| '''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 |
| |
| ''' |
| |
| __all__ = [ |
| 'ChainMap', |
| 'Counter', |
| 'OrderedDict', |
| 'UserDict', |
| 'UserList', |
| 'UserString', |
| 'defaultdict', |
| 'deque', |
| 'namedtuple', |
| ] |
| |
| import _collections_abc |
| import sys as _sys |
| |
| from itertools import chain as _chain |
| from itertools import repeat as _repeat |
| from itertools import starmap as _starmap |
| from keyword import iskeyword as _iskeyword |
| from operator import eq as _eq |
| from operator import itemgetter as _itemgetter |
| from reprlib import recursive_repr as _recursive_repr |
| from _weakref import proxy as _proxy |
| |
| try: |
| from _collections import deque |
| except ImportError: |
| pass |
| else: |
| _collections_abc.MutableSequence.register(deque) |
| |
| try: |
| from _collections import defaultdict |
| except ImportError: |
| pass |
| |
| |
| ################################################################################ |
| ### OrderedDict |
| ################################################################################ |
| |
| class _OrderedDictKeysView(_collections_abc.KeysView): |
| |
| def __reversed__(self): |
| yield from reversed(self._mapping) |
| |
| class _OrderedDictItemsView(_collections_abc.ItemsView): |
| |
| def __reversed__(self): |
| for key in reversed(self._mapping): |
| yield (key, self._mapping[key]) |
| |
| class _OrderedDictValuesView(_collections_abc.ValuesView): |
| |
| def __reversed__(self): |
| for key in reversed(self._mapping): |
| yield self._mapping[key] |
| |
| class _Link(object): |
| __slots__ = 'prev', 'next', 'key', '__weakref__' |
| |
| 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). |
| # The sentinel is in self.__hardroot with a weakref proxy in self.__root. |
| # The prev links are weakref proxies (to prevent circular references). |
| # Individual links are kept alive by the hard reference in self.__map. |
| # Those hard references disappear when a key is deleted from an OrderedDict. |
| |
| def __init__(self, other=(), /, **kwds): |
| '''Initialize an ordered dictionary. The signature is the same as |
| regular dictionaries. Keyword argument order is preserved. |
| ''' |
| try: |
| self.__root |
| except AttributeError: |
| self.__hardroot = _Link() |
| self.__root = root = _proxy(self.__hardroot) |
| root.prev = root.next = root |
| self.__map = {} |
| self.__update(other, **kwds) |
| |
| def __setitem__(self, key, value, |
| dict_setitem=dict.__setitem__, proxy=_proxy, Link=_Link): |
| '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: |
| self.__map[key] = link = Link() |
| root = self.__root |
| last = root.prev |
| link.prev, link.next, link.key = last, root, key |
| last.next = link |
| root.prev = proxy(link) |
| 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 = self.__map.pop(key) |
| link_prev = link.prev |
| link_next = link.next |
| link_prev.next = link_next |
| link_next.prev = link_prev |
| link.prev = None |
| link.next = None |
| |
| def __iter__(self): |
| 'od.__iter__() <==> iter(od)' |
| # Traverse the linked list in order. |
| root = self.__root |
| curr = root.next |
| while curr is not root: |
| yield curr.key |
| curr = curr.next |
| |
| def __reversed__(self): |
| 'od.__reversed__() <==> reversed(od)' |
| # Traverse the linked list in reverse order. |
| root = self.__root |
| curr = root.prev |
| while curr is not root: |
| yield curr.key |
| curr = curr.prev |
| |
| def clear(self): |
| 'od.clear() -> None. Remove all items from od.' |
| root = self.__root |
| root.prev = root.next = root |
| self.__map.clear() |
| dict.clear(self) |
| |
| def popitem(self, last=True): |
| '''Remove and return a (key, value) pair from the dictionary. |
| |
| Pairs are returned in LIFO order if last is true or FIFO order if false. |
| ''' |
| if not self: |
| raise KeyError('dictionary is empty') |
| root = self.__root |
| if last: |
| link = root.prev |
| link_prev = link.prev |
| link_prev.next = root |
| root.prev = link_prev |
| else: |
| link = root.next |
| link_next = link.next |
| root.next = link_next |
| link_next.prev = root |
| key = link.key |
| del self.__map[key] |
| value = dict.pop(self, key) |
| return key, value |
| |
| def move_to_end(self, key, last=True): |
| '''Move an existing element to the end (or beginning if last is false). |
| |
| Raise KeyError if the element does not exist. |
| ''' |
| link = self.__map[key] |
| link_prev = link.prev |
| link_next = link.next |
| soft_link = link_next.prev |
| link_prev.next = link_next |
| link_next.prev = link_prev |
| root = self.__root |
