diff --git "a/lib/python3.11/site-packages/more_itertools/more.py" "b/lib/python3.11/site-packages/more_itertools/more.py"
new file mode 100644--- /dev/null
+++ "b/lib/python3.11/site-packages/more_itertools/more.py"
@@ -0,0 +1,4569 @@
+import warnings
+
+from collections import Counter, defaultdict, deque, abc
+from collections.abc import Sequence
+from functools import cached_property, partial, reduce, wraps
+from heapq import heapify, heapreplace, heappop
+from itertools import (
+ chain,
+ compress,
+ count,
+ cycle,
+ dropwhile,
+ groupby,
+ islice,
+ repeat,
+ starmap,
+ takewhile,
+ tee,
+ zip_longest,
+ product,
+)
+from math import exp, factorial, floor, log
+from queue import Empty, Queue
+from random import random, randrange, uniform
+from operator import itemgetter, mul, sub, gt, lt, ge, le
+from sys import hexversion, maxsize
+from time import monotonic
+
+from .recipes import (
+ _marker,
+ _zip_equal,
+ UnequalIterablesError,
+ consume,
+ flatten,
+ pairwise,
+ powerset,
+ take,
+ unique_everseen,
+ all_equal,
+ batched,
+)
+
+__all__ = [
+ 'AbortThread',
+ 'SequenceView',
+ 'UnequalIterablesError',
+ 'adjacent',
+ 'all_unique',
+ 'always_iterable',
+ 'always_reversible',
+ 'bucket',
+ 'callback_iter',
+ 'chunked',
+ 'chunked_even',
+ 'circular_shifts',
+ 'collapse',
+ 'combination_index',
+ 'combination_with_replacement_index',
+ 'consecutive_groups',
+ 'constrained_batches',
+ 'consumer',
+ 'count_cycle',
+ 'countable',
+ 'difference',
+ 'distinct_combinations',
+ 'distinct_permutations',
+ 'distribute',
+ 'divide',
+ 'duplicates_everseen',
+ 'duplicates_justseen',
+ 'exactly_n',
+ 'filter_except',
+ 'first',
+ 'gray_product',
+ 'groupby_transform',
+ 'ichunked',
+ 'iequals',
+ 'ilen',
+ 'interleave',
+ 'interleave_evenly',
+ 'interleave_longest',
+ 'intersperse',
+ 'is_sorted',
+ 'islice_extended',
+ 'iterate',
+ 'last',
+ 'locate',
+ 'longest_common_prefix',
+ 'lstrip',
+ 'make_decorator',
+ 'map_except',
+ 'map_if',
+ 'map_reduce',
+ 'mark_ends',
+ 'minmax',
+ 'nth_or_last',
+ 'nth_permutation',
+ 'nth_product',
+ 'nth_combination_with_replacement',
+ 'numeric_range',
+ 'one',
+ 'only',
+ 'outer_product',
+ 'padded',
+ 'partial_product',
+ 'partitions',
+ 'peekable',
+ 'permutation_index',
+ 'product_index',
+ 'raise_',
+ 'repeat_each',
+ 'repeat_last',
+ 'replace',
+ 'rlocate',
+ 'rstrip',
+ 'run_length',
+ 'sample',
+ 'seekable',
+ 'set_partitions',
+ 'side_effect',
+ 'sliced',
+ 'sort_together',
+ 'split_after',
+ 'split_at',
+ 'split_before',
+ 'split_into',
+ 'split_when',
+ 'spy',
+ 'stagger',
+ 'strip',
+ 'strictly_n',
+ 'substrings',
+ 'substrings_indexes',
+ 'takewhile_inclusive',
+ 'time_limited',
+ 'unique_in_window',
+ 'unique_to_each',
+ 'unzip',
+ 'value_chain',
+ 'windowed',
+ 'windowed_complete',
+ 'with_iter',
+ 'zip_broadcast',
+ 'zip_equal',
+ 'zip_offset',
+]
+
+
+def chunked(iterable, n, strict=False):
+ """Break *iterable* into lists of length *n*:
+
+ >>> list(chunked([1, 2, 3, 4, 5, 6], 3))
+ [[1, 2, 3], [4, 5, 6]]
+
+ By the default, the last yielded list will have fewer than *n* elements
+ if the length of *iterable* is not divisible by *n*:
+
+ >>> list(chunked([1, 2, 3, 4, 5, 6, 7, 8], 3))
+ [[1, 2, 3], [4, 5, 6], [7, 8]]
+
+ To use a fill-in value instead, see the :func:`grouper` recipe.
+
+ If the length of *iterable* is not divisible by *n* and *strict* is
+ ``True``, then ``ValueError`` will be raised before the last
+ list is yielded.
+
+ """
+ iterator = iter(partial(take, n, iter(iterable)), [])
+ if strict:
+ if n is None:
+ raise ValueError('n must not be None when using strict mode.')
+
+ def ret():
+ for chunk in iterator:
+ if len(chunk) != n:
+ raise ValueError('iterable is not divisible by n.')
+ yield chunk
+
+ return iter(ret())
+ else:
+ return iterator
+
+
+def first(iterable, default=_marker):
+ """Return the first item of *iterable*, or *default* if *iterable* is
+ empty.
+
+ >>> first([0, 1, 2, 3])
+ 0
+ >>> first([], 'some default')
+ 'some default'
+
+ If *default* is not provided and there are no items in the iterable,
+ raise ``ValueError``.
+
+ :func:`first` is useful when you have a generator of expensive-to-retrieve
+ values and want any arbitrary one. It is marginally shorter than
+ ``next(iter(iterable), default)``.
+
+ """
+ try:
+ return next(iter(iterable))
+ except StopIteration as e:
+ if default is _marker:
+ raise ValueError(
+ 'first() was called on an empty iterable, and no '
+ 'default value was provided.'
+ ) from e
+ return default
+
+
+def last(iterable, default=_marker):
+ """Return the last item of *iterable*, or *default* if *iterable* is
+ empty.
+
+ >>> last([0, 1, 2, 3])
+ 3
+ >>> last([], 'some default')
+ 'some default'
+
+ If *default* is not provided and there are no items in the iterable,
+ raise ``ValueError``.
+ """
+ try:
+ if isinstance(iterable, Sequence):
+ return iterable[-1]
+ # Work around https://bugs.python.org/issue38525
+ elif hasattr(iterable, '__reversed__') and (hexversion != 0x030800F0):
+ return next(reversed(iterable))
+ else:
+ return deque(iterable, maxlen=1)[-1]
+ except (IndexError, TypeError, StopIteration):
+ if default is _marker:
+ raise ValueError(
+ 'last() was called on an empty iterable, and no default was '
+ 'provided.'
+ )
+ return default
+
+
+def nth_or_last(iterable, n, default=_marker):
+ """Return the nth or the last item of *iterable*,
+ or *default* if *iterable* is empty.
+
+ >>> nth_or_last([0, 1, 2, 3], 2)
+ 2
+ >>> nth_or_last([0, 1], 2)
+ 1
+ >>> nth_or_last([], 0, 'some default')
+ 'some default'
+
+ If *default* is not provided and there are no items in the iterable,
+ raise ``ValueError``.
+ """
+ return last(islice(iterable, n + 1), default=default)
+
+
+class peekable:
+ """Wrap an iterator to allow lookahead and prepending elements.
+
+ Call :meth:`peek` on the result to get the value that will be returned
+ by :func:`next`. This won't advance the iterator:
+
+ >>> p = peekable(['a', 'b'])
+ >>> p.peek()
+ 'a'
+ >>> next(p)
+ 'a'
+
+ Pass :meth:`peek` a default value to return that instead of raising
+ ``StopIteration`` when the iterator is exhausted.
+
+ >>> p = peekable([])
+ >>> p.peek('hi')
+ 'hi'
+
+ peekables also offer a :meth:`prepend` method, which "inserts" items
+ at the head of the iterable:
+
+ >>> p = peekable([1, 2, 3])
+ >>> p.prepend(10, 11, 12)
+ >>> next(p)
+ 10
+ >>> p.peek()
+ 11
+ >>> list(p)
+ [11, 12, 1, 2, 3]
+
+ peekables can be indexed. Index 0 is the item that will be returned by
+ :func:`next`, index 1 is the item after that, and so on:
+ The values up to the given index will be cached.
+
+ >>> p = peekable(['a', 'b', 'c', 'd'])
+ >>> p[0]
+ 'a'
+ >>> p[1]
+ 'b'
+ >>> next(p)
+ 'a'
+
+ Negative indexes are supported, but be aware that they will cache the
+ remaining items in the source iterator, which may require significant
+ storage.
+
+ To check whether a peekable is exhausted, check its truth value:
+
+ >>> p = peekable(['a', 'b'])
+ >>> if p: # peekable has items
+ ... list(p)
+ ['a', 'b']
+ >>> if not p: # peekable is exhausted
+ ... list(p)
+ []
+
+ """
+
+ def __init__(self, iterable):
+ self._it = iter(iterable)
+ self._cache = deque()
+
+ def __iter__(self):
+ return self
+
+ def __bool__(self):
+ try:
+ self.peek()
+ except StopIteration:
+ return False
+ return True
+
+ def peek(self, default=_marker):
+ """Return the item that will be next returned from ``next()``.
+
+ Return ``default`` if there are no items left. If ``default`` is not
+ provided, raise ``StopIteration``.
+
+ """
+ if not self._cache:
+ try:
+ self._cache.append(next(self._it))
+ except StopIteration:
+ if default is _marker:
+ raise
+ return default
+ return self._cache[0]
+
+ def prepend(self, *items):
+ """Stack up items to be the next ones returned from ``next()`` or
+ ``self.peek()``. The items will be returned in
+ first in, first out order::
+
+ >>> p = peekable([1, 2, 3])
+ >>> p.prepend(10, 11, 12)
+ >>> next(p)
+ 10
+ >>> list(p)
+ [11, 12, 1, 2, 3]
+
+ It is possible, by prepending items, to "resurrect" a peekable that
+ previously raised ``StopIteration``.
+
+ >>> p = peekable([])
+ >>> next(p)
+ Traceback (most recent call last):
+ ...
+ StopIteration
+ >>> p.prepend(1)
+ >>> next(p)
+ 1
+ >>> next(p)
+ Traceback (most recent call last):
+ ...
+ StopIteration
+
+ """
+ self._cache.extendleft(reversed(items))
+
+ def __next__(self):
+ if self._cache:
+ return self._cache.popleft()
+
+ return next(self._it)
+
+ def _get_slice(self, index):
+ # Normalize the slice's arguments
+ step = 1 if (index.step is None) else index.step
+ if step > 0:
+ start = 0 if (index.start is None) else index.start
+ stop = maxsize if (index.stop is None) else index.stop
+ elif step < 0:
+ start = -1 if (index.start is None) else index.start
+ stop = (-maxsize - 1) if (index.stop is None) else index.stop
+ else:
+ raise ValueError('slice step cannot be zero')
+
+ # If either the start or stop index is negative, we'll need to cache
+ # the rest of the iterable in order to slice from the right side.
+ if (start < 0) or (stop < 0):
+ self._cache.extend(self._it)
+ # Otherwise we'll need to find the rightmost index and cache to that
+ # point.
+ else:
+ n = min(max(start, stop) + 1, maxsize)
+ cache_len = len(self._cache)
+ if n >= cache_len:
+ self._cache.extend(islice(self._it, n - cache_len))
+
+ return list(self._cache)[index]
+
+ def __getitem__(self, index):
+ if isinstance(index, slice):
+ return self._get_slice(index)
+
+ cache_len = len(self._cache)
+ if index < 0:
+ self._cache.extend(self._it)
+ elif index >= cache_len:
+ self._cache.extend(islice(self._it, index + 1 - cache_len))
+
+ return self._cache[index]
+
+
+def consumer(func):
+ """Decorator that automatically advances a PEP-342-style "reverse iterator"
+ to its first yield point so you don't have to call ``next()`` on it
+ manually.
+
+ >>> @consumer
+ ... def tally():
+ ... i = 0
+ ... while True:
+ ... print('Thing number %s is %s.' % (i, (yield)))
+ ... i += 1
+ ...
+ >>> t = tally()
+ >>> t.send('red')
+ Thing number 0 is red.
+ >>> t.send('fish')
+ Thing number 1 is fish.
+
+ Without the decorator, you would have to call ``next(t)`` before
+ ``t.send()`` could be used.
+
+ """
+
+ @wraps(func)
+ def wrapper(*args, **kwargs):
+ gen = func(*args, **kwargs)
+ next(gen)
+ return gen
+
+ return wrapper
+
+
+def ilen(iterable):
+ """Return the number of items in *iterable*.
+
+ >>> ilen(x for x in range(1000000) if x % 3 == 0)
+ 333334
+
+ This consumes the iterable, so handle with care.
+
+ """
+ # This approach was selected because benchmarks showed it's likely the
+ # fastest of the known implementations at the time of writing.
+ # See GitHub tracker: #236, #230.
+ counter = count()
+ deque(zip(iterable, counter), maxlen=0)
+ return next(counter)
+
+
+def iterate(func, start):
+ """Return ``start``, ``func(start)``, ``func(func(start))``, ...
+
+ >>> from itertools import islice
+ >>> list(islice(iterate(lambda x: 2*x, 1), 10))
+ [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]
+
+ """
+ while True:
+ yield start
+ try:
+ start = func(start)
+ except StopIteration:
+ break
+
+
+def with_iter(context_manager):
+ """Wrap an iterable in a ``with`` statement, so it closes once exhausted.
+
+ For example, this will close the file when the iterator is exhausted::
+
+ upper_lines = (line.upper() for line in with_iter(open('foo')))
+
+ Any context manager which returns an iterable is a candidate for
+ ``with_iter``.
+
+ """
+ with context_manager as iterable:
+ yield from iterable
+
+
+def one(iterable, too_short=None, too_long=None):
+ """Return the first item from *iterable*, which is expected to contain only
+ that item. Raise an exception if *iterable* is empty or has more than one
+ item.
+
+ :func:`one` is useful for ensuring that an iterable contains only one item.
+ For example, it can be used to retrieve the result of a database query
+ that is expected to return a single row.
+
+ If *iterable* is empty, ``ValueError`` will be raised. You may specify a
+ different exception with the *too_short* keyword:
+
+ >>> it = []
+ >>> one(it) # doctest: +IGNORE_EXCEPTION_DETAIL
+ Traceback (most recent call last):
+ ...
+ ValueError: too many items in iterable (expected 1)'
+ >>> too_short = IndexError('too few items')
+ >>> one(it, too_short=too_short) # doctest: +IGNORE_EXCEPTION_DETAIL
+ Traceback (most recent call last):
+ ...
+ IndexError: too few items
+
+ Similarly, if *iterable* contains more than one item, ``ValueError`` will
+ be raised. You may specify a different exception with the *too_long*
+ keyword:
+
+ >>> it = ['too', 'many']
+ >>> one(it) # doctest: +IGNORE_EXCEPTION_DETAIL
+ Traceback (most recent call last):
+ ...
+ ValueError: Expected exactly one item in iterable, but got 'too',
+ 'many', and perhaps more.
+ >>> too_long = RuntimeError
+ >>> one(it, too_long=too_long) # doctest: +IGNORE_EXCEPTION_DETAIL
+ Traceback (most recent call last):
+ ...
