Doc/library/collections.rst

:mod:`collections` --- High-performance container datatypes
===========================================================

.. module:: collections
   :synopsis: High-performance datatypes
.. moduleauthor:: Raymond Hettinger <python@rcn.com>
.. sectionauthor:: Raymond Hettinger <python@rcn.com>

.. versionadded:: 2.4

.. testsetup:: *

   from collections import *
   import itertools
   __name__ = '<doctest>'

This module implements high-performance container datatypes.  Currently,
there are four datatypes, :class:`Counter`, :class:`deque`, :class:`OrderedDict` and
:class:`defaultdict`, and one datatype factory function, :func:`namedtuple`.

The specialized containers provided in this module provide alternatives
to Python's general purpose built-in containers, :class:`dict`,
:class:`list`, :class:`set`, and :class:`tuple`.

.. versionchanged:: 2.4
   Added :class:`deque`.

.. versionchanged:: 2.5
   Added :class:`defaultdict`.

.. versionchanged:: 2.6
   Added :func:`namedtuple` and added abstract base classes.

.. versionchanged:: 2.7
   Added :class:`Counter` and :class:`OrderedDict`.

In addition to containers, the collections module provides some ABCs
(abstract base classes) that can be used to test whether a class
provides a particular interface, for example, whether it is hashable or
a mapping.


ABCs - abstract base classes
----------------------------

The collections module offers the following ABCs:

=========================  =====================  ======================  ====================================================
ABC                        Inherits               Abstract Methods        Mixin Methods
=========================  =====================  ======================  ====================================================
:class:`Container`                                ``__contains__``
:class:`Hashable`                                 ``__hash__``
:class:`Iterable`                                 ``__iter__``
:class:`Iterator`          :class:`Iterable`      ``next``                ``__iter__``
:class:`Sized`                                    ``__len__``
:class:`Callable`                                 ``__call__``

:class:`Sequence`          :class:`Sized`,        ``__getitem__``         ``__contains__``. ``__iter__``, ``__reversed__``.
                           :class:`Iterable`,                             ``index``, and ``count``
                           :class:`Container`

:class:`MutableSequence`   :class:`Sequence`      ``__setitem__``         Inherited Sequence methods and
                                                  ``__delitem__``,        ``append``, ``reverse``, ``extend``, ``pop``,
                                                  and ``insert``          ``remove``, and ``__iadd__``

:class:`Set`               :class:`Sized`,                                ``__le__``, ``__lt__``, ``__eq__``, ``__ne__``,
                           :class:`Iterable`,                             ``__gt__``, ``__ge__``, ``__and__``, ``__or__``
                           :class:`Container`                             ``__sub__``, ``__xor__``, and ``isdisjoint``

:class:`MutableSet`        :class:`Set`           ``add`` and             Inherited Set methods and
                                                  ``discard``             ``clear``, ``pop``, ``remove``, ``__ior__``,
                                                                          ``__iand__``, ``__ixor__``, and ``__isub__``

:class:`Mapping`           :class:`Sized`,        ``__getitem__``         ``__contains__``, ``keys``, ``items``, ``values``,
                           :class:`Iterable`,                             ``get``, ``__eq__``, and ``__ne__``
                           :class:`Container`

:class:`MutableMapping`    :class:`Mapping`       ``__setitem__`` and     Inherited Mapping methods and
                                                  ``__delitem__``         ``pop``, ``popitem``, ``clear``, ``update``,
                                                                          and ``setdefault``


:class:`MappingView`       :class:`Sized`                                 ``__len__``
:class:`KeysView`          :class:`MappingView`,                          ``__contains__``,
                           :class:`Set`                                   ``__iter__``
:class:`ItemsView`         :class:`MappingView`,                          ``__contains__``,
                           :class:`Set`                                   ``__iter__``
:class:`ValuesView`        :class:`MappingView`                           ``__contains__``, ``__iter__``
=========================  =====================  ======================  ====================================================

These ABCs allow us to ask classes or instances if they provide
particular functionality, for example::

    size = None
    if isinstance(myvar, collections.Sized):
        size = len(myvar)