| if last: |
| last = root.prev |
| link.prev = last |
| link.next = root |
| root.prev = soft_link |
| last.next = link |
| else: |
| first = root.next |
| link.prev = root |
| link.next = first |
| first.prev = soft_link |
| root.next = link |
| |
| def __sizeof__(self): |
| sizeof = _sys.getsizeof |
| n = len(self) + 1 # number of links including root |
| size = sizeof(self.__dict__) # instance dictionary |
| size += sizeof(self.__map) * 2 # internal dict and inherited dict |
| size += sizeof(self.__hardroot) * n # link objects |
| size += sizeof(self.__root) * n # proxy objects |
| return size |
| |
| update = __update = _collections_abc.MutableMapping.update |
| |
| def keys(self): |
| "D.keys() -> a set-like object providing a view on D's keys" |
| return _OrderedDictKeysView(self) |
| |
| def items(self): |
| "D.items() -> a set-like object providing a view on D's items" |
| return _OrderedDictItemsView(self) |
| |
| def values(self): |
| "D.values() -> an object providing a view on D's values" |
| return _OrderedDictValuesView(self) |
| |
| __ne__ = _collections_abc.MutableMapping.__ne__ |
| |
| __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. |
| |
| ''' |
| marker = self.__marker |
| result = dict.pop(self, key, marker) |
| if result is not marker: |
| # The same as in __delitem__(). |
| link = self.__map.pop(key) |
| link_prev = link.prev |
| link_next = link.next |
| link_prev.next = link_next |
| link_next.prev = link_prev |
| link.prev = None |
| link.next = None |
| return result |
| if default is marker: |
| raise KeyError(key) |
| return default |
| |
| def setdefault(self, key, default=None): |
| '''Insert key with a value of default if key is not in the dictionary. |
| |
| Return the value for key if key is in the dictionary, else default. |
| ''' |
| if key in self: |
| return self[key] |
| self[key] = default |
| return default |
| |
| @_recursive_repr() |
| def __repr__(self): |
| 'od.__repr__() <==> repr(od)' |
| if not self: |
| return '%s()' % (self.__class__.__name__,) |
| return '%s(%r)' % (self.__class__.__name__, list(self.items())) |
| |
| def __reduce__(self): |
| 'Return state information for pickling' |
| state = self.__getstate__() |
| if state: |
| if isinstance(state, tuple): |
| state, slots = state |
| else: |
| slots = {} |
| state = state.copy() |
| slots = slots.copy() |
| for k in vars(OrderedDict()): |
| state.pop(k, None) |
| slots.pop(k, None) |
| if slots: |
| state = state, slots |
| else: |
| state = state or None |
| return self.__class__, (), state, None, iter(self.items()) |
| |
| def copy(self): |
| 'od.copy() -> a shallow copy of od' |
| return self.__class__(self) |
| |
| @classmethod |
| def fromkeys(cls, iterable, value=None): |
| '''Create a new ordered dictionary with keys from iterable and values set to value. |
| ''' |
| 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(map(_eq, self, other)) |
| return dict.__eq__(self, other) |
| |
| def __ior__(self, other): |
| self.update(other) |
| return self |
| |
| def __or__(self, other): |
| if not isinstance(other, dict): |
| return NotImplemented |
| new = self.__class__(self) |
| new.update(other) |
| return new |
| |
| def __ror__(self, other): |
| if not isinstance(other, dict): |
| return NotImplemented |
| new = self.__class__(other) |
| new.update(self) |
| return new |
| |
| |
| try: |
| from _collections import OrderedDict |
| except ImportError: |
| # Leave the pure Python version in place. |
| pass |
| |
| |
| ################################################################################ |
| ### namedtuple |
| ################################################################################ |
| |
| try: |
| from _collections import _tuplegetter |
| except ImportError: |
| _tuplegetter = lambda index, doc: property(_itemgetter(index), doc=doc) |
| |
| def namedtuple(typename, field_names, *, rename=False, defaults=None, module=None): |
| """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 accessible 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, str): |
| field_names = field_names.replace(',', ' ').split() |
| field_names = list(map(str, field_names)) |
| typename = _sys.intern(str(typename)) |
| |
| if rename: |
| seen = set() |
| for index, name in enumerate(field_names): |
| if (not name.isidentifier() |
| or _iskeyword(name) |
| or name.startswith('_') |
| or name in seen): |
| field_names[index] = f'_{index}' |
| seen.add(name) |
| |
| for name in [typename] + field_names: |
| if type(name) is not str: |
| raise TypeError('Type names and field names must be strings') |
| if not name.isidentifier(): |
