"collections" --- Container datatypes
*************************************

**Source code:** Lib/collections/__init__.py

======================================================================

This module implements specialized container datatypes providing
alternatives to Python's general purpose built-in containers, "dict",
"list", "set", and "tuple".

+-----------------------+----------------------------------------------------------------------+
| "namedtuple()"        | factory function for creating tuple subclasses with named fields     |
+-----------------------+----------------------------------------------------------------------+
| "deque"               | list-like container with fast appends and pops on either end         |
+-----------------------+----------------------------------------------------------------------+
| "ChainMap"            | dict-like class for creating a single view of multiple mappings      |
+-----------------------+----------------------------------------------------------------------+
| "Counter"             | dict subclass for counting *hashable* objects                        |
+-----------------------+----------------------------------------------------------------------+
| "OrderedDict"         | dict subclass that remembers the order entries were added            |
+-----------------------+----------------------------------------------------------------------+
| "defaultdict"         | dict subclass that calls a factory function to supply missing values |
+-----------------------+----------------------------------------------------------------------+
| "UserDict"            | wrapper around dictionary objects for easier dict subclassing        |
+-----------------------+----------------------------------------------------------------------+
| "UserList"            | wrapper around list objects for easier list subclassing              |
+-----------------------+----------------------------------------------------------------------+
| "UserString"          | wrapper around string objects for easier string subclassing          |
+-----------------------+----------------------------------------------------------------------+


"ChainMap" objects
==================

New in version 3.3.

A "ChainMap" class is provided for quickly linking a number of
mappings so they can be treated as a single unit.  It is often much
faster than creating a new dictionary and running multiple "update()"
calls.

The class can be used to simulate nested scopes and is useful in
templating.

class collections.ChainMap(*maps)

   A "ChainMap" groups multiple dicts or other mappings together to
   create a single, updateable view.  If no *maps* are specified, a
   single empty dictionary is provided so that a new chain always has
   at least one mapping.

   The underlying mappings are stored in a list.  That list is public
   and can be accessed or updated using the *maps* attribute.  There
   is no other state.

   Lookups search the underlying mappings successively until a key is
   found.  In contrast, writes, updates, and deletions only operate on
   the first mapping.

   A "ChainMap" incorporates the underlying mappings by reference.
   So, if one of the underlying mappings gets updated, those changes
   will be reflected in "ChainMap".

   All of the usual dictionary methods are supported.  In addition,
   there is a *maps* attribute, a method for creating new subcontexts,
   and a property for accessing all but the first mapping:

   maps

      A user updateable list of mappings.  The list is ordered from
      first-searched to last-searched.  It is the only stored state
      and can be modified to change which mappings are searched.  The
      list should always contain at least one mapping.

   new_child(m=None, **kwargs)

      Returns a new "ChainMap" containing a new map followed by all of
      the maps in the current instance.  If "m" is specified, it
      becomes the new map at the front of the list of mappings; if not
      specified, an empty dict is used, so that a call to
      "d.new_child()" is equivalent to: "ChainMap({}, *d.maps)". If
      any keyword arguments are specified, they update passed map or
      new empty dict. This method is used for creating subcontexts
      that can be updated without altering values in any of the parent
      mappings.

      Changed in version 3.4: The optional "m" parameter was added.

      Changed in version 3.10: Keyword arguments support was added.

   parents

      Property returning a new "ChainMap" containing all of the maps
      in the current instance except the first one.  This is useful
      for skipping the first map in the search.  Use cases are similar
      to those for the "nonlocal" keyword used in *nested scopes*.
      The use cases also parallel those for the built-in "super()"
      function.  A reference to "d.parents" is equivalent to:
      "ChainMap(*d.maps[1:])".

   Note, the iteration order of a "ChainMap()" is determined by
   scanning the mappings last to first:

      >>> baseline = {'music': 'bach', 'art': 'rembrandt'}
      >>> adjustments = {'art': 'van gogh', 'opera': 'carmen'}
      >>> list(ChainMap(adjustments, baseline))
      ['music', 'art', 'opera']

   This gives the same ordering as a series of "dict.update()" calls
   starting with the last mapping:

      >>> combined = baseline.copy()
      >>> combined.update(adjustments)
      >>> list(combined)
      ['music', 'art', 'opera']

   Changed in version 3.9: Added support for "|" and "|=" operators,
   specified in **PEP 584**.

See also:

  * The MultiContext class in the Enthought CodeTools package has
    options to support writing to any mapping in the chain.