+ RuntimeError
+
+ Note that :func:`one` attempts to advance *iterable* twice to ensure there
+ is only one item. See :func:`spy` or :func:`peekable` to check iterable
+ contents less destructively.
+
+ """
+ it = iter(iterable)
+
+ try:
+ first_value = next(it)
+ except StopIteration as e:
+ raise (
+ too_short or ValueError('too few items in iterable (expected 1)')
+ ) from e
+
+ try:
+ second_value = next(it)
+ except StopIteration:
+ pass
+ else:
+ msg = (
+ 'Expected exactly one item in iterable, but got {!r}, {!r}, '
+ 'and perhaps more.'.format(first_value, second_value)
+ )
+ raise too_long or ValueError(msg)
+
+ return first_value
+
+
+def raise_(exception, *args):
+ raise exception(*args)
+
+
+def strictly_n(iterable, n, too_short=None, too_long=None):
+ """Validate that *iterable* has exactly *n* items and return them if
+ it does. If it has fewer than *n* items, call function *too_short*
+ with those items. If it has more than *n* items, call function
+ *too_long* with the first ``n + 1`` items.
+
+ >>> iterable = ['a', 'b', 'c', 'd']
+ >>> n = 4
+ >>> list(strictly_n(iterable, n))
+ ['a', 'b', 'c', 'd']
+
+ By default, *too_short* and *too_long* are functions that raise
+ ``ValueError``.
+
+ >>> list(strictly_n('ab', 3)) # doctest: +IGNORE_EXCEPTION_DETAIL
+ Traceback (most recent call last):
+ ...
+ ValueError: too few items in iterable (got 2)
+
+ >>> list(strictly_n('abc', 2)) # doctest: +IGNORE_EXCEPTION_DETAIL
+ Traceback (most recent call last):
+ ...
+ ValueError: too many items in iterable (got at least 3)
+
+ You can instead supply functions that do something else.
+ *too_short* will be called with the number of items in *iterable*.
+ *too_long* will be called with `n + 1`.
+
+ >>> def too_short(item_count):
+ ... raise RuntimeError
+ >>> it = strictly_n('abcd', 6, too_short=too_short)
+ >>> list(it) # doctest: +IGNORE_EXCEPTION_DETAIL
+ Traceback (most recent call last):
+ ...
+ RuntimeError
+
+ >>> def too_long(item_count):
+ ... print('The boss is going to hear about this')
+ >>> it = strictly_n('abcdef', 4, too_long=too_long)
+ >>> list(it)
+ The boss is going to hear about this
+ ['a', 'b', 'c', 'd']
+
+ """
+ if too_short is None:
+ too_short = lambda item_count: raise_(
+ ValueError,
+ 'Too few items in iterable (got {})'.format(item_count),
+ )
+
+ if too_long is None:
+ too_long = lambda item_count: raise_(
+ ValueError,
+ 'Too many items in iterable (got at least {})'.format(item_count),
+ )
+
+ it = iter(iterable)
+ for i in range(n):
+ try:
+ item = next(it)
+ except StopIteration:
+ too_short(i)
+ return
+ else:
+ yield item
+
+ try:
+ next(it)
+ except StopIteration:
+ pass
+ else:
+ too_long(n + 1)
+
+
+def distinct_permutations(iterable, r=None):
+ """Yield successive distinct permutations of the elements in *iterable*.
+
+ >>> sorted(distinct_permutations([1, 0, 1]))
+ [(0, 1, 1), (1, 0, 1), (1, 1, 0)]
+
+ Equivalent to ``set(permutations(iterable))``, except duplicates are not
+ generated and thrown away. For larger input sequences this is much more
+ efficient.
+
+ Duplicate permutations arise when there are duplicated elements in the
+ input iterable. The number of items returned is
+ `n! / (x_1! * x_2! * ... * x_n!)`, where `n` is the total number of
+ items input, and each `x_i` is the count of a distinct item in the input
+ sequence.
+
+ If *r* is given, only the *r*-length permutations are yielded.
+
+ >>> sorted(distinct_permutations([1, 0, 1], r=2))
+ [(0, 1), (1, 0), (1, 1)]
+ >>> sorted(distinct_permutations(range(3), r=2))
+ [(0, 1), (0, 2), (1, 0), (1, 2), (2, 0), (2, 1)]
+
+ """
+
+ # Algorithm: https://w.wiki/Qai
+ def _full(A):
+ while True:
+ # Yield the permutation we have
+ yield tuple(A)
+
+ # Find the largest index i such that A[i] < A[i + 1]
+ for i in range(size - 2, -1, -1):
+ if A[i] < A[i + 1]:
+ break
+ # If no such index exists, this permutation is the last one
+ else:
+ return
+
+ # Find the largest index j greater than j such that A[i] < A[j]
+ for j in range(size - 1, i, -1):
+ if A[i] < A[j]:
+ break
+
+ # Swap the value of A[i] with that of A[j], then reverse the
+ # sequence from A[i + 1] to form the new permutation
+ A[i], A[j] = A[j], A[i]
+ A[i + 1 :] = A[: i - size : -1] # A[i + 1:][::-1]
+
+ # Algorithm: modified from the above
+ def _partial(A, r):
+ # Split A into the first r items and the last r items
+ head, tail = A[:r], A[r:]
+ right_head_indexes = range(r - 1, -1, -1)
+ left_tail_indexes = range(len(tail))
+
+ while True:
+ # Yield the permutation we have
+ yield tuple(head)
+
+ # Starting from the right, find the first index of the head with
+ # value smaller than the maximum value of the tail - call it i.
+ pivot = tail[-1]
+ for i in right_head_indexes:
+ if head[i] < pivot:
+ break
+ pivot = head[i]
+ else:
+ return
+
+ # Starting from the left, find the first value of the tail
+ # with a value greater than head[i] and swap.
+ for j in left_tail_indexes:
+ if tail[j] > head[i]:
+ head[i], tail[j] = tail[j], head[i]
+ break
+ # If we didn't find one, start from the right and find the first
+ # index of the head with a value greater than head[i] and swap.
+ else:
+ for j in right_head_indexes:
+ if head[j] > head[i]:
+ head[i], head[j] = head[j], head[i]
+ break
+
+ # Reverse head[i + 1:] and swap it with tail[:r - (i + 1)]
+ tail += head[: i - r : -1] # head[i + 1:][::-1]
+ i += 1
+ head[i:], tail[:] = tail[: r - i], tail[r - i :]
+
+ items = sorted(iterable)
+
+ size = len(items)
+ if r is None:
+ r = size
+
+ if 0 < r <= size:
+ return _full(items) if (r == size) else _partial(items, r)
+
+ return iter(() if r else ((),))
+
+
+def intersperse(e, iterable, n=1):
+ """Intersperse filler element *e* among the items in *iterable*, leaving
+ *n* items between each filler element.
+
+ >>> list(intersperse('!', [1, 2, 3, 4, 5]))
+ [1, '!', 2, '!', 3, '!', 4, '!', 5]
+
+ >>> list(intersperse(None, [1, 2, 3, 4, 5], n=2))
+ [1, 2, None, 3, 4, None, 5]
+
+ """
+ if n == 0:
+ raise ValueError('n must be > 0')
+ elif n == 1:
+ # interleave(repeat(e), iterable) -> e, x_0, e, x_1, e, x_2...
+ # islice(..., 1, None) -> x_0, e, x_1, e, x_2...
+ return islice(interleave(repeat(e), iterable), 1, None)
+ else:
+ # interleave(filler, chunks) -> [e], [x_0, x_1], [e], [x_2, x_3]...
+ # islice(..., 1, None) -> [x_0, x_1], [e], [x_2, x_3]...
+ # flatten(...) -> x_0, x_1, e, x_2, x_3...
+ filler = repeat([e])
+ chunks = chunked(iterable, n)
+ return flatten(islice(interleave(filler, chunks), 1, None))
+
+
+def unique_to_each(*iterables):
+ """Return the elements from each of the input iterables that aren't in the
+ other input iterables.
+
+ For example, suppose you have a set of packages, each with a set of
+ dependencies::
+
+ {'pkg_1': {'A', 'B'}, 'pkg_2': {'B', 'C'}, 'pkg_3': {'B', 'D'}}
+
+ If you remove one package, which dependencies can also be removed?
+
+ If ``pkg_1`` is removed, then ``A`` is no longer necessary - it is not
+ associated with ``pkg_2`` or ``pkg_3``. Similarly, ``C`` is only needed for
+ ``pkg_2``, and ``D`` is only needed for ``pkg_3``::
+
+ >>> unique_to_each({'A', 'B'}, {'B', 'C'}, {'B', 'D'})
+ [['A'], ['C'], ['D']]
+
+ If there are duplicates in one input iterable that aren't in the others
+ they will be duplicated in the output. Input order is preserved::
+
+ >>> unique_to_each("mississippi", "missouri")
+ [['p', 'p'], ['o', 'u', 'r']]
+
+ It is assumed that the elements of each iterable are hashable.
+
+ """
+ pool = [list(it) for it in iterables]
+ counts = Counter(chain.from_iterable(map(set, pool)))
+ uniques = {element for element in counts if counts[element] == 1}
+ return [list(filter(uniques.__contains__, it)) for it in pool]
+
+
+def windowed(seq, n, fillvalue=None, step=1):
+ """Return a sliding window of width *n* over the given iterable.
+
+ >>> all_windows = windowed([1, 2, 3, 4, 5], 3)
+ >>> list(all_windows)
+ [(1, 2, 3), (2, 3, 4), (3, 4, 5)]
+
+ When the window is larger than the iterable, *fillvalue* is used in place
+ of missing values:
+
+ >>> list(windowed([1, 2, 3], 4))
+ [(1, 2, 3, None)]
+
+ Each window will advance in increments of *step*:
+
+ >>> list(windowed([1, 2, 3, 4, 5, 6], 3, fillvalue='!', step=2))
+ [(1, 2, 3), (3, 4, 5), (5, 6, '!')]
+
+ To slide into the iterable's items, use :func:`chain` to add filler items
+ to the left:
+
+ >>> iterable = [1, 2, 3, 4]
+ >>> n = 3
+ >>> padding = [None] * (n - 1)
+ >>> list(windowed(chain(padding, iterable), 3))
+ [(None, None, 1), (None, 1, 2), (1, 2, 3), (2, 3, 4)]
+ """
+ if n < 0:
+ raise ValueError('n must be >= 0')
+ if n == 0:
+ yield tuple()
+ return
+ if step < 1:
+ raise ValueError('step must be >= 1')
+
+ window = deque(maxlen=n)
+ i = n
+ for _ in map(window.append, seq):
+ i -= 1
+ if not i:
+ i = step
+ yield tuple(window)
+
+ size = len(window)
+ if size == 0:
+ return
+ elif size < n:
+ yield tuple(chain(window, repeat(fillvalue, n - size)))
+ elif 0 < i < min(step, n):
+ window += (fillvalue,) * i
+ yield tuple(window)
+
+
+def substrings(iterable):
+ """Yield all of the substrings of *iterable*.
+
+ >>> [''.join(s) for s in substrings('more')]
+ ['m', 'o', 'r', 'e', 'mo', 'or', 're', 'mor', 'ore', 'more']
+
+ Note that non-string iterables can also be subdivided.
+
+ >>> list(substrings([0, 1, 2]))
+ [(0,), (1,), (2,), (0, 1), (1, 2), (0, 1, 2)]
+
+ """
+ # The length-1 substrings
+ seq = []
+ for item in iter(iterable):
+ seq.append(item)
+ yield (item,)
+ seq = tuple(seq)
+ item_count = len(seq)
+
+ # And the rest
+ for n in range(2, item_count + 1):
+ for i in range(item_count - n + 1):
+ yield seq[i : i + n]
+
+
+def substrings_indexes(seq, reverse=False):
+ """Yield all substrings and their positions in *seq*
+
+ The items yielded will be a tuple of the form ``(substr, i, j)``, where
+ ``substr == seq[i:j]``.
+
+ This function only works for iterables that support slicing, such as
+ ``str`` objects.
+
+ >>> for item in substrings_indexes('more'):
+ ... print(item)
+ ('m', 0, 1)
+ ('o', 1, 2)
+ ('r', 2, 3)
+ ('e', 3, 4)
+ ('mo', 0, 2)
+ ('or', 1, 3)
+ ('re', 2, 4)
+ ('mor', 0, 3)
+ ('ore', 1, 4)
+ ('more', 0, 4)
+
+ Set *reverse* to ``True`` to yield the same items in the opposite order.
+
+
+ """
+ r = range(1, len(seq) + 1)
+ if reverse:
+ r = reversed(r)
+ return (
+ (seq[i : i + L], i, i + L) for L in r for i in range(len(seq) - L + 1)
+ )
+
+
+class bucket:
+ """Wrap *iterable* and return an object that buckets it iterable into
+ child iterables based on a *key* function.
+
+ >>> iterable = ['a1', 'b1', 'c1', 'a2', 'b2', 'c2', 'b3']
+ >>> s = bucket(iterable, key=lambda x: x[0]) # Bucket by 1st character
+ >>> sorted(list(s)) # Get the keys
+ ['a', 'b', 'c']
+ >>> a_iterable = s['a']
+ >>> next(a_iterable)
+ 'a1'
+ >>> next(a_iterable)
+ 'a2'
+ >>> list(s['b'])
+ ['b1', 'b2', 'b3']
+
+ The original iterable will be advanced and its items will be cached until
+ they are used by the child iterables. This may require significant storage.
+
+ By default, attempting to select a bucket to which no items belong will
+ exhaust the iterable and cache all values.
+ If you specify a *validator* function, selected buckets will instead be
+ checked against it.
+
+ >>> from itertools import count
+ >>> it = count(1, 2) # Infinite sequence of odd numbers
+ >>> key = lambda x: x % 10 # Bucket by last digit
+ >>> validator = lambda x: x in {1, 3, 5, 7, 9} # Odd digits only
+ >>> s = bucket(it, key=key, validator=validator)
+ >>> 2 in s
+ False
+ >>> list(s[2])
+ []
+
+ """
+
+ def __init__(self, iterable, key, validator=None):
+ self._it = iter(iterable)
+ self._key = key
+ self._cache = defaultdict(deque)
+ self._validator = validator or (lambda x: True)
+
+ def __contains__(self, value):
+ if not self._validator(value):
+ return False
+
+ try:
+ item = next(self[value])
+ except StopIteration:
+ return False
+ else:
+ self._cache[value].appendleft(item)
+
+ return True
+
+ def _get_values(self, value):
+ """
+ Helper to yield items from the parent iterator that match *value*.
+ Items that don't match are stored in the local cache as they
+ are encountered.
+ """
+ while True:
+ # If we've cached some items that match the target value, emit
+ # the first one and evict it from the cache.
+ if self._cache[value]:
+ yield self._cache[value].popleft()
+ # Otherwise we need to advance the parent iterator to search for
+ # a matching item, caching the rest.
+ else:
+ while True:
+ try:
+ item = next(self._it)
+ except StopIteration:
+ return
+ item_value = self._key(item)
+ if item_value == value:
+ yield item
+ break
+ elif self._validator(item_value):
+ self._cache[item_value].append(item)
+
+ def __iter__(self):
+ for item in self._it:
+ item_value = self._key(item)
+ if self._validator(item_value):
+ self._cache[item_value].append(item)
+
+ yield from self._cache.keys()
+
+ def __getitem__(self, value):
+ if not self._validator(value):
+ return iter(())
+
+ return self._get_values(value)
+
+
+def spy(iterable, n=1):
+ """Return a 2-tuple with a list containing the first *n* elements of
+ *iterable*, and an iterator with the same items as *iterable*.