| raise ValueError('Type names and field names must be valid ' |
| f'identifiers: {name!r}') |
| if _iskeyword(name): |
| raise ValueError('Type names and field names cannot be a ' |
| f'keyword: {name!r}') |
| |
| seen = set() |
| for name in field_names: |
| if name.startswith('_') and not rename: |
| raise ValueError('Field names cannot start with an underscore: ' |
| f'{name!r}') |
| if name in seen: |
| raise ValueError(f'Encountered duplicate field name: {name!r}') |
| seen.add(name) |
| |
| field_defaults = {} |
| if defaults is not None: |
| defaults = tuple(defaults) |
| if len(defaults) > len(field_names): |
| raise TypeError('Got more default values than field names') |
| field_defaults = dict(reversed(list(zip(reversed(field_names), |
| reversed(defaults))))) |
| |
| # Variables used in the methods and docstrings |
| field_names = tuple(map(_sys.intern, field_names)) |
| num_fields = len(field_names) |
| arg_list = ', '.join(field_names) |
| if num_fields == 1: |
| arg_list += ',' |
| repr_fmt = '(' + ', '.join(f'{name}=%r' for name in field_names) + ')' |
| tuple_new = tuple.__new__ |
| _dict, _tuple, _len, _map, _zip = dict, tuple, len, map, zip |
| |
| # Create all the named tuple methods to be added to the class namespace |
| |
| namespace = { |
| '_tuple_new': tuple_new, |
| '__builtins__': {}, |
| '__name__': f'namedtuple_{typename}', |
| } |
| code = f'lambda _cls, {arg_list}: _tuple_new(_cls, ({arg_list}))' |
| __new__ = eval(code, namespace) |
| __new__.__name__ = '__new__' |
| __new__.__doc__ = f'Create new instance of {typename}({arg_list})' |
| if defaults is not None: |
| __new__.__defaults__ = defaults |
| |
| @classmethod |
| def _make(cls, iterable): |
| result = tuple_new(cls, iterable) |
| if _len(result) != num_fields: |
| raise TypeError(f'Expected {num_fields} arguments, got {len(result)}') |
| return result |
| |
| _make.__func__.__doc__ = (f'Make a new {typename} object from a sequence ' |
| 'or iterable') |
| |
| def _replace(self, /, **kwds): |
| result = self._make(_map(kwds.pop, field_names, self)) |
| if kwds: |
| raise ValueError(f'Got unexpected field names: {list(kwds)!r}') |
| return result |
| |
| _replace.__doc__ = (f'Return a new {typename} object replacing specified ' |
| 'fields with new values') |
| |
| def __repr__(self): |
| 'Return a nicely formatted representation string' |
| return self.__class__.__name__ + repr_fmt % self |
| |
| def _asdict(self): |
| 'Return a new dict which maps field names to their values.' |
| return _dict(_zip(self._fields, self)) |
| |
| def __getnewargs__(self): |
| 'Return self as a plain tuple. Used by copy and pickle.' |
| return _tuple(self) |
| |
| # Modify function metadata to help with introspection and debugging |
| for method in ( |
| __new__, |
| _make.__func__, |
| _replace, |
| __repr__, |
| _asdict, |
| __getnewargs__, |
| ): |
| method.__qualname__ = f'{typename}.{method.__name__}' |
| |
| # Build-up the class namespace dictionary |
| # and use type() to build the result class |
| class_namespace = { |
| '__doc__': f'{typename}({arg_list})', |
| '__slots__': (), |
| '_fields': field_names, |
| '_field_defaults': field_defaults, |
| '__new__': __new__, |
| '_make': _make, |
| '_replace': _replace, |
| '__repr__': __repr__, |
| '_asdict': _asdict, |
| '__getnewargs__': __getnewargs__, |
| '__match_args__': field_names, |
| } |
| for index, name in enumerate(field_names): |
| doc = _sys.intern(f'Alias for field number {index}') |
| class_namespace[name] = _tuplegetter(index, doc) |
| |
| result = type(typename, (tuple,), class_namespace) |
| |
| # For pickling to work, the __module__ variable needs to be set to the frame |
| # where the named tuple is created. Bypass this step in environments where |
| # sys._getframe is not defined (Jython for example) or sys._getframe is not |
| # defined for arguments greater than 0 (IronPython), or where the user has |
| # specified a particular module. |
| if module is None: |
| try: |
| module = _sys._getframe(1).f_globals.get('__name__', '__main__') |
| except (AttributeError, ValueError): |
| pass |
| if module is not None: |
| result.__module__ = module |
| |
| return result |
| |
| |
| ######################################################################## |
| ### Counter |
| ######################################################################## |
| |
| def _count_elements(mapping, iterable): |
| 'Tally elements from the iterable.' |
| mapping_get = mapping.get |
| for elem in iterable: |
| mapping[elem] = mapping_get(elem, 0) + 1 |
| |
| try: # Load C helper function if available |
| from _collections import _count_elements |
