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+__all__ = ['Counter', 'deque', 'defaultdict', 'namedtuple', 'OrderedDict']
+# For bootstrapping reasons, the collection ABCs are defined in _abcoll.py.
+# They should however be considered an integral part of collections.py.
+from _abcoll import *
+import _abcoll
+__all__ += _abcoll.__all__
+
+from _collections import deque, defaultdict
+from operator import itemgetter as _itemgetter, eq as _eq
+from keyword import iskeyword as _iskeyword
+import sys as _sys
+import heapq as _heapq
+from itertools import repeat as _repeat, chain as _chain, starmap as _starmap
+from itertools import imap as _imap
+
+try:
+ from thread import get_ident as _get_ident
+except ImportError:
+ from dummy_thread import get_ident as _get_ident
+
+
+################################################################################
+### OrderedDict
+################################################################################
+
+class OrderedDict(dict):
+ 'Dictionary that remembers insertion order'
+ # An inherited dict maps keys to values.
+ # The inherited dict provides __getitem__, __len__, __contains__, and get.
+ # The remaining methods are order-aware.
+ # Big-O running times for all methods are the same as regular dictionaries.
+
+ # The internal self.__map dict maps keys to links in a doubly linked list.
+ # The circular doubly linked list starts and ends with a sentinel element.
+ # The sentinel element never gets deleted (this simplifies the algorithm).
+ # Each link is stored as a list of length three: [PREV, NEXT, KEY].
+
+ def __init__(self, *args, **kwds):
+ '''Initialize an ordered dictionary. The signature is the same as
+ regular dictionaries, but keyword arguments are not recommended because
+ their insertion order is arbitrary.
+
+ '''
+ if len(args) > 1:
+ raise TypeError('expected at most 1 arguments, got %d' % len(args))
+ try:
+ self.__root
+ except AttributeError:
+ self.__root = root = [] # sentinel node
+ root[:] = [root, root, None]
+ self.__map = {}
+ self.__update(*args, **kwds)
+
+ def __setitem__(self, key, value, dict_setitem=dict.__setitem__):
+ 'od.__setitem__(i, y) <==> od[i]=y'
+ # Setting a new item creates a new link at the end of the linked list,
+ # and the inherited dictionary is updated with the new key/value pair.
+ if key not in self:
+ root = self.__root
+ last = root[0]
+ last[1] = root[0] = self.__map[key] = [last, root, key]
+ return dict_setitem(self, key, value)
+
+ def __delitem__(self, key, dict_delitem=dict.__delitem__):
+ 'od.__delitem__(y) <==> del od[y]'
+ # Deleting an existing item uses self.__map to find the link which gets
+ # removed by updating the links in the predecessor and successor nodes.
+ dict_delitem(self, key)
+ link_prev, link_next, _ = self.__map.pop(key)
+ link_prev[1] = link_next # update link_prev[NEXT]
+ link_next[0] = link_prev # update link_next[PREV]
+
+ def __iter__(self):
+ 'od.__iter__() <==> iter(od)'
+ # Traverse the linked list in order.
+ root = self.__root
+ curr = root[1] # start at the first node
+ while curr is not root:
+ yield curr[2] # yield the curr[KEY]
+ curr = curr[1] # move to next node
+
+ def __reversed__(self):
+ 'od.__reversed__() <==> reversed(od)'
+ # Traverse the linked list in reverse order.
+ root = self.__root
+ curr = root[0] # start at the last node
+ while curr is not root:
+ yield curr[2] # yield the curr[KEY]
+ curr = curr[0] # move to previous node
+
+ def clear(self):
+ 'od.clear() -> None. Remove all items from od.'
