
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(L)

   Extend the list by appending all the items in the given list;
   equivalent to ``a[len(a):] = L``.

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.index(x)

   Return the index in the list of the first item whose value is *x*.
   It is an error if there is no such item.

list.count(x)

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

list.sort()

   Sort the items of the list, in place.

list.reverse()

   Reverse the elements of the list, in place.

An example that uses most of the list methods:

   >>> a = [66.25, 333, 333, 1, 1234.5]
   >>> print a.count(333), a.count(66.25), a.count('x')
   2 1 0
   >>> a.insert(2, -1)
   >>> a.append(333)
   >>> a
   [66.25, 333, -1, 333, 1, 1234.5, 333]
   >>> a.index(333)
   1
   >>> a.remove(333)
   >>> a
   [66.25, -1, 333, 1, 1234.5, 333]
   >>> a.reverse()
   >>> a
   [333, 1234.5, 1, 333, -1, 66.25]
   >>> a.sort()
   >>> a
   [-1, 1, 66.25, 333, 333, 1234.5]


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'])


Functional Programming Tools
----------------------------

There are three built-in functions that are very useful when used with
lists: ``filter()``, ``map()``, and ``reduce()``.

``filter(function, sequence)`` returns a sequence consisting of those
items from the sequence for which ``function(item)`` is true. If
*sequence* is a ``string`` or ``tuple``, the result will be of the
same type; otherwise, it is always a ``list``. For example, to compute
a sequence of numbers not divisible by 2 or 3:

   >>> def f(x): return x % 2 != 0 and x % 3 != 0
   ...
   >>> filter(f, range(2, 25))
   [5, 7, 11, 13, 17, 19, 23]

``map(function, sequence)`` calls ``function(item)`` for each of the
sequence's items and returns a list of the return values.  For
example, to compute some cubes:

   >>> def cube(x): return x*x*x
   ...
   >>> map(cube, range(1, 11))
   [1, 8, 27, 64, 125, 216, 343, 512, 729, 1000]

More than one sequence may be passed; the function must then have as
many arguments as there are sequences and is called with the
corresponding item from each sequence (or ``None`` if some sequence is
shorter than another).  For example:

   >>> seq = range(8)
   >>> def add(x, y): return x+y
   ...
   >>> map(add, seq, seq)
   [0, 2, 4, 6, 8, 10, 12, 14]

``reduce(function, sequence)`` returns a single value constructed by
calling the binary function *function* on the first two items of the
sequence, then on the result and the next item, and so on.  For
example, to compute the sum of the numbers 1 through 10:

   >>> def add(x,y): return x+y
   ...
   >>> reduce(add, range(1, 11))
   55

If there's only one item in the sequence, its value is returned; if
the sequence is empty, an exception is raised.

A third argument can be passed to indicate the starting value.  In
this case the starting value is returned for an empty sequence, and
the function is first applied to the starting value and the first
sequence item, then to the result and the next item, and so on.  For
example,

   >>> def sum(seq):
   ...     def add(x,y): return x+y
   ...     return reduce(add, seq, 0)
   ...
   >>> sum(range(1, 11))
   55
   >>> sum([])
   0

Don't use this example's definition of ``sum()``: since summing
numbers is such a common need, a built-in function ``sum(sequence)``
is already provided, and works exactly like this.


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]

We can obtain the same result with:

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

This is also equivalent to ``squares = map(lambda x: x**2,
range(10))``, but it's 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
       [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:

   >>> 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 --- str, unicode, list, tuple,
bytearray, buffer, xrange*).  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 an 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
the list of variables on the left to have the same number of elements
as the length of 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']
   >>> fruit = set(basket)               # create a set without duplicates
   >>> fruit
   set(['orange', 'pear', 'apple', 'banana'])
   >>> 'orange' in fruit                 # fast membership testing
   True
   >>> 'crabgrass' in fruit
   False

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

The ``keys()`` method of a dictionary object returns a list of all the
keys used in the dictionary, in arbitrary order (if you want it
sorted, just apply the ``sorted()`` function to it).  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}
   >>> tel.keys()
   ['guido', 'irv', 'jack']
   >>> 'guido' in tel
   True