| except ImportError: |
| pass |
| |
| 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().__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 total(self): |
| 'Sum of the counts' |
| return sum(self.values()) |
| |
| 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('abracadabra').most_common(3) |
| [('a', 5), ('b', 2), ('r', 2)] |
| |
| ''' |
| # Emulate Bag.sortedByCount from Smalltalk |
| if n is None: |
| return sorted(self.items(), key=_itemgetter(1), reverse=True) |
| |
| # Lazy import to speedup Python startup time |
| import heapq |
| return heapq.nlargest(n, self.items(), 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 |
| >>> import math |
| >>> prime_factors = Counter({2: 2, 3: 3, 17: 1}) |
| >>> math.prod(prime_factors.elements()) |
| 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.items())) |
| |
| # Override dict methods where necessary |
| |
| @classmethod |
| def fromkeys(cls, iterable, v=None): |
| # There is no equivalent method for counters because the semantics |
| # would be ambiguous in cases such as Counter.fromkeys('aaabbc', v=2). |
| # Initializing counters to zero values isn't necessary because zero |
| # is already the default value for counter lookups. Initializing |
| # to one is easily accomplished with Counter(set(iterable)). For |
| # more exotic cases, create a dictionary first using a dictionary |
| # comprehension or dict.fromkeys(). |
| 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, _collections_abc.Mapping): |
| if self: |
| self_get = self.get |
| for elem, count in iterable.items(): |
| self[elem] = count + self_get(elem, 0) |
| else: |
| # fast path when counter is empty |
| super().update(iterable) |
| else: |
| _count_elements(self, iterable) |
| 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, _collections_abc.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().__delitem__(elem) |
| |
| def __repr__(self): |
| if not self: |
| return f'{self.__class__.__name__}()' |
| try: |
| # dict() preserves the ordering returned by most_common() |
| d = dict(self.most_common()) |
| except TypeError: |
| # handle case where values are not orderable |
| d = dict(self) |
| return f'{self.__class__.__name__}({d!r})' |
| |
| # 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() |
| # |
| # 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. |
| # |
| # When the multiplicities are all zero or one, multiset operations |
| # are guaranteed to be equivalent to the corresponding operations |
| # for regular sets. |
| # Given counter multisets such as: |
| # cp = Counter(a=1, b=0, c=1) |
| # cq = Counter(c=1, d=0, e=1) |
| # The corresponding regular sets would be: |
| # sp = {'a', 'c'} |
| # sq = {'c', 'e'} |
| # All of the following relations would hold: |
| # set(cp + cq) == sp | sq |
| # set(cp - cq) == sp - sq |
| # set(cp | cq) == sp | sq |
| # set(cp & cq) == sp & sq |
| # (cp == cq) == (sp == sq) |
| # (cp != cq) == (sp != sq) |
| # (cp <= cq) == (sp <= sq) |
| # (cp < cq) == (sp < sq) |
| # (cp >= cq) == (sp >= sq) |
| # (cp > cq) == (sp > sq) |
| |
| def __eq__(self, other): |
| 'True if all counts agree. Missing counts are treated as zero.' |
| if not isinstance(other, Counter): |
| return NotImplemented |
| return all(self[e] == other[e] for c in (self, other) for e in c) |
| |
| def __ne__(self, other): |
| 'True if any counts disagree. Missing counts are treated as zero.' |
| if not isinstance(other, Counter): |
| return NotImplemented |
| return not self == other |
| |
| def __le__(self, other): |
| 'True if all counts in self are a subset of those in other.' |
| if not isinstance(other, Counter): |
| return NotImplemented |
| return all(self[e] <= other[e] for c in (self, other) for e in c) |
| |
| def __lt__(self, other): |
| 'True if all counts in self are a proper subset of those in other.' |
| if not isinstance(other, Counter): |
| return NotImplemented |
| return self <= other and self != other |
| |
| def __ge__(self, other): |
| 'True if all counts in self are a superset of those in other.' |
| if not isinstance(other, Counter): |
| return NotImplemented |
| return all(self[e] >= other[e] for c in (self, other) for e in c) |
| |
| def __gt__(self, other): |
| 'True if all counts in self are a proper superset of those in other.' |
| if not isinstance(other, Counter): |
| return NotImplemented |
| return self >= other and self != other |
| |
| 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 |
| |
| def __pos__(self): |
| 'Adds an empty counter, effectively stripping negative and zero counts' |
| result = Counter() |