Several of the ABCs are also useful as mixins that make it easier to develop
classes supporting container APIs.  For example, to write a class supporting
the full :class:`Set` API, it only necessary to supply the three underlying
abstract methods: :meth:`__contains__`, :meth:`__iter__`, and :meth:`__len__`.
The ABC supplies the remaining methods such as :meth:`__and__` and
:meth:`isdisjoint` ::

    class ListBasedSet(collections.Set):
         ''' Alternate set implementation favoring space over speed
             and not requiring the set elements to be hashable. '''
         def __init__(self, iterable):
             self.elements = lst = []
             for value in iterable:
                 if value not in lst:
                     lst.append(value)
         def __iter__(self):
             return iter(self.elements)
         def __contains__(self, value):
             return value in self.elements
         def __len__(self):
             return len(self.elements)

    s1 = ListBasedSet('abcdef')
    s2 = ListBasedSet('defghi')
    overlap = s1 & s2            # The __and__() method is supported automatically

Notes on using :class:`Set` and :class:`MutableSet` as a mixin:

(1)
   Since some set operations create new sets, the default mixin methods need
   a way to create new instances from an iterable. The class constructor is
   assumed to have a signature in the form ``ClassName(iterable)``.
   That assumption is factored-out to an internal classmethod called
   :meth:`_from_iterable` which calls ``cls(iterable)`` to produce a new set.
   If the :class:`Set` mixin is being used in a class with a different
   constructor signature, you will need to override :meth:`from_iterable`
   with a classmethod that can construct new instances from
   an iterable argument.

(2)
   To override the comparisons (presumably for speed, as the
   semantics are fixed), redefine :meth:`__le__` and
   then the other operations will automatically follow suit.

(3)
   The :class:`Set` mixin provides a :meth:`_hash` method to compute a hash value
   for the set; however, :meth:`__hash__` is not defined because not all sets
   are hashable or immutable.  To add set hashabilty using mixins,
   inherit from both :meth:`Set` and :meth:`Hashable`, then define
   ``__hash__ = Set._hash``.

.. seealso::

   * `OrderedSet recipe <http://code.activestate.com/recipes/576694/>`_ for an
     example built on :class:`MutableSet`.

   * For more about ABCs, see the :mod:`abc` module and :pep:`3119`.


:class:`Counter` objects
------------------------

A counter tool is provided to support convenient and rapid tallies.
For example::

    >>> # Tally occurrences of words in a list
    >>> cnt = Counter()
    >>> for word in ['red', 'blue', 'red', 'green', 'blue', 'blue']:
    ...     cnt[word] += 1
    >>> cnt
    Counter({'blue': 3, 'red': 2, 'green': 1})

    >>> # Find the ten most common words in Hamlet
    >>> import re
    >>> words = re.findall('\w+', open('hamlet.txt').read().lower())
    >>> Counter(words).most_common(10)
    [('the', 1143), ('and', 966), ('to', 762), ('of', 669), ('i', 631),
     ('you', 554),  ('a', 546), ('my', 514), ('hamlet', 471), ('in', 451)]

.. class:: Counter([iterable-or-mapping])

   A :class:`Counter` is a :class:`dict` subclass for counting hashable objects.
   It is an unordered collection where elements are stored as dictionary keys
   and their counts are stored as dictionary values.  Counts are allowed to be
   any integer value including zero or negative counts.  The :class:`Counter`
   class is similar to bags or multisets in other languages.

   Elements are counted from an *iterable* or initialized from another
   *mapping* (or counter):

        >>> c = Counter()                           # a new, empty counter
        >>> c = Counter('gallahad')                 # a new counter from an iterable
        >>> c = Counter({'red': 4, 'blue': 2})      # a new counter from a mapping
        >>> c = Counter(cats=4, dogs=8)             # a new counter from keyword args

   Counter objects have a dictionary interface except that they return a zero
   count for missing items instead of raising a :exc:`KeyError`:

        >>> c = Counter(['eggs', 'ham'])
        >>> c['bacon']                              # count of a missing element is zero
        0

   Setting a count to zero does not remove an element from a counter.
   Use ``del`` to remove it entirely:

        >>> c['sausage'] = 0                        # counter entry with a zero count
        >>> del c['sausage']                        # del actually removes the entry

   .. versionadded:: 2.7


   Counter objects support two methods beyond those available for all
   dictionaries:

   .. method:: elements()

      Return an iterator over elements repeating each as many times as its
      count.  Elements are returned in arbitrary order.  If an element's count
      is less than one, :meth:`elements` will ignore it.

