x)

This is all I will say about functions for the moment. We will go into more details later.

String functions

reference

Now that we have a better idea of what functions are, we can have a look at functions available to us by default in Python that let us work on the data types we have seen.

I’ll just put a bunch of examples in the code block below. You can always look them up in the documentation.

>>> s = "Shake it off.    "
>>> s_clean = s.strip()
>>> print(s_clean)
"Shake it off."
>>> print(s)
"Shake it off.    "
>>> s.replace("off", "on")
"Shake it on.    "
>>> print(s)
"Shake it off.    "
>>> len(s_clean) #length of the string
17
>>> s_clean.upper()
"SHAKE IT OFF."

Sometimes you want to include some information that you computed into a string to print to the user. Say you have a function that squares a number and you want to display a nice message to the user saying “you asked me to square [number] and the result is [number squared]”. This is called string formatting. There is a very useful function in Python that lets you do this. It’s called format() and it is an attribute of the str class.

def square(x):
	return x*x

x = 5
x_squared = square(x)

#all of the following are equivalent.

msg_str = "You gave me {0} and I got {1}".format(x, x_squared)

msg_str = "You gave me {} and I got {}".format(x, x_squared)

msg_str = "You gave me {adam} and I got {eve}".format(adam=x, eve=x_squared)

Good news! In Python 3.6 we get a brand new feature which makes this even easier! It’s called the f-string. All you have to do is put an f before the string quotes and python will automatically know that you want to format that string (without having to call the format() function). And it will use the names that are already in the namespace without having to pass them as input to the format(name1, name2) function. You can even evaluate Python expressions inside the string! Example:

>>> x = 5
>>> x_squared = square(x)
 
>>> msg_str = f"You gave me {x} and I got {x_squared}"

>>> msg_str = f"You gave me {x} and I got {x**x}"

>>> print(msg_str)
'You gave me 5 and I got 25'

Exercises

  1. Write a function called repeat(s, n) that takes a str object s and returns a string that is copied n times. Example: repeat("hi ", 3) should give hi hi hi.
  2. Write a function called suffix_reverse(s, n) that takes as input a str object s and int object n. First, it prints a string that looks like this. "You gave me the string 'We were living in Paris' and the number 5". Then, it returns the last n characters of s in reverse order. (Hint: if you want to include quotation marks in a string, use the escape character \. e.g.
>>> s = "Plato said, \"Only the dead have seen the end of war \"."
>>> print(s)
>>> "Plato said, "Only the dead have seen the end of war"."

Escape characters tell Python to treat the next character differently. In this case it tells Python to include the next " in the string and not treat it as the beginning of a new string.

Conditional Statements

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When you write your code in a .py file and give it to the interpreter it executes one line at a time from the top of the file until it reaches the bottom. What if we want our program to behave differently depending on some conditions? More specifically, what if we want certain parts of the code to execute only if some condition is true? This amounts to endowing python programs with the ability to make decisions.

To to this, we introduce the if statement. A statement in python is a line of code that does not produce a new object or modifies any values. Instead, it gives the interpreter some directions on how to execute the program. Think of statements as road signs.

We’ve already seen the name binding statement x = 5 which binds the name x to the object 5. Here python isn’t computing any new values or performing any operations, it’s just an instruction so the interpreter remembers a name for you.

Ok, back to the if statement. Let me just give an example.

x = 5
y = 2
if x > y == True:
	print("x is bigger")
print("done")

This is what the interpreter does as it reads from top to bottom:

  1. Bind the name x to the object 5
  2. Bind the name y to the object 2
  3. Evaluate expression after if. If result is True execute code that is indented. Otherwise, skip indented code.
  4. Execute print statement.

So now we have some code whose execution depends on something else. Here it depends on the value of x and y. Try setting x=2 and y=5 and see what happens. You should see that the line print("x is bigger") never gets reached.