| for elem, count in self.items(): |
| if count > 0: |
| result[elem] = count |
| return result |
| |
| def __neg__(self): |
| '''Subtracts from an empty counter. Strips positive and zero counts, |
| and flips the sign on negative counts. |
| |
| ''' |
| result = Counter() |
| for elem, count in self.items(): |
| if count < 0: |
| result[elem] = 0 - count |
| return result |
| |
| def _keep_positive(self): |
| '''Internal method to strip elements with a negative or zero count''' |
| nonpositive = [elem for elem, count in self.items() if not count > 0] |
| for elem in nonpositive: |
| del self[elem] |
| return self |
| |
| def __iadd__(self, other): |
| '''Inplace add from another counter, keeping only positive counts. |
| |
| >>> c = Counter('abbb') |
| >>> c += Counter('bcc') |
| >>> c |
| Counter({'b': 4, 'c': 2, 'a': 1}) |
| |
| ''' |
| for elem, count in other.items(): |
| self[elem] += count |
| return self._keep_positive() |
| |
| def __isub__(self, other): |
| '''Inplace subtract counter, but keep only results with positive counts. |
| |
| >>> c = Counter('abbbc') |
| >>> c -= Counter('bccd') |
| >>> c |
| Counter({'b': 2, 'a': 1}) |
| |
| ''' |
| for elem, count in other.items(): |
| self[elem] -= count |
| return self._keep_positive() |
| |
| def __ior__(self, other): |
| '''Inplace union is the maximum of value from either counter. |
| |
| >>> c = Counter('abbb') |
| >>> c |= Counter('bcc') |
| >>> c |
| Counter({'b': 3, 'c': 2, 'a': 1}) |
| |
| ''' |
| for elem, other_count in other.items(): |
| count = self[elem] |
| if other_count > count: |
| self[elem] = other_count |
| return self._keep_positive() |
| |
| def __iand__(self, other): |
| '''Inplace intersection is the minimum of corresponding counts. |
| |
| >>> c = Counter('abbb') |
| >>> c &= Counter('bcc') |
| >>> c |
| Counter({'b': 1}) |
| |
| ''' |
| for elem, count in self.items(): |
| other_count = other[elem] |
| if other_count < count: |
| self[elem] = other_count |
| return self._keep_positive() |
| |
| |
| ######################################################################## |
| ### ChainMap |
| ######################################################################## |
| |
| class ChainMap(_collections_abc.MutableMapping): |
| ''' A ChainMap groups multiple dicts (or other mappings) together |
| to create a single, updateable view. |
| |
| 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. |
| |
| ''' |
| |
| def __init__(self, *maps): |
| '''Initialize a ChainMap by setting *maps* to the given mappings. |
| If no mappings are provided, a single empty dictionary is used. |
| |
| ''' |
| self.maps = list(maps) or [{}] # always at least one map |
| |
| def __missing__(self, key): |
| raise KeyError(key) |
| |
| def __getitem__(self, key): |
| for mapping in self.maps: |
| try: |
| return mapping[key] # can't use 'key in mapping' with defaultdict |
| except KeyError: |
| pass |
| return self.__missing__(key) # support subclasses that define __missing__ |
| |
| def get(self, key, default=None): |
| return self[key] if key in self else default |
| |
| def __len__(self): |
| return len(set().union(*self.maps)) # reuses stored hash values if possible |
| |
| def __iter__(self): |
| d = {} |
| for mapping in reversed(self.maps): |
| d.update(dict.fromkeys(mapping)) # reuses stored hash values if possible |
| return iter(d) |
| |
| def __contains__(self, key): |
| return any(key in m for m in self.maps) |
| |
| def __bool__(self): |
| return any(self.maps) |
| |
| @_recursive_repr() |
| def __repr__(self): |
| return f'{self.__class__.__name__}({", ".join(map(repr, self.maps))})' |
| |
| @classmethod |
| def fromkeys(cls, iterable, *args): |
| 'Create a ChainMap with a single dict created from the iterable.' |
| return cls(dict.fromkeys(iterable, *args)) |
| |
| def copy(self): |
| 'New ChainMap or subclass with a new copy of maps[0] and refs to maps[1:]' |
| return self.__class__(self.maps[0].copy(), *self.maps[1:]) |
| |
| __copy__ = copy |
| |
| def new_child(self, m=None, **kwargs): # like Django's Context.push() |
| '''New ChainMap with a new map followed by all previous maps. |
| If no map is provided, an empty dict is used. |
| Keyword arguments update the map or new empty dict. |
| ''' |
| if m is None: |
| m = kwargs |
| elif kwargs: |
| m.update(kwargs) |
| return self.__class__(m, *self.maps) |
| |
| @property |
| def parents(self): # like Django's Context.pop() |
| 'New ChainMap from maps[1:].' |
| return self.__class__(*self.maps[1:]) |
| |
| def __setitem__(self, key, value): |
| self.maps[0][key] = value |
| |
| def __delitem__(self, key): |
| try: |
