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How to Think Like a Computer Scientist

Chapter 8

Lists

A list is an ordered set of values, where each value is identified by an index. The values that make up a list are called its elements. Lists are similar to strings, which are ordered sets of characters, except that the elements of a list can have any type. Lists and strings and other things that behave like ordered sets are called sequences.

8.1 List values

There are several ways to create a new list; the simplest is to enclose the elements in square brackets ([ and ]):

[10, 20, 30, 40] ["spam", "bungee", "swallow"]

The first example is a list of four integers. The second is a list of three strings. The elements of a list don't have to be the same type. The following list contains a string, a float, an integer, and (mirabile dictu) another list:

["hello", 2.0, 5, [10, 20]]

A list within another list is said to be nested.

Lists that contain consecutive integers are common, so Python provides a simple way to create them:

>>> range(1,5) [1, 2, 3, 4]

The range function takes two arguments and returns a list that contains all the integers from the first to the second, including the first but not including the second!

There are two other forms of range. With a single argument, it creates a list that starts at 0:

>>> range(10) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

If there is a third argument, it specifies the space between successive values, which is called the step size. This example counts from 1 to 10 by steps of 2:

>>> range(1, 10, 2) [1, 3, 5, 7, 9]

Finally, there is a special list that contains no elements. It is called the empty list, and it is denoted [].

With all these ways to create lists, it would be disappointing if we couldn't assign list values to variables or pass lists as arguments to functions. We can.

vocabulary = ["ameliorate", "castigate", "defenestrate"] numbers = [17, 123] empty = [] print vocabulary, numbers, empty ['ameliorate', 'castigate', 'defenestrate'] [17, 123] []

8.2 Accessing elements

The syntax for accessing the elements of a list is the same as the syntax for accessing the characters of a string the bracket operator ([]). The expression inside the brackets specifies the index. Remember that the indices start at 0:

print numbers[0] numbers[1] = 5

The bracket operator can appear anywhere in an expression. When it appears on the left side of an assignment, it changes one of the elements in the list, so the one-eth element of numbers, which used to be 123, is now 5.

Any integer expression can be used as an index:

>>> numbers[3-2] 5 >>> numbers[1.0] TypeError: sequence index must be integer

If you try to read or write an element that does not exist, you get a runtime error:

>>> numbers[2] = 5 IndexError: list assignment index out of range

If an index has a negative value, it counts backward from the end of the list:

>>> numbers[-1] 5 >>> numbers[-2] 17 >>> numbers[-3] IndexError: list index out of range

numbers[-1] is the last element of the list, numbers[-2] is the second to last, and numbers[-3] doesn't exist.

It is common to use a loop variable as a list index.

horsemen = ["war", "famine", "pestilence", "death"] i = 0 while i < 4: print horsemen[i] i = i + 1

This while loop counts from 0 to 4. When the loop variable i is 4, the condition fails and the loop terminates. So the body of the loop is only executed when i is 0, 1, 2, and 3.

Each time through the loop, the variable i is used as an index into the list, printing the i-eth element. This pattern of computation is called a list traversal.

8.3 List length

The function len returns the length of a list. It is a good idea to use this value as the upper bound of a loop instead of a constant. That way, if the size of the list changes, you won't have to go through the program changing all the loops; they will work correctly for any size list:

horsemen = ["war", "famine", "pestilence", "death"] i = 0 while i < len(horsemen): print horsemen[i] i = i + 1

The last time the body of the loop is executed, i is len(horsemen) - 1, which is the index of the last element. When i is equal to len(horsemen), the condition fails and the body is not executed, which is a good thing, because len(horsemen) is not a legal index.

Although a list can contain another list, the nested list still counts as a single element. The length of this list is four:

['spam!', 1, ['Brie', 'Roquefort', 'Pol le Veq'], [1, 2, 3]]

As an exercise, write a loop that traverses the previous list and prints the length of each element. What happens if you send an integer to len?

8.4 List membership

in is a boolean operator that tests membership in a sequence. We used it in Section 7.10 with strings, but it also works with lists and other sequences:

>>> horsemen = ['war', 'famine', 'pestilence', 'death'] >>> 'pestilence' in horsemen True >>> 'debauchery' in horsemen False

Since "pestilence" is a member of the horsemen list, the in operator returns true. Since "debauchery" is not in the list, in returns false.

