Chapter 4 Lists and Sequences

This chapter will cover using lists in Python, which is a data type representing a sequence of data values. A list is a fundamental data type in Python, and key to writing almost all practical programs. Lists are used to store and organize large sets of data (and computer programs usually deal with lots of data). This chapter covers how to create and access lists, as well as a number of related sequence structures. Note in practice, using lists also means using loops, which are covered in the chapter Iterating with Loops.

4.1 What is a List?

A list is a mutable, ordered sequence of values that are all stored in a single variable. For example, you can make a list names that contains the strings “Sarah”, “Amit”, and “Zhang”, or a list one_to_seventy that stores the numbers from 1 to 70. Each value in a list is referred to as an element of that list; thus your names list would have 3 elements: "Sarah", "Amit", and "Zhang".

Lists are written as literals inside of square brackets ([]), with each element in the list separated by a comma (,):

# A list of names
names = ["Sarah", "Amit", "Zhang"]

# A list of numbers (lists can contain "duplicate" values)
numbers = [1, 2, 2, 3, 5, 8]

# Lists can contain different types of values (including other lists!)
things = ["raindrops", 2, True, [5, 1, 1]]

# Lists can be empty (with no elements)
empty = []

Style Requirement: List variables should be named using plurals (names, numbers, etc.), because lists hold multiple values!

4.2 List Indices

You can refer to individual elements in a list by their index, which is the number of their position in the list. Lists are zero-indexed, which means that positions are counted starting at 0. For example, in the list:

vowels = ['a', 'e', 'i', 'o', 'u']

The 'a' (the first element) is at index 0, 'e' (the second element) is at index 1, and so on. This also means that the last element can be found at the index length_of_list - 1.

You can retrieve an element from a list using bracket notation: you refer to the element at a particular index of a list by writing the name of the list, followed by square brackets ([]) that contain the index of interest:

# Create the `names` list
names = ["Sarah", "Amit", "Zhang"]

# Access the element at index 0
name_first = names[0]
print(name_first) # Sarah

# Access the element at index 2
name_third = names[2]
print(name_third) # Zhang

# Accessing an index not in the list will give an error
name_fourth = names[3] # IndexError!

# Negative indices count backwards from the end
name_last = names[-1] # Zhang
name_second_to_last = names[-2] # Amit

The value inside the square brackets can be any expression that resolves to an integer, including variables:

# Access the element at index `3-2` (1)
names[3-2]  # "Amit"

last_index = len(names) - 1  # last index is length of list - 1
names[last_index]  # "Zhang"

# Don't forget to subtract one from the length!
names[len(names)]  # IndexError!
# Using an index of `-1` is a better way to get the last element

The most important thing to note about lists is that an indexed reference to a list element (e.g., names[0]) is effectively a variable in its own right: you can think of names[0], names[1], and names[2] as being equivalent to having variables names_0, names_1, names_2 (each of which has its own value). Lists effectively provide a “shortcut” for having lots and lots of variables that are all related; you can “collect” those variables into a list!

  • As a metaphor: you can think of a list as a “hotel” full of values, and each index as the “room number” of that value. For example, the value “Zhang” lives at room #2. The value names[2] refers to “the value that lives in room #2” (similar to how a bellhop might refer to a customer)

Because list references are variables, they can be used anywhere that a “normal” variable can be. In particular, this means that variables can be assigned to them, allowing the list to be mutated (changed):

# A list of school supplies
school_supplies = ["Backpack", "Laptop", "Pen"]

# Assign a new value to the element at index 2; replaces "Pen" with "Pencil"
school_supplies[2] = "Pencil"

print(school_supplies)  # ['Backpack', 'Laptop', 'Pencil']

# You can only assign values to elements that exist in the list!
school_supplies[3] = "Paper"  # IndexError!
  • Following the hotel metaphor: names[2] = "Yash" would mean “the value ‘Yash’ is now living in room #2”.