| del self.maps[0][key] |
| except KeyError: |
| raise KeyError(f'Key not found in the first mapping: {key!r}') |
| |
| def popitem(self): |
| 'Remove and return an item pair from maps[0]. Raise KeyError is maps[0] is empty.' |
| try: |
| return self.maps[0].popitem() |
| except KeyError: |
| raise KeyError('No keys found in the first mapping.') |
| |
| def pop(self, key, *args): |
| 'Remove *key* from maps[0] and return its value. Raise KeyError if *key* not in maps[0].' |
| try: |
| return self.maps[0].pop(key, *args) |
| except KeyError: |
| raise KeyError(f'Key not found in the first mapping: {key!r}') |
| |
| def clear(self): |
| 'Clear maps[0], leaving maps[1:] intact.' |
| self.maps[0].clear() |
| |
| def __ior__(self, other): |
| self.maps[0].update(other) |
| return self |
| |
| def __or__(self, other): |
| if not isinstance(other, _collections_abc.Mapping): |
| return NotImplemented |
| m = self.copy() |
| m.maps[0].update(other) |
| return m |
| |
| def __ror__(self, other): |
| if not isinstance(other, _collections_abc.Mapping): |
| return NotImplemented |
| m = dict(other) |
| for child in reversed(self.maps): |
| m.update(child) |
| return self.__class__(m) |
| |
| |
| ################################################################################ |
| ### UserDict |
| ################################################################################ |
| |
| class UserDict(_collections_abc.MutableMapping): |
| |
| # Start by filling-out the abstract methods |
| def __init__(self, dict=None, /, **kwargs): |
| self.data = {} |
| if dict is not None: |
| self.update(dict) |
| if kwargs: |
| self.update(kwargs) |
| |
| def __len__(self): |
| return len(self.data) |
| |
| def __getitem__(self, key): |
| if key in self.data: |
| return self.data[key] |
| if hasattr(self.__class__, "__missing__"): |
| return self.__class__.__missing__(self, key) |
| raise KeyError(key) |
| |
| def __setitem__(self, key, item): |
| self.data[key] = item |
| |
| def __delitem__(self, key): |
| del self.data[key] |
| |
| def __iter__(self): |
| return iter(self.data) |
| |
| # Modify __contains__ to work correctly when __missing__ is present |
| def __contains__(self, key): |
| return key in self.data |
| |
| # Now, add the methods in dicts but not in MutableMapping |
| def __repr__(self): |
| return repr(self.data) |
| |
| def __or__(self, other): |
| if isinstance(other, UserDict): |
| return self.__class__(self.data | other.data) |
| if isinstance(other, dict): |
| return self.__class__(self.data | other) |
| return NotImplemented |
| |
| def __ror__(self, other): |
| if isinstance(other, UserDict): |
| return self.__class__(other.data | self.data) |
| if isinstance(other, dict): |
| return self.__class__(other | self.data) |
| return NotImplemented |
| |
| def __ior__(self, other): |
| if isinstance(other, UserDict): |
| self.data |= other.data |
| else: |
| self.data |= other |
| return self |
| |
| def __copy__(self): |
| inst = self.__class__.__new__(self.__class__) |
| inst.__dict__.update(self.__dict__) |
| # Create a copy and avoid triggering descriptors |
| inst.__dict__["data"] = self.__dict__["data"].copy() |
| return inst |
| |
| def copy(self): |
| if self.__class__ is UserDict: |
| return UserDict(self.data.copy()) |
| import copy |
| data = self.data |
| try: |
| self.data = {} |
| c = copy.copy(self) |
| finally: |
| self.data = data |
| c.update(self) |
| return c |
| |
| @classmethod |
| def fromkeys(cls, iterable, value=None): |
| d = cls() |
| for key in iterable: |
| d[key] = value |
| return d |
| |
| |
| ################################################################################ |
| ### UserList |
| ################################################################################ |
| |
| class UserList(_collections_abc.MutableSequence): |
| """A more or less complete user-defined wrapper around list objects.""" |
| |
| def __init__(self, initlist=None): |
| self.data = [] |
| if initlist is not None: |
| # XXX should this accept an arbitrary sequence? |
| if type(initlist) == type(self.data): |
| self.data[:] = initlist |
| elif isinstance(initlist, UserList): |
| self.data[:] = initlist.data[:] |
| else: |
| self.data = list(initlist) |
| |
| def __repr__(self): |
| return repr(self.data) |
| |
| def __lt__(self, other): |
| return self.data < self.__cast(other) |
| |
| def __le__(self, other): |
| return self.data <= self.__cast(other) |
| |
| def __eq__(self, other): |
| return self.data == self.__cast(other) |
| |
| def __gt__(self, other): |
| return self.data > self.__cast(other) |
| |
| def __ge__(self, other): |