We can use the not in combination with in to test whether an element is not a member of a list:

>>> 'debauchery' not in horsemen True

8.5 Lists and `for` loops

The for loop we saw in Section 7.3 also works with lists. The generalized syntax of a for loop is:

for VARIABLE in LIST: BODY

This statement is equivalent to:

i = 0 while i < len(LIST): VARIABLE = LIST[i] BODY i = i + 1

The for loop is more concise because we can eliminate the loop variable, i. Here is the previous loop written with a for loop.

for horseman in horsemen: print horseman

It almost reads like English: "For (every) horseman in (the list of) horsemen, print (the name of the) horseman."

Any list expression can be used in a for loop:

for number in range(20): if number % 2 == 0: print number for fruit in ["banana", "apple", "quince"]: print "I like to eat " + fruit + "s!"

The first example prints all the even numbers between zero and nineteen. The second example expresses enthusiasm for various fruits.

8.6 List operations

The + operator concatenates lists:

>>> a = [1, 2, 3] >>> b = [4, 5, 6] >>> c = a + b >>> print c [1, 2, 3, 4, 5, 6]

Similarly, the * operator repeats a list a given number of times:

>>> [0] * 4 [0, 0, 0, 0] >>> [1, 2, 3] * 3 [1, 2, 3, 1, 2, 3, 1, 2, 3]

The first example repeats [0] four times. The second example repeats the list [1, 2, 3] three times.

8.7 List slices

The slice operations we saw in Section 7.4 also work on lists:

>>> list = ['a', 'b', 'c', 'd', 'e', 'f'] >>> list[1:3] ['b', 'c'] >>> list[:4] ['a', 'b', 'c', 'd'] >>> list[3:] ['d', 'e', 'f']

If you omit the first index, the slice starts at the beginning. If you omit the second, the slice goes to the end. So if you omit both, the slice is really a copy of the whole list.

>>> list[:] ['a', 'b', 'c', 'd', 'e', 'f']

8.8 Lists are mutable

Unlike strings, lists are mutable, which means we can change their elements. Using the bracket operator on the left side of an assignment, we can update one of the elements:

>>> fruit = ["banana", "apple", "quince"] >>> fruit[0] = "pear" >>> fruit[-1] = "orange" >>> print fruit ['pear', 'apple', 'orange']

With the slice operator we can update several elements at once:

>>> list = ['a', 'b', 'c', 'd', 'e', 'f'] >>> list[1:3] = ['x', 'y'] >>> print list ['a', 'x', 'y', 'd', 'e', 'f']

We can also remove elements from a list by assigning the empty list to them:

>>> list = ['a', 'b', 'c', 'd', 'e', 'f'] >>> list[1:3] = [] >>> print list ['a', 'd', 'e', 'f']

And we can add elements to a list by squeezing them into an empty slice at the desired location:

>>> list = ['a', 'd', 'f'] >>> list[1:1] = ['b', 'c'] >>> print list ['a', 'b', 'c', 'd', 'f'] >>> list[4:4] = ['e'] >>> print list ['a', 'b', 'c', 'd', 'e', 'f']

8.9 List deletion

Using slices to delete list elements can be awkward, and therefore error-prone. Python provides an alternative that is more readable.

del removes an element from a list:

>>> a = ['one', 'two', 'three'] >>> del a[1] >>> a ['one', 'three']

As you might expect, del handles negative indices and causes a runtime error if the index is out of range.

You can use a slice as an index for del:

>>> list = ['a', 'b', 'c', 'd', 'e', 'f'] >>> del list[1:5] >>> print list ['a', 'f']

As usual, slices select all the elements up to, but not including, the second index.

8.10 Objects and values

If we execute these assignment statements,

a = "banana" b = "banana"

we know that a and b will refer to a string with the letters "banana". But we can't tell whether they point to the same string.

There are two possible states:

In one case, a and b refer to two different things that have the same value. In the second case, they refer to the same thing. These "things" have names they are called objects. An object is something a variable can refer to.

Every object has a unique identifier, which we can obtain with the id function. By printing the identifier of a and b, we can tell whether they refer to the same object.

>>> id(a) 135044008 >>> id(b) 135044008

In fact, we get the same identifier twice, which means that Python only created one string, and both a and b refer to it.

Interestingly, lists behave differently. When we create two lists, we get two objects:

>>> a = [1, 2, 3] >>> b = [1, 2, 3] >>> id(a) 135045528 >>> id(b) 135041704

So the state diagram looks like this:

a and b have the same value but do not refer to the same object.

8.11 Aliasing

Since variables refer to objects, if we assign one variable to another, both variables refer to the same object:

>>> a = [1, 2, 3] >>> b = a

In this case, the state diagram looks like this:

Because the same list has two different names, a and b, we say that it is aliased. Changes made with one alias affect the other:

>>> b[0] = 5 >>> print a [5, 2, 3]

Although this behavior can be useful, it is sometimes unexpected or undesirable. In general, it is safer to avoid aliasing when you are working with mutable objects. Of course, for immutable objects, there's no problem. That's why Python is free to alias strings when it sees an opportunity to economize.