+ root = self.__root
+ root[:] = [root, root, None]
+ self.__map.clear()
+ dict.clear(self)
+
+ # -- the following methods do not depend on the internal structure --
+
+ def keys(self):
+ 'od.keys() -> list of keys in od'
+ return list(self)
+
+ def values(self):
+ 'od.values() -> list of values in od'
+ return [self[key] for key in self]
+
+ def items(self):
+ 'od.items() -> list of (key, value) pairs in od'
+ return [(key, self[key]) for key in self]
+
+ def iterkeys(self):
+ 'od.iterkeys() -> an iterator over the keys in od'
+ return iter(self)
+
+ def itervalues(self):
+ 'od.itervalues -> an iterator over the values in od'
+ for k in self:
+ yield self[k]
+
+ def iteritems(self):
+ 'od.iteritems -> an iterator over the (key, value) pairs in od'
+ for k in self:
+ yield (k, self[k])
+
+ update = MutableMapping.update
+
+ __update = update # let subclasses override update without breaking __init__
+
+ __marker = object()
+
+ def pop(self, key, default=__marker):
+ '''od.pop(k[,d]) -> v, remove specified key and return the corresponding
+ value. If key is not found, d is returned if given, otherwise KeyError
+ is raised.
+
+ '''
+ if key in self:
+ result = self[key]
+ del self[key]
+ return result
+ if default is self.__marker:
+ raise KeyError(key)
+ return default
+
+ def setdefault(self, key, default=None):
+ 'od.setdefault(k[,d]) -> od.get(k,d), also set od[k]=d if k not in od'
+ if key in self:
+ return self[key]
+ self[key] = default
+ return default
+
+ def popitem(self, last=True):
+ '''od.popitem() -> (k, v), return and remove a (key, value) pair.
+ Pairs are returned in LIFO order if last is true or FIFO order if false.
+
+ '''
+ if not self:
+ raise KeyError('dictionary is empty')
+ key = next(reversed(self) if last else iter(self))
+ value = self.pop(key)
+ return key, value
+
+ def __repr__(self, _repr_running={}):
+ 'od.__repr__() <==> repr(od)'
+ call_key = id(self), _get_ident()
+ if call_key in _repr_running:
+ return '...'
+ _repr_running[call_key] = 1
+ try:
+ if not self:
+ return '%s()' % (self.__class__.__name__,)
+ return '%s(%r)' % (self.__class__.__name__, self.items())
+ finally:
+ del _repr_running[call_key]
+
+ def __reduce__(self):
+ 'Return state information for pickling'
+ items = [[k, self[k]] for k in self]
+ inst_dict = vars(self).copy()
+ for k in vars(OrderedDict()):
+ inst_dict.pop(k, None)
+ if inst_dict:
+ return (self.__class__, (items,), inst_dict)
+ return self.__class__, (items,)
+
+ def copy(self):
+ 'od.copy() -> a shallow copy of od'
+ return self.__class__(self)
+
+ @classmethod
+ def fromkeys(cls, iterable, value=None):
+ '''OD.fromkeys(S[, v]) -> New ordered dictionary with keys from S.
+ If not specified, the value defaults to None.
+
+ '''
+ self = cls()
+ for key in iterable:
+ self[key] = value
+ return self
+
+ def __eq__(self, other):
+ '''od.__eq__(y) <==> od==y. Comparison to another OD is order-sensitive
+ while comparison to a regular mapping is order-insensitive.