+ This allows you to "look ahead" at the items in the iterable without
+ advancing it.
+
+ There is one item in the list by default:
+
+ >>> iterable = 'abcdefg'
+ >>> head, iterable = spy(iterable)
+ >>> head
+ ['a']
+ >>> list(iterable)
+ ['a', 'b', 'c', 'd', 'e', 'f', 'g']
+
+ You may use unpacking to retrieve items instead of lists:
+
+ >>> (head,), iterable = spy('abcdefg')
+ >>> head
+ 'a'
+ >>> (first, second), iterable = spy('abcdefg', 2)
+ >>> first
+ 'a'
+ >>> second
+ 'b'
+
+ The number of items requested can be larger than the number of items in
+ the iterable:
+
+ >>> iterable = [1, 2, 3, 4, 5]
+ >>> head, iterable = spy(iterable, 10)
+ >>> head
+ [1, 2, 3, 4, 5]
+ >>> list(iterable)
+ [1, 2, 3, 4, 5]
+
+ """
+ it = iter(iterable)
+ head = take(n, it)
+
+ return head.copy(), chain(head, it)
+
+
+def interleave(*iterables):
+ """Return a new iterable yielding from each iterable in turn,
+ until the shortest is exhausted.
+
+ >>> list(interleave([1, 2, 3], [4, 5], [6, 7, 8]))
+ [1, 4, 6, 2, 5, 7]
+
+ For a version that doesn't terminate after the shortest iterable is
+ exhausted, see :func:`interleave_longest`.
+
+ """
+ return chain.from_iterable(zip(*iterables))
+
+
+def interleave_longest(*iterables):
+ """Return a new iterable yielding from each iterable in turn,
+ skipping any that are exhausted.
+
+ >>> list(interleave_longest([1, 2, 3], [4, 5], [6, 7, 8]))
+ [1, 4, 6, 2, 5, 7, 3, 8]
+
+ This function produces the same output as :func:`roundrobin`, but may
+ perform better for some inputs (in particular when the number of iterables
+ is large).
+
+ """
+ i = chain.from_iterable(zip_longest(*iterables, fillvalue=_marker))
+ return (x for x in i if x is not _marker)
+
+
+def interleave_evenly(iterables, lengths=None):
+ """
+ Interleave multiple iterables so that their elements are evenly distributed
+ throughout the output sequence.
+
+ >>> iterables = [1, 2, 3, 4, 5], ['a', 'b']
+ >>> list(interleave_evenly(iterables))
+ [1, 2, 'a', 3, 4, 'b', 5]
+
+ >>> iterables = [[1, 2, 3], [4, 5], [6, 7, 8]]
+ >>> list(interleave_evenly(iterables))
+ [1, 6, 4, 2, 7, 3, 8, 5]
+
+ This function requires iterables of known length. Iterables without
+ ``__len__()`` can be used by manually specifying lengths with *lengths*:
+
+ >>> from itertools import combinations, repeat
+ >>> iterables = [combinations(range(4), 2), ['a', 'b', 'c']]
+ >>> lengths = [4 * (4 - 1) // 2, 3]
+ >>> list(interleave_evenly(iterables, lengths=lengths))
+ [(0, 1), (0, 2), 'a', (0, 3), (1, 2), 'b', (1, 3), (2, 3), 'c']
+
+ Based on Bresenham's algorithm.
+ """
+ if lengths is None:
+ try:
+ lengths = [len(it) for it in iterables]
+ except TypeError:
+ raise ValueError(
+ 'Iterable lengths could not be determined automatically. '
+ 'Specify them with the lengths keyword.'
+ )
+ elif len(iterables) != len(lengths):
+ raise ValueError('Mismatching number of iterables and lengths.')
+
+ dims = len(lengths)
+
+ # sort iterables by length, descending
+ lengths_permute = sorted(
+ range(dims), key=lambda i: lengths[i], reverse=True
+ )
+ lengths_desc = [lengths[i] for i in lengths_permute]
+ iters_desc = [iter(iterables[i]) for i in lengths_permute]
+
+ # the longest iterable is the primary one (Bresenham: the longest
+ # distance along an axis)
+ delta_primary, deltas_secondary = lengths_desc[0], lengths_desc[1:]
+ iter_primary, iters_secondary = iters_desc[0], iters_desc[1:]
+ errors = [delta_primary // dims] * len(deltas_secondary)
+
+ to_yield = sum(lengths)
+ while to_yield:
+ yield next(iter_primary)
+ to_yield -= 1
+ # update errors for each secondary iterable
+ errors = [e - delta for e, delta in zip(errors, deltas_secondary)]
+
+ # those iterables for which the error is negative are yielded
+ # ("diagonal step" in Bresenham)
+ for i, e in enumerate(errors):
+ if e < 0:
+ yield next(iters_secondary[i])
+ to_yield -= 1
+ errors[i] += delta_primary
+
+
+def collapse(iterable, base_type=None, levels=None):
+ """Flatten an iterable with multiple levels of nesting (e.g., a list of
+ lists of tuples) into non-iterable types.
+
+ >>> iterable = [(1, 2), ([3, 4], [[5], [6]])]
+ >>> list(collapse(iterable))
+ [1, 2, 3, 4, 5, 6]
+
+ Binary and text strings are not considered iterable and
+ will not be collapsed.
+
+ To avoid collapsing other types, specify *base_type*:
+
+ >>> iterable = ['ab', ('cd', 'ef'), ['gh', 'ij']]
+ >>> list(collapse(iterable, base_type=tuple))
+ ['ab', ('cd', 'ef'), 'gh', 'ij']
+
+ Specify *levels* to stop flattening after a certain level:
+
+ >>> iterable = [('a', ['b']), ('c', ['d'])]
+ >>> list(collapse(iterable)) # Fully flattened
+ ['a', 'b', 'c', 'd']
+ >>> list(collapse(iterable, levels=1)) # Only one level flattened
+ ['a', ['b'], 'c', ['d']]
+
+ """
+
+ def walk(node, level):
+ if (
+ ((levels is not None) and (level > levels))
+ or isinstance(node, (str, bytes))
+ or ((base_type is not None) and isinstance(node, base_type))
+ ):
+ yield node
+ return
+
+ try:
+ tree = iter(node)
+ except TypeError:
+ yield node
+ return
+ else:
+ for child in tree:
+ yield from walk(child, level + 1)
+
+ yield from walk(iterable, 0)
+
+
+def side_effect(func, iterable, chunk_size=None, before=None, after=None):
+ """Invoke *func* on each item in *iterable* (or on each *chunk_size* group
+ of items) before yielding the item.
+
+ `func` must be a function that takes a single argument. Its return value
+ will be discarded.
+
+ *before* and *after* are optional functions that take no arguments. They
+ will be executed before iteration starts and after it ends, respectively.
+
+ `side_effect` can be used for logging, updating progress bars, or anything
+ that is not functionally "pure."
+
+ Emitting a status message:
+
+ >>> from more_itertools import consume
+ >>> func = lambda item: print('Received {}'.format(item))
+ >>> consume(side_effect(func, range(2)))
+ Received 0
+ Received 1
+
+ Operating on chunks of items:
+
+ >>> pair_sums = []
+ >>> func = lambda chunk: pair_sums.append(sum(chunk))
+ >>> list(side_effect(func, [0, 1, 2, 3, 4, 5], 2))
+ [0, 1, 2, 3, 4, 5]
+ >>> list(pair_sums)
+ [1, 5, 9]
+
+ Writing to a file-like object:
+
+ >>> from io import StringIO
+ >>> from more_itertools import consume
+ >>> f = StringIO()
+ >>> func = lambda x: print(x, file=f)
+ >>> before = lambda: print(u'HEADER', file=f)
+ >>> after = f.close
+ >>> it = [u'a', u'b', u'c']
+ >>> consume(side_effect(func, it, before=before, after=after))
+ >>> f.closed
+ True
+
+ """
+ try:
+ if before is not None:
+ before()
+
+ if chunk_size is None:
+ for item in iterable:
+ func(item)
+ yield item
+ else:
+ for chunk in chunked(iterable, chunk_size):
+ func(chunk)
+ yield from chunk
+ finally:
+ if after is not None:
+ after()
+
+
+def sliced(seq, n, strict=False):
+ """Yield slices of length *n* from the sequence *seq*.
+
+ >>> list(sliced((1, 2, 3, 4, 5, 6), 3))
+ [(1, 2, 3), (4, 5, 6)]
+
+ By the default, the last yielded slice will have fewer than *n* elements
+ if the length of *seq* is not divisible by *n*:
+
+ >>> list(sliced((1, 2, 3, 4, 5, 6, 7, 8), 3))
+ [(1, 2, 3), (4, 5, 6), (7, 8)]
+
+ If the length of *seq* is not divisible by *n* and *strict* is
+ ``True``, then ``ValueError`` will be raised before the last
+ slice is yielded.
+
+ This function will only work for iterables that support slicing.
+ For non-sliceable iterables, see :func:`chunked`.
+
+ """
+ iterator = takewhile(len, (seq[i : i + n] for i in count(0, n)))
+ if strict:
+
+ def ret():
+ for _slice in iterator:
+ if len(_slice) != n:
+ raise ValueError("seq is not divisible by n.")
+ yield _slice
+
+ return iter(ret())
+ else:
+ return iterator
+
+
+def split_at(iterable, pred, maxsplit=-1, keep_separator=False):
+ """Yield lists of items from *iterable*, where each list is delimited by
+ an item where callable *pred* returns ``True``.
+
+ >>> list(split_at('abcdcba', lambda x: x == 'b'))
+ [['a'], ['c', 'd', 'c'], ['a']]
+
+ >>> list(split_at(range(10), lambda n: n % 2 == 1))
+ [[0], [2], [4], [6], [8], []]
+
+ At most *maxsplit* splits are done. If *maxsplit* is not specified or -1,
+ then there is no limit on the number of splits:
+
+ >>> list(split_at(range(10), lambda n: n % 2 == 1, maxsplit=2))
+ [[0], [2], [4, 5, 6, 7, 8, 9]]
+
+ By default, the delimiting items are not included in the output.
+ To include them, set *keep_separator* to ``True``.
+
+ >>> list(split_at('abcdcba', lambda x: x == 'b', keep_separator=True))
+ [['a'], ['b'], ['c', 'd', 'c'], ['b'], ['a']]
+
+ """
+ if maxsplit == 0:
+ yield list(iterable)
+ return
+
+ buf = []
+ it = iter(iterable)
+ for item in it:
+ if pred(item):
+ yield buf
+ if keep_separator:
+ yield [item]
+ if maxsplit == 1:
+ yield list(it)
+ return
+ buf = []
+ maxsplit -= 1
+ else:
+ buf.append(item)
+ yield buf
+
+
+def split_before(iterable, pred, maxsplit=-1):
+ """Yield lists of items from *iterable*, where each list ends just before
+ an item for which callable *pred* returns ``True``:
+
+ >>> list(split_before('OneTwo', lambda s: s.isupper()))
+ [['O', 'n', 'e'], ['T', 'w', 'o']]
+
+ >>> list(split_before(range(10), lambda n: n % 3 == 0))
+ [[0, 1, 2], [3, 4, 5], [6, 7, 8], [9]]
+
+ At most *maxsplit* splits are done. If *maxsplit* is not specified or -1,
+ then there is no limit on the number of splits:
+
+ >>> list(split_before(range(10), lambda n: n % 3 == 0, maxsplit=2))
+ [[0, 1, 2], [3, 4, 5], [6, 7, 8, 9]]
+ """
+ if maxsplit == 0:
+ yield list(iterable)
+ return
+
+ buf = []
+ it = iter(iterable)
+ for item in it:
+ if pred(item) and buf:
+ yield buf
+ if maxsplit == 1:
+ yield [item] + list(it)
+ return
+ buf = []
+ maxsplit -= 1
+ buf.append(item)
+ if buf:
+ yield buf
+
+
+def split_after(iterable, pred, maxsplit=-1):
+ """Yield lists of items from *iterable*, where each list ends with an
+ item where callable *pred* returns ``True``:
+
+ >>> list(split_after('one1two2', lambda s: s.isdigit()))
+ [['o', 'n', 'e', '1'], ['t', 'w', 'o', '2']]
+
+ >>> list(split_after(range(10), lambda n: n % 3 == 0))
+ [[0], [1, 2, 3], [4, 5, 6], [7, 8, 9]]
+
+ At most *maxsplit* splits are done. If *maxsplit* is not specified or -1,
+ then there is no limit on the number of splits:
+
+ >>> list(split_after(range(10), lambda n: n % 3 == 0, maxsplit=2))
+ [[0], [1, 2, 3], [4, 5, 6, 7, 8, 9]]
+
+ """
+ if maxsplit == 0:
+ yield list(iterable)
+ return
+
+ buf = []
+ it = iter(iterable)
+ for item in it:
+ buf.append(item)
+ if pred(item) and buf:
+ yield buf
+ if maxsplit == 1:
+ buf = list(it)
+ if buf:
+ yield buf
+ return
+ buf = []
+ maxsplit -= 1
+ if buf:
+ yield buf
+
+
+def split_when(iterable, pred, maxsplit=-1):
+ """Split *iterable* into pieces based on the output of *pred*.
+ *pred* should be a function that takes successive pairs of items and
+ returns ``True`` if the iterable should be split in between them.
+
+ For example, to find runs of increasing numbers, split the iterable when
+ element ``i`` is larger than element ``i + 1``:
+
+ >>> list(split_when([1, 2, 3, 3, 2, 5, 2, 4, 2], lambda x, y: x > y))
+ [[1, 2, 3, 3], [2, 5], [2, 4], [2]]
+
+ At most *maxsplit* splits are done. If *maxsplit* is not specified or -1,
+ then there is no limit on the number of splits:
+
+ >>> list(split_when([1, 2, 3, 3, 2, 5, 2, 4, 2],
+ ... lambda x, y: x > y, maxsplit=2))
+ [[1, 2, 3, 3], [2, 5], [2, 4, 2]]
+
+ """
+ if maxsplit == 0:
+ yield list(iterable)
+ return
+
+ it = iter(iterable)
+ try:
+ cur_item = next(it)
+ except StopIteration:
+ return
+
+ buf = [cur_item]
+ for next_item in it:
+ if pred(cur_item, next_item):
+ yield buf
+ if maxsplit == 1:
+ yield [next_item] + list(it)
+ return
+ buf = []
+ maxsplit -= 1
+
+ buf.append(next_item)
+ cur_item = next_item
+
+ yield buf
+
+
+def split_into(iterable, sizes):
+ """Yield a list of sequential items from *iterable* of length 'n' for each
+ integer 'n' in *sizes*.
+
+ >>> list(split_into([1,2,3,4,5,6], [1,2,3]))
+ [[1], [2, 3], [4, 5, 6]]
+
+ If the sum of *sizes* is smaller than the length of *iterable*, then the
+ remaining items of *iterable* will not be returned.