  * Django's Context class for templating is a read-only chain of
    mappings.  It also features pushing and popping of contexts
    similar to the "new_child()" method and the "parents" property.

  * The Nested Contexts recipe has options to control whether writes
    and other mutations apply only to the first mapping or to any
    mapping in the chain.

  * A greatly simplified read-only version of Chainmap.


"ChainMap" Examples and Recipes
-------------------------------

This section shows various approaches to working with chained maps.

Example of simulating Python's internal lookup chain:

   import builtins
   pylookup = ChainMap(locals(), globals(), vars(builtins))

Example of letting user specified command-line arguments take
precedence over environment variables which in turn take precedence
over default values:

   import os, argparse

   defaults = {'color': 'red', 'user': 'guest'}

   parser = argparse.ArgumentParser()
   parser.add_argument('-u', '--user')
   parser.add_argument('-c', '--color')
   namespace = parser.parse_args()
   command_line_args = {k: v for k, v in vars(namespace).items() if v is not None}

   combined = ChainMap(command_line_args, os.environ, defaults)
   print(combined['color'])
   print(combined['user'])

Example patterns for using the "ChainMap" class to simulate nested
contexts:

   c = ChainMap()        # Create root context
   d = c.new_child()     # Create nested child context
   e = c.new_child()     # Child of c, independent from d
   e.maps[0]             # Current context dictionary -- like Python's locals()
   e.maps[-1]            # Root context -- like Python's globals()
   e.parents             # Enclosing context chain -- like Python's nonlocals

   d['x'] = 1            # Set value in current context
   d['x']                # Get first key in the chain of contexts
   del d['x']            # Delete from current context
   list(d)               # All nested values
   k in d                # Check all nested values
   len(d)                # Number of nested values
   d.items()             # All nested items
   dict(d)               # Flatten into a regular dictionary

The "ChainMap" class only makes updates (writes and deletions) to the
first mapping in the chain while lookups will search the full chain.
However, if deep writes and deletions are desired, it is easy to make
a subclass that updates keys found deeper in the chain:

   class DeepChainMap(ChainMap):
       'Variant of ChainMap that allows direct updates to inner scopes'

       def __setitem__(self, key, value):
           for mapping in self.maps:
               if key in mapping:
                   mapping[key] = value
                   return
           self.maps[0][key] = value

       def __delitem__(self, key):
           for mapping in self.maps:
               if key in mapping:
                   del mapping[key]
                   return
           raise KeyError(key)

   >>> d = DeepChainMap({'zebra': 'black'}, {'elephant': 'blue'}, {'lion': 'yellow'})
   >>> d['lion'] = 'orange'         # update an existing key two levels down
   >>> d['snake'] = 'red'           # new keys get added to the topmost dict
   >>> del d['elephant']            # remove an existing key one level down
   >>> d                            # display result
   DeepChainMap({'zebra': 'black', 'snake': 'red'}, {}, {'lion': 'orange'})


"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(r'\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 collections.Counter([iterable-or-mapping])

   A "Counter" is a "dict" subclass for counting *hashable* objects.
   It is a 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
   "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 "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

   New in version 3.1.

   Changed in version 3.7: As a "dict" subclass, "Counter" inherited
   the capability to remember insertion order.  Math operations on
   *Counter* objects also preserve order.  Results are ordered
   according to when an element is first encountered in the left
   operand and then by the order encountered in the right operand.

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

   elements()

      Return an iterator over elements repeating each as many times as
      its count.  Elements are returned in the order first
      encountered. If an element's count is less than one,
      "elements()" will ignore it.

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

   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 omitted or "None",
      "most_common()" returns *all* elements in the counter. Elements
      with equal counts are ordered in the order first encountered:

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

   subtract([iterable-or-mapping])

      Elements are subtracted from an *iterable* or from another
      *mapping* (or counter).  Like "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)
      >>> c
      Counter({'a': 3, 'b': 0, 'c': -3, 'd': -6})

      New in version 3.2.

   total()

      Compute the sum of the counts.

      >>> c = Counter(a=10, b=5, c=0)
      >>> c.total()
      15

      New in version 3.10.

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

   fromkeys(iterable)

      This class method is not implemented for "Counter" objects.

   update([iterable-or-mapping])

      Elements are counted from an *iterable* or added-in from another
      *mapping* (or counter).  Like "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.

Counters support rich comparison operators for equality, subset, and
superset relationships: "==", "!=", "<", "<=", ">", ">=". All of those
tests treat missing elements as having zero counts so that
"Counter(a=1) == Counter(a=1, b=0)" returns true.