+
+ '''
+ if isinstance(other, OrderedDict):
+ return dict.__eq__(self, other) and all(_imap(_eq, self, other))
+ return dict.__eq__(self, other)
+
+ def __ne__(self, other):
+ 'od.__ne__(y) <==> od!=y'
+ return not self == other
+
+ # -- the following methods support python 3.x style dictionary views --
+
+ def viewkeys(self):
+ "od.viewkeys() -> a set-like object providing a view on od's keys"
+ return KeysView(self)
+
+ def viewvalues(self):
+ "od.viewvalues() -> an object providing a view on od's values"
+ return ValuesView(self)
+
+ def viewitems(self):
+ "od.viewitems() -> a set-like object providing a view on od's items"
+ return ItemsView(self)
+
+
+################################################################################
+### namedtuple
+################################################################################
+
+_class_template = '''\
+class {typename}(tuple):
+ '{typename}({arg_list})'
+
+ __slots__ = ()
+
+ _fields = {field_names!r}
+
+ def __new__(_cls, {arg_list}):
+ 'Create new instance of {typename}({arg_list})'
+ return _tuple.__new__(_cls, ({arg_list}))
+
+ @classmethod
+ def _make(cls, iterable, new=tuple.__new__, len=len):
+ 'Make a new {typename} object from a sequence or iterable'
+ result = new(cls, iterable)
+ if len(result) != {num_fields:d}:
+ raise TypeError('Expected {num_fields:d} arguments, got %d' % len(result))
+ return result
+
+ def __repr__(self):
+ 'Return a nicely formatted representation string'
+ return '{typename}({repr_fmt})' % self
+
+ def _asdict(self):
+ 'Return a new OrderedDict which maps field names to their values'
+ return OrderedDict(zip(self._fields, self))
+
+ def _replace(_self, **kwds):
+ 'Return a new {typename} object replacing specified fields with new values'
+ result = _self._make(map(kwds.pop, {field_names!r}, _self))
+ if kwds:
+ raise ValueError('Got unexpected field names: %r' % kwds.keys())
+ return result
+
+ def __getnewargs__(self):
+ 'Return self as a plain tuple. Used by copy and pickle.'
+ return tuple(self)
+
+{field_defs}
+'''
+
+_repr_template = '{name}=%r'
+
+_field_template = '''\
+ {name} = _property(_itemgetter({index:d}), doc='Alias for field number {index:d}')
+'''
+
+def namedtuple(typename, field_names, verbose=False, rename=False):
+ """Returns a new subclass of tuple with named fields.
+
+ >>> Point = namedtuple('Point', ['x', 'y'])
+ >>> Point.__doc__ # docstring for the new class
+ 'Point(x, y)'
+ >>> p = Point(11, y=22) # instantiate with positional args or keywords
+ >>> p[0] + p[1] # indexable like a plain tuple
+ 33
+ >>> x, y = p # unpack like a regular tuple
+ >>> x, y
+ (11, 22)
+ >>> p.x + p.y # fields also accessable by name
+ 33
+ >>> d = p._asdict() # convert to a dictionary
+ >>> d['x']
+ 11
+ >>> Point(**d) # convert from a dictionary
+ Point(x=11, y=22)
+ >>> p._replace(x=100) # _replace() is like str.replace() but targets named fields
+ Point(x=100, y=22)
+
+ """
+
+ # Validate the field names. At the user's option, either generate an error
+ # message or automatically replace the field name with a valid name.
+ if isinstance(field_names, basestring):
+ field_names = field_names.replace(',', ' ').split()
+ field_names = map(str, field_names)
+ if rename:
+ seen = set()
+ for index, name in enumerate(field_names):
+ if (not all(c.isalnum() or c=='_' for c in name)
+ or _iskeyword(name)
+ or not name
+ or name[0].isdigit()
+ or name.startswith('_')
+ or name in seen):
+ field_names[index] = '_%d' % index
+ seen.add(name)
+ for name in [typename] + field_names:
+ if not all(c.isalnum() or c=='_' for c in name):
+ raise ValueError('Type names and field names can only contain '
+ 'alphanumeric characters and underscores: %r' % name)
+ if _iskeyword(name):
+ raise ValueError('Type names and field names cannot be a '
+ 'keyword: %r' % name)
+ if name[0].isdigit():
+ raise ValueError('Type names and field names cannot start with '
+ 'a number: %r' % name)
+ seen = set()
+ for name in field_names:
+ if name.startswith('_') and not rename:
+ raise ValueError('Field names cannot start with an underscore: '
+ '%r' % name)
+ if name in seen:
+ raise ValueError('Encountered duplicate field name: %r' % name)
+ seen.add(name)
+
+ # Fill-in the class template
+ class_definition = _class_template.format(
+ typename = typename,
+ field_names = tuple(field_names),
+ num_fields = len(field_names),
+ arg_list = repr(tuple(field_names)).replace("'", "")[1:-1],
+ repr_fmt = ', '.join(_repr_template.format(name=name)
+ for name in field_names),
+ field_defs = '\n'.join(_field_template.format(index=index, name=name)
+ for index, name in enumerate(field_names))
+ )
+ if verbose:
+ print class_definition
+
+ # Execute the template string in a temporary namespace and support
+ # tracing utilities by setting a value for frame.f_globals['__name__']
+ namespace = dict(_itemgetter=_itemgetter, __name__='namedtuple_%s' % typename,
+ OrderedDict=OrderedDict, _property=property, _tuple=tuple)
+ try:
+ exec class_definition in namespace
+ except SyntaxError as e:
+ raise SyntaxError(e.message + ':\n' + class_definition)
+ result = namespace[typename]
+
+ # For pickling to work, the __module__ variable needs to be set to the frame
+ # where the named tuple is created. Bypass this step in enviroments where
+ # sys._getframe is not defined (Jython for example) or sys._getframe is not
+ # defined for arguments greater than 0 (IronPython).