8.12 Cloning lists

If we want to modify a list and also keep a copy of the original, we need to be able to make a copy of the list itself, not just the reference. This process is sometimes called cloning, to avoid the ambiguity of the word "copy."

The easiest way to clone a list is to use the slice operator:

>>> a = [1, 2, 3] >>> b = a[:] >>> print b [1, 2, 3]

Taking any slice of a creates a new list. In this case the slice happens to consist of the whole list.

Now we are free to make changes to b without worrying about a:

>>> b[0] = 5 >>> print a [1, 2, 3]

As an exercise, draw a state diagram for a and b before and after this change.

8.13 List parameters

Passing a list as an argument actually passes a reference to the list, not a copy of the list. For example, the function head takes a list as an argument and returns the first element:

def head(list): return list[0]

Here's how it is used:

>>> numbers = [1, 2, 3] >>> head(numbers) 1

The parameter list and the variable numbers are aliases for the same object. The state diagram looks like this:

Since the list object is shared by two frames, we drew it between them.

If a function modifies a list parameter, the caller sees the change. For example, deleteHead removes the first element from a list:

def deleteHead(list): del list[0]

Here's how deleteHead is used:

>>> numbers = [1, 2, 3] >>> deleteHead(numbers) >>> print numbers [2, 3]

If a function returns a list, it returns a reference to the list. For example, tail returns a list that contains all but the first element of the given list:

def tail(list): return list[1:]

Here's how tail is used:

>>> numbers = [1, 2, 3] >>> rest = tail(numbers) >>> print rest [2, 3]

Because the return value was created with the slice operator, it is a new list. Creating rest, and any subsequent changes to rest, have no effect on numbers.

8.14 Nested lists

A nested list is a list that appears as an element in another list. In this list, the three-eth element is a nested list:

>>> list = ["hello", 2.0, 5, [10, 20]]

If we print list[3], we get [10, 20]. To extract an element from the nested list, we can proceed in two steps:

>>> elt = list[3] >>> elt[0] 10

Or we can combine them:

>>> list[3][1] 20

Bracket operators evaluate from left to right, so this expression gets the three-eth element of list and extracts the one-eth element from it.

8.15 Matrices

Nested lists are often used to represent matrices. For example, the matrix:

might be represented as:

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

matrix is a list with three elements, where each element is a row of the matrix. We can select an entire row from the matrix in the usual way:

>>> matrix[1] [4, 5, 6]

Or we can extract a single element from the matrix using the double-index form:

>>> matrix[1][1] 5

The first index selects the row, and the second index selects the column. Although this way of representing matrices is common, it is not the only possibility. A small variation is to use a list of columns instead of a list of rows. Later we will see a more radical alternative using a dictionary.

8.16 Strings and lists

Two of the most useful functions in the string module involve lists of strings. The split function breaks a string into a list of words. By default, any number of whitespace characters is considered a word boundary:

>>> import string >>> song = "The rain in Spain..." >>> string.split(song) ['The', 'rain', 'in', 'Spain...']

An optional argument called a delimiter can be used to specify which characters to use as word boundaries. The following example uses the string ai as the delimiter:

>>> string.split(song, 'ai') ['The r', 'n in Sp', 'n...']

Notice that the delimiter doesn't appear in the list.

The join function is the inverse of split. It takes a list of strings and concatenates the elements with a space between each pair:

>>> list = ['The', 'rain', 'in', 'Spain...'] >>> string.join(list) 'The rain in Spain...'

Like split, join takes an optional delimiter that is inserted between elements:

>>> string.join(list, '_') 'The_rain_in_Spain...'

As an exercise, describe the relationship between string.join(string.split(song)) and song. Are they the same for all strings? When would they be different?

8.17 Glossary

list: A named collection of objects, where each object is identified by an index.
index: An integer variable or value that indicates an element of a list.
element: One of the values in a list (or other sequence). The bracket operator selects elements of a list.
sequence: Any of the data types that consist of an ordered set of elements, with each element identified by an index.
nested list: A list that is an element of another list.
list traversal: The sequential accessing of each element in a list.
object: A thing to which a variable can refer.
aliases: Multiple variables that contain references to the same object.
clone: To create a new object that has the same value as an existing object. Copying a reference to an object creates an alias but doesn't clone the object.
delimiter: A character or string used to indicate where a string should be split.