| return self.data >= self.__cast(other) |
| |
| def __cast(self, other): |
| return other.data if isinstance(other, UserList) else other |
| |
| def __contains__(self, item): |
| return item in self.data |
| |
| def __len__(self): |
| return len(self.data) |
| |
| def __getitem__(self, i): |
| if isinstance(i, slice): |
| return self.__class__(self.data[i]) |
| else: |
| return self.data[i] |
| |
| def __setitem__(self, i, item): |
| self.data[i] = item |
| |
| def __delitem__(self, i): |
| del self.data[i] |
| |
| def __add__(self, other): |
| if isinstance(other, UserList): |
| return self.__class__(self.data + other.data) |
| elif isinstance(other, type(self.data)): |
| return self.__class__(self.data + other) |
| return self.__class__(self.data + list(other)) |
| |
| def __radd__(self, other): |
| if isinstance(other, UserList): |
| return self.__class__(other.data + self.data) |
| elif isinstance(other, type(self.data)): |
| return self.__class__(other + self.data) |
| return self.__class__(list(other) + self.data) |
| |
| def __iadd__(self, other): |
| if isinstance(other, UserList): |
| self.data += other.data |
| elif isinstance(other, type(self.data)): |
| self.data += other |
| else: |
| self.data += list(other) |
| return self |
| |
| def __mul__(self, n): |
| return self.__class__(self.data * n) |
| |
| __rmul__ = __mul__ |
| |
| def __imul__(self, n): |
| self.data *= n |
| return self |
| |
| def __copy__(self): |
| inst = self.__class__.__new__(self.__class__) |
| inst.__dict__.update(self.__dict__) |
| # Create a copy and avoid triggering descriptors |
| inst.__dict__["data"] = self.__dict__["data"][:] |
| return inst |
| |
| def append(self, item): |
| self.data.append(item) |
| |
| def insert(self, i, item): |
| self.data.insert(i, item) |
| |
| def pop(self, i=-1): |
| return self.data.pop(i) |
| |
| def remove(self, item): |
| self.data.remove(item) |
| |
| def clear(self): |
| self.data.clear() |
| |
| def copy(self): |
| return self.__class__(self) |
| |
| def count(self, item): |
| return self.data.count(item) |
| |
| def index(self, item, *args): |
| return self.data.index(item, *args) |
| |
| def reverse(self): |
| self.data.reverse() |
| |
| def sort(self, /, *args, **kwds): |
| self.data.sort(*args, **kwds) |
| |
| def extend(self, other): |
| if isinstance(other, UserList): |
| self.data.extend(other.data) |
| else: |
| self.data.extend(other) |
| |
| |
| ################################################################################ |
| ### UserString |
| ################################################################################ |
| |
| class UserString(_collections_abc.Sequence): |
| |
| def __init__(self, seq): |
| if isinstance(seq, str): |
| self.data = seq |
| elif isinstance(seq, UserString): |
| self.data = seq.data[:] |
| else: |
| self.data = str(seq) |
| |
| def __str__(self): |
| return str(self.data) |
| |
| def __repr__(self): |
| return repr(self.data) |
| |
| def __int__(self): |
| return int(self.data) |
| |
| def __float__(self): |
| return float(self.data) |
| |
| def __complex__(self): |
| return complex(self.data) |
| |
| def __hash__(self): |
| return hash(self.data) |
| |
| def __getnewargs__(self): |
| return (self.data[:],) |
| |
| def __eq__(self, string): |
| if isinstance(string, UserString): |
| return self.data == string.data |
| return self.data == string |
| |
| def __lt__(self, string): |
| if isinstance(string, UserString): |
| return self.data < string.data |
| return self.data < string |
| |
| def __le__(self, string): |
| if isinstance(string, UserString): |
| return self.data <= string.data |
| return self.data <= string |
| |
| def __gt__(self, string): |
| if isinstance(string, UserString): |
| return self.data > string.data |
| return self.data > string |
| |
| def __ge__(self, string): |
| if isinstance(string, UserString): |
| return self.data >= string.data |
| return self.data >= string |
| |
| def __contains__(self, char): |
| if isinstance(char, UserString): |
| char = char.data |
| return char in self.data |
| |
| def __len__(self): |
| return len(self.data) |
| |
| def __getitem__(self, index): |
| return self.__class__(self.data[index]) |
| |
| def __add__(self, other): |
| if isinstance(other, UserString): |
| return self.__class__(self.data + other.data) |
| elif isinstance(other, str): |
| return self.__class__(self.data + other) |
| return self.__class__(self.data + str(other)) |
| |
| def __radd__(self, other): |
| if isinstance(other, str): |
| return self.__class__(other + self.data) |
| return self.__class__(str(other) + self.data) |
| |
| def __mul__(self, n): |