            >>> c = Counter(a=4, b=2, c=0, d=-2)
            >>> list(c.elements())
            ['a', 'a', 'a', 'a', 'b', 'b']

   .. method:: most_common([n])

      Return a list of the *n* most common elements and their counts from the
      most common to the least.  If *n* is not specified, :func:`most_common`
      returns *all* elements in the counter.  Elements with equal counts are
      ordered arbitrarily:

            >>> Counter('abracadabra').most_common(3)
            [('a', 5), ('r', 2), ('b', 2)]

   .. method:: subtract([iterable-or-mapping])

      Elements are subtracted from an *iterable* or from another *mapping*
      (or counter).  Like :meth:`dict.update` but subtracts counts instead
      of replacing them.  Both inputs and outputs may be zero or negative.

            >>> c = Counter(a=4, b=2, c=0, d=-2)
            >>> d = Counter(a=1, b=2, c=3, d=4)
            >>> c.subtract(d)
            Counter({'a': 3, 'b': 0, 'c': -3, 'd': -6})

   The usual dictionary methods are available for :class:`Counter` objects
   except for two which work differently for counters.

   .. method:: fromkeys(iterable)

      This class method is not implemented for :class:`Counter` objects.

   .. method:: update([iterable-or-mapping])

      Elements are counted from an *iterable* or added-in from another
      *mapping* (or counter).  Like :meth:`dict.update` but adds counts
      instead of replacing them.  Also, the *iterable* is expected to be a
      sequence of elements, not a sequence of ``(key, value)`` pairs.

Common patterns for working with :class:`Counter` objects::

    sum(c.values())                 # total of all counts
    c.clear()                       # reset all counts
    list(c)                         # list unique elements
    set(c)                          # convert to a set
    dict(c)                         # convert to a regular dictionary
    c.items()                       # convert to a list of (elem, cnt) pairs
    Counter(dict(list_of_pairs))    # convert from a list of (elem, cnt) pairs
    c.most_common()[:-n:-1]         # n least common elements
    c += Counter()                  # remove zero and negative counts

Several mathematical operations are provided for combining :class:`Counter`
objects to produce multisets (counters that have counts greater than zero).
Addition and subtraction combine counters by adding or subtracting the counts
of corresponding elements.  Intersection and union return the minimum and
maximum of corresponding counts.  Each operation can accept inputs with signed
counts, but the output will exclude results with counts of zero or less.

    >>> c = Counter(a=3, b=1)
    >>> d = Counter(a=1, b=2)
    >>> c + d                       # add two counters together:  c[x] + d[x]
    Counter({'a': 4, 'b': 3})
    >>> c - d                       # subtract (keeping only positive counts)
    Counter({'a': 2})
    >>> c & d                       # intersection:  min(c[x], d[x])
    Counter({'a': 1, 'b': 1})
    >>> c | d                       # union:  max(c[x], d[x])
    Counter({'a': 3, 'b': 2})

.. seealso::

    * `Counter class <http://code.activestate.com/recipes/576611/>`_
      adapted for Python 2.5 and an early `Bag recipe
      <http://code.activestate.com/recipes/259174/>`_ for Python 2.4.

    * `Bag class <http://www.gnu.org/software/smalltalk/manual-base/html_node/Bag.html>`_
      in Smalltalk.

    * Wikipedia entry for `Multisets <http://en.wikipedia.org/wiki/Multiset>`_\.

    * `C++ multisets <http://www.demo2s.com/Tutorial/Cpp/0380__set-multiset/Catalog0380__set-multiset.htm>`_
      tutorial with examples.

    * For mathematical operations on multisets and their use cases, see
      *Knuth, Donald. The Art of Computer Programming Volume II,
      Section 4.6.3, Exercise 19*\.

    * To enumerate all distinct multisets of a given size over a given set of
      elements, see :func:`itertools.combinations_with_replacement`.

          map(Counter, combinations_with_replacement('ABC', 2)) --> AA AB AC BB BC CC


:class:`deque` objects
----------------------

.. class:: deque([iterable[, maxlen]])

   Returns a new deque object initialized left-to-right (using :meth:`append`) with
   data from *iterable*.  If *iterable* is not specified, the new deque is empty.