+ try:
+ result.__module__ = _sys._getframe(1).f_globals.get('__name__', '__main__')
+ except (AttributeError, ValueError):
+ pass
+
+ return result
+
+
+########################################################################
+### Counter
+########################################################################
+
+class Counter(dict):
+ '''Dict subclass for counting hashable items. Sometimes called a bag
+ or multiset. Elements are stored as dictionary keys and their counts
+ are stored as dictionary values.
+
+ >>> c = Counter('abcdeabcdabcaba') # count elements from a string
+
+ >>> c.most_common(3) # three most common elements
+ [('a', 5), ('b', 4), ('c', 3)]
+ >>> sorted(c) # list all unique elements
+ ['a', 'b', 'c', 'd', 'e']
+ >>> ''.join(sorted(c.elements())) # list elements with repetitions
+ 'aaaaabbbbcccdde'
+ >>> sum(c.values()) # total of all counts
+ 15
+
+ >>> c['a'] # count of letter 'a'
+ 5
+ >>> for elem in 'shazam': # update counts from an iterable
+ ... c[elem] += 1 # by adding 1 to each element's count
+ >>> c['a'] # now there are seven 'a'
+ 7
+ >>> del c['b'] # remove all 'b'
+ >>> c['b'] # now there are zero 'b'
+ 0
+
+ >>> d = Counter('simsalabim') # make another counter
+ >>> c.update(d) # add in the second counter
+ >>> c['a'] # now there are nine 'a'
+ 9
+
+ >>> c.clear() # empty the counter
+ >>> c
+ Counter()
+
+ Note: If a count is set to zero or reduced to zero, it will remain
+ in the counter until the entry is deleted or the counter is cleared:
+
+ >>> c = Counter('aaabbc')
+ >>> c['b'] -= 2 # reduce the count of 'b' by two
+ >>> c.most_common() # 'b' is still in, but its count is zero
+ [('a', 3), ('c', 1), ('b', 0)]
+
+ '''
+ # References:
+ # http://en.wikipedia.org/wiki/Multiset
+ # http://www.gnu.org/software/smalltalk/manual-base/html_node/Bag.html
+ # http://www.demo2s.com/Tutorial/Cpp/0380__set-multiset/Catalog0380__set-multiset.htm
+ # http://code.activestate.com/recipes/259174/
+ # Knuth, TAOCP Vol. II section 4.6.3
+
+ def __init__(self, iterable=None, **kwds):
+ '''Create a new, empty Counter object. And if given, count elements
+ from an input iterable. Or, initialize the count from another mapping
+ of elements to their counts.
+
+ >>> c = Counter() # a new, empty counter
+ >>> c = Counter('gallahad') # a new counter from an iterable
+ >>> c = Counter({'a': 4, 'b': 2}) # a new counter from a mapping
+ >>> c = Counter(a=4, b=2) # a new counter from keyword args
+
+ '''
+ super(Counter, self).__init__()
+ self.update(iterable, **kwds)
+
+ def __missing__(self, key):
+ 'The count of elements not in the Counter is zero.'
+ # Needed so that self[missing_item] does not raise KeyError
+ return 0
+
+ def most_common(self, n=None):
+ '''List the n most common elements and their counts from the most
+ common to the least. If n is None, then list all element counts.