Syntax: To write an if statement you use the key word if followed by a boolean expression which evaluates to either True or False and you end the line with a colon :. Anything you want python to execute if the condition evaluates to True you place one tab in.

What if you have several cases that you want to test? Use the elif statement (short for “else if”).

x = 10
y = 8
if x > y:
	print("x is bigger")
elif x < y:
	print("x is smaller")
else:
	print("x and y are equal")

You can have as many elif in a row. It is not necessary that they end with an else statement but it is usually good practice to deal with an else case. Python goes through the conditions one at a time. As soon as it encounters the first True condition it executes its code and skips the rest of the cases. So the order of your statements can sometimes be important.

jon = "Stark"
tyrion = "Lannister"

if len(jon) == len(tyrion):
	print("same length")
elif jon[2] == tyrion[1]:
	print("both a")
elif jon[1] == tyron[-3]:
	print("both t")
else:
	print("hello")

In this case, both elif blocks evaluate to True but only the first one will actually execute since python skips the rest as soon as it finds one that is True.

If none of the if or elif statements evaluated to True then the else block will execute. You can also use an else after an if block.

In the jon and tyrion example, if you wanted both elif blocks to execute you could put them both in if statements.

if jon[2] == tyrion[1]:
	print("both a")
if jon[1] == tyrion[-3]:
	print("both t")

Here, both print calls will execute as they belong to independent if statements.

Exercises

  1. Write a function called xor(a, b) that takes two bool objects and returns True only if one of a or b is true and False otherwise.
  2. Write a function called is_palindrome(s) that takes one string sand returns True if s is palindromes, i.e. it reads the same forwards and backwards.

Containers: Lists, Tuples, and Sets

reference

Until now we have been dealing with individual objects, each floating around in memory on their own. We’ve been binding individual str or bool objects to names and performing operations of them.

However, the world is full of collections of things: the days of the week, genes in a genome, grades in a class, names of past lovers, petals on a flower, etc. We would like to be able to have some kind of container for these things that lets us work with them efficiently.

So python has some more built-in types that we can use as containers for other objects. The main ones are lists, tuples, and sets.

Lists: the mutable container

This is how you store an empty list object

mylist = []

This is how you store a list with some stuff already in it.

stuff = ["pencil", "books", "calculator", "phone"]
#is much better than
thing1 = "pencil"
thing2 = "books"
thing3 = "calculator"
thing4 = "phone"

If you want to access one of the things in the list, you just use its name and tell python which position in the list you want to access.

>>> print(stuff[1])
"books"

You can use exactly the same kind of indexing and slicing as with strings (see above).

>>> print(stuff[1::2])
['books', 'phone']

Lists are mutable which means we can modify the value of a list object. A useful example is the attribute of the list type, list.append(object). This function adds an object to the end of the list, essentially modifying the value of the list.

>>> id(stuff)
4339084744
>>> stuff.append("laptop")
>>> print(stuff)
["pencil", "books", "calculator", "phone", "laptop"]
#same id, same object. different value
>>> id(stuff)
4339084744 
>>> stuff[0] = "binder"
#lists can hold objects of different types.
stuff.append(3000)

Since lists are objects and lists hold objects, it follows that lists can hold other lists. This kind of construction is often useful in many programming problems. In math, we often work with matrices which in Python can be thought of as lists of lists.

mat = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

This represents a matrix that looks like this:

\[mat = \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}\]

Each list in the list mat would represent one of the rows in the matrix.

Let’s say we want to change the $6$ to a $0$.

mat[1][2] = 0

Why does this work?

>>> print(mat[1])
[4, 5, 0]
>>> print(mat[1][2]
0

We can ask Python if a certain value is stored in a list using the in keyword.

>>> mylist = [1, 2, 3, 4]
>>> 4 in mylist
True
>>> 0 in mylist
False
# The in keyword only checks one level of nesting.
>>> mymat = [[1, 2, 3], [4, 5, 6]]
>>> 3 in mylist
False
>>> [1, 2, 3] in mylist
True
>>> 3 in mylist[0]
True

Tuples: the immutable container

A tuple can hold the same kinds of objects as a list. The only difference is that tuples are immutable. For this reason, they are often used to store things that you don’t want to change, and whose index you want to always represent the same thing.