+
+ >>> list(split_into([1,2,3,4,5,6], [2,3]))
+ [[1, 2], [3, 4, 5]]
+
+ If the sum of *sizes* is larger than the length of *iterable*, fewer items
+ will be returned in the iteration that overruns *iterable* and further
+ lists will be empty:
+
+ >>> list(split_into([1,2,3,4], [1,2,3,4]))
+ [[1], [2, 3], [4], []]
+
+ When a ``None`` object is encountered in *sizes*, the returned list will
+ contain items up to the end of *iterable* the same way that itertools.slice
+ does:
+
+ >>> list(split_into([1,2,3,4,5,6,7,8,9,0], [2,3,None]))
+ [[1, 2], [3, 4, 5], [6, 7, 8, 9, 0]]
+
+ :func:`split_into` can be useful for grouping a series of items where the
+ sizes of the groups are not uniform. An example would be where in a row
+ from a table, multiple columns represent elements of the same feature
+ (e.g. a point represented by x,y,z) but, the format is not the same for
+ all columns.
+ """
+ # convert the iterable argument into an iterator so its contents can
+ # be consumed by islice in case it is a generator
+ it = iter(iterable)
+
+ for size in sizes:
+ if size is None:
+ yield list(it)
+ return
+ else:
+ yield list(islice(it, size))
+
+
+def padded(iterable, fillvalue=None, n=None, next_multiple=False):
+ """Yield the elements from *iterable*, followed by *fillvalue*, such that
+ at least *n* items are emitted.
+
+ >>> list(padded([1, 2, 3], '?', 5))
+ [1, 2, 3, '?', '?']
+
+ If *next_multiple* is ``True``, *fillvalue* will be emitted until the
+ number of items emitted is a multiple of *n*::
+
+ >>> list(padded([1, 2, 3, 4], n=3, next_multiple=True))
+ [1, 2, 3, 4, None, None]
+
+ If *n* is ``None``, *fillvalue* will be emitted indefinitely.
+
+ """
+ it = iter(iterable)
+ if n is None:
+ yield from chain(it, repeat(fillvalue))
+ elif n < 1:
+ raise ValueError('n must be at least 1')
+ else:
+ item_count = 0
+ for item in it:
+ yield item
+ item_count += 1
+
+ remaining = (n - item_count) % n if next_multiple else n - item_count
+ for _ in range(remaining):
+ yield fillvalue
+
+
+def repeat_each(iterable, n=2):
+ """Repeat each element in *iterable* *n* times.
+
+ >>> list(repeat_each('ABC', 3))
+ ['A', 'A', 'A', 'B', 'B', 'B', 'C', 'C', 'C']
+ """
+ return chain.from_iterable(map(repeat, iterable, repeat(n)))
+
+
+def repeat_last(iterable, default=None):
+ """After the *iterable* is exhausted, keep yielding its last element.
+
+ >>> list(islice(repeat_last(range(3)), 5))
+ [0, 1, 2, 2, 2]
+
+ If the iterable is empty, yield *default* forever::
+
+ >>> list(islice(repeat_last(range(0), 42), 5))
+ [42, 42, 42, 42, 42]
+
+ """
+ item = _marker
+ for item in iterable:
+ yield item
+ final = default if item is _marker else item
+ yield from repeat(final)
+
+
+def distribute(n, iterable):
+ """Distribute the items from *iterable* among *n* smaller iterables.
+
+ >>> group_1, group_2 = distribute(2, [1, 2, 3, 4, 5, 6])
+ >>> list(group_1)
+ [1, 3, 5]
+ >>> list(group_2)
+ [2, 4, 6]
+
+ If the length of *iterable* is not evenly divisible by *n*, then the
+ length of the returned iterables will not be identical:
+
+ >>> children = distribute(3, [1, 2, 3, 4, 5, 6, 7])
+ >>> [list(c) for c in children]
+ [[1, 4, 7], [2, 5], [3, 6]]
+
+ If the length of *iterable* is smaller than *n*, then the last returned
+ iterables will be empty:
+
+ >>> children = distribute(5, [1, 2, 3])
+ >>> [list(c) for c in children]
+ [[1], [2], [3], [], []]
+
+ This function uses :func:`itertools.tee` and may require significant
+ storage. If you need the order items in the smaller iterables to match the
+ original iterable, see :func:`divide`.
+
+ """
+ if n < 1:
+ raise ValueError('n must be at least 1')
+
+ children = tee(iterable, n)
+ return [islice(it, index, None, n) for index, it in enumerate(children)]
+
+
+def stagger(iterable, offsets=(-1, 0, 1), longest=False, fillvalue=None):
+ """Yield tuples whose elements are offset from *iterable*.
+ The amount by which the `i`-th item in each tuple is offset is given by
+ the `i`-th item in *offsets*.
+
+ >>> list(stagger([0, 1, 2, 3]))
+ [(None, 0, 1), (0, 1, 2), (1, 2, 3)]
+ >>> list(stagger(range(8), offsets=(0, 2, 4)))
+ [(0, 2, 4), (1, 3, 5), (2, 4, 6), (3, 5, 7)]
+
+ By default, the sequence will end when the final element of a tuple is the
+ last item in the iterable. To continue until the first element of a tuple
+ is the last item in the iterable, set *longest* to ``True``::
+
+ >>> list(stagger([0, 1, 2, 3], longest=True))
+ [(None, 0, 1), (0, 1, 2), (1, 2, 3), (2, 3, None), (3, None, None)]
+
+ By default, ``None`` will be used to replace offsets beyond the end of the
+ sequence. Specify *fillvalue* to use some other value.
+
+ """
+ children = tee(iterable, len(offsets))
+
+ return zip_offset(
+ *children, offsets=offsets, longest=longest, fillvalue=fillvalue
+ )
+
+
+def zip_equal(*iterables):
+ """``zip`` the input *iterables* together, but raise
+ ``UnequalIterablesError`` if they aren't all the same length.
+
+ >>> it_1 = range(3)
+ >>> it_2 = iter('abc')
+ >>> list(zip_equal(it_1, it_2))
+ [(0, 'a'), (1, 'b'), (2, 'c')]
+
+ >>> it_1 = range(3)
+ >>> it_2 = iter('abcd')
+ >>> list(zip_equal(it_1, it_2)) # doctest: +IGNORE_EXCEPTION_DETAIL
+ Traceback (most recent call last):
+ ...
+ more_itertools.more.UnequalIterablesError: Iterables have different
+ lengths
+
+ """
+ if hexversion >= 0x30A00A6:
+ warnings.warn(
+ (
+ 'zip_equal will be removed in a future version of '
+ 'more-itertools. Use the builtin zip function with '
+ 'strict=True instead.'
+ ),
+ DeprecationWarning,
+ )
+
+ return _zip_equal(*iterables)
+
+
+def zip_offset(*iterables, offsets, longest=False, fillvalue=None):
+ """``zip`` the input *iterables* together, but offset the `i`-th iterable
+ by the `i`-th item in *offsets*.
+
+ >>> list(zip_offset('0123', 'abcdef', offsets=(0, 1)))
+ [('0', 'b'), ('1', 'c'), ('2', 'd'), ('3', 'e')]
+
+ This can be used as a lightweight alternative to SciPy or pandas to analyze
+ data sets in which some series have a lead or lag relationship.
+
+ By default, the sequence will end when the shortest iterable is exhausted.
+ To continue until the longest iterable is exhausted, set *longest* to
+ ``True``.
+
+ >>> list(zip_offset('0123', 'abcdef', offsets=(0, 1), longest=True))
+ [('0', 'b'), ('1', 'c'), ('2', 'd'), ('3', 'e'), (None, 'f')]
+
+ By default, ``None`` will be used to replace offsets beyond the end of the
+ sequence. Specify *fillvalue* to use some other value.
+
+ """
+ if len(iterables) != len(offsets):
+ raise ValueError("Number of iterables and offsets didn't match")
+
+ staggered = []
+ for it, n in zip(iterables, offsets):
+ if n < 0:
+ staggered.append(chain(repeat(fillvalue, -n), it))
+ elif n > 0:
+ staggered.append(islice(it, n, None))
+ else:
+ staggered.append(it)
+
+ if longest:
+ return zip_longest(*staggered, fillvalue=fillvalue)
+
+ return zip(*staggered)
+
+
+def sort_together(iterables, key_list=(0,), key=None, reverse=False):
+ """Return the input iterables sorted together, with *key_list* as the
+ priority for sorting. All iterables are trimmed to the length of the
+ shortest one.
+
+ This can be used like the sorting function in a spreadsheet. If each
+ iterable represents a column of data, the key list determines which
+ columns are used for sorting.
+
+ By default, all iterables are sorted using the ``0``-th iterable::
+
+ >>> iterables = [(4, 3, 2, 1), ('a', 'b', 'c', 'd')]
+ >>> sort_together(iterables)
+ [(1, 2, 3, 4), ('d', 'c', 'b', 'a')]
+
+ Set a different key list to sort according to another iterable.
+ Specifying multiple keys dictates how ties are broken::
+
+ >>> iterables = [(3, 1, 2), (0, 1, 0), ('c', 'b', 'a')]
+ >>> sort_together(iterables, key_list=(1, 2))
+ [(2, 3, 1), (0, 0, 1), ('a', 'c', 'b')]
+
+ To sort by a function of the elements of the iterable, pass a *key*
+ function. Its arguments are the elements of the iterables corresponding to
+ the key list::
+
+ >>> names = ('a', 'b', 'c')
+ >>> lengths = (1, 2, 3)
+ >>> widths = (5, 2, 1)
+ >>> def area(length, width):
+ ... return length * width
+ >>> sort_together([names, lengths, widths], key_list=(1, 2), key=area)
+ [('c', 'b', 'a'), (3, 2, 1), (1, 2, 5)]
+
+ Set *reverse* to ``True`` to sort in descending order.
+
+ >>> sort_together([(1, 2, 3), ('c', 'b', 'a')], reverse=True)
+ [(3, 2, 1), ('a', 'b', 'c')]
+
+ """
+ if key is None:
+ # if there is no key function, the key argument to sorted is an
+ # itemgetter
+ key_argument = itemgetter(*key_list)
+ else:
+ # if there is a key function, call it with the items at the offsets
+ # specified by the key function as arguments
+ key_list = list(key_list)
+ if len(key_list) == 1:
+ # if key_list contains a single item, pass the item at that offset
+ # as the only argument to the key function
+ key_offset = key_list[0]
+ key_argument = lambda zipped_items: key(zipped_items[key_offset])
+ else:
+ # if key_list contains multiple items, use itemgetter to return a
+ # tuple of items, which we pass as *args to the key function
+ get_key_items = itemgetter(*key_list)
+ key_argument = lambda zipped_items: key(
+ *get_key_items(zipped_items)
+ )
+
+ return list(
+ zip(*sorted(zip(*iterables), key=key_argument, reverse=reverse))
+ )
+
+
+def unzip(iterable):
+ """The inverse of :func:`zip`, this function disaggregates the elements
+ of the zipped *iterable*.
+
+ The ``i``-th iterable contains the ``i``-th element from each element
+ of the zipped iterable. The first element is used to determine the
+ length of the remaining elements.
+
+ >>> iterable = [('a', 1), ('b', 2), ('c', 3), ('d', 4)]
+ >>> letters, numbers = unzip(iterable)
+ >>> list(letters)
+ ['a', 'b', 'c', 'd']
+ >>> list(numbers)
+ [1, 2, 3, 4]
+
+ This is similar to using ``zip(*iterable)``, but it avoids reading
+ *iterable* into memory. Note, however, that this function uses
+ :func:`itertools.tee` and thus may require significant storage.
+
+ """
+ head, iterable = spy(iter(iterable))
+ if not head:
+ # empty iterable, e.g. zip([], [], [])
+ return ()
+ # spy returns a one-length iterable as head
+ head = head[0]
+ iterables = tee(iterable, len(head))
+
+ def itemgetter(i):
+ def getter(obj):
+ try:
+ return obj[i]
+ except IndexError:
+ # basically if we have an iterable like
+ # iter([(1, 2, 3), (4, 5), (6,)])
+ # the second unzipped iterable would fail at the third tuple
+ # since it would try to access tup[1]
+ # same with the third unzipped iterable and the second tuple
+ # to support these "improperly zipped" iterables,
+ # we create a custom itemgetter
+ # which just stops the unzipped iterables
+ # at first length mismatch
+ raise StopIteration
+
+ return getter
+
+ return tuple(map(itemgetter(i), it) for i, it in enumerate(iterables))
+
+
+def divide(n, iterable):
+ """Divide the elements from *iterable* into *n* parts, maintaining
+ order.
+
+ >>> group_1, group_2 = divide(2, [1, 2, 3, 4, 5, 6])
+ >>> list(group_1)
+ [1, 2, 3]
+ >>> list(group_2)
+ [4, 5, 6]
+
+ If the length of *iterable* is not evenly divisible by *n*, then the
+ length of the returned iterables will not be identical:
+
+ >>> children = divide(3, [1, 2, 3, 4, 5, 6, 7])
+ >>> [list(c) for c in children]
+ [[1, 2, 3], [4, 5], [6, 7]]
+
+ If the length of the iterable is smaller than n, then the last returned
+ iterables will be empty:
+
+ >>> children = divide(5, [1, 2, 3])
+ >>> [list(c) for c in children]
+ [[1], [2], [3], [], []]
+
+ This function will exhaust the iterable before returning and may require
+ significant storage. If order is not important, see :func:`distribute`,
+ which does not first pull the iterable into memory.
+
+ """
+ if n < 1:
+ raise ValueError('n must be at least 1')
+
+ try:
+ iterable[:0]
+ except TypeError:
+ seq = tuple(iterable)
+ else:
+ seq = iterable
+
+ q, r = divmod(len(seq), n)
+
+ ret = []
+ stop = 0
+ for i in range(1, n + 1):
+ start = stop
+ stop += q + 1 if i <= r else q
+ ret.append(iter(seq[start:stop]))
+
+ return ret
+
+
+def always_iterable(obj, base_type=(str, bytes)):
+ """If *obj* is iterable, return an iterator over its items::
+
+ >>> obj = (1, 2, 3)
+ >>> list(always_iterable(obj))
+ [1, 2, 3]
+
+ If *obj* is not iterable, return a one-item iterable containing *obj*::
+
+ >>> obj = 1
+ >>> list(always_iterable(obj))
+ [1]
+
+ If *obj* is ``None``, return an empty iterable:
+
+ >>> obj = None
+ >>> list(always_iterable(None))
+ []
+
+ By default, binary and text strings are not considered iterable::
+
+ >>> obj = 'foo'
+ >>> list(always_iterable(obj))
+ ['foo']
+
+ If *base_type* is set, objects for which ``isinstance(obj, base_type)``
+ returns ``True`` won't be considered iterable.
+
+ >>> obj = {'a': 1}
+ >>> list(always_iterable(obj)) # Iterate over the dict's keys
+ ['a']
+ >>> list(always_iterable(obj, base_type=dict)) # Treat dicts as a unit
+ [{'a': 1}]
+
+ Set *base_type* to ``None`` to avoid any special handling and treat objects
+ Python considers iterable as iterable:
+
+ >>> obj = 'foo'
+ >>> list(always_iterable(obj, base_type=None))
+ ['f', 'o', 'o']
+ """
+ if obj is None:
+ return iter(())
+
+ if (base_type is not None) and isinstance(obj, base_type):
+ return iter((obj,))
+
+ try:
+ return iter(obj)
+ except TypeError:
+ return iter((obj,))
+
+
+def adjacent(predicate, iterable, distance=1):
+ """Return an iterable over `(bool, item)` tuples where the `item` is
+ drawn from *iterable* and the `bool` indicates whether
+ that item satisfies the *predicate* or is adjacent to an item that does.