+
+ >>> Counter('abcdeabcdabcaba').most_common(3)
+ [('a', 5), ('b', 4), ('c', 3)]
+
+ '''
+ # Emulate Bag.sortedByCount from Smalltalk
+ if n is None:
+ return sorted(self.iteritems(), key=_itemgetter(1), reverse=True)
+ return _heapq.nlargest(n, self.iteritems(), key=_itemgetter(1))
+
+ def elements(self):
+ '''Iterator over elements repeating each as many times as its count.
+
+ >>> c = Counter('ABCABC')
+ >>> sorted(c.elements())
+ ['A', 'A', 'B', 'B', 'C', 'C']
+
+ # Knuth's example for prime factors of 1836: 2**2 * 3**3 * 17**1
+ >>> prime_factors = Counter({2: 2, 3: 3, 17: 1})
+ >>> product = 1
+ >>> for factor in prime_factors.elements(): # loop over factors
+ ... product *= factor # and multiply them
+ >>> product
+ 1836
+
+ Note, if an element's count has been set to zero or is a negative
+ number, elements() will ignore it.
+
+ '''
+ # Emulate Bag.do from Smalltalk and Multiset.begin from C++.
+ return _chain.from_iterable(_starmap(_repeat, self.iteritems()))
+
+ # Override dict methods where necessary
+
+ @classmethod
+ def fromkeys(cls, iterable, v=None):
+ # There is no equivalent method for counters because setting v=1
+ # means that no element can have a count greater than one.
+ raise NotImplementedError(
+ 'Counter.fromkeys() is undefined. Use Counter(iterable) instead.')
+
+ def update(self, iterable=None, **kwds):
+ '''Like dict.update() but add counts instead of replacing them.
+
+ Source can be an iterable, a dictionary, or another Counter instance.
+
+ >>> c = Counter('which')
+ >>> c.update('witch') # add elements from another iterable
+ >>> d = Counter('watch')
+ >>> c.update(d) # add elements from another counter
+ >>> c['h'] # four 'h' in which, witch, and watch
+ 4
+
+ '''
+ # The regular dict.update() operation makes no sense here because the
+ # replace behavior results in the some of original untouched counts
+ # being mixed-in with all of the other counts for a mismash that
+ # doesn't have a straight-forward interpretation in most counting
+ # contexts. Instead, we implement straight-addition. Both the inputs
+ # and outputs are allowed to contain zero and negative counts.
+
+ if iterable is not None:
+ if isinstance(iterable, Mapping):
+ if self:
+ self_get = self.get
+ for elem, count in iterable.iteritems():
+ self[elem] = self_get(elem, 0) + count
+ else:
+ super(Counter, self).update(iterable) # fast path when counter is empty
+ else:
+ self_get = self.get
+ for elem in iterable:
+ self[elem] = self_get(elem, 0) + 1
+ if kwds:
+ self.update(kwds)
+
+ def subtract(self, iterable=None, **kwds):
+ '''Like dict.update() but subtracts counts instead of replacing them.
+ Counts can be reduced below zero. Both the inputs and outputs are
+ allowed to contain zero and negative counts.
+
+ Source can be an iterable, a dictionary, or another Counter instance.
+
+ >>> c = Counter('which')
+ >>> c.subtract('witch') # subtract elements from another iterable
+ >>> c.subtract(Counter('watch')) # subtract elements from another counter
+ >>> c['h'] # 2 in which, minus 1 in witch, minus 1 in watch
+ 0
+ >>> c['w'] # 1 in which, minus 1 in witch, minus 1 in watch
+ -1
+
+ '''
+ if iterable is not None:
+ self_get = self.get
+ if isinstance(iterable, Mapping):
+ for elem, count in iterable.items():
+ self[elem] = self_get(elem, 0) - count
+ else:
+ for elem in iterable:
+ self[elem] = self_get(elem, 0) - 1
+ if kwds:
+ self.subtract(kwds)
+
+ def copy(self):
+ 'Return a shallow copy.'