Let’s say I wanted to keep track of the student ID of each person in the class. Since people can add or drop the class, I would probably want to keep that information in a list cause it’s easy to grow or shrink a list. Okay so I have a list where each element is a student’s info. Now how should I fill that list? Let’s say I only ever care about the student’s name and their McGill ID. These things don’t change. So I’m tempted to use a tuple. So my code would look something like this.

>>> students = [("John", 260452134), ("Mary", 2601502135), ("Rose", 2001202933)]

That’s a list of tuples. Let’s say a new student joins the class.

>>> students.append(("Tracy", 2601002231))

and now the list has one more tuple representing the student “Tracy”’s info.

Because the tuples are immutable I know that the name string will always be at index 0 and the ID will be at index 1 of a particular tuple.

So let’s say I want the ID of the most recently added student, I would just do

>>> most_recent = students[-1][1] #this will be the ID number.

Because lists can grow and shrink we can’t be sure that the index will always hold the same kind of information.

Tuples also have the advantage of being faster to access and more memory efficient. Because the size of a tuple is fixed, Python can know exactly how much memory it needs to reserve for that tuple. On the other hand, a list can always grow so python may often have to over-compensate in case you decide to make the list bigger.

Just to make sure, let’s try to modify a tuple and see what happens.

>>> mytup = ("Carlos", 5558116519)
>>> mytup[0] = "Dante"
TypeError: 'tuple' object does not support item assignment

Naturally, we can understand that there is no append() function for tuples.

However, if a tuple contains a mutable object, we can modify that.

>>> tuptup = ([1, 2, 3], "Hello")
>>> tuptup[0].append(4)
>>> print(tuptup)
([1, 2, 3, 4], "Hello")

Sets: the container for unique things

The other major container in Python is the set. Sets work like math sets if you’ve studied them. In a set, every element is unique, and the elements are unordered. Having this kind of guarantee is often useful as you try to solve more and more problems. Along with this container, Python provides some very useful functions which implement set operations. Some examples will clarify all this.

A recap on how to initialize the containers:

mylist = [1, 2, 3] 
mytup = (1, 2, 3)
myset = {1, 2, 3} #note empty set is set() not {}

You can store a set with the curly braces.

Here are some other ways to start a set. Whenever you give duplicate elements (will evaluate to true with the == opearator) to the set, only the unique elements will be included in the set.

>>> myset = set([1, 2, 3, 3, 4])
>>> myset = set("AAACCGGAG") #will keep only unique characters
>>> print(myset)
{'G', 'A'}
>>>len(myset)
2

Set methods and operations

The main set operations can be called as operations or methods. Here are some examples.

>>> novels = set({"dante", "wilde", "hemigway", "nietzche", "rand"})
>>> philosophy = set(["spinoza", "nietzche", "schoppenhauer", "spinoza", "rand"])
#elements in philosophy and novels
>>> philosophy.intersection(novels)
{'nietzche', 'rand'}
>>> philosophy & novels
{'nietzche', 'rand'}
#elements in philosophy but NOT in novels
>>> philosophy.difference(novels)
{'spinoza', 'schoppenhauer'}
>>> philosophy - novels
{'spinoza', 'schoppenhauer'}

If you would like to add an element to the set, use the set.add(element) function. This makes sure you are not adding any duplicates to the set.

>>> philosophy.add("kant") #adds kant
>>> philosophy.add("spinoza") #does nothing

here is a complete list of set operations and methods.

Exercises

  1. Use sets to print the number of unique letters in the following string: “subdermatoglyphic”.
  2. Create a list containing the prime numbers from 0 to 100.