Just as with variables: if the list index (e.g., my_list[index]) is on the left side of an assignment, it means the variable (which “slot” in the list). If it is on the right side of an assignment, it means the value (which element is in that slot).

letters = ['a', 'b', 'c']

letters[0] = 'q'  # `letters[0]` is the variable we assign to
first_letter = letters[0]  # `letters[0]` is the value assigned

Note that it is also possible to select multiple, consecutive elements from a list by specifying a slice. A slice is written as the starting and ending indices separated by a colon (:); the starting index is included and the ending index is excluded. For example:

letters = ['a', 'b', 'c', 'd', 'e', 'f']

# Indices 1 through 3 (non-inclusive)
letters[1:3]  # ['b', 'c']

# Indices 3 to the end (inclusive)
letters[3:]  # ['d', 'e', 'f']

# Indices up to 3 (non-inclusive)
letters[:3]  # ['a', 'b', 'c']

# Indices 2 to (2 from end) (non-inclusive)
letters[2:-2]  # ['c', 'd'], the `e` is excluded

# All the indices. This produces a new list with the same contents!

4.3 List Operations and Methods

Lists support a number of different operations and methods (functions), some of which are demonstrated below:

# Use addition (+) to combine lists
['a', 'b'] + [1, 2]  # ['a', 'b', 1, 2]

# Multiplication (*) performs multiple additions
[1, 2] * 3  # [1, 2, 1, 2, 1, 2]

# A sample list
letters = ['a', 'b', 'c', 'd']

# Add value to end of list
letters.append('x')  # add 'x' at end

# Add value in middle of list
letters.insert(2, 'y')  # put 'y' at index 2 (everyone else shifts over)

# Remove from end of list ("pop off")
letters.pop()  # removes and returns the last item (`x`)

# Remove from middle
letters.pop(2)  # removes and returns item at index 2 (`y`)

# Remove specific value
letters.remove('c')  # remove the first 'c' in the list; nothing returned

# Remove all elements

Note that list methods such as append() or clear() usually mutate the existing list value and then return None. In comparison, string methods (such as lower() or replace()) will return a different string value. This is because lists can be changed, but strings cannot (strings are immutable).

In general, if you call a list method, you won’t assign the result to a value. But if you call a string method, you will assign the result to a value

When comparing lists using a relational operator (e.g., == or >), the operation is applied to the lists member-wise: the first element in each list is compared, and in the case of a “tie” then the second element in each list are compared, and so on. In practice, this means that (a) you can use == to compare the contents of lists, and (b) a list is “smaller” than another if its first element(s) is smaller than the other’s first element(s).

But be careful: just because two lists have the same contents (are ==) does not mean that they are the same list! In particular, two lists can be different objects (values) but still have the same contents. In Python, you can test whether two values are actually the same value (as opposed to having the same contents) using the is operator.

# With strings, literals are shared (because they cannot be mutated)
str_a = "banana"  # `str_a` labels string literal "banana"
str_b = "banana"  # `str_b` labels string literal "banana"

# Both variables label the same (literal) value
str_a is str_b  # True

# With lists, each list created is a different object!
list_a = [1,2,3]  # `list_a` labels a new list [1,2,3]
list_b = [1,2,3]  # `list_b` labels a new list [1,2,3]

list_a == list_b  # True, have same values as contents
list_a is list_b  # False, are two different objects

list_c = list_a  # `list_c` labels the value that `list_a` labels
list_a is list_c  # True, both labels are on the same object

# Modify the list!
list_a[0] = 10
print(list_b[0])  # 1 (is a different list, so not changed)
print(list_c[0])  # 10 (is the same list, so is changed)

Keeping track of whether a new list has been created is particularly important when using lists as arguments to functions. Function arguments are local variables that are assigned the passed value—if this value is a list, then the assigned variable will refer to the same list, and any modifications to the argument will affect the value outside of the function:

# A version of a function that modifies the list
def delete_first(a_list):
    a_list.pop(0)  # modifies the given value

letters = ['a','b','c']
delete_first(letters)  # call function
print(letters)  # ['b', 'c'], variable is changed