   Deques are a generalization of stacks and queues (the name is pronounced "deck"
   and is short for "double-ended queue").  Deques support thread-safe, memory
   efficient appends and pops from either side of the deque with approximately the
   same O(1) performance in either direction.

   Though :class:`list` objects support similar operations, they are optimized for
   fast fixed-length operations and incur O(n) memory movement costs for
   ``pop(0)`` and ``insert(0, v)`` operations which change both the size and
   position of the underlying data representation.

   .. versionadded:: 2.4

   If *maxlen* is not specified or is *None*, deques may grow to an
   arbitrary length.  Otherwise, the deque is bounded to the specified maximum
   length.  Once a bounded length deque is full, when new items are added, a
   corresponding number of items are discarded from the opposite end.  Bounded
   length deques provide functionality similar to the ``tail`` filter in
   Unix. They are also useful for tracking transactions and other pools of data
   where only the most recent activity is of interest.

   .. versionchanged:: 2.6
      Added *maxlen* parameter.

   Deque objects support the following methods:


   .. method:: append(x)

      Add *x* to the right side of the deque.


   .. method:: appendleft(x)

      Add *x* to the left side of the deque.


   .. method:: clear()

      Remove all elements from the deque leaving it with length 0.


   .. method:: count(x)

      Count the number of deque elements equal to *x*.

      .. versionadded:: 2.7

   .. method:: extend(iterable)

      Extend the right side of the deque by appending elements from the iterable
      argument.


   .. method:: extendleft(iterable)

      Extend the left side of the deque by appending elements from *iterable*.
      Note, the series of left appends results in reversing the order of
      elements in the iterable argument.


   .. method:: pop()

      Remove and return an element from the right side of the deque. If no
      elements are present, raises an :exc:`IndexError`.


   .. method:: popleft()

      Remove and return an element from the left side of the deque. If no
      elements are present, raises an :exc:`IndexError`.


   .. method:: remove(value)

      Removed the first occurrence of *value*.  If not found, raises a
      :exc:`ValueError`.

      .. versionadded:: 2.5

   .. method:: reverse()

      Reverse the elements of the deque in-place and then return ``None``.

      .. versionadded:: 2.7

   .. method:: rotate(n)

      Rotate the deque *n* steps to the right.  If *n* is negative, rotate to
      the left.  Rotating one step to the right is equivalent to:
      ``d.appendleft(d.pop())``.


   Deque objects also provide one read-only attribute:

   .. attribute:: maxlen

      Maximum size of a deque or *None* if unbounded.

      .. versionadded:: 2.7


In addition to the above, deques support iteration, pickling, ``len(d)``,
``reversed(d)``, ``copy.copy(d)``, ``copy.deepcopy(d)``, membership testing with
the :keyword:`in` operator, and subscript references such as ``d[-1]``.  Indexed
access is O(1) at both ends but slows to O(n) in the middle.  For fast random
access, use lists instead.

Example:

.. doctest::

   >>> from collections import deque
   >>> d = deque('ghi')                 # make a new deque with three items
   >>> for elem in d:                   # iterate over the deque's elements
   ...     print elem.upper()
   G
   H
   I

   >>> d.append('j')                    # add a new entry to the right side
   >>> d.appendleft('f')                # add a new entry to the left side
   >>> d                                # show the representation of the deque
   deque(['f', 'g', 'h', 'i', 'j'])

   >>> d.pop()                          # return and remove the rightmost item
   'j'
   >>> d.popleft()                      # return and remove the leftmost item
   'f'
   >>> list(d)                          # list the contents of the deque
   ['g', 'h', 'i']
   >>> d[0]                             # peek at leftmost item
   'g'
   >>> d[-1]                            # peek at rightmost item
   'i'

   >>> list(reversed(d))                # list the contents of a deque in reverse
   ['i', 'h', 'g']
   >>> 'h' in d                         # search the deque
   True
   >>> d.extend('jkl')                  # add multiple elements at once
   >>> d
   deque(['g', 'h', 'i', 'j', 'k', 'l'])
   >>> d.rotate(1)                      # right rotation
   >>> d
   deque(['l', 'g', 'h', 'i', 'j', 'k'])
   >>> d.rotate(-1)                     # left rotation
   >>> d
   deque(['g', 'h', 'i', 'j', 'k', 'l'])

   >>> deque(reversed(d))               # make a new deque in reverse order
   deque(['l', 'k', 'j', 'i', 'h', 'g'])
   >>> d.clear()                        # empty the deque
   >>> d.pop()                          # cannot pop from an empty deque
   Traceback (most recent call last):
     File "<pyshell#6>", line 1, in -toplevel-
       d.pop()
   IndexError: pop from an empty deque

   >>> d.extendleft('abc')              # extendleft() reverses the input order
   >>> d
   deque(['c', 'b', 'a'])


:class:`deque` Recipes
^^^^^^^^^^^^^^^^^^^^^^

This section shows various approaches to working with deques.