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 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(xrange(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

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

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

To change a sequence you are iterating over while inside the loop (for
example to duplicate certain items), it is recommended that you first
make a copy.  Looping over a sequence does not implicitly make a copy.
The slice notation makes this especially convenient:

   >>> words = ['cat', 'window', 'defenestrate']
   >>> for w in words[:]:  # Loop over a slice copy of the entire list.
   ...     if len(w) > 6:
   ...         words.insert(0, w)
   ...
   >>> words
   ['defenestrate', 'cat', 'window', 'defenestrate']


More on Conditions
==================

The conditions used in ``while`` and ``if`` statements can contain any
operators, not just comparisons.

The comparison operators ``in`` and ``not in`` check whether a value
occurs (does not occur) in a sequence.  The operators ``is`` and ``is
not`` compare whether two objects are really the same object; this
only matters for mutable objects like lists.  All comparison operators
have the same priority, which is lower than that of all numerical
operators.

Comparisons can be chained.  For example, ``a < b == c`` tests whether
``a`` is less than ``b`` and moreover ``b`` equals ``c``.

Comparisons may be combined using the Boolean operators ``and`` and
``or``, and the outcome of a comparison (or of any other Boolean
expression) may be negated with ``not``.  These have lower priorities
than comparison operators; between them, ``not`` has the highest
priority and ``or`` the lowest, so that ``A and not B or C`` is
equivalent to ``(A and (not B)) or C``. As always, parentheses can be
used to express the desired composition.

The Boolean operators ``and`` and ``or`` are so-called *short-circuit*
operators: their arguments are evaluated from left to right, and
evaluation stops as soon as the outcome is determined.  For example,
if ``A`` and ``C`` are true but ``B`` is false, ``A and B and C`` does
not evaluate the expression ``C``.  When used as a general value and
not as a Boolean, the return value of a short-circuit operator is the
last evaluated argument.

It is possible to assign the result of a comparison or other Boolean
expression to a variable.  For example,

   >>> string1, string2, string3 = '', 'Trondheim', 'Hammer Dance'
   >>> non_null = string1 or string2 or string3
   >>> non_null
   'Trondheim'

Note that in Python, unlike C, assignment cannot occur inside
expressions. C programmers may grumble about this, but it avoids a
common class of problems encountered in C programs: typing ``=`` in an
expression when ``==`` was intended.


Comparing Sequences and Other Types
===================================

Sequence objects may be compared to other objects with the same
sequence type. The comparison uses *lexicographical* ordering: first
the first two items are compared, and if they differ this determines
the outcome of the comparison; if they are equal, the next two items
are compared, and so on, until either sequence is exhausted. If two
items to be compared are themselves sequences of the same type, the
lexicographical comparison is carried out recursively.  If all items
of two sequences compare equal, the sequences are considered equal. If
one sequence is an initial sub-sequence of the other, the shorter
sequence is the smaller (lesser) one.  Lexicographical ordering for
strings uses the ASCII ordering for individual characters.  Some
examples of comparisons between sequences of the same type:

   (1, 2, 3)              < (1, 2, 4)
   [1, 2, 3]              < [1, 2, 4]
   'ABC' < 'C' < 'Pascal' < 'Python'
   (1, 2, 3, 4)           < (1, 2, 4)
   (1, 2)                 < (1, 2, -1)
   (1, 2, 3)             == (1.0, 2.0, 3.0)
   (1, 2, ('aa', 'ab'))   < (1, 2, ('abc', 'a'), 4)

Note that comparing objects of different types is legal.  The outcome
is deterministic but arbitrary: the types are ordered by their name.
Thus, a list is always smaller than a string, a string is always
smaller than a tuple, etc. [1] Mixed numeric types are compared
according to their numeric value, so 0 equals 0.0, etc.

-[ Footnotes ]-

[1] The rules for comparing objects of different types should not be
    relied upon; they may change in a future version of the language.