| return self.__class__(self.data * n) |
| |
| __rmul__ = __mul__ |
| |
| def __mod__(self, args): |
| return self.__class__(self.data % args) |
| |
| def __rmod__(self, template): |
| return self.__class__(str(template) % self) |
| |
| # the following methods are defined in alphabetical order: |
| def capitalize(self): |
| return self.__class__(self.data.capitalize()) |
| |
| def casefold(self): |
| return self.__class__(self.data.casefold()) |
| |
| def center(self, width, *args): |
| return self.__class__(self.data.center(width, *args)) |
| |
| def count(self, sub, start=0, end=_sys.maxsize): |
| if isinstance(sub, UserString): |
| sub = sub.data |
| return self.data.count(sub, start, end) |
| |
| def removeprefix(self, prefix, /): |
| if isinstance(prefix, UserString): |
| prefix = prefix.data |
| return self.__class__(self.data.removeprefix(prefix)) |
| |
| def removesuffix(self, suffix, /): |
| if isinstance(suffix, UserString): |
| suffix = suffix.data |
| return self.__class__(self.data.removesuffix(suffix)) |
| |
| def encode(self, encoding='utf-8', errors='strict'): |
| encoding = 'utf-8' if encoding is None else encoding |
| errors = 'strict' if errors is None else errors |
| return self.data.encode(encoding, errors) |
| |
| def endswith(self, suffix, start=0, end=_sys.maxsize): |
| return self.data.endswith(suffix, start, end) |
| |
| def expandtabs(self, tabsize=8): |
| return self.__class__(self.data.expandtabs(tabsize)) |
| |
| def find(self, sub, start=0, end=_sys.maxsize): |
| if isinstance(sub, UserString): |
| sub = sub.data |
| return self.data.find(sub, start, end) |
| |
| def format(self, /, *args, **kwds): |
| return self.data.format(*args, **kwds) |
| |
| def format_map(self, mapping): |
| return self.data.format_map(mapping) |
| |
| def index(self, sub, start=0, end=_sys.maxsize): |
| return self.data.index(sub, start, end) |
| |
| def isalpha(self): |
| return self.data.isalpha() |
| |
| def isalnum(self): |
| return self.data.isalnum() |
| |
| def isascii(self): |
| return self.data.isascii() |
| |
| def isdecimal(self): |
| return self.data.isdecimal() |
| |
| def isdigit(self): |
| return self.data.isdigit() |
| |
| def isidentifier(self): |
| return self.data.isidentifier() |
| |
| def islower(self): |
| return self.data.islower() |
| |
| def isnumeric(self): |
| return self.data.isnumeric() |
| |
| def isprintable(self): |
| return self.data.isprintable() |
| |
| def isspace(self): |
| return self.data.isspace() |
| |
| def istitle(self): |
| return self.data.istitle() |
| |
| def isupper(self): |
| return self.data.isupper() |
| |
| def join(self, seq): |
| return self.data.join(seq) |
| |
| def ljust(self, width, *args): |
| return self.__class__(self.data.ljust(width, *args)) |
| |
| def lower(self): |
| return self.__class__(self.data.lower()) |
| |
| def lstrip(self, chars=None): |
| return self.__class__(self.data.lstrip(chars)) |
| |
| maketrans = str.maketrans |
| |
| def partition(self, sep): |
| return self.data.partition(sep) |
| |
| def replace(self, old, new, maxsplit=-1): |
| if isinstance(old, UserString): |
| old = old.data |
| if isinstance(new, UserString): |
| new = new.data |
| return self.__class__(self.data.replace(old, new, maxsplit)) |
| |
| def rfind(self, sub, start=0, end=_sys.maxsize): |
| if isinstance(sub, UserString): |
| sub = sub.data |
| return self.data.rfind(sub, start, end) |
| |
| def rindex(self, sub, start=0, end=_sys.maxsize): |
| return self.data.rindex(sub, start, end) |
| |
| def rjust(self, width, *args): |
| return self.__class__(self.data.rjust(width, *args)) |
| |
| def rpartition(self, sep): |
| return self.data.rpartition(sep) |
| |
| def rstrip(self, chars=None): |
| return self.__class__(self.data.rstrip(chars)) |
| |
| def split(self, sep=None, maxsplit=-1): |
| return self.data.split(sep, maxsplit) |
| |
| def rsplit(self, sep=None, maxsplit=-1): |
| return self.data.rsplit(sep, maxsplit) |
| |
| def splitlines(self, keepends=False): |
| return self.data.splitlines(keepends) |
| |
| def startswith(self, prefix, start=0, end=_sys.maxsize): |
| return self.data.startswith(prefix, start, end) |
| |
| def strip(self, chars=None): |
| return self.__class__(self.data.strip(chars)) |
| |
| def swapcase(self): |
| return self.__class__(self.data.swapcase()) |
| |
| def title(self): |
| return self.__class__(self.data.title()) |
| |
| def translate(self, *args): |
| return self.__class__(self.data.translate(*args)) |
| |
| def upper(self): |
| return self.__class__(self.data.upper()) |
| |
| def zfill(self, width): |
| return self.__class__(self.data.zfill(width)) |