Loops

Now that we have containers with a bunch of things in them. We want to be able to quickly perform operations on them. This is where loops come in. Loops are simply a way to repeat a set of python commands a certain number of times. This saves you from a lot of copy pasting of the same code.

The simplest loop is the while loop. Loops are statements like the if statement. They don’t make any operations on their own, they just tell the interpreter how to execute your code.

Here is an example of the simplest possible loop:

while True:
	print(""" This life as you now live it and have lived it,
	 you will have to live once more and innumerable times 
	 more; and there will be nothing new in it, 
	 but every pain and every joy and every thought and sigh
	 and everything unutterably small or great in your life
	 will have to return to you, all in the same succession
	 and sequence - even this spider and this moonlight
	 between the trees, and even this moment and I myself. 
	 The eternal hourglass of existence is turned
	 upside down again and again, and you with it, 
	 speck of dust!""")

When python encounters the while statement it evaluates the boolean expression to its right. If it sees a statement that is True and enters the loop body (one tab in) and executes the code inside it. Once it has marched through the code in the loop body it goes back to the while statement and evaluates the boolean expression to its right. If it sees something that is True it goes back into the loop body and executes again and goes back to the top and repeats. In this example, that loop will never stop executing since the condition never changes and we will have Nietzche’s quote repeated forever. This is called an infinite loop and you generally want to avoid them.

Here’s an example of a while loop that does terminate.

x = 100
while x > 0:
	print("The original is unfaithful to the translation.")
	x = x - 1

Here are the steps the interpreter takes:

  1. Bind x to 100
  2. Evaluate boolean expression 100 > 0 result is True.
  3. Continue inside loop body
  4. Print Jorge Luis Borges quote
  5. Evaluate expression x-1 get value of 99 and bind it to name x
  6. Go back to while statement and evaluate 99 > 0 this is True.
  7. Repeat
  8. When x=0 the while condition will be False and the interpreter will skip the loop body.

The for loop

The while and the for loop can be used interchangeably and can both accomplish the same tasks. However, in some cases is it more convenient to use one over the other. Typically, for loops are used when you know how many iterations of the loop you need or when you are iterating over some kind of container like a list, set, or tuple.

These are the main ingredients of a for loop:

  1. the for keyword
  2. a name whose value is updated after each iteration (loop variable)
  3. the in keyword
  4. an iterable
  5. A colon :
  6. The loop body (everything tabbed at least once after the loop header.

This is what a typical for loop looks like:

mylist = [1, 2, 3, 4, "watermelon", "tree", 939] #the iterable

for n in mylist: #n is the loop variable
	print(f"The value of n is now {n}")
	print("Moving to next iteration.")

Let’s break down what happens at each step.

  1. Python sees that you are binding the name mylist to the list object defined on the right.
  2. It reaches the for statement so it knows it is about to repeat some code.
  3. Python binds the first value in the list 1 to the name n
  4. Python enters the loop body and executes the code inside of it one by one. It does the first print function which prints something like “The value of n is now 1”
  5. Then it reaches the next print call and so we see `“Moving to next iteration.”
  6. Python sees nothing else is tabbed in so it is done executing the loop body.
  7. Python goes back to the loop header and this time binds the name n to the second object in the list.
  8. We repeat this process until the name n has been bound to every item in the list.

Python has a few very useful functions that make working with for loops a lot easier: enumerate, zip, and range.

The enumerate function yields a tuple in the form (index, item) for every iteration in the loop.

>>> b = ["adam", "eve", "bob"]
>>> for en in enumerate(b):
>>> 	print(en)
(0, "adam")
(1, "eve")
(2, "bob")

This comes in handy when you want to do something to the items in the list but also need to know their position.

We can use variable unpacking to assign a name to the index and the item in one shot.

