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Python 3.6.5 Documentation > Data Structures

Data Structures
***************

This chapter describes some things you’ve learned about already in
more detail, and adds some new things as well.

More on Lists
=============

The list data type has some more methods. Here are all of the methods
of list objects:

list.append(x)

Add an item to the end of the list. Equivalent to "a[len(a):] =
[x]".

list.extend(iterable)

Extend the list by appending all the items from the iterable.
Equivalent to "a[len(a):] = iterable".

list.insert(i, x)

Insert an item at a given position. The first argument is the
index of the element before which to insert, so "a.insert(0, x)"
inserts at the front of the list, and "a.insert(len(a), x)" is
equivalent to "a.append(x)".

list.remove(x)

Remove the first item from the list whose value is *x*. It is an
error if there is no such item.

list.pop([i])

Remove the item at the given position in the list, and return it.
If no index is specified, "a.pop()" removes and returns the last
item in the list. (The square brackets around the *i* in the
method signature denote that the parameter is optional, not that
you should type square brackets at that position. You will see
this notation frequently in the Python Library Reference.)

list.clear()

Remove all items from the list. Equivalent to "del a[:]".

list.index(x[, start[, end]])

Return zero-based index in the list of the first item whose value
is *x*. Raises a "ValueError" if there is no such item.

The optional arguments *start* and *end* are interpreted as in the
slice notation and are used to limit the search to a particular
subsequence of the list. The returned index is computed relative
to the beginning of the full sequence rather than the *start*
argument.

list.count(x)

Return the number of times *x* appears in the list.

list.sort(key=None, reverse=False)

Sort the items of the list in place (the arguments can be used for
sort customization, see "sorted()" for their explanation).

list.reverse()

Reverse the elements of the list in place.

list.copy()

Return a shallow copy of the list. Equivalent to "a[:]".

An example that uses most of the list methods:

>>> fruits = ['orange', 'apple', 'pear', 'banana', 'kiwi', 'apple', 'banana']
>>> fruits.count('apple')
2
>>> fruits.count('tangerine')
0
>>> fruits.index('banana')
3
>>> fruits.index('banana', 4) # Find next banana starting a position 4
6
>>> fruits.reverse()
>>> fruits
['banana', 'apple', 'kiwi', 'banana', 'pear', 'apple', 'orange']
>>> fruits.append('grape')
>>> fruits
['banana', 'apple', 'kiwi', 'banana', 'pear', 'apple', 'orange', 'grape']
>>> fruits.sort()
>>> fruits
['apple', 'apple', 'banana', 'banana', 'grape', 'kiwi', 'orange', 'pear']
>>> fruits.pop()
'pear'

You might have noticed that methods like "insert", "remove" or "sort"
that only modify the list have no return value printed – they return
the default "None". [1] This is a design principle for all mutable
data structures in Python.

Using Lists as Stacks
---------------------

The list methods make it very easy to use a list as a stack, where the
last element added is the first element retrieved (“last-in, first-
out”). To add an item to the top of the stack, use "append()". To
retrieve an item from the top of the stack, use "pop()" without an
explicit index. For example:

>>> stack = [3, 4, 5]
>>> stack.append(6)
>>> stack.append(7)
>>> stack
[3, 4, 5, 6, 7]
>>> stack.pop()
7
>>> stack
[3, 4, 5, 6]
>>> stack.pop()
6
>>> stack.pop()
5
>>> stack
[3, 4]

Using Lists as Queues
---------------------

It is also possible to use a list as a queue, where the first element
added is the first element retrieved (“first-in, first-out”); however,
lists are not efficient for this purpose. While appends and pops from
the end of list are fast, doing inserts or pops from the beginning of
a list is slow (because all of the other elements have to be shifted
by one).

To implement a queue, use "collections.deque" which was designed to
have fast appends and pops from both ends. For example:

>>> from collections import deque
>>> queue = deque(["Eric", "John", "Michael"])
>>> queue.append("Terry") # Terry arrives
>>> queue.append("Graham") # Graham arrives
>>> queue.popleft() # The first to arrive now leaves
'Eric'
>>> queue.popleft() # The second to arrive now leaves
'John'
>>> queue # Remaining queue in order of arrival
deque(['Michael', 'Terry', 'Graham'])

List Comprehensions
-------------------

List comprehensions provide a concise way to create lists. Common
applications are to make new lists where each element is the result of
some operations applied to each member of another sequence or
iterable, or to create a subsequence of those elements that satisfy a
certain condition.