+
+ For example, to find whether items are adjacent to a ``3``::
+
+ >>> list(adjacent(lambda x: x == 3, range(6)))
+ [(False, 0), (False, 1), (True, 2), (True, 3), (True, 4), (False, 5)]
+
+ Set *distance* to change what counts as adjacent. For example, to find
+ whether items are two places away from a ``3``:
+
+ >>> list(adjacent(lambda x: x == 3, range(6), distance=2))
+ [(False, 0), (True, 1), (True, 2), (True, 3), (True, 4), (True, 5)]
+
+ This is useful for contextualizing the results of a search function.
+ For example, a code comparison tool might want to identify lines that
+ have changed, but also surrounding lines to give the viewer of the diff
+ context.
+
+ The predicate function will only be called once for each item in the
+ iterable.
+
+ See also :func:`groupby_transform`, which can be used with this function
+ to group ranges of items with the same `bool` value.
+
+ """
+ # Allow distance=0 mainly for testing that it reproduces results with map()
+ if distance < 0:
+ raise ValueError('distance must be at least 0')
+
+ i1, i2 = tee(iterable)
+ padding = [False] * distance
+ selected = chain(padding, map(predicate, i1), padding)
+ adjacent_to_selected = map(any, windowed(selected, 2 * distance + 1))
+ return zip(adjacent_to_selected, i2)
+
+
+def groupby_transform(iterable, keyfunc=None, valuefunc=None, reducefunc=None):
+ """An extension of :func:`itertools.groupby` that can apply transformations
+ to the grouped data.
+
+ * *keyfunc* is a function computing a key value for each item in *iterable*
+ * *valuefunc* is a function that transforms the individual items from
+ *iterable* after grouping
+ * *reducefunc* is a function that transforms each group of items
+
+ >>> iterable = 'aAAbBBcCC'
+ >>> keyfunc = lambda k: k.upper()
+ >>> valuefunc = lambda v: v.lower()
+ >>> reducefunc = lambda g: ''.join(g)
+ >>> list(groupby_transform(iterable, keyfunc, valuefunc, reducefunc))
+ [('A', 'aaa'), ('B', 'bbb'), ('C', 'ccc')]
+
+ Each optional argument defaults to an identity function if not specified.
+
+ :func:`groupby_transform` is useful when grouping elements of an iterable
+ using a separate iterable as the key. To do this, :func:`zip` the iterables
+ and pass a *keyfunc* that extracts the first element and a *valuefunc*
+ that extracts the second element::
+
+ >>> from operator import itemgetter
+ >>> keys = [0, 0, 1, 1, 1, 2, 2, 2, 3]
+ >>> values = 'abcdefghi'
+ >>> iterable = zip(keys, values)
+ >>> grouper = groupby_transform(iterable, itemgetter(0), itemgetter(1))
+ >>> [(k, ''.join(g)) for k, g in grouper]
+ [(0, 'ab'), (1, 'cde'), (2, 'fgh'), (3, 'i')]
+
+ Note that the order of items in the iterable is significant.
+ Only adjacent items are grouped together, so if you don't want any
+ duplicate groups, you should sort the iterable by the key function.
+
+ """
+ ret = groupby(iterable, keyfunc)
+ if valuefunc:
+ ret = ((k, map(valuefunc, g)) for k, g in ret)
+ if reducefunc:
+ ret = ((k, reducefunc(g)) for k, g in ret)
+
+ return ret
+
+
+class numeric_range(abc.Sequence, abc.Hashable):
+ """An extension of the built-in ``range()`` function whose arguments can
+ be any orderable numeric type.
+
+ With only *stop* specified, *start* defaults to ``0`` and *step*
+ defaults to ``1``. The output items will match the type of *stop*:
+
+ >>> list(numeric_range(3.5))
+ [0.0, 1.0, 2.0, 3.0]
+
+ With only *start* and *stop* specified, *step* defaults to ``1``. The
+ output items will match the type of *start*:
+
+ >>> from decimal import Decimal
+ >>> start = Decimal('2.1')
+ >>> stop = Decimal('5.1')
+ >>> list(numeric_range(start, stop))
+ [Decimal('2.1'), Decimal('3.1'), Decimal('4.1')]
+
+ With *start*, *stop*, and *step* specified the output items will match
+ the type of ``start + step``:
+
+ >>> from fractions import Fraction
+ >>> start = Fraction(1, 2) # Start at 1/2
+ >>> stop = Fraction(5, 2) # End at 5/2
+ >>> step = Fraction(1, 2) # Count by 1/2
+ >>> list(numeric_range(start, stop, step))
+ [Fraction(1, 2), Fraction(1, 1), Fraction(3, 2), Fraction(2, 1)]
+
+ If *step* is zero, ``ValueError`` is raised. Negative steps are supported:
+
+ >>> list(numeric_range(3, -1, -1.0))
+ [3.0, 2.0, 1.0, 0.0]
+
+ Be aware of the limitations of floating point numbers; the representation
+ of the yielded numbers may be surprising.
+
+ ``datetime.datetime`` objects can be used for *start* and *stop*, if *step*
+ is a ``datetime.timedelta`` object:
+
+ >>> import datetime
+ >>> start = datetime.datetime(2019, 1, 1)
+ >>> stop = datetime.datetime(2019, 1, 3)
+ >>> step = datetime.timedelta(days=1)
+ >>> items = iter(numeric_range(start, stop, step))
+ >>> next(items)
+ datetime.datetime(2019, 1, 1, 0, 0)
+ >>> next(items)
+ datetime.datetime(2019, 1, 2, 0, 0)
+
+ """
+
+ _EMPTY_HASH = hash(range(0, 0))
+
+ def __init__(self, *args):
+ argc = len(args)
+ if argc == 1:
+ (self._stop,) = args
+ self._start = type(self._stop)(0)
+ self._step = type(self._stop - self._start)(1)
+ elif argc == 2:
+ self._start, self._stop = args
+ self._step = type(self._stop - self._start)(1)
+ elif argc == 3:
+ self._start, self._stop, self._step = args
+ elif argc == 0:
+ raise TypeError(
+ 'numeric_range expected at least '
+ '1 argument, got {}'.format(argc)
+ )
+ else:
+ raise TypeError(
+ 'numeric_range expected at most '
+ '3 arguments, got {}'.format(argc)
+ )
+
+ self._zero = type(self._step)(0)
+ if self._step == self._zero:
+ raise ValueError('numeric_range() arg 3 must not be zero')
+ self._growing = self._step > self._zero
+
+ def __bool__(self):
+ if self._growing:
+ return self._start < self._stop
+ else:
+ return self._start > self._stop
+
+ def __contains__(self, elem):
+ if self._growing:
+ if self._start <= elem < self._stop:
+ return (elem - self._start) % self._step == self._zero
+ else:
+ if self._start >= elem > self._stop:
+ return (self._start - elem) % (-self._step) == self._zero
+
+ return False
+
+ def __eq__(self, other):
+ if isinstance(other, numeric_range):
+ empty_self = not bool(self)
+ empty_other = not bool(other)
+ if empty_self or empty_other:
+ return empty_self and empty_other # True if both empty
+ else:
+ return (
+ self._start == other._start
+ and self._step == other._step
+ and self._get_by_index(-1) == other._get_by_index(-1)
+ )
+ else:
+ return False
+
+ def __getitem__(self, key):
+ if isinstance(key, int):
+ return self._get_by_index(key)
+ elif isinstance(key, slice):
+ step = self._step if key.step is None else key.step * self._step
+
+ if key.start is None or key.start <= -self._len:
+ start = self._start
+ elif key.start >= self._len:
+ start = self._stop
+ else: # -self._len < key.start < self._len
+ start = self._get_by_index(key.start)
+
+ if key.stop is None or key.stop >= self._len:
+ stop = self._stop
+ elif key.stop <= -self._len:
+ stop = self._start
+ else: # -self._len < key.stop < self._len
+ stop = self._get_by_index(key.stop)
+
+ return numeric_range(start, stop, step)
+ else:
+ raise TypeError(
+ 'numeric range indices must be '
+ 'integers or slices, not {}'.format(type(key).__name__)
+ )
+
+ def __hash__(self):
+ if self:
+ return hash((self._start, self._get_by_index(-1), self._step))
+ else:
+ return self._EMPTY_HASH
+
+ def __iter__(self):
+ values = (self._start + (n * self._step) for n in count())
+ if self._growing:
+ return takewhile(partial(gt, self._stop), values)
+ else:
+ return takewhile(partial(lt, self._stop), values)
+
+ def __len__(self):
+ return self._len
+
+ @cached_property
+ def _len(self):
+ if self._growing:
+ start = self._start
+ stop = self._stop
+ step = self._step
+ else:
+ start = self._stop
+ stop = self._start
+ step = -self._step
+ distance = stop - start
+ if distance <= self._zero:
+ return 0
+ else: # distance > 0 and step > 0: regular euclidean division
+ q, r = divmod(distance, step)
+ return int(q) + int(r != self._zero)
+
+ def __reduce__(self):
+ return numeric_range, (self._start, self._stop, self._step)
+
+ def __repr__(self):
+ if self._step == 1:
+ return "numeric_range({}, {})".format(
+ repr(self._start), repr(self._stop)
+ )
+ else:
+ return "numeric_range({}, {}, {})".format(
+ repr(self._start), repr(self._stop), repr(self._step)
+ )
+
+ def __reversed__(self):
+ return iter(
+ numeric_range(
+ self._get_by_index(-1), self._start - self._step, -self._step
+ )
+ )
+
+ def count(self, value):
+ return int(value in self)
+
+ def index(self, value):
+ if self._growing:
+ if self._start <= value < self._stop:
+ q, r = divmod(value - self._start, self._step)
+ if r == self._zero:
+ return int(q)
+ else:
+ if self._start >= value > self._stop:
+ q, r = divmod(self._start - value, -self._step)
+ if r == self._zero:
+ return int(q)
+
+ raise ValueError("{} is not in numeric range".format(value))
+
+ def _get_by_index(self, i):
+ if i < 0:
+ i += self._len
+ if i < 0 or i >= self._len:
+ raise IndexError("numeric range object index out of range")
+ return self._start + i * self._step
+
+
+def count_cycle(iterable, n=None):
+ """Cycle through the items from *iterable* up to *n* times, yielding
+ the number of completed cycles along with each item. If *n* is omitted the
+ process repeats indefinitely.
+
+ >>> list(count_cycle('AB', 3))
+ [(0, 'A'), (0, 'B'), (1, 'A'), (1, 'B'), (2, 'A'), (2, 'B')]
+
+ """
+ iterable = tuple(iterable)
+ if not iterable:
+ return iter(())
+ counter = count() if n is None else range(n)
+ return ((i, item) for i in counter for item in iterable)
+
+
+def mark_ends(iterable):
+ """Yield 3-tuples of the form ``(is_first, is_last, item)``.
+
+ >>> list(mark_ends('ABC'))
+ [(True, False, 'A'), (False, False, 'B'), (False, True, 'C')]
+
+ Use this when looping over an iterable to take special action on its first
+ and/or last items:
+
+ >>> iterable = ['Header', 100, 200, 'Footer']
+ >>> total = 0
+ >>> for is_first, is_last, item in mark_ends(iterable):
+ ... if is_first:
+ ... continue # Skip the header
+ ... if is_last:
+ ... continue # Skip the footer
+ ... total += item
+ >>> print(total)
+ 300
+ """
+ it = iter(iterable)
+
+ try:
+ b = next(it)
+ except StopIteration:
+ return
+
+ try:
+ for i in count():
+ a = b
+ b = next(it)
+ yield i == 0, False, a
+
+ except StopIteration:
+ yield i == 0, True, a
+
+
+def locate(iterable, pred=bool, window_size=None):
+ """Yield the index of each item in *iterable* for which *pred* returns
+ ``True``.
+
+ *pred* defaults to :func:`bool`, which will select truthy items:
+
+ >>> list(locate([0, 1, 1, 0, 1, 0, 0]))
+ [1, 2, 4]
+
+ Set *pred* to a custom function to, e.g., find the indexes for a particular
+ item.
+
+ >>> list(locate(['a', 'b', 'c', 'b'], lambda x: x == 'b'))
+ [1, 3]
+
+ If *window_size* is given, then the *pred* function will be called with
+ that many items. This enables searching for sub-sequences:
+
+ >>> iterable = [0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]
+ >>> pred = lambda *args: args == (1, 2, 3)
+ >>> list(locate(iterable, pred=pred, window_size=3))
+ [1, 5, 9]
+
+ Use with :func:`seekable` to find indexes and then retrieve the associated
+ items:
+
+ >>> from itertools import count
+ >>> from more_itertools import seekable
+ >>> source = (3 * n + 1 if (n % 2) else n // 2 for n in count())
+ >>> it = seekable(source)
+ >>> pred = lambda x: x > 100
+ >>> indexes = locate(it, pred=pred)
+ >>> i = next(indexes)
+ >>> it.seek(i)
+ >>> next(it)
+ 106
+
+ """
+ if window_size is None:
+ return compress(count(), map(pred, iterable))
+
+ if window_size < 1:
+ raise ValueError('window size must be at least 1')
+
+ it = windowed(iterable, window_size, fillvalue=_marker)
+ return compress(count(), starmap(pred, it))
+
+
+def longest_common_prefix(iterables):
+ """Yield elements of the longest common prefix amongst given *iterables*.
+
+ >>> ''.join(longest_common_prefix(['abcd', 'abc', 'abf']))
+ 'ab'
+
+ """
+ return (c[0] for c in takewhile(all_equal, zip(*iterables)))
+
+
+def lstrip(iterable, pred):
+ """Yield the items from *iterable*, but strip any from the beginning
+ for which *pred* returns ``True``.
+
+ For example, to remove a set of items from the start of an iterable:
+
+ >>> iterable = (None, False, None, 1, 2, None, 3, False, None)
+ >>> pred = lambda x: x in {None, False, ''}
+ >>> list(lstrip(iterable, pred))
+ [1, 2, None, 3, False, None]
+
+ This function is analogous to to :func:`str.lstrip`, and is essentially
+ an wrapper for :func:`itertools.dropwhile`.
+
+ """
+ return dropwhile(pred, iterable)
+
+
+def rstrip(iterable, pred):
+ """Yield the items from *iterable*, but strip any from the end
+ for which *pred* returns ``True``.
+
+ For example, to remove a set of items from the end of an iterable:
+
+ >>> iterable = (None, False, None, 1, 2, None, 3, False, None)
+ >>> pred = lambda x: x in {None, False, ''}
+ >>> list(rstrip(iterable, pred))
+ [None, False, None, 1, 2, None, 3]
+
+ This function is analogous to :func:`str.rstrip`.
+
+ """
+ cache = []
+ cache_append = cache.append
+ cache_clear = cache.clear
+ for x in iterable:
+ if pred(x):
+ cache_append(x)
+ else:
+ yield from cache
+ cache_clear()
+ yield x
+
+
+def strip(iterable, pred):
+ """Yield the items from *iterable*, but strip any from the
+ beginning and end for which *pred* returns ``True``.
+
+ For example, to remove a set of items from both ends of an iterable:
+
+ >>> iterable = (None, False, None, 1, 2, None, 3, False, None)
+ >>> pred = lambda x: x in {None, False, ''}
+ >>> list(strip(iterable, pred))
+ [1, 2, None, 3]
+
+ This function is analogous to :func:`str.strip`.