#variable unpacking
>>> my_tup = ("bob", "joe")
>>> b, j = my_tup
>>> print(b)
"bob"
>>> print(j)
"joe"

Using this in the loop header with the enumerate function looks like this:

for i, item in ["dog", "cat"]:
	print(f"index: {i}, item: {item}")

The zip function is similar to the enumerate function but it yields a tuple of items in two or more lists.

animals = ["dog", "cat", "human"]
legs = [4, 4, 2]
tail = [1, 1, 0]
for a, l, t in zip(animals, legs, tail):
	print(f"{a} has {l} legs and {t} tails"})

The range function yields a number for every iteration in the for loop within some specified range.

#numbers from 0 to 9
for i in range(10):
	print(i)

#numbers from 4 to 9
for i in range(4, 9):
	print(i)

#numbers from 0 to 0 taking steps of size 2
for i in range(0, 10, 2):
	print(i) #0 2 4 6 8

List and Set Comprehensions

You will often want to do something to every element in a list, or create a new list efficiently. Python lets you do this in one line using what it calls comprehensions. Comprehensions can be used go create lists, sets, and dictionaries.

Here’s a basic example of a list comprehension and we’ll break it down.

zero_to_one_hundred = [n for n in range(101)]

The list zero_to_one_hundred would contain the numbers 0 to 100.

If we didn’t have list comprehensions, we would have to do something like this to store the same list:

zero_to_one_hundred = []
for n in range(101):
	zerp_to_one_hundred.append(n)

These are both equivalent, but the list comprehension is obviously much quicker to write.

So basically whatever expression comes before the for is appended to the list, and the for loop takes you from one item to another.

An even more basic list comprehension would be this:

>>> ones = [1 for _ in range(10)]
>>> print(ones)
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

This would create a list with 10 entries all with value 1.

To the left of the for you can add any expression and the value of the expression gets added to the list.

>>> [x*x for x in range(5)]
[0, 1, 4, 9, 16]

You just wrote a quadratic function evaluated from 0 to 5 in one line.

Another handy thing with comprehensions is the conditional statement. Say we want a list that only contains the square of even numbers.

>>> [x*x for x in range(5) if x % 2 == 0]
[0, 4, 16]

So you can put an if statement that can act on the loop variable and if it evaluates to true, it will append the current value of the loop variable x to the list, and skip it otherwise.

This is equivalent to:

even_squares = []
for x in range(5):
	if x % 2 == 0:
		even_squares.append(x*x)
	else:
		continue

As you can see, list comprehensions can save us a lot of coding time.

All these examples were used to create lists, but we can use a similar syntax to create sets and dictionaries.

For sets we can do something like this:

>>> fruits = ["apple", "banana", "banana", "banana"]
>>> fruit_set = {f for f in fruits}
{"apple", "banana"}
>>> {f + "_carlos" for f in fruits}
{"banana_carlos", "apple_carlos"}

You can also include conditionals when building sets just as before.

Dictionary comprehensions have a little extra syntax which is the key:value mapping.

Say I want to map every number from 0 to 4 to its square. Here, we still use the curly braces like with the sets, but the colon tells python that this is a dictionary and not a set.

>>> square_map  = {x:x*x for x in range(5)}
>>> print(square_map)
{0: 0, 1: 1, 2: 4, 3: 9, 4: 16}
>>> square_map[3]
9

Nested Loops

Loops repeat whatever is inside the loop body until the continue condition evaluates to false. Turns you you can put pretty much any Python code in the loop body, including another loop. We call a loop inside a loop a nested loop.

Nested loops come up when trying to solve many types of problems so it’s good to keep them in mind. The usual case is when you want to do repeat some operations on every element of a list, or when working with matrices (lists of lists). Here are some examples.

nums = [1, 2, 3]
for n in nums:
	for a in ["dog", "cat"]:
		print(f"{n}, {a}")	

1, dog
1, cat
2, dog
2, cat
3, dog
3, cat

So you can see that for every item in the outer loop, the inner loop executes fully.

Nested list comprehensions

We can also turn nested loops into nested list comprehensions. This starts to get a little messy so make sure you really want to do a list comprehension instead of a regular loop.