For example, assume we want to create a list of squares, like:

>>> squares = []
>>> for x in range(10):
... squares.append(x**2)
...
>>> squares
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

Note that this creates (or overwrites) a variable named "x" that still
exists after the loop completes. We can calculate the list of squares
without any side effects using:

squares = list(map(lambda x: x**2, range(10)))

or, equivalently:

squares = [x**2 for x in range(10)]

which is more concise and readable.

A list comprehension consists of brackets containing an expression
followed by a "for" clause, then zero or more "for" or "if" clauses.
The result will be a new list resulting from evaluating the expression
in the context of the "for" and "if" clauses which follow it. For
example, this listcomp combines the elements of two lists if they are
not equal:

>>> [(x, y) for x in [1,2,3] for y in [3,1,4] if x != y]
[(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]

and it’s equivalent to:

>>> combs = []
>>> for x in [1,2,3]:
... for y in [3,1,4]:
... if x != y:
... combs.append((x, y))
...
>>> combs
[(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]

Note how the order of the "for" and "if" statements is the same in
both these snippets.

If the expression is a tuple (e.g. the "(x, y)" in the previous
example), it must be parenthesized.

>>> vec = [-4, -2, 0, 2, 4]
>>> # create a new list with the values doubled
>>> [x*2 for x in vec]
[-8, -4, 0, 4, 8]
>>> # filter the list to exclude negative numbers
>>> [x for x in vec if x >= 0]
[0, 2, 4]
>>> # apply a function to all the elements
>>> [abs(x) for x in vec]
[4, 2, 0, 2, 4]
>>> # call a method on each element
>>> freshfruit = [' banana', ' loganberry ', 'passion fruit ']
>>> [weapon.strip() for weapon in freshfruit]
['banana', 'loganberry', 'passion fruit']
>>> # create a list of 2-tuples like (number, square)
>>> [(x, x**2) for x in range(6)]
[(0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)]
>>> # the tuple must be parenthesized, otherwise an error is raised
>>> [x, x**2 for x in range(6)]
File "<stdin>", line 1, in <module>
[x, x**2 for x in range(6)]
^
SyntaxError: invalid syntax
>>> # flatten a list using a listcomp with two 'for'
>>> vec = [[1,2,3], [4,5,6], [7,8,9]]
>>> [num for elem in vec for num in elem]
[1, 2, 3, 4, 5, 6, 7, 8, 9]

List comprehensions can contain complex expressions and nested
functions:

>>> from math import pi
>>> [str(round(pi, i)) for i in range(1, 6)]
['3.1', '3.14', '3.142', '3.1416', '3.14159']

Nested List Comprehensions
--------------------------

The initial expression in a list comprehension can be any arbitrary
expression, including another list comprehension.

Consider the following example of a 3x4 matrix implemented as a list
of 3 lists of length 4:

>>> matrix = [
... [1, 2, 3, 4],
... [5, 6, 7, 8],
... [9, 10, 11, 12],
... ]

The following list comprehension will transpose rows and columns:

>>> [[row[i] for row in matrix] for i in range(4)]
[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]

As we saw in the previous section, the nested listcomp is evaluated in
the context of the "for" that follows it, so this example is
equivalent to:

>>> transposed = []
>>> for i in range(4):
... transposed.append([row[i] for row in matrix])
...
>>> transposed
[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]

which, in turn, is the same as:

>>> transposed = []
>>> for i in range(4):
... # the following 3 lines implement the nested listcomp
... transposed_row = []
... for row in matrix:
... transposed_row.append(row[i])
... transposed.append(transposed_row)
...
>>> transposed
[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]

In the real world, you should prefer built-in functions to complex
flow statements. The "zip()" function would do a great job for this
use case:

>>> list(zip(*matrix))
[(1, 5, 9), (2, 6, 10), (3, 7, 11), (4, 8, 12)]

See Unpacking Argument Lists for details on the asterisk in this line.

The "del" statement
===================

There is a way to remove an item from a list given its index instead
of its value: the "del" statement. This differs from the "pop()"
method which returns a value. The "del" statement can also be used to
remove slices from a list or clear the entire list (which we did
earlier by assignment of an empty list to the slice). For example:

>>> a = [-1, 1, 66.25, 333, 333, 1234.5]
>>> del a[0]
>>> a
[1, 66.25, 333, 333, 1234.5]
>>> del a[2:4]
>>> a
[1, 66.25, 1234.5]
>>> del a[:]
>>> a
[]

"del" can also be used to delete entire variables:

>>> del a

Referencing the name "a" hereafter is an error (at least until another
value is assigned to it). We’ll find other uses for "del" later.