New in version 3.10: Rich comparison operations were added.

Changed in version 3.10: In equality tests, missing elements are
treated as having zero counts. Formerly, "Counter(a=3)" and
"Counter(a=3, b=0)" were considered distinct.

Common patterns for working with "Counter" objects:

   c.total()                       # 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:-1]       # n least common elements
   +c                              # remove zero and negative counts

Several mathematical operations are provided for combining "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.
Equality and inclusion compare 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})
   >>> c == d                      # equality:  c[x] == d[x]
   False
   >>> c <= d                      # inclusion:  c[x] <= d[x]
   False

Unary addition and subtraction are shortcuts for adding an empty
counter or subtracting from an empty counter.

>>> c = Counter(a=2, b=-4)
>>> +c
Counter({'a': 2})
>>> -c
Counter({'b': 4})

New in version 3.3: Added support for unary plus, unary minus, and in-
place multiset operations.

Note:

  Counters were primarily designed to work with positive integers to
  represent running counts; however, care was taken to not
  unnecessarily preclude use cases needing other types or negative
  values.  To help with those use cases, this section documents the
  minimum range and type restrictions.

  * The "Counter" class itself is a dictionary subclass with no
    restrictions on its keys and values.  The values are intended to
    be numbers representing counts, but you *could* store anything in
    the value field.

  * The "most_common()" method requires only that the values be
    orderable.

  * For in-place operations such as "c[key] += 1", the value type need
    only support addition and subtraction.  So fractions, floats, and
    decimals would work and negative values are supported.  The same
    is also true for "update()" and "subtract()" which allow negative
    and zero values for both inputs and outputs.

  * The multiset methods are designed only for use cases with positive
    values. The inputs may be negative or zero, but only outputs with
    positive values are created.  There are no type restrictions, but
    the value type needs to support addition, subtraction, and
    comparison.

  * The "elements()" method requires integer counts.  It ignores zero
    and negative counts.

See also:

  * Bag class in Smalltalk.

  * Wikipedia entry for Multisets.

  * C++ multisets 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 "itertools.combinations_with_replacement()":

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


"deque" objects
===============

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

   Returns a new deque object initialized left-to-right (using
   "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 "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.

   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.

   Deque objects support the following methods:

   append(x)

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

   appendleft(x)

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

   clear()

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

   copy()

      Create a shallow copy of the deque.

      New in version 3.5.

   count(x)

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

      New in version 3.2.

   extend(iterable)

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

   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.

   index(x[, start[, stop]])

      Return the position of *x* in the deque (at or after index
      *start* and before index *stop*).  Returns the first match or
      raises "ValueError" if not found.

      New in version 3.5.

   insert(i, x)

      Insert *x* into the deque at position *i*.

      If the insertion would cause a bounded deque to grow beyond
      *maxlen*, an "IndexError" is raised.

      New in version 3.5.

   pop()

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

   popleft()

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

   remove(value)

      Remove the first occurrence of *value*.  If not found, raises a
      "ValueError".

   reverse()

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

      New in version 3.2.

   rotate(n=1)

      Rotate the deque *n* steps to the right.  If *n* is negative,
      rotate to the left.

      When the deque is not empty, rotating one step to the right is
      equivalent to "d.appendleft(d.pop())", and rotating one step to
      the left is equivalent to "d.append(d.popleft())".

   Deque objects also provide one read-only attribute:

   maxlen

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

      New in version 3.1.

In addition to the above, deques support iteration, pickling,
"len(d)", "reversed(d)", "copy.copy(d)", "copy.deepcopy(d)",
membership testing with the "in" operator, and subscript references
such as "d[0]" to access the first element.  Indexed access is O(1) at
both ends but slows to O(n) in the middle.  For fast random access,
use lists instead.

Starting in version 3.5, deques support "__add__()", "__mul__()", and
"__imul__()".

Example:

   >>> 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'])


"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'
       with open(filename) as f:
           return deque(f, 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
       # https://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 / n

A round-robin scheduler can be implemented with input iterators stored
in a "deque".  Values are yielded from the active iterator in position
zero.  If that iterator is exhausted, it can be removed with
"popleft()"; otherwise, it can be cycled back to the end with the
"rotate()" method:

   def roundrobin(*iterables):
       "roundrobin('ABC', 'D', 'EF') --> A D E B F C"
       iterators = deque(map(iter, iterables))
       while iterators:
           try:
               while True:
                   yield next(iterators[0])
                   iterators.rotate(-1)
           except StopIteration:
               # Remove an exhausted iterator.
               iterators.popleft()

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

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

To implement "deque" slicing, use a similar approach applying
"rotate()" to bring a target element to the left side of the deque.
Remove old entries with "popleft()", add new entries with "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".