+
+ """
+ return rstrip(lstrip(iterable, pred), pred)
+
+
+class islice_extended:
+ """An extension of :func:`itertools.islice` that supports negative values
+ for *stop*, *start*, and *step*.
+
+ >>> iterable = iter('abcdefgh')
+ >>> list(islice_extended(iterable, -4, -1))
+ ['e', 'f', 'g']
+
+ Slices with negative values require some caching of *iterable*, but this
+ function takes care to minimize the amount of memory required.
+
+ For example, you can use a negative step with an infinite iterator:
+
+ >>> from itertools import count
+ >>> list(islice_extended(count(), 110, 99, -2))
+ [110, 108, 106, 104, 102, 100]
+
+ You can also use slice notation directly:
+
+ >>> iterable = map(str, count())
+ >>> it = islice_extended(iterable)[10:20:2]
+ >>> list(it)
+ ['10', '12', '14', '16', '18']
+
+ """
+
+ def __init__(self, iterable, *args):
+ it = iter(iterable)
+ if args:
+ self._iterable = _islice_helper(it, slice(*args))
+ else:
+ self._iterable = it
+
+ def __iter__(self):
+ return self
+
+ def __next__(self):
+ return next(self._iterable)
+
+ def __getitem__(self, key):
+ if isinstance(key, slice):
+ return islice_extended(_islice_helper(self._iterable, key))
+
+ raise TypeError('islice_extended.__getitem__ argument must be a slice')
+
+
+def _islice_helper(it, s):
+ start = s.start
+ stop = s.stop
+ if s.step == 0:
+ raise ValueError('step argument must be a non-zero integer or None.')
+ step = s.step or 1
+
+ if step > 0:
+ start = 0 if (start is None) else start
+
+ if start < 0:
+ # Consume all but the last -start items
+ cache = deque(enumerate(it, 1), maxlen=-start)
+ len_iter = cache[-1][0] if cache else 0
+
+ # Adjust start to be positive
+ i = max(len_iter + start, 0)
+
+ # Adjust stop to be positive
+ if stop is None:
+ j = len_iter
+ elif stop >= 0:
+ j = min(stop, len_iter)
+ else:
+ j = max(len_iter + stop, 0)
+
+ # Slice the cache
+ n = j - i
+ if n <= 0:
+ return
+
+ for index, item in islice(cache, 0, n, step):
+ yield item
+ elif (stop is not None) and (stop < 0):
+ # Advance to the start position
+ next(islice(it, start, start), None)
+
+ # When stop is negative, we have to carry -stop items while
+ # iterating
+ cache = deque(islice(it, -stop), maxlen=-stop)
+
+ for index, item in enumerate(it):
+ cached_item = cache.popleft()
+ if index % step == 0:
+ yield cached_item
+ cache.append(item)
+ else:
+ # When both start and stop are positive we have the normal case
+ yield from islice(it, start, stop, step)
+ else:
+ start = -1 if (start is None) else start
+
+ if (stop is not None) and (stop < 0):
+ # Consume all but the last items
+ n = -stop - 1
+ cache = deque(enumerate(it, 1), maxlen=n)
+ len_iter = cache[-1][0] if cache else 0
+
+ # If start and stop are both negative they are comparable and
+ # we can just slice. Otherwise we can adjust start to be negative
+ # and then slice.
+ if start < 0:
+ i, j = start, stop
+ else:
+ i, j = min(start - len_iter, -1), None
+
+ for index, item in list(cache)[i:j:step]:
+ yield item
+ else:
+ # Advance to the stop position
+ if stop is not None:
+ m = stop + 1
+ next(islice(it, m, m), None)
+
+ # stop is positive, so if start is negative they are not comparable
+ # and we need the rest of the items.
+ if start < 0:
+ i = start
+ n = None
+ # stop is None and start is positive, so we just need items up to
+ # the start index.
+ elif stop is None:
+ i = None
+ n = start + 1
+ # Both stop and start are positive, so they are comparable.
+ else:
+ i = None
+ n = start - stop
+ if n <= 0:
+ return
+
+ cache = list(islice(it, n))
+
+ yield from cache[i::step]
+
+
+def always_reversible(iterable):
+ """An extension of :func:`reversed` that supports all iterables, not
+ just those which implement the ``Reversible`` or ``Sequence`` protocols.
+
+ >>> print(*always_reversible(x for x in range(3)))
+ 2 1 0
+
+ If the iterable is already reversible, this function returns the
+ result of :func:`reversed()`. If the iterable is not reversible,
+ this function will cache the remaining items in the iterable and
+ yield them in reverse order, which may require significant storage.
+ """
+ try:
+ return reversed(iterable)
+ except TypeError:
+ return reversed(list(iterable))
+
+
+def consecutive_groups(iterable, ordering=lambda x: x):
+ """Yield groups of consecutive items using :func:`itertools.groupby`.
+ The *ordering* function determines whether two items are adjacent by
+ returning their position.
+
+ By default, the ordering function is the identity function. This is
+ suitable for finding runs of numbers:
+
+ >>> iterable = [1, 10, 11, 12, 20, 30, 31, 32, 33, 40]
+ >>> for group in consecutive_groups(iterable):
+ ... print(list(group))
+ [1]
+ [10, 11, 12]
+ [20]
+ [30, 31, 32, 33]
+ [40]
+
+ For finding runs of adjacent letters, try using the :meth:`index` method
+ of a string of letters:
+
+ >>> from string import ascii_lowercase
+ >>> iterable = 'abcdfgilmnop'
+ >>> ordering = ascii_lowercase.index
+ >>> for group in consecutive_groups(iterable, ordering):
+ ... print(list(group))
+ ['a', 'b', 'c', 'd']
+ ['f', 'g']
+ ['i']
+ ['l', 'm', 'n', 'o', 'p']
+
+ Each group of consecutive items is an iterator that shares it source with
+ *iterable*. When an an output group is advanced, the previous group is
+ no longer available unless its elements are copied (e.g., into a ``list``).
+
+ >>> iterable = [1, 2, 11, 12, 21, 22]
+ >>> saved_groups = []
+ >>> for group in consecutive_groups(iterable):
+ ... saved_groups.append(list(group)) # Copy group elements
+ >>> saved_groups
+ [[1, 2], [11, 12], [21, 22]]
+
+ """
+ for k, g in groupby(
+ enumerate(iterable), key=lambda x: x[0] - ordering(x[1])
+ ):
+ yield map(itemgetter(1), g)
+
+
+def difference(iterable, func=sub, *, initial=None):
+ """This function is the inverse of :func:`itertools.accumulate`. By default
+ it will compute the first difference of *iterable* using
+ :func:`operator.sub`:
+
+ >>> from itertools import accumulate
+ >>> iterable = accumulate([0, 1, 2, 3, 4]) # produces 0, 1, 3, 6, 10
+ >>> list(difference(iterable))
+ [0, 1, 2, 3, 4]
+
+ *func* defaults to :func:`operator.sub`, but other functions can be
+ specified. They will be applied as follows::
+
+ A, B, C, D, ... --> A, func(B, A), func(C, B), func(D, C), ...
+
+ For example, to do progressive division:
+
+ >>> iterable = [1, 2, 6, 24, 120]
+ >>> func = lambda x, y: x // y
+ >>> list(difference(iterable, func))
+ [1, 2, 3, 4, 5]
+
+ If the *initial* keyword is set, the first element will be skipped when
+ computing successive differences.
+
+ >>> it = [10, 11, 13, 16] # from accumulate([1, 2, 3], initial=10)
+ >>> list(difference(it, initial=10))
+ [1, 2, 3]
+
+ """
+ a, b = tee(iterable)
+ try:
+ first = [next(b)]
+ except StopIteration:
+ return iter([])
+
+ if initial is not None:
+ first = []
+
+ return chain(first, map(func, b, a))
+
+
+class SequenceView(Sequence):
+ """Return a read-only view of the sequence object *target*.
+
+ :class:`SequenceView` objects are analogous to Python's built-in
+ "dictionary view" types. They provide a dynamic view of a sequence's items,
+ meaning that when the sequence updates, so does the view.
+
+ >>> seq = ['0', '1', '2']
+ >>> view = SequenceView(seq)
+ >>> view
+ SequenceView(['0', '1', '2'])
+ >>> seq.append('3')
+ >>> view
+ SequenceView(['0', '1', '2', '3'])
+
+ Sequence views support indexing, slicing, and length queries. They act
+ like the underlying sequence, except they don't allow assignment:
+
+ >>> view[1]
+ '1'
+ >>> view[1:-1]
+ ['1', '2']
+ >>> len(view)
+ 4
+
+ Sequence views are useful as an alternative to copying, as they don't
+ require (much) extra storage.
+
+ """
+
+ def __init__(self, target):
+ if not isinstance(target, Sequence):
+ raise TypeError
+ self._target = target
+
+ def __getitem__(self, index):
+ return self._target[index]
+
+ def __len__(self):
+ return len(self._target)
+
+ def __repr__(self):
+ return '{}({})'.format(self.__class__.__name__, repr(self._target))
+
+
+class seekable:
+ """Wrap an iterator to allow for seeking backward and forward. This
+ progressively caches the items in the source iterable so they can be
+ re-visited.
+
+ Call :meth:`seek` with an index to seek to that position in the source
+ iterable.
+
+ To "reset" an iterator, seek to ``0``:
+
+ >>> from itertools import count
+ >>> it = seekable((str(n) for n in count()))
+ >>> next(it), next(it), next(it)
+ ('0', '1', '2')
+ >>> it.seek(0)
+ >>> next(it), next(it), next(it)
+ ('0', '1', '2')
+ >>> next(it)
+ '3'
+
+ You can also seek forward:
+
+ >>> it = seekable((str(n) for n in range(20)))
+ >>> it.seek(10)
+ >>> next(it)
+ '10'
+ >>> it.relative_seek(-2) # Seeking relative to the current position
+ >>> next(it)
+ '9'
+ >>> it.seek(20) # Seeking past the end of the source isn't a problem
+ >>> list(it)
+ []
+ >>> it.seek(0) # Resetting works even after hitting the end
+ >>> next(it), next(it), next(it)
+ ('0', '1', '2')
+
+ Call :meth:`peek` to look ahead one item without advancing the iterator:
+
+ >>> it = seekable('1234')
+ >>> it.peek()
+ '1'
+ >>> list(it)
+ ['1', '2', '3', '4']
+ >>> it.peek(default='empty')
+ 'empty'
+
+ Before the iterator is at its end, calling :func:`bool` on it will return
+ ``True``. After it will return ``False``:
+
+ >>> it = seekable('5678')
+ >>> bool(it)
+ True
+ >>> list(it)
+ ['5', '6', '7', '8']
+ >>> bool(it)
+ False
+
+ You may view the contents of the cache with the :meth:`elements` method.
+ That returns a :class:`SequenceView`, a view that updates automatically:
+
+ >>> it = seekable((str(n) for n in range(10)))
+ >>> next(it), next(it), next(it)
+ ('0', '1', '2')
+ >>> elements = it.elements()
+ >>> elements
+ SequenceView(['0', '1', '2'])
+ >>> next(it)
+ '3'
+ >>> elements
+ SequenceView(['0', '1', '2', '3'])
+
+ By default, the cache grows as the source iterable progresses, so beware of
+ wrapping very large or infinite iterables. Supply *maxlen* to limit the
+ size of the cache (this of course limits how far back you can seek).
+
+ >>> from itertools import count
+ >>> it = seekable((str(n) for n in count()), maxlen=2)
+ >>> next(it), next(it), next(it), next(it)
+ ('0', '1', '2', '3')
+ >>> list(it.elements())
+ ['2', '3']
+ >>> it.seek(0)
+ >>> next(it), next(it), next(it), next(it)
+ ('2', '3', '4', '5')
+ >>> next(it)
+ '6'
+
+ """
+
+ def __init__(self, iterable, maxlen=None):
+ self._source = iter(iterable)
+ if maxlen is None:
+ self._cache = []
+ else:
+ self._cache = deque([], maxlen)
+ self._index = None
+
+ def __iter__(self):
+ return self
+
+ def __next__(self):
+ if self._index is not None:
+ try:
+ item = self._cache[self._index]
+ except IndexError:
+ self._index = None
+ else:
+ self._index += 1
+ return item
+
+ item = next(self._source)
+ self._cache.append(item)
+ return item
+
+ def __bool__(self):
+ try:
+ self.peek()
+ except StopIteration:
+ return False
+ return True
+
+ def peek(self, default=_marker):
+ try:
+ peeked = next(self)
+ except StopIteration:
+ if default is _marker:
+ raise
+ return default
+ if self._index is None:
+ self._index = len(self._cache)
+ self._index -= 1
+ return peeked
+
+ def elements(self):
+ return SequenceView(self._cache)
+
+ def seek(self, index):
+ self._index = index
+ remainder = index - len(self._cache)
+ if remainder > 0:
+ consume(self, remainder)
+
+ def relative_seek(self, count):
+ index = len(self._cache)
+ self.seek(max(index + count, 0))
+
+
+class run_length:
+ """
+ :func:`run_length.encode` compresses an iterable with run-length encoding.
+ It yields groups of repeated items with the count of how many times they
+ were repeated:
+
+ >>> uncompressed = 'abbcccdddd'
+ >>> list(run_length.encode(uncompressed))
+ [('a', 1), ('b', 2), ('c', 3), ('d', 4)]
+
+ :func:`run_length.decode` decompresses an iterable that was previously
+ compressed with run-length encoding. It yields the items of the
+ decompressed iterable:
+
+ >>> compressed = [('a', 1), ('b', 2), ('c', 3), ('d', 4)]
+ >>> list(run_length.decode(compressed))
+ ['a', 'b', 'b', 'c', 'c', 'c', 'd', 'd', 'd', 'd']
+
+ """
+
+ @staticmethod
+ def encode(iterable):
+ return ((k, ilen(g)) for k, g in groupby(iterable))
+
+ @staticmethod
+ def decode(iterable):
+ return chain.from_iterable(repeat(k, n) for k, n in iterable)
+
+
+def exactly_n(iterable, n, predicate=bool):
+ """Return ``True`` if exactly ``n`` items in the iterable are ``True``
+ according to the *predicate* function.
+
+ >>> exactly_n([True, True, False], 2)
+ True
+ >>> exactly_n([True, True, False], 1)
+ False
+ >>> exactly_n([0, 1, 2, 3, 4, 5], 3, lambda x: x < 3)
+ True
+
+ The iterable will be advanced until ``n + 1`` truthy items are encountered,
+ so avoid calling it on infinite iterables.
+
+ """
+ return len(take(n + 1, filter(predicate, iterable))) == n
+
+
+def circular_shifts(iterable):
+ """Return a list of circular shifts of *iterable*.
+
+ >>> circular_shifts(range(4))
+ [(0, 1, 2, 3), (1, 2, 3, 0), (2, 3, 0, 1), (3, 0, 1, 2)]
+ """
+ lst = list(iterable)
+ return take(len(lst), windowed(cycle(lst), len(lst)))
+
+
+def make_decorator(wrapping_func, result_index=0):
+ """Return a decorator version of *wrapping_func*, which is a function that
+ modifies an iterable. *result_index* is the position in that function's
+ signature where the iterable goes.
+
+ This lets you use itertools on the "production end," i.e. at function
+ definition. This can augment what the function returns without changing the
+ function's code.