Tuples and Sequences
====================

We saw that lists and strings have many common properties, such as
indexing and slicing operations. They are two examples of *sequence*
data types (see Sequence Types — list, tuple, range). Since Python is
an evolving language, other sequence data types may be added. There
is also another standard sequence data type: the *tuple*.

A tuple consists of a number of values separated by commas, for
instance:

>>> t = 12345, 54321, 'hello!'
>>> t[0]
12345
>>> t
(12345, 54321, 'hello!')
>>> # Tuples may be nested:
... u = t, (1, 2, 3, 4, 5)
>>> u
((12345, 54321, 'hello!'), (1, 2, 3, 4, 5))
>>> # Tuples are immutable:
... t[0] = 88888
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: 'tuple' object does not support item assignment
>>> # but they can contain mutable objects:
... v = ([1, 2, 3], [3, 2, 1])
>>> v
([1, 2, 3], [3, 2, 1])

As you see, on output tuples are always enclosed in parentheses, so
that nested tuples are interpreted correctly; they may be input with
or without surrounding parentheses, although often parentheses are
necessary anyway (if the tuple is part of a larger expression). It is
not possible to assign to the individual items of a tuple, however it
is possible to create tuples which contain mutable objects, such as
lists.

Though tuples may seem similar to lists, they are often used in
different situations and for different purposes. Tuples are
*immutable*, and usually contain a heterogeneous sequence of elements
that are accessed via unpacking (see later in this section) or
indexing (or even by attribute in the case of "namedtuples"). Lists
are *mutable*, and their elements are usually homogeneous and are
accessed by iterating over the list.

A special problem is the construction of tuples containing 0 or 1
items: the syntax has some extra quirks to accommodate these. Empty
tuples are constructed by an empty pair of parentheses; a tuple with
one item is constructed by following a value with a comma (it is not
sufficient to enclose a single value in parentheses). Ugly, but
effective. For example:

>>> empty = ()
>>> singleton = 'hello', # <-- note trailing comma
>>> len(empty)
0
>>> len(singleton)
1
>>> singleton
('hello',)

The statement "t = 12345, 54321, 'hello!'" is an example of *tuple
packing*: the values "12345", "54321" and "'hello!'" are packed
together in a tuple. The reverse operation is also possible:

>>> x, y, z = t

This is called, appropriately enough, *sequence unpacking* and works
for any sequence on the right-hand side. Sequence unpacking requires
that there are as many variables on the left side of the equals sign
as there are elements in the sequence. Note that multiple assignment
is really just a combination of tuple packing and sequence unpacking.

Sets
====

Python also includes a data type for *sets*. A set is an unordered
collection with no duplicate elements. Basic uses include membership
testing and eliminating duplicate entries. Set objects also support
mathematical operations like union, intersection, difference, and
symmetric difference.

Curly braces or the "set()" function can be used to create sets.
Note: to create an empty set you have to use "set()", not "{}"; the
latter creates an empty dictionary, a data structure that we discuss
in the next section.

Here is a brief demonstration:

>>> basket = {'apple', 'orange', 'apple', 'pear', 'orange', 'banana'}
>>> print(basket) # show that duplicates have been removed
{'orange', 'banana', 'pear', 'apple'}
>>> 'orange' in basket # fast membership testing
True
>>> 'crabgrass' in basket
False

>>> # Demonstrate set operations on unique letters from two words
...
>>> a = set('abracadabra')
>>> b = set('alacazam')
>>> a # unique letters in a
{'a', 'r', 'b', 'c', 'd'}
>>> a - b # letters in a but not in b
{'r', 'd', 'b'}
>>> a | b # letters in a or b or both
{'a', 'c', 'r', 'd', 'b', 'm', 'z', 'l'}
>>> a & b # letters in both a and b
{'a', 'c'}
>>> a ^ b # letters in a or b but not both
{'r', 'd', 'b', 'm', 'z', 'l'}

Similarly to list comprehensions, set comprehensions are also
supported:

>>> a = {x for x in 'abracadabra' if x not in 'abc'}
>>> a
{'r', 'd'}

Dictionaries
============

Another useful data type built into Python is the *dictionary* (see
Mapping Types — dict). Dictionaries are sometimes found in other
languages as “associative memories” or “associative arrays”. Unlike
sequences, which are indexed by a range of numbers, dictionaries are
indexed by *keys*, which can be any immutable type; strings and
numbers can always be keys. Tuples can be used as keys if they
contain only strings, numbers, or tuples; if a tuple contains any
mutable object either directly or indirectly, it cannot be used as a
key. You can’t use lists as keys, since lists can be modified in place
using index assignments, slice assignments, or methods like "append()"
and "extend()".