"defaultdict" objects
=====================

class collections.defaultdict(default_factory=None, /[, ...])

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

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

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

   __missing__(key)

      If the "default_factory" attribute is "None", this raises a
      "KeyError" exception with the *key* as argument.

      If "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 "default_factory" raises an exception this exception
      is propagated unchanged.

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

      Note that "__missing__()" is *not* called for any operations
      besides "__getitem__()". This means that "get()" will, like
      normal dictionaries, return "None" as a default rather than
      using "default_factory".

   "defaultdict" objects support the following instance variable:

   default_factory

      This attribute is used by the "__missing__()" method; it is
      initialized from the first argument to the constructor, if
      present, or to "None", if absent.

   Changed in version 3.9: Added merge ("|") and update ("|=")
   operators, specified in **PEP 584**.


"defaultdict" Examples
----------------------

Using "list" as the "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)
...
>>> sorted(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
"default_factory" function which returns an empty "list".  The
"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 "list.append()" operation
adds another value to the list. This technique is simpler and faster
than an equivalent technique using "dict.setdefault()":

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

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

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

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

The function "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 a lambda function which can supply any
constant value (not just zero):

>>> def constant_factory(value):
...     return lambda: value
...
>>> 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 "default_factory" to "set" makes the "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)
...
>>> sorted(d.items())
[('blue', {2, 4}), ('red', {1, 3})]


"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.

collections.namedtuple(typename, field_names, *, rename=False, defaults=None, module=None)

   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 "__repr__()" method which
   lists the tuple contents in a "name=value" format.

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

   *defaults* can be "None" or an *iterable* of default values. Since
   fields with a default value must come after any fields without a
   default, the *defaults* are applied to the rightmost parameters.
   For example, if the fieldnames are "['x', 'y', 'z']" and the
   defaults are "(1, 2)", then "x" will be a required argument, "y"
   will default to "1", and "z" will default to "2".

   If *module* is defined, the "__module__" attribute of the named
   tuple is set to that value.

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

   To support pickling, the named tuple class should be assigned to a
   variable that matches *typename*.

   Changed in version 3.1: Added support for *rename*.

   Changed in version 3.6: The *verbose* and *rename* parameters
   became keyword-only arguments.

   Changed in version 3.6: Added the *module* parameter.

   Changed in version 3.7: Removed the *verbose* parameter and the
   "_source" attribute.

   Changed in version 3.7: Added the *defaults* parameter and the
   "_field_defaults" attribute.

   >>> # Basic example
   >>> Point = namedtuple('Point', ['x', 'y'])
   >>> 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 "csv" or "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 two attributes.  To prevent conflicts
with field names, the method and attribute names start with an
underscore.

classmethod somenamedtuple._make(iterable)

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

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

somenamedtuple._asdict()

   Return a new "dict" which maps field names to their corresponding
   values:

      >>> p = Point(x=11, y=22)
      >>> p._asdict()
      {'x': 11, 'y': 22}

   Changed in version 3.1: Returns an "OrderedDict" instead of a
   regular "dict".

   Changed in version 3.8: Returns a regular "dict" instead of an
   "OrderedDict". As of Python 3.7, regular dicts are guaranteed to be
   ordered.  If the extra features of "OrderedDict" are required, the
   suggested remediation is to cast the result to the desired type:
   "OrderedDict(nt._asdict())".

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())

somenamedtuple._fields

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

      >>> 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)

somenamedtuple._field_defaults

   Dictionary mapping field names to default values.

      >>> Account = namedtuple('Account', ['type', 'balance'], defaults=[0])
      >>> Account._field_defaults
      {'balance': 0}
      >>> Account('premium')
      Account(type='premium', balance=0)

To retrieve a field whose name is stored in a string, use the
"getattr()" function:

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

To convert a dictionary to a named tuple, use the double-star-operator
(as described in Unpacking Argument Lists):

>>> 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 "_fields" attribute:

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

Docstrings can be customized by making direct assignments to the
"__doc__" fields:

>>> Book = namedtuple('Book', ['id', 'title', 'authors'])
>>> Book.__doc__ += ': Hardcover book in active collection'
>>> Book.id.__doc__ = '13-digit ISBN'
>>> Book.title.__doc__ = 'Title of first printing'
>>> Book.authors.__doc__ = 'List of authors sorted by last name'

Changed in version 3.5: Property docstrings became writeable.