# A version of a function that does not modify the list
def delete_first_local(a_list):
    shorter_list = a_list[1:]  
    a_list = shorter_list # creates new local variable (replacing old local var)

letters = ['a','b','c']
delete_first_local(letters)  # call function
print(letters)  # ['a', 'b', 'c'], variable is not changed

4.4 Nested Lists

As noted at the start of the chapter, lists elements can be of any data type (and any combination of data types)—including other lists! These “lists of lists” are known as nested lists or 2-dimensional lists (or 3d-lists for a “list of lists of lists”, etc). Nested lists are most commonly used to represent information such as tables or matrices.

Nested lists work exactly like normal lists—the elements just happen to themselves be indexable:

# A list of different dinners available at a fancy party
# This list has 4 elements, each of which is a list of 3 string elements
# (the indentation is just for human readability)
dinner_options = [
    ["chicken", "mashed potatoes", "mixed veggies"],
    ["steak", "seasoned potatoes", "asparagus"],
    ["fish", "seasoned rice", "green beans"],
    ["portobello steak", "seasoned rice", "green beans"]

len(dinner_options) # 4; there are 4 elements in the "outer" list
fish_option = dinner_options[2]  # ["fish", "seasoned rice", "green beans"]

# Because `fish_option` is a list, we can reference its elements by index
print(fish_option[0])  # "fish"

In this example, fish_option is a variable that refers to a list, and thus its elements can be accessed by index using bracket notation. But as with any operator or function, it is also possible to use bracket notation on an anonymous value (e.g., a literal value that has not been assigned to a variable). That is, because dinner_options[2] is a list, we can use bracket notation refer to an element of that list without assigning it to a variable first:

# Access the 2th element's 0th element
dinner_options[2][0]  # "fish"

This “pair of brackets” notation allows you to easily access elements within nested lists. This is particularly useful for 2d-lists that represent tables as a list of “rows” (often data records), each of which is a list of “column cells” (often data features):

# A simple table of values
table = [ ['aa','ab','ac','ad'],
          ['ca','cb','cc','cd'] ]

row_index = 1  # cells starting with 'b'
col_index = 3  # cells ending with 'd'
table[row_index][col_index]  # "bd", the cell at (row, col)

4.5 Other Sequences

In Python, lists are the most common example of a sequence data structure. But there are other types of sequences as well.

For example, strings are indexed sequences of characters. Thus you can use bracket notation to refer to individual letters, and many string methods make use of the character’s index:

# Define a string
message_str = "Hello world"

# Access individual letters using bracket notation
first_letter = message_str[0]

# Can also slice to select multiple letters (substrings)
message_str[1:5]  # "ello"

# Use a method find the index of the character 'w'
message_str.find('w')  # 6

It is possible to convert other sequences (such as strings) into a list variable by using the built-in list() function (similar how you converted numbers into strings with the str() function):

# Convert a string into a list
list("hello")  # ['h', 'e', 'l', 'l', 'o']

4.5.1 Ranges

Another common sequence type is a range. A range represents a sequence of integers. You create a range sequence by using the built-in range() function. This function. The range() function can be called with different arguments depending on the range and spread of numbers you wish to use:

# One argument produces a range of numbers from 0 to the argument (not inclusive)
range(10) # produces `0, 1, 2, 3, 4, 5, 6, 7, 8, 9`

# Two arguments produce a range of numbers from the first argument (inclusive) 
# to the second argument (not inclusive)
range(3,10) # produces `3, 4, 5, 6, 7, 8, 9`

# Three arguments produces a range of numbers from the first argument (inclusive)
# to the second argument (not inclusive), stepping by the third argument
range(0, 10, 3) # produces `0, 3, 6, 9`; every 3rd number from 0 to 9

The fact that the “ending” argument is non-inclusive is related to how sequences are zero-index. range(10) produces a sequence of 10 values; but because it starts at 0, the sequence ends at 9. When counting from 0, the 10th number is 9. This way a single argument refers to “how many numbers you want”, rather than “what number you will end on”.