Bounded length deques provide functionality similar to the ``tail`` filter
in Unix::

   def tail(filename, n=10):
       'Return the last n lines of a file'
       return deque(open(filename), n)

Another approach to using deques is to maintain a sequence of recently
added elements by appending to the right and popping to the left::

    def moving_average(iterable, n=3):
        # moving_average([40, 30, 50, 46, 39, 44]) --> 40.0 42.0 45.0 43.0
        # http://en.wikipedia.org/wiki/Moving_average
        it = iter(iterable)
        d = deque(itertools.islice(it, n-1))
        d.appendleft(0)
        s = sum(d)
        for elem in it:
            s += elem - d.popleft()
            d.append(elem)
            yield s / float(n)

The :meth:`rotate` method provides a way to implement :class:`deque` slicing and
deletion.  For example, a pure Python implementation of ``del d[n]`` relies on
the :meth:`rotate` method to position elements to be popped::

   def delete_nth(d, n):
       d.rotate(-n)
       d.popleft()
       d.rotate(n)

To implement :class:`deque` slicing, use a similar approach applying
:meth:`rotate` to bring a target element to the left side of the deque. Remove
old entries with :meth:`popleft`, add new entries with :meth:`extend`, and then
reverse the rotation.
With minor variations on that approach, it is easy to implement Forth style
stack manipulations such as ``dup``, ``drop``, ``swap``, ``over``, ``pick``,
``rot``, and ``roll``.


:class:`defaultdict` objects
----------------------------

.. class:: defaultdict([default_factory[, ...]])

   Returns a new dictionary-like object.  :class:`defaultdict` is a subclass of the
   built-in :class:`dict` class.  It overrides one method and adds one writable
   instance variable.  The remaining functionality is the same as for the
   :class:`dict` class and is not documented here.

   The first argument provides the initial value for the :attr:`default_factory`
   attribute; it defaults to ``None``. All remaining arguments are treated the same
   as if they were passed to the :class:`dict` constructor, including keyword
   arguments.

   .. versionadded:: 2.5

   :class:`defaultdict` objects support the following method in addition to the
   standard :class:`dict` operations:


   .. method:: defaultdict.__missing__(key)

      If the :attr:`default_factory` attribute is ``None``, this raises a
      :exc:`KeyError` exception with the *key* as argument.

      If :attr:`default_factory` is not ``None``, it is called without arguments
      to provide a default value for the given *key*, this value is inserted in
      the dictionary for the *key*, and returned.

      If calling :attr:`default_factory` raises an exception this exception is
      propagated unchanged.

      This method is called by the :meth:`__getitem__` method of the
      :class:`dict` class when the requested key is not found; whatever it
      returns or raises is then returned or raised by :meth:`__getitem__`.


   :class:`defaultdict` objects support the following instance variable:


   .. attribute:: defaultdict.default_factory

      This attribute is used by the :meth:`__missing__` method; it is
      initialized from the first argument to the constructor, if present, or to
      ``None``, if absent.


:class:`defaultdict` Examples
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Using :class:`list` as the :attr:`default_factory`, it is easy to group a
sequence of key-value pairs into a dictionary of lists:

   >>> s = [('yellow', 1), ('blue', 2), ('yellow', 3), ('blue', 4), ('red', 1)]
   >>> d = defaultdict(list)
   >>> for k, v in s:
   ...     d[k].append(v)
   ...
   >>> d.items()
   [('blue', [2, 4]), ('red', [1]), ('yellow', [1, 3])]

When each key is encountered for the first time, it is not already in the
mapping; so an entry is automatically created using the :attr:`default_factory`
function which returns an empty :class:`list`.  The :meth:`list.append`
operation then attaches the value to the new list.  When keys are encountered
again, the look-up proceeds normally (returning the list for that key) and the
:meth:`list.append` operation adds another value to the list. This technique is
simpler and faster than an equivalent technique using :meth:`dict.setdefault`:

   >>> d = {}
   >>> for k, v in s:
   ...     d.setdefault(k, []).append(v)
   ...
   >>> d.items()
   [('blue', [2, 4]), ('red', [1]), ('yellow', [1, 3])]

Setting the :attr:`default_factory` to :class:`int` makes the
:class:`defaultdict` useful for counting (like a bag or multiset in other
languages):

   >>> s = 'mississippi'
   >>> d = defaultdict(int)
   >>> for k in s:
   ...     d[k] += 1
   ...
   >>> d.items()
   [('i', 4), ('p', 2), ('s', 4), ('m', 1)]

When a letter is first encountered, it is missing from the mapping, so the
:attr:`default_factory` function calls :func:`int` to supply a default count of
zero.  The increment operation then builds up the count for each letter.

The function :func:`int` which always returns zero is just a special case of
constant functions.  A faster and more flexible way to create constant functions
is to use :func:`itertools.repeat` which can supply any constant value (not just
zero):

   >>> def constant_factory(value):
   ...     return itertools.repeat(value).next
   >>> d = defaultdict(constant_factory('<missing>'))
   >>> d.update(name='John', action='ran')
   >>> '%(name)s %(action)s to %(object)s' % d
   'John ran to <missing>'

Setting the :attr:`default_factory` to :class:`set` makes the
:class:`defaultdict` useful for building a dictionary of sets:

   >>> s = [('red', 1), ('blue', 2), ('red', 3), ('blue', 4), ('red', 1), ('blue', 4)]
   >>> d = defaultdict(set)
   >>> for k, v in s:
   ...     d[k].add(v)
   ...
   >>> d.items()
   [('blue', set([2, 4])), ('red', set([1, 3]))]


:func:`namedtuple` Factory Function for Tuples with Named Fields
----------------------------------------------------------------

Named tuples assign meaning to each position in a tuple and allow for more readable,
self-documenting code.  They can be used wherever regular tuples are used, and
they add the ability to access fields by name instead of position index.

.. function:: namedtuple(typename, field_names, [verbose], [rename])

   Returns a new tuple subclass named *typename*.  The new subclass is used to
   create tuple-like objects that have fields accessible by attribute lookup as
   well as being indexable and iterable.  Instances of the subclass also have a
   helpful docstring (with typename and field_names) and a helpful :meth:`__repr__`
   method which lists the tuple contents in a ``name=value`` format.

   The *field_names* are a single string with each fieldname separated by whitespace
   and/or commas, for example ``'x y'`` or ``'x, y'``.  Alternatively, *field_names*
   can be a sequence of strings such as ``['x', 'y']``.

   Any valid Python identifier may be used for a fieldname except for names
   starting with an underscore.  Valid identifiers consist of letters, digits,
   and underscores but do not start with a digit or underscore and cannot be
   a :mod:`keyword` such as *class*, *for*, *return*, *global*, *pass*, *print*,
   or *raise*.

   If *rename* is true, invalid fieldnames are automatically replaced
   with positional names.  For example, ``['abc', 'def', 'ghi', 'abc']`` is
   converted to ``['abc', '_1', 'ghi', '_3']``, eliminating the keyword
   ``def`` and the duplicate fieldname ``abc``.

   If *verbose* is true, the class definition is printed just before being built.

   Named tuple instances do not have per-instance dictionaries, so they are
   lightweight and require no more memory than regular tuples.

   .. versionadded:: 2.6

   .. versionchanged:: 2.7
      added support for *rename*.