See also:

  * See "typing.NamedTuple" for a way to add type hints for named
    tuples.  It also provides an elegant notation using the "class"
    keyword:

       class Component(NamedTuple):
           part_number: int
           weight: float
           description: Optional[str] = None

  * See "types.SimpleNamespace()" for a mutable namespace based on an
    underlying dictionary instead of a tuple.

  * The "dataclasses" module provides a decorator and functions for
    automatically adding generated special methods to user-defined
    classes.


"OrderedDict" objects
=====================

Ordered dictionaries are just like regular dictionaries but have some
extra capabilities relating to ordering operations.  They have become
less important now that the built-in "dict" class gained the ability
to remember insertion order (this new behavior became guaranteed in
Python 3.7).

Some differences from "dict" still remain:

* The regular "dict" was designed to be very good at mapping
  operations.  Tracking insertion order was secondary.

* The "OrderedDict" was designed to be good at reordering operations.
  Space efficiency, iteration speed, and the performance of update
  operations were secondary.

* The "OrderedDict" algorithm can handle frequent reordering
  operations better than "dict".  As shown in the recipes below, this
  makes it suitable for implementing various kinds of LRU caches.

* The equality operation for "OrderedDict" checks for matching order.

  A regular "dict" can emulate the order sensitive equality test with
  "p == q and all(k1 == k2 for k1, k2 in zip(p, q))".

* The "popitem()" method of "OrderedDict" has a different signature.
  It accepts an optional argument to specify which item is popped.

  A regular "dict" can emulate OrderedDict's "od.popitem(last=True)"
  with "d.popitem()" which is guaranteed to pop the rightmost (last)
  item.

  A regular "dict" can emulate OrderedDict's "od.popitem(last=False)"
  with "(k := next(iter(d)), d.pop(k))" which will return and remove
  the leftmost (first) item if it exists.

* "OrderedDict" has a "move_to_end()" method to efficiently reposition
  an element to an endpoint.

  A regular "dict" can emulate OrderedDict's "od.move_to_end(k,
  last=True)" with "d[k] = d.pop(k)" which will move the key and its
  associated value to the rightmost (last) position.

  A regular "dict" does not have an efficient equivalent for
  OrderedDict's "od.move_to_end(k, last=False)" which moves the key
  and its associated value to the leftmost (first) position.

* Until Python 3.8, "dict" lacked a "__reversed__()" method.

class collections.OrderedDict([items])

   Return an instance of a "dict" subclass that has methods
   specialized for rearranging dictionary order.

   New in version 3.1.

   popitem(last=True)

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

   move_to_end(key, last=True)

      Move an existing *key* to either end of an ordered dictionary.
      The item is moved to the right end if *last* is true (the
      default) or to the beginning if *last* is false.  Raises
      "KeyError" if the *key* does not exist:

         >>> d = OrderedDict.fromkeys('abcde')
         >>> d.move_to_end('b')
         >>> ''.join(d)
         'acdeb'
         >>> d.move_to_end('b', last=False)
         >>> ''.join(d)
         'bacde'

      New in version 3.2.

In addition to the usual mapping methods, ordered dictionaries also
support reverse iteration using "reversed()".

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

Changed in version 3.5: The items, keys, and values *views* of
"OrderedDict" now support reverse iteration using "reversed()".

Changed in version 3.6: With the acceptance of **PEP 468**, order is
retained for keyword arguments passed to the "OrderedDict" constructor
and its "update()" method.

Changed in version 3.9: Added merge ("|") and update ("|=") operators,
specified in **PEP 584**.


"OrderedDict" Examples and Recipes
----------------------------------

It is straightforward to create an ordered dictionary variant that
remembers the order the keys were *last* inserted. If a new entry
overwrites an existing entry, the original insertion position is
changed and moved to the end:

   class LastUpdatedOrderedDict(OrderedDict):
       'Store items in the order the keys were last added'

       def __setitem__(self, key, value):
           super().__setitem__(key, value)
           self.move_to_end(key)

An "OrderedDict" would also be useful for implementing variants of
"functools.lru_cache()":

   from collections import OrderedDict
   from time import time

   class TimeBoundedLRU:
       "LRU Cache that invalidates and refreshes old entries."

       def __init__(self, func, maxsize=128, maxage=30):
           self.cache = OrderedDict()      # { args : (timestamp, result)}
           self.func = func
           self.maxsize = maxsize
           self.maxage = maxage

       def __call__(self, *args):
           if args in self.cache:
               self.cache.move_to_end(args)
               timestamp, result = self.cache[args]
               if time() - timestamp <= self.maxage:
                   return result
           result = self.func(*args)
           self.cache[args] = time(), result
           if len(self.cache) > self.maxsize:
               self.cache.popitem(0)
           return result

   class MultiHitLRUCache:
       """ LRU cache that defers caching a result until
           it has been requested multiple times.