So let’s say I want to build a grid that looks like a telephone number pad (without the zero). Let’s do it the explicit way:

number_pad = []
for i in range(3):
	row = []
	for j in range(3):
		row.append(j + 1 + (3 * i))
	number_pad(row)
print(number_pad)		

[[1, 2, 3], [4, 5, 6], [7, 8, 9]]

Let’s turn that into a list comprehension.

#using the line continuation character \ so the line 
#doesn't go too far off the screen
#but this is still just one line according to python
number_pad = [[j + 1 + (3 * i) for j in range(3)]\
	 for i in range(3)]

[[1, 2, 3], [4, 5, 6], [7, 8, 9]]

So you see this behaves with the same logic as a single list comprehension. You have an outer for loop that is appending stuff to a list. In this case what it is appending is itself a list generated by a list comprehension.

Exercises

  1. Make a telephone number pad but instead of numbers, the keys are strings with the word equivalent of the number. i.e. “one”, “two”, “three”, … etc.
  2. Create a list that evaluates the function $\frac{x}{x-1}$ from 1 to 100 and skips an $x$ if $x-1 = 0$.

Functions

Why use functions?

Functions are an essential part of programming in python. They let us store pieces of code that we can then re-use any number of times.

A function is just some Python code that we assign a name to and works on some input (arguments) to produce an output.

An easy example is a piece of python code that computes the mean of some list of numbers. Clearly this is a useful task that we may want to repeat more than once on many different lists. So let’s tell python to remember it and give it a name.

No function:

nums = [1, 2, 3]
nums2 = [2, 3, 4, 5]

tot = 0
for n in nums:
	tot += n
print(tot / len(nums)

tot = 0
for n in nums2:
	tot += n
print(tot / len(nums2)

With functions:

nums = [1, 2, 3]
nums2 = [2, 3, 4, 5]

def mean(li):
	tot = 0
	for n in li:
		tot += n
	return tot / len(li)

print(mean(nums))
print(mean(nums2))

You see we only had to write the code to compute a mean once. And we were able to call the function on different lists to compute their mean.

The anatomy of a function

Code to be placed inside a function has to follow some rules so Python understands it as a function definition.

Every function starts with a function header this is the first line of a function and gives us a lot of information on how it behaves.

  1. The def keyword tells python that we are going to define a function.
  2. The name of the function, in this case mean acts just like any other name in python.
  3. The function arguments in round brackets (). The arguments are objects that are passed to the function which can then be used inside the function.

The function body is the code that executes as part of the function and if everything that is tabbed once after the function header.

The return statement spits out any object that is accessible by the function and ends the execution of the function.

Let’s go over the definition of another function to see what happens step by step.

def square(x):
	result = x * x
	return result
num = 5
num_squared = square(num)

Let’s to from top to bottom:

  1. We reach a function header, python knows that it will store a function with the name square that takes one argument x as input.
  2. The code inside the function body is not executed, it is just stored.
  3. We reach num = 5 this is a simple name-object binding.
  4. Now we have another name-object binding but first we have to evaluate the object on the right which is square(num).
  5. Python sees the name of a function is being called square so it looks for a function definition with that name. It finds it above. We are passing num to the function so the object bound to the name num is then bound to the name x which will live inside the square function body.
  6. Now we execute the function’s code. x was bound to the object with the name num when we called the function so now we can use it to bind x * x to the name result.
  7. Then we return the object with the name result so square(sum) evaluates to 25 and we can finish binding it to the name num_squared.

That was a moutful. But now we can use this super useful function ad nauseum.

For example, let’s square every number up to 100 while also practicing list comprehensions.

squares = [square(x) for x in range(100)]

Namespaces + Functions

Functions define their own local namespace.

In that book which is my memory, On the first page of the chapter that is the day when I first met you, Appear the words, ‘Here begins a new life’. (Dante Alighieri, Vita Nuova)

Exception Handling

Dictionaries

Reading and Writing Files