Example:

.. doctest::
   :options: +NORMALIZE_WHITESPACE

   >>> Point = namedtuple('Point', 'x y', verbose=True)
   class Point(tuple):
           'Point(x, y)'
   <BLANKLINE>
           __slots__ = ()
   <BLANKLINE>
           _fields = ('x', 'y')
   <BLANKLINE>
           def __new__(_cls, x, y):
               'Create a new instance of Point(x, y)'
               return _tuple.__new__(_cls, (x, y))
   <BLANKLINE>
           @classmethod
           def _make(cls, iterable, new=tuple.__new__, len=len):
               'Make a new Point object from a sequence or iterable'
               result = new(cls, iterable)
               if len(result) != 2:
                   raise TypeError('Expected 2 arguments, got %d' % len(result))
               return result
   <BLANKLINE>
           def __repr__(self):
               'Return a nicely formatted representation string'
               return 'Point(x=%r, y=%r)' % self
   <BLANKLINE>
           def _asdict(self):
               'Return a new OrderedDict which maps field names to their values'
               return OrderedDict(zip(self._fields, self))
   <BLANKLINE>
           def _replace(_self, **kwds):
               'Return a new Point object replacing specified fields with new values'
               result = _self._make(map(kwds.pop, ('x', 'y'), _self))
               if kwds:
                   raise ValueError('Got unexpected field names: %r' % kwds.keys())
               return result
   <BLANKLINE>
           def __getnewargs__(self):
               'Return self as a plain tuple.   Used by copy and pickle.'
               return tuple(self)
   <BLANKLINE>
           x = _property(_itemgetter(0), doc='Alias for field number 0')
           y = _property(_itemgetter(1), doc='Alias for field number 1')

   >>> p = Point(11, y=22)     # instantiate with positional or keyword arguments
   >>> p[0] + p[1]             # indexable like the plain tuple (11, 22)
   33
   >>> x, y = p                # unpack like a regular tuple
   >>> x, y
   (11, 22)
   >>> p.x + p.y               # fields also accessible by name
   33
   >>> p                       # readable __repr__ with a name=value style
   Point(x=11, y=22)

Named tuples are especially useful for assigning field names to result tuples returned
by the :mod:`csv` or :mod:`sqlite3` modules::

   EmployeeRecord = namedtuple('EmployeeRecord', 'name, age, title, department, paygrade')

   import csv
   for emp in map(EmployeeRecord._make, csv.reader(open("employees.csv", "rb"))):
       print emp.name, emp.title

   import sqlite3
   conn = sqlite3.connect('/companydata')
   cursor = conn.cursor()
   cursor.execute('SELECT name, age, title, department, paygrade FROM employees')
   for emp in map(EmployeeRecord._make, cursor.fetchall()):
       print emp.name, emp.title

In addition to the methods inherited from tuples, named tuples support
three additional methods and one attribute.  To prevent conflicts with
field names, the method and attribute names start with an underscore.

.. method:: somenamedtuple._make(iterable)

   Class method that makes a new instance from an existing sequence or iterable.

   .. doctest::

      >>> t = [11, 22]
      >>> Point._make(t)
      Point(x=11, y=22)

.. method:: somenamedtuple._asdict()

   Return a new :class:`OrderedDict` which maps field names to their corresponding
   values::

      >>> p._asdict()
      OrderedDict([('x', 11), ('y', 22)])

   .. versionchanged:: 2.7
      Returns an :class:`OrderedDict` instead of a regular :class:`dict`.

.. method:: somenamedtuple._replace(kwargs)

   Return a new instance of the named tuple replacing specified fields with new
   values::

      >>> p = Point(x=11, y=22)
      >>> p._replace(x=33)
      Point(x=33, y=22)

      >>> for partnum, record in inventory.items():
      ...     inventory[partnum] = record._replace(price=newprices[partnum], timestamp=time.now())

.. attribute:: somenamedtuple._fields

   Tuple of strings listing the field names.  Useful for introspection
   and for creating new named tuple types from existing named tuples.

   .. doctest::

      >>> p._fields            # view the field names
      ('x', 'y')

      >>> Color = namedtuple('Color', 'red green blue')
      >>> Pixel = namedtuple('Pixel', Point._fields + Color._fields)
      >>> Pixel(11, 22, 128, 255, 0)
      Pixel(x=11, y=22, red=128, green=255, blue=0)

To retrieve a field whose name is stored in a string, use the :func:`getattr`
function:

    >>> getattr(p, 'x')
    11

To convert a dictionary to a named tuple, use the double-star-operator
(as described in :ref:`tut-unpacking-arguments`):

   >>> d = {'x': 11, 'y': 22}
   >>> Point(**d)
   Point(x=11, y=22)

Since a named tuple is a regular Python class, it is easy to add or change
functionality with a subclass.  Here is how to add a calculated field and
a fixed-width print format:

    >>> class Point(namedtuple('Point', 'x y')):
    ...     __slots__ = ()
    ...     @property
    ...     def hypot(self):
    ...         return (self.x ** 2 + self.y ** 2) ** 0.5
    ...     def __str__(self):
    ...         return 'Point: x=%6.3f  y=%6.3f  hypot=%6.3f' % (self.x, self.y, self.hypot)

    >>> for p in Point(3, 4), Point(14, 5/7.):
    ...     print p
    Point: x= 3.000  y= 4.000  hypot= 5.000
    Point: x=14.000  y= 0.714  hypot=14.018

The subclass shown above sets ``__slots__`` to an empty tuple.  This helps
keep memory requirements low by preventing the creation of instance dictionaries.

Subclassing is not useful for adding new, stored fields.  Instead, simply
create a new named tuple type from the :attr:`_fields` attribute:

    >>> Point3D = namedtuple('Point3D', Point._fields + ('z',))

Default values can be implemented by using :meth:`_replace` to
customize a prototype instance:

    >>> Account = namedtuple('Account', 'owner balance transaction_count')
    >>> default_account = Account('<owner name>', 0.0, 0)
    >>> johns_account = default_account._replace(owner='John')

Enumerated constants can be implemented with named tuples, but it is simpler
and more efficient to use a simple class declaration:

    >>> Status = namedtuple('Status', 'open pending closed')._make(range(3))
    >>> Status.open, Status.pending, Status.closed
    (0, 1, 2)
    >>> class Status:
    ...     open, pending, closed = range(3)

.. seealso::

   `Named tuple recipe <http://code.activestate.com/recipes/500261/>`_
   adapted for Python 2.4.


:class:`OrderedDict` objects
----------------------------

Ordered dictionaries are just like regular dictionaries but they remember the
order that items were inserted.  When iterating over an ordered dictionary,
the items are returned in the order their keys were first added.

.. class:: OrderedDict([items])

   Return an instance of a dict subclass, supporting the usual :class:`dict`
   methods.  An *OrderedDict* is a dict that remembers the order that keys
   were first inserted. If a new entry overwrites an existing entry, the
   original insertion position is left unchanged.  Deleting an entry and
   reinserting it will move it to the end.

   .. versionadded:: 2.7

.. method:: OrderedDict.popitem(last=True)

   The :meth:`popitem` method for ordered dictionaries returns and removes
   a (key, value) pair.  The pairs are returned in LIFO order if *last* is
   true or FIFO order if false.

In addition to the usual mapping methods, ordered dictionaries also support
reverse iteration using :func:`reversed`.

Equality tests between :class:`OrderedDict` objects are order-sensitive
and are implemented as ``list(od1.items())==list(od2.items())``.
Equality tests between :class:`OrderedDict` objects and other
:class:`Mapping` objects are order-insensitive like regular dictionaries.
This allows :class:`OrderedDict` objects to be substituted anywhere a
regular dictionary is used.

The :class:`OrderedDict` constructor and :meth:`update` method both accept
keyword arguments, but their order is lost because Python's function call
semantics pass-in keyword arguments using a regular unordered dictionary.

.. seealso::

   `Equivalent OrderedDict recipe <http://code.activestate.com/recipes/576693/>`_
   that runs on Python 2.4 or later.

Since an ordered dictionary remembers its insertion order, it can be used
in conjuction with sorting to make a sorted dictionary::

    >>> # regular unsorted dictionary
    >>> d = {'banana': 3, 'apple':4, 'pear': 1, 'orange': 2}

    >>> # dictionary sorted by key
    >>> OrderedDict(sorted(d.items(), key=lambda t: t[0]))
    OrderedDict([('apple', 4), ('banana', 3), ('orange', 2), ('pear', 1)])

    >>> # dictionary sorted by value
    >>> OrderedDict(sorted(d.items(), key=lambda t: t[1]))
    OrderedDict([('pear', 1), ('orange', 2), ('banana', 3), ('apple', 4)])

    >>> # dictionary sorted by length of the key string
    >>> OrderedDict(sorted(d.items(), key=lambda t: len(t[0])))
    OrderedDict([('pear', 1), ('apple', 4), ('orange', 2), ('banana', 3)])

The new sorted dictionaries maintain their sort order when entries
are deleted.  But when new keys are added, the keys are appended
to the end and the sort is not maintained.