           To avoid flushing the LRU cache with one-time requests,
           we don't cache until a request has been made more than once.

       """

       def __init__(self, func, maxsize=128, maxrequests=4096, cache_after=1):
           self.requests = OrderedDict()   # { uncached_key : request_count }
           self.cache = OrderedDict()      # { cached_key : function_result }
           self.func = func
           self.maxrequests = maxrequests  # max number of uncached requests
           self.maxsize = maxsize          # max number of stored return values
           self.cache_after = cache_after

       def __call__(self, *args):
           if args in self.cache:
               self.cache.move_to_end(args)
               return self.cache[args]
           result = self.func(*args)
           self.requests[args] = self.requests.get(args, 0) + 1
           if self.requests[args] <= self.cache_after:
               self.requests.move_to_end(args)
               if len(self.requests) > self.maxrequests:
                   self.requests.popitem(0)
           else:
               self.requests.pop(args, None)
               self.cache[args] = result
               if len(self.cache) > self.maxsize:
                   self.cache.popitem(0)
           return result


"UserDict" objects
==================

The class, "UserDict" acts as a wrapper around dictionary objects. The
need for this class has been partially supplanted by the ability to
subclass directly from "dict"; however, this class can be easier to
work with because the underlying dictionary is accessible as an
attribute.

class collections.UserDict([initialdata])

   Class that simulates a dictionary.  The instance's contents are
   kept in a regular dictionary, which is accessible via the "data"
   attribute of "UserDict" instances.  If *initialdata* is provided,
   "data" is initialized with its contents; note that a reference to
   *initialdata* will not be kept, allowing it to be used for other
   purposes.

   In addition to supporting the methods and operations of mappings,
   "UserDict" instances provide the following attribute:

   data

      A real dictionary used to store the contents of the "UserDict"
      class.


"UserList" objects
==================

This class acts as a wrapper around list objects.  It is a useful base
class for your own list-like classes which can inherit from them and
override existing methods or add new ones.  In this way, one can add
new behaviors to lists.

The need for this class has been partially supplanted by the ability
to subclass directly from "list"; however, this class can be easier to
work with because the underlying list is accessible as an attribute.

class collections.UserList([list])

   Class that simulates a list.  The instance's contents are kept in a
   regular list, which is accessible via the "data" attribute of
   "UserList" instances.  The instance's contents are initially set to
   a copy of *list*, defaulting to the empty list "[]".  *list* can be
   any iterable, for example a real Python list or a "UserList"
   object.

   In addition to supporting the methods and operations of mutable
   sequences, "UserList" instances provide the following attribute:

   data

      A real "list" object used to store the contents of the
      "UserList" class.

**Subclassing requirements:** Subclasses of "UserList" are expected to
offer a constructor which can be called with either no arguments or
one argument.  List operations which return a new sequence attempt to
create an instance of the actual implementation class.  To do so, it
assumes that the constructor can be called with a single parameter,
which is a sequence object used as a data source.

If a derived class does not wish to comply with this requirement, all
of the special methods supported by this class will need to be
overridden; please consult the sources for information about the
methods which need to be provided in that case.


"UserString" objects
====================

The class, "UserString" acts as a wrapper around string objects. The
need for this class has been partially supplanted by the ability to
subclass directly from "str"; however, this class can be easier to
work with because the underlying string is accessible as an attribute.

class collections.UserString(seq)

   Class that simulates a string object.  The instance's content is
   kept in a regular string object, which is accessible via the "data"
   attribute of "UserString" instances.  The instance's contents are
   initially set to a copy of *seq*.  The *seq* argument can be any
   object which can be converted into a string using the built-in
   "str()" function.

   In addition to supporting the methods and operations of strings,
   "UserString" instances provide the following attribute:

   data

      A real "str" object used to store the contents of the
      "UserString" class.

   Changed in version 3.5: New methods "__getnewargs__", "__rmod__",
   "casefold", "format_map", "isprintable", and "maketrans".