+ return self.__class__(self)
+
+ def __reduce__(self):
+ return self.__class__, (dict(self),)
+
+ def __delitem__(self, elem):
+ 'Like dict.__delitem__() but does not raise KeyError for missing values.'
+ if elem in self:
+ super(Counter, self).__delitem__(elem)
+
+ def __repr__(self):
+ if not self:
+ return '%s()' % self.__class__.__name__
+ items = ', '.join(map('%r: %r'.__mod__, self.most_common()))
+ return '%s({%s})' % (self.__class__.__name__, items)
+
+ # Multiset-style mathematical operations discussed in:
+ # Knuth TAOCP Volume II section 4.6.3 exercise 19
+ # and at http://en.wikipedia.org/wiki/Multiset
+ #
+ # Outputs guaranteed to only include positive counts.
+ #
+ # To strip negative and zero counts, add-in an empty counter:
+ # c += Counter()
+
+ def __add__(self, other):
+ '''Add counts from two counters.
+
+ >>> Counter('abbb') + Counter('bcc')
+ Counter({'b': 4, 'c': 2, 'a': 1})
+
+ '''
+ if not isinstance(other, Counter):
+ return NotImplemented
+ result = Counter()
+ for elem, count in self.items():
+ newcount = count + other[elem]
+ if newcount > 0:
+ result[elem] = newcount
+ for elem, count in other.items():
+ if elem not in self and count > 0:
+ result[elem] = count
+ return result
+
+ def __sub__(self, other):
+ ''' Subtract count, but keep only results with positive counts.
+
+ >>> Counter('abbbc') - Counter('bccd')
+ Counter({'b': 2, 'a': 1})
+
+ '''
+ if not isinstance(other, Counter):
+ return NotImplemented
+ result = Counter()
+ for elem, count in self.items():
+ newcount = count - other[elem]
+ if newcount > 0:
+ result[elem] = newcount
+ for elem, count in other.items():
+ if elem not in self and count < 0:
+ result[elem] = 0 - count
+ return result
+
+ def __or__(self, other):
+ '''Union is the maximum of value in either of the input counters.
+
+ >>> Counter('abbb') | Counter('bcc')
+ Counter({'b': 3, 'c': 2, 'a': 1})
+
+ '''
+ if not isinstance(other, Counter):
+ return NotImplemented
+ result = Counter()
+ for elem, count in self.items():
+ other_count = other[elem]
+ newcount = other_count if count < other_count else count
+ if newcount > 0:
+ result[elem] = newcount
+ for elem, count in other.items():
+ if elem not in self and count > 0:
+ result[elem] = count
+ return result
+
+ def __and__(self, other):
+ ''' Intersection is the minimum of corresponding counts.
+
+ >>> Counter('abbb') & Counter('bcc')
+ Counter({'b': 1})
+
+ '''
+ if not isinstance(other, Counter):
+ return NotImplemented
+ result = Counter()
+ for elem, count in self.items():
+ other_count = other[elem]
+ newcount = count if count < other_count else other_count
+ if newcount > 0:
+ result[elem] = newcount
+ return result
+
+
+if __name__ == '__main__':
+ # verify that instances can be pickled
+ from cPickle import loads, dumps
+ Point = namedtuple('Point', 'x, y', True)
+ p = Point(x=10, y=20)
+ assert p == loads(dumps(p))
+
+ # test and demonstrate ability to override methods
+ 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
+
+ class Point(namedtuple('Point', 'x y')):
+ 'Point class with optimized _make() and _replace() without error-checking'
+ __slots__ = ()
+ _make = classmethod(tuple.__new__)
+ def _replace(self, _map=map, **kwds):
+ return self._make(_map(kwds.get, ('x', 'y'), self))
+
+ print Point(11, 22)._replace(x=100)
+
+ Point3D = namedtuple('Point3D', Point._fields + ('z',))
+ print Point3D.__doc__
+
+ import doctest
+ TestResults = namedtuple('TestResults', 'failed attempted')
+ print TestResults(*doctest.testmod())