+
+ For example, to produce a decorator version of :func:`chunked`:
+
+ >>> from more_itertools import chunked
+ >>> chunker = make_decorator(chunked, result_index=0)
+ >>> @chunker(3)
+ ... def iter_range(n):
+ ... return iter(range(n))
+ ...
+ >>> list(iter_range(9))
+ [[0, 1, 2], [3, 4, 5], [6, 7, 8]]
+
+ To only allow truthy items to be returned:
+
+ >>> truth_serum = make_decorator(filter, result_index=1)
+ >>> @truth_serum(bool)
+ ... def boolean_test():
+ ... return [0, 1, '', ' ', False, True]
+ ...
+ >>> list(boolean_test())
+ [1, ' ', True]
+
+ The :func:`peekable` and :func:`seekable` wrappers make for practical
+ decorators:
+
+ >>> from more_itertools import peekable
+ >>> peekable_function = make_decorator(peekable)
+ >>> @peekable_function()
+ ... def str_range(*args):
+ ... return (str(x) for x in range(*args))
+ ...
+ >>> it = str_range(1, 20, 2)
+ >>> next(it), next(it), next(it)
+ ('1', '3', '5')
+ >>> it.peek()
+ '7'
+ >>> next(it)
+ '7'
+
+ """
+
+ # See https://sites.google.com/site/bbayles/index/decorator_factory for
+ # notes on how this works.
+ def decorator(*wrapping_args, **wrapping_kwargs):
+ def outer_wrapper(f):
+ def inner_wrapper(*args, **kwargs):
+ result = f(*args, **kwargs)
+ wrapping_args_ = list(wrapping_args)
+ wrapping_args_.insert(result_index, result)
+ return wrapping_func(*wrapping_args_, **wrapping_kwargs)
+
+ return inner_wrapper
+
+ return outer_wrapper
+
+ return decorator
+
+
+def map_reduce(iterable, keyfunc, valuefunc=None, reducefunc=None):
+ """Return a dictionary that maps the items in *iterable* to categories
+ defined by *keyfunc*, transforms them with *valuefunc*, and
+ then summarizes them by category with *reducefunc*.
+
+ *valuefunc* defaults to the identity function if it is unspecified.
+ If *reducefunc* is unspecified, no summarization takes place:
+
+ >>> keyfunc = lambda x: x.upper()
+ >>> result = map_reduce('abbccc', keyfunc)
+ >>> sorted(result.items())
+ [('A', ['a']), ('B', ['b', 'b']), ('C', ['c', 'c', 'c'])]
+
+ Specifying *valuefunc* transforms the categorized items:
+
+ >>> keyfunc = lambda x: x.upper()
+ >>> valuefunc = lambda x: 1
+ >>> result = map_reduce('abbccc', keyfunc, valuefunc)
+ >>> sorted(result.items())
+ [('A', [1]), ('B', [1, 1]), ('C', [1, 1, 1])]
+
+ Specifying *reducefunc* summarizes the categorized items:
+
+ >>> keyfunc = lambda x: x.upper()
+ >>> valuefunc = lambda x: 1
+ >>> reducefunc = sum
+ >>> result = map_reduce('abbccc', keyfunc, valuefunc, reducefunc)
+ >>> sorted(result.items())
+ [('A', 1), ('B', 2), ('C', 3)]
+
+ You may want to filter the input iterable before applying the map/reduce
+ procedure:
+
+ >>> all_items = range(30)
+ >>> items = [x for x in all_items if 10 <= x <= 20] # Filter
+ >>> keyfunc = lambda x: x % 2 # Evens map to 0; odds to 1
+ >>> categories = map_reduce(items, keyfunc=keyfunc)
+ >>> sorted(categories.items())
+ [(0, [10, 12, 14, 16, 18, 20]), (1, [11, 13, 15, 17, 19])]
+ >>> summaries = map_reduce(items, keyfunc=keyfunc, reducefunc=sum)
+ >>> sorted(summaries.items())
+ [(0, 90), (1, 75)]
+
+ Note that all items in the iterable are gathered into a list before the
+ summarization step, which may require significant storage.
+
+ The returned object is a :obj:`collections.defaultdict` with the
+ ``default_factory`` set to ``None``, such that it behaves like a normal
+ dictionary.
+
+ """
+ valuefunc = (lambda x: x) if (valuefunc is None) else valuefunc
+
+ ret = defaultdict(list)
+ for item in iterable:
+ key = keyfunc(item)
+ value = valuefunc(item)
+ ret[key].append(value)
+
+ if reducefunc is not None:
+ for key, value_list in ret.items():
+ ret[key] = reducefunc(value_list)
+
+ ret.default_factory = None
+ return ret
+
+
+def rlocate(iterable, pred=bool, window_size=None):
+ """Yield the index of each item in *iterable* for which *pred* returns
+ ``True``, starting from the right and moving left.
+
+ *pred* defaults to :func:`bool`, which will select truthy items:
+
+ >>> list(rlocate([0, 1, 1, 0, 1, 0, 0])) # Truthy at 1, 2, and 4
+ [4, 2, 1]
+
+ Set *pred* to a custom function to, e.g., find the indexes for a particular
+ item:
+
+ >>> iterable = iter('abcb')
+ >>> pred = lambda x: x == 'b'
+ >>> list(rlocate(iterable, pred))
+ [3, 1]
+
+ If *window_size* is given, then the *pred* function will be called with
+ that many items. This enables searching for sub-sequences:
+
+ >>> iterable = [0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]
+ >>> pred = lambda *args: args == (1, 2, 3)
+ >>> list(rlocate(iterable, pred=pred, window_size=3))
+ [9, 5, 1]
+
+ Beware, this function won't return anything for infinite iterables.
+ If *iterable* is reversible, ``rlocate`` will reverse it and search from
+ the right. Otherwise, it will search from the left and return the results
+ in reverse order.
+
+ See :func:`locate` to for other example applications.
+
+ """
+ if window_size is None:
+ try:
+ len_iter = len(iterable)
+ return (len_iter - i - 1 for i in locate(reversed(iterable), pred))
+ except TypeError:
+ pass
+
+ return reversed(list(locate(iterable, pred, window_size)))
+
+
+def replace(iterable, pred, substitutes, count=None, window_size=1):
+ """Yield the items from *iterable*, replacing the items for which *pred*
+ returns ``True`` with the items from the iterable *substitutes*.
+
+ >>> iterable = [1, 1, 0, 1, 1, 0, 1, 1]
+ >>> pred = lambda x: x == 0
+ >>> substitutes = (2, 3)
+ >>> list(replace(iterable, pred, substitutes))
+ [1, 1, 2, 3, 1, 1, 2, 3, 1, 1]
+
+ If *count* is given, the number of replacements will be limited:
+
+ >>> iterable = [1, 1, 0, 1, 1, 0, 1, 1, 0]
+ >>> pred = lambda x: x == 0
+ >>> substitutes = [None]
+ >>> list(replace(iterable, pred, substitutes, count=2))
+ [1, 1, None, 1, 1, None, 1, 1, 0]
+
+ Use *window_size* to control the number of items passed as arguments to
+ *pred*. This allows for locating and replacing subsequences.
+
+ >>> iterable = [0, 1, 2, 5, 0, 1, 2, 5]
+ >>> window_size = 3
+ >>> pred = lambda *args: args == (0, 1, 2) # 3 items passed to pred
+ >>> substitutes = [3, 4] # Splice in these items
+ >>> list(replace(iterable, pred, substitutes, window_size=window_size))
+ [3, 4, 5, 3, 4, 5]
+
+ """
+ if window_size < 1:
+ raise ValueError('window_size must be at least 1')
+
+ # Save the substitutes iterable, since it's used more than once
+ substitutes = tuple(substitutes)
+
+ # Add padding such that the number of windows matches the length of the
+ # iterable
+ it = chain(iterable, [_marker] * (window_size - 1))
+ windows = windowed(it, window_size)
+
+ n = 0
+ for w in windows:
+ # If the current window matches our predicate (and we haven't hit
+ # our maximum number of replacements), splice in the substitutes
+ # and then consume the following windows that overlap with this one.
+ # For example, if the iterable is (0, 1, 2, 3, 4...)
+ # and the window size is 2, we have (0, 1), (1, 2), (2, 3)...
+ # If the predicate matches on (0, 1), we need to zap (0, 1) and (1, 2)
+ if pred(*w):
+ if (count is None) or (n < count):
+ n += 1
+ yield from substitutes
+ consume(windows, window_size - 1)
+ continue
+
+ # If there was no match (or we've reached the replacement limit),
+ # yield the first item from the window.
+ if w and (w[0] is not _marker):
+ yield w[0]
+
+
+def partitions(iterable):
+ """Yield all possible order-preserving partitions of *iterable*.
+
+ >>> iterable = 'abc'
+ >>> for part in partitions(iterable):
+ ... print([''.join(p) for p in part])
+ ['abc']
+ ['a', 'bc']
+ ['ab', 'c']
+ ['a', 'b', 'c']
+
+ This is unrelated to :func:`partition`.
+
+ """
+ sequence = list(iterable)
+ n = len(sequence)
+ for i in powerset(range(1, n)):
+ yield [sequence[i:j] for i, j in zip((0,) + i, i + (n,))]
+
+
+def set_partitions(iterable, k=None):
+ """
+ Yield the set partitions of *iterable* into *k* parts. Set partitions are
+ not order-preserving.
+
+ >>> iterable = 'abc'
+ >>> for part in set_partitions(iterable, 2):
+ ... print([''.join(p) for p in part])
+ ['a', 'bc']
+ ['ab', 'c']
+ ['b', 'ac']
+
+
+ If *k* is not given, every set partition is generated.
+
+ >>> iterable = 'abc'
+ >>> for part in set_partitions(iterable):
+ ... print([''.join(p) for p in part])
+ ['abc']
+ ['a', 'bc']
+ ['ab', 'c']
+ ['b', 'ac']
+ ['a', 'b', 'c']
+
+ """
+ L = list(iterable)
+ n = len(L)
+ if k is not None:
+ if k < 1:
+ raise ValueError(
+ "Can't partition in a negative or zero number of groups"
+ )
+ elif k > n:
+ return
+
+ def set_partitions_helper(L, k):
+ n = len(L)
+ if k == 1:
+ yield [L]
+ elif n == k:
+ yield [[s] for s in L]
+ else:
+ e, *M = L
+ for p in set_partitions_helper(M, k - 1):
+ yield [[e], *p]
+ for p in set_partitions_helper(M, k):
+ for i in range(len(p)):
+ yield p[:i] + [[e] + p[i]] + p[i + 1 :]
+
+ if k is None:
+ for k in range(1, n + 1):
+ yield from set_partitions_helper(L, k)
+ else:
+ yield from set_partitions_helper(L, k)
+
+
+class time_limited:
+ """
+ Yield items from *iterable* until *limit_seconds* have passed.
+ If the time limit expires before all items have been yielded, the
+ ``timed_out`` parameter will be set to ``True``.
+
+ >>> from time import sleep
+ >>> def generator():
+ ... yield 1
+ ... yield 2
+ ... sleep(0.2)
+ ... yield 3
+ >>> iterable = time_limited(0.1, generator())
+ >>> list(iterable)
+ [1, 2]
+ >>> iterable.timed_out
+ True
+
+ Note that the time is checked before each item is yielded, and iteration
+ stops if the time elapsed is greater than *limit_seconds*. If your time
+ limit is 1 second, but it takes 2 seconds to generate the first item from
+ the iterable, the function will run for 2 seconds and not yield anything.
+
+ """
+
+ def __init__(self, limit_seconds, iterable):
+ if limit_seconds < 0:
+ raise ValueError('limit_seconds must be positive')
+ self.limit_seconds = limit_seconds
+ self._iterable = iter(iterable)
+ self._start_time = monotonic()
+ self.timed_out = False
+
+ def __iter__(self):
+ return self
+
+ def __next__(self):
+ item = next(self._iterable)
+ if monotonic() - self._start_time > self.limit_seconds:
+ self.timed_out = True
+ raise StopIteration
+
+ return item
+
+
+def only(iterable, default=None, too_long=None):
+ """If *iterable* has only one item, return it.
+ If it has zero items, return *default*.
+ If it has more than one item, raise the exception given by *too_long*,
+ which is ``ValueError`` by default.
+
+ >>> only([], default='missing')
+ 'missing'
+ >>> only([1])
+ 1
+ >>> only([1, 2]) # doctest: +IGNORE_EXCEPTION_DETAIL
+ Traceback (most recent call last):
+ ...
+ ValueError: Expected exactly one item in iterable, but got 1, 2,
+ and perhaps more.'
+ >>> only([1, 2], too_long=TypeError) # doctest: +IGNORE_EXCEPTION_DETAIL
+ Traceback (most recent call last):
+ ...
+ TypeError
+
+ Note that :func:`only` attempts to advance *iterable* twice to ensure there
+ is only one item. See :func:`spy` or :func:`peekable` to check
+ iterable contents less destructively.
+ """
+ it = iter(iterable)
+ first_value = next(it, default)
+
+ try:
+ second_value = next(it)
+ except StopIteration:
+ pass
+ else:
+ msg = (
+ 'Expected exactly one item in iterable, but got {!r}, {!r}, '
+ 'and perhaps more.'.format(first_value, second_value)
+ )
+ raise too_long or ValueError(msg)
+
+ return first_value
+
+
+class _IChunk:
+ def __init__(self, iterable, n):
+ self._it = islice(iterable, n)
+ self._cache = deque()
+
+ def fill_cache(self):
+ self._cache.extend(self._it)
+
+ def __iter__(self):
+ return self
+
+ def __next__(self):
+ try:
+ return next(self._it)
+ except StopIteration:
+ if self._cache:
+ return self._cache.popleft()
+ else:
+ raise
+
+
+def ichunked(iterable, n):
+ """Break *iterable* into sub-iterables with *n* elements each.
+ :func:`ichunked` is like :func:`chunked`, but it yields iterables
+ instead of lists.
+
+ If the sub-iterables are read in order, the elements of *iterable*
+ won't be stored in memory.
+ If they are read out of order, :func:`itertools.tee` is used to cache
+ elements as necessary.
+
+ >>> from itertools import count
+ >>> all_chunks = ichunked(count(), 4)
+ >>> c_1, c_2, c_3 = next(all_chunks), next(all_chunks), next(all_chunks)
+ >>> list(c_2) # c_1's elements have been cached; c_3's haven't been
+ [4, 5, 6, 7]
+ >>> list(c_1)
+ [0, 1, 2, 3]
+ >>> list(c_3)
+ [8, 9, 10, 11]
+
+ """
+ source = peekable(iter(iterable))
+ ichunk_marker = object()
+ while True:
+ # Check to see whether we're at the end of the source iterable
+ item = source.peek(ichunk_marker)
+ if item is ichunk_marker:
+ return
+
+ chunk = _IChunk(source, n)
+ yield chunk
+
+ # Advance the source iterable and fill previous chunk's cache
+ chunk.fill_cache()
+
+
+def iequals(*iterables):
+ """Return ``True`` if all given *iterables* are equal to each other,
+ which means that they contain the same elements in the same order.
+
+ The function is useful for comparing iterables of different data types
+ or iterables that do not support equality checks.
+
+ >>> iequals("abc", ['a', 'b', 'c'], ('a', 'b', 'c'), iter("abc"))
+ True
+
+ >>> iequals("abc", "acb")
+ False
+
+ Not to be confused with :func:`all_equals`, which checks whether all
+ elements of iterable are equal to each other.