It is best to think of a dictionary as an unordered set of *key:
value* pairs, with the requirement that the keys are unique (within
one dictionary). A pair of braces creates an empty dictionary: "{}".
Placing a comma-separated list of key:value pairs within the braces
adds initial key:value pairs to the dictionary; this is also the way
dictionaries are written on output.

The main operations on a dictionary are storing a value with some key
and extracting the value given the key. It is also possible to delete
a key:value pair with "del". If you store using a key that is already
in use, the old value associated with that key is forgotten. It is an
error to extract a value using a non-existent key.

Performing "list(d.keys())" on a dictionary returns a list of all the
keys used in the dictionary, in arbitrary order (if you want it
sorted, just use "sorted(d.keys())" instead). [2] To check whether a
single key is in the dictionary, use the "in" keyword.

Here is a small example using a dictionary:

>>> tel = {'jack': 4098, 'sape': 4139}
>>> tel['guido'] = 4127
>>> tel
{'sape': 4139, 'guido': 4127, 'jack': 4098}
>>> tel['jack']
4098
>>> del tel['sape']
>>> tel['irv'] = 4127
>>> tel
{'guido': 4127, 'irv': 4127, 'jack': 4098}
>>> list(tel.keys())
['irv', 'guido', 'jack']
>>> sorted(tel.keys())
['guido', 'irv', 'jack']
>>> 'guido' in tel
True
>>> 'jack' not in tel
False

The "dict()" constructor builds dictionaries directly from sequences
of key-value pairs:

>>> dict([('sape', 4139), ('guido', 4127), ('jack', 4098)])
{'sape': 4139, 'jack': 4098, 'guido': 4127}

In addition, dict comprehensions can be used to create dictionaries
from arbitrary key and value expressions:

>>> {x: x**2 for x in (2, 4, 6)}
{2: 4, 4: 16, 6: 36}

When the keys are simple strings, it is sometimes easier to specify
pairs using keyword arguments:

>>> dict(sape=4139, guido=4127, jack=4098)
{'sape': 4139, 'jack': 4098, 'guido': 4127}

Looping Techniques
==================

When looping through dictionaries, the key and corresponding value can
be retrieved at the same time using the "items()" method.

>>> knights = {'gallahad': 'the pure', 'robin': 'the brave'}
>>> for k, v in knights.items():
... print(k, v)
...
gallahad the pure
robin the brave

When looping through a sequence, the position index and corresponding
value can be retrieved at the same time using the "enumerate()"
function.

>>> for i, v in enumerate(['tic', 'tac', 'toe']):
... print(i, v)
...
0 tic
1 tac
2 toe

To loop over two or more sequences at the same time, the entries can
be paired with the "zip()" function.

>>> questions = ['name', 'quest', 'favorite color']
>>> answers = ['lancelot', 'the holy grail', 'blue']
>>> for q, a in zip(questions, answers):
... print('What is your {0}? It is {1}.'.format(q, a))
...
What is your name? It is lancelot.
What is your quest? It is the holy grail.
What is your favorite color? It is blue.

To loop over a sequence in reverse, first specify the sequence in a
forward direction and then call the "reversed()" function.

>>> for i in reversed(range(1, 10, 2)):
... print(i)
...
9
7
5
3
1

To loop over a sequence in sorted order, use the "sorted()" function
which returns a new sorted list while leaving the source unaltered.

>>> basket = ['apple', 'orange', 'apple', 'pear', 'orange', 'banana']
>>> for f in sorted(set(basket)):
... print(f)
...
apple
banana
orange
pear

It is sometimes tempting to change a list while you are looping over
it; however, it is often simpler and safer to create a new list
instead.

>>> import math
>>> raw_data = [56.2, float('NaN'), 51.7, 55.3, 52.5, float('NaN'), 47.8]
>>> filtered_data = []
>>> for value in raw_data:
... if not math.isnan(value):
... filtered_data.append(value)
...
>>> filtered_data
[56.2, 51.7, 55.3, 52.5, 47.8]