You can access individual elements of a range using bracket notation. Note though that ranges are immutable, which means you can’t assign a different value to a range element.

Importantly, ranges are different than lists! If you print out a range, you won’t see the whole sequence of numbers. You can convert the range into a list by using the list() function (though again, you don’t commonly want to do this).

one_to_five = range(1,6)
print(one_to_five) # range(1, 6)

one_to_five_list = list(one_to_five)
print(one_to_five_list) # [1, 2, 3, 4, 5]

Ranges are most commonly used when doing iteration, as they provide a clean way to specify the number of times you want to do something (or to track which element of a list you’re on). See Iterating with Loops for more details on when to use ranges.

4.5.2 Tuples

While lists are mutable (changeable) sequences of data, tuples represent immutable sequences of data. These are useful if you want to enforce that a data value won’t be changed, such as for a function argument (or a dictionary key; see Chapter 10). Indeed, many built-in Python functions utilize tuples.

Tuples are written as comma-separated sequences of values. They are often placed inside parentheses for clarity (to help indicate the start and end of the tuple values):

# A tuple with 3 elements
letters_tuple = ('a', 'b', 'c')
print(letters_tuple)  # ('a', 'b', 'c')

# Also is a tuple with 3 elements (written without parentheses)
numbers_tuple = 1, 2, 3
print(numbers_tuple)  # (1, 2, 3)

# A tuple representing a person's name, age, and whether they are hungry
# Tuple values have _implied_ meanings, which should be explained in comments
hungry_person = ('Ada', 28, True)

# In English, tuple variables may be named based on the number of elements
a_triple = (1,2,3)
a_double = (4,5)
a_single = (6,)  # extra comma indicates is a tuple, not just the int `6`
empty = ()  # an empty expression is a tuple!

# For fun
type(())  # <class 'tuple'> (type of empty expression)

It’s important to note that while you often write tuples in parentheses (and they are printed in parentheses), it is the commas that makes a sequence of literals into a tuple. The parentheses act just like like they do in mathematical expressions—they are only necessary to clarify ambiguity in the order-of-operations. You will find that some “idiomatic” expressions using tuples forgo the parentheses, making the syntax look more magical than it is!

Elements in tuples can be accessed by index using bracket notation, just like the elements in lists. However, tuples cannot be modified, so you cannot assign a new value to an index in a tuple:

# A tuple with 3 elements
letter_triple = ('a','b','c')

# Access with bracket notation
print(letter_triple[0])  # 'a'

# Can use slices as an index
print(letter_triple[1:3])  # ('b','c'), a tuple

# Cannot assign values to tuple elements
letter_triple[0] = 'q'  # TypeError!

Tuples can be compared using relational operators just like lists, and have the same “member-wise” comparison behavior described above. This makes it easy to order the immutable tuples just like you would order numbers or strings.

Finally, tuples provide one additional useful feature. The Python interpreter uses tuples to perform multiple assignments, where you assign multiple values to multiple variables in a single statement. You have already been able to assign multiple, comma-separated values to a single tuple variable (a process called packing). But Python also supports having a single sequential value (e.g., a tuple) be assigned to multiple, comma-separate variables (a process called unpacking)!

# A tuple with 3 elements (omitting parentheses)
a_triple = 1, 2, 3  # assign multiple values to single variable (packing)
print(a_triple)  # (1, 2, 3)

x, y, z = (1,2,3)  # assign single tuple value to multiple variables (unpacking)
print(x)  # 1
print(y)  # 2
print(z)  # 3

# The VALUE in this statement is evaluated as a tuple, and then is assigned to
# multiple variables!
a, b, c = x, y, z  # a=x; b=y; c=z

# The same process can be used to swap values!
a, b = b, a

This is mostly a useful shortcut (syntactical sugar), but is also used by some idiomatic Python constructions.