+
+ """
+ return all(map(all_equal, zip_longest(*iterables, fillvalue=object())))
+
+
+def distinct_combinations(iterable, r):
+ """Yield the distinct combinations of *r* items taken from *iterable*.
+
+ >>> list(distinct_combinations([0, 0, 1], 2))
+ [(0, 0), (0, 1)]
+
+ Equivalent to ``set(combinations(iterable))``, except duplicates are not
+ generated and thrown away. For larger input sequences this is much more
+ efficient.
+
+ """
+ if r < 0:
+ raise ValueError('r must be non-negative')
+ elif r == 0:
+ yield ()
+ return
+ pool = tuple(iterable)
+ generators = [unique_everseen(enumerate(pool), key=itemgetter(1))]
+ current_combo = [None] * r
+ level = 0
+ while generators:
+ try:
+ cur_idx, p = next(generators[-1])
+ except StopIteration:
+ generators.pop()
+ level -= 1
+ continue
+ current_combo[level] = p
+ if level + 1 == r:
+ yield tuple(current_combo)
+ else:
+ generators.append(
+ unique_everseen(
+ enumerate(pool[cur_idx + 1 :], cur_idx + 1),
+ key=itemgetter(1),
+ )
+ )
+ level += 1
+
+
+def filter_except(validator, iterable, *exceptions):
+ """Yield the items from *iterable* for which the *validator* function does
+ not raise one of the specified *exceptions*.
+
+ *validator* is called for each item in *iterable*.
+ It should be a function that accepts one argument and raises an exception
+ if that item is not valid.
+
+ >>> iterable = ['1', '2', 'three', '4', None]
+ >>> list(filter_except(int, iterable, ValueError, TypeError))
+ ['1', '2', '4']
+
+ If an exception other than one given by *exceptions* is raised by
+ *validator*, it is raised like normal.
+ """
+ for item in iterable:
+ try:
+ validator(item)
+ except exceptions:
+ pass
+ else:
+ yield item
+
+
+def map_except(function, iterable, *exceptions):
+ """Transform each item from *iterable* with *function* and yield the
+ result, unless *function* raises one of the specified *exceptions*.
+
+ *function* is called to transform each item in *iterable*.
+ It should accept one argument.
+
+ >>> iterable = ['1', '2', 'three', '4', None]
+ >>> list(map_except(int, iterable, ValueError, TypeError))
+ [1, 2, 4]
+
+ If an exception other than one given by *exceptions* is raised by
+ *function*, it is raised like normal.
+ """
+ for item in iterable:
+ try:
+ yield function(item)
+ except exceptions:
+ pass
+
+
+def map_if(iterable, pred, func, func_else=lambda x: x):
+ """Evaluate each item from *iterable* using *pred*. If the result is
+ equivalent to ``True``, transform the item with *func* and yield it.
+ Otherwise, transform the item with *func_else* and yield it.
+
+ *pred*, *func*, and *func_else* should each be functions that accept
+ one argument. By default, *func_else* is the identity function.
+
+ >>> from math import sqrt
+ >>> iterable = list(range(-5, 5))
+ >>> iterable
+ [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4]
+ >>> list(map_if(iterable, lambda x: x > 3, lambda x: 'toobig'))
+ [-5, -4, -3, -2, -1, 0, 1, 2, 3, 'toobig']
+ >>> list(map_if(iterable, lambda x: x >= 0,
+ ... lambda x: f'{sqrt(x):.2f}', lambda x: None))
+ [None, None, None, None, None, '0.00', '1.00', '1.41', '1.73', '2.00']
+ """
+ for item in iterable:
+ yield func(item) if pred(item) else func_else(item)
+
+
+def _sample_unweighted(iterable, k):
+ # Implementation of "Algorithm L" from the 1994 paper by Kim-Hung Li:
+ # "Reservoir-Sampling Algorithms of Time Complexity O(n(1+log(N/n)))".
+
+ # Fill up the reservoir (collection of samples) with the first `k` samples
+ reservoir = take(k, iterable)
+
+ # Generate random number that's the largest in a sample of k U(0,1) numbers
+ # Largest order statistic: https://en.wikipedia.org/wiki/Order_statistic
+ W = exp(log(random()) / k)
+
+ # The number of elements to skip before changing the reservoir is a random
+ # number with a geometric distribution. Sample it using random() and logs.
+ next_index = k + floor(log(random()) / log(1 - W))
+
+ for index, element in enumerate(iterable, k):
+ if index == next_index:
+ reservoir[randrange(k)] = element
+ # The new W is the largest in a sample of k U(0, `old_W`) numbers
+ W *= exp(log(random()) / k)
+ next_index += floor(log(random()) / log(1 - W)) + 1
+
+ return reservoir
+
+
+def _sample_weighted(iterable, k, weights):
+ # Implementation of "A-ExpJ" from the 2006 paper by Efraimidis et al. :
+ # "Weighted random sampling with a reservoir".
+
+ # Log-transform for numerical stability for weights that are small/large
+ weight_keys = (log(random()) / weight for weight in weights)
+
+ # Fill up the reservoir (collection of samples) with the first `k`
+ # weight-keys and elements, then heapify the list.
+ reservoir = take(k, zip(weight_keys, iterable))
+ heapify(reservoir)
+
+ # The number of jumps before changing the reservoir is a random variable
+ # with an exponential distribution. Sample it using random() and logs.
+ smallest_weight_key, _ = reservoir[0]
+ weights_to_skip = log(random()) / smallest_weight_key
+
+ for weight, element in zip(weights, iterable):
+ if weight >= weights_to_skip:
+ # The notation here is consistent with the paper, but we store
+ # the weight-keys in log-space for better numerical stability.
+ smallest_weight_key, _ = reservoir[0]
+ t_w = exp(weight * smallest_weight_key)
+ r_2 = uniform(t_w, 1) # generate U(t_w, 1)
+ weight_key = log(r_2) / weight
+ heapreplace(reservoir, (weight_key, element))
+ smallest_weight_key, _ = reservoir[0]
+ weights_to_skip = log(random()) / smallest_weight_key
+ else:
+ weights_to_skip -= weight
+
+ # Equivalent to [element for weight_key, element in sorted(reservoir)]
+ return [heappop(reservoir)[1] for _ in range(k)]
+
+
+def sample(iterable, k, weights=None):
+ """Return a *k*-length list of elements chosen (without replacement)
+ from the *iterable*. Like :func:`random.sample`, but works on iterables
+ of unknown length.
+
+ >>> iterable = range(100)
+ >>> sample(iterable, 5) # doctest: +SKIP
+ [81, 60, 96, 16, 4]
+
+ An iterable with *weights* may also be given:
+
+ >>> iterable = range(100)
+ >>> weights = (i * i + 1 for i in range(100))
+ >>> sampled = sample(iterable, 5, weights=weights) # doctest: +SKIP
+ [79, 67, 74, 66, 78]
+
+ The algorithm can also be used to generate weighted random permutations.
+ The relative weight of each item determines the probability that it
+ appears late in the permutation.
+
+ >>> data = "abcdefgh"
+ >>> weights = range(1, len(data) + 1)
+ >>> sample(data, k=len(data), weights=weights) # doctest: +SKIP
+ ['c', 'a', 'b', 'e', 'g', 'd', 'h', 'f']
+ """
+ if k == 0:
+ return []
+
+ iterable = iter(iterable)
+ if weights is None:
+ return _sample_unweighted(iterable, k)
+ else:
+ weights = iter(weights)
+ return _sample_weighted(iterable, k, weights)
+
+
+def is_sorted(iterable, key=None, reverse=False, strict=False):
+ """Returns ``True`` if the items of iterable are in sorted order, and
+ ``False`` otherwise. *key* and *reverse* have the same meaning that they do
+ in the built-in :func:`sorted` function.
+
+ >>> is_sorted(['1', '2', '3', '4', '5'], key=int)
+ True
+ >>> is_sorted([5, 4, 3, 1, 2], reverse=True)
+ False
+
+ If *strict*, tests for strict sorting, that is, returns ``False`` if equal
+ elements are found:
+
+ >>> is_sorted([1, 2, 2])
+ True
+ >>> is_sorted([1, 2, 2], strict=True)
+ False
+
+ The function returns ``False`` after encountering the first out-of-order
+ item. If there are no out-of-order items, the iterable is exhausted.
+ """
+
+ compare = (le if reverse else ge) if strict else (lt if reverse else gt)
+ it = iterable if key is None else map(key, iterable)
+ return not any(starmap(compare, pairwise(it)))
+
+
+class AbortThread(BaseException):
+ pass
+
+
+class callback_iter:
+ """Convert a function that uses callbacks to an iterator.
+
+ Let *func* be a function that takes a `callback` keyword argument.
+ For example:
+
+ >>> def func(callback=None):
+ ... for i, c in [(1, 'a'), (2, 'b'), (3, 'c')]:
+ ... if callback:
+ ... callback(i, c)
+ ... return 4
+
+
+ Use ``with callback_iter(func)`` to get an iterator over the parameters
+ that are delivered to the callback.
+
+ >>> with callback_iter(func) as it:
+ ... for args, kwargs in it:
+ ... print(args)
+ (1, 'a')
+ (2, 'b')
+ (3, 'c')
+
+ The function will be called in a background thread. The ``done`` property
+ indicates whether it has completed execution.
+
+ >>> it.done
+ True
+
+ If it completes successfully, its return value will be available
+ in the ``result`` property.
+
+ >>> it.result
+ 4
+
+ Notes:
+
+ * If the function uses some keyword argument besides ``callback``, supply
+ *callback_kwd*.
+ * If it finished executing, but raised an exception, accessing the
+ ``result`` property will raise the same exception.
+ * If it hasn't finished executing, accessing the ``result``
+ property from within the ``with`` block will raise ``RuntimeError``.
+ * If it hasn't finished executing, accessing the ``result`` property from
+ outside the ``with`` block will raise a
+ ``more_itertools.AbortThread`` exception.
+ * Provide *wait_seconds* to adjust how frequently the it is polled for
+ output.
+
+ """
+
+ def __init__(self, func, callback_kwd='callback', wait_seconds=0.1):
+ self._func = func
+ self._callback_kwd = callback_kwd
+ self._aborted = False
+ self._future = None
+ self._wait_seconds = wait_seconds
+ # Lazily import concurrent.future
+ self._executor = __import__(
+ 'concurrent.futures'
+ ).futures.ThreadPoolExecutor(max_workers=1)
+ self._iterator = self._reader()
+
+ def __enter__(self):
+ return self
+
+ def __exit__(self, exc_type, exc_value, traceback):
+ self._aborted = True
+ self._executor.shutdown()
+
+ def __iter__(self):
+ return self
+
+ def __next__(self):
+ return next(self._iterator)
+
+ @property
+ def done(self):
+ if self._future is None:
+ return False
+ return self._future.done()
+
+ @property
+ def result(self):
+ if not self.done:
+ raise RuntimeError('Function has not yet completed')
+
+ return self._future.result()
+
+ def _reader(self):
+ q = Queue()
+
+ def callback(*args, **kwargs):
+ if self._aborted:
+ raise AbortThread('canceled by user')
+
+ q.put((args, kwargs))
+
+ self._future = self._executor.submit(
+ self._func, **{self._callback_kwd: callback}
+ )
+
+ while True:
+ try:
+ item = q.get(timeout=self._wait_seconds)
+ except Empty:
+ pass
+ else:
+ q.task_done()
+ yield item
+
+ if self._future.done():
+ break
+
+ remaining = []
+ while True:
+ try:
+ item = q.get_nowait()
+ except Empty:
+ break
+ else:
+ q.task_done()
+ remaining.append(item)
+ q.join()
+ yield from remaining
+
+
+def windowed_complete(iterable, n):
+ """
+ Yield ``(beginning, middle, end)`` tuples, where:
+
+ * Each ``middle`` has *n* items from *iterable*
+ * Each ``beginning`` has the items before the ones in ``middle``
+ * Each ``end`` has the items after the ones in ``middle``
+
+ >>> iterable = range(7)
+ >>> n = 3
+ >>> for beginning, middle, end in windowed_complete(iterable, n):
+ ... print(beginning, middle, end)
+ () (0, 1, 2) (3, 4, 5, 6)
+ (0,) (1, 2, 3) (4, 5, 6)
+ (0, 1) (2, 3, 4) (5, 6)
+ (0, 1, 2) (3, 4, 5) (6,)
+ (0, 1, 2, 3) (4, 5, 6) ()
+
+ Note that *n* must be at least 0 and most equal to the length of
+ *iterable*.
+
+ This function will exhaust the iterable and may require significant
+ storage.
+ """
+ if n < 0:
+ raise ValueError('n must be >= 0')
+
+ seq = tuple(iterable)
+ size = len(seq)
+
+ if n > size:
+ raise ValueError('n must be <= len(seq)')
+
+ for i in range(size - n + 1):
+ beginning = seq[:i]
+ middle = seq[i : i + n]
+ end = seq[i + n :]
+ yield beginning, middle, end
+
+
+def all_unique(iterable, key=None):
+ """
+ Returns ``True`` if all the elements of *iterable* are unique (no two
+ elements are equal).
+
+ >>> all_unique('ABCB')
+ False
+
+ If a *key* function is specified, it will be used to make comparisons.
+
+ >>> all_unique('ABCb')
+ True
+ >>> all_unique('ABCb', str.lower)
+ False
+
+ The function returns as soon as the first non-unique element is
+ encountered. Iterables with a mix of hashable and unhashable items can
+ be used, but the function will be slower for unhashable items.
+ """
+ seenset = set()
+ seenset_add = seenset.add
+ seenlist = []
+ seenlist_add = seenlist.append
+ for element in map(key, iterable) if key else iterable:
+ try:
+ if element in seenset:
+ return False
+ seenset_add(element)
+ except TypeError:
+ if element in seenlist:
+ return False
+ seenlist_add(element)
+ return True
+
+
+def nth_product(index, *args):
+ """Equivalent to ``list(product(*args))[index]``.
+
+ The products of *args* can be ordered lexicographically.
+ :func:`nth_product` computes the product at sort position *index* without
+ computing the previous products.
+
+ >>> nth_product(8, range(2), range(2), range(2), range(2))
+ (1, 0, 0, 0)
+
+ ``IndexError`` will be raised if the given *index* is invalid.
+ """
+ pools = list(map(tuple, reversed(args)))
+ ns = list(map(len, pools))
+
+ c = reduce(mul, ns)
+
+ if index < 0:
+ index += c
+
+ if not 0 <= index < c:
+ raise IndexError
+
+ result = []
+ for pool, n in zip(pools, ns):
+ result.append(pool[index % n])
+ index //= n
+
+ return tuple(reversed(result))
+
+
+def nth_permutation(iterable, r, index):
+ """Equivalent to ``list(permutations(iterable, r))[index]```
+
+ The subsequences of *iterable* that are of length *r* where order is
+ important can be ordered lexicographically. :func:`nth_permutation`
+ computes the subsequence at sort position *index* directly, without
+ computing the previous subsequences.
+
+ >>> nth_permutation('ghijk', 2, 5)
+ ('h', 'i')
+
+ ``ValueError`` will be raised If *r* is negative or greater than the length
+ of *iterable*.
+ ``IndexError`` will be raised if the given *index* is invalid.
+ """
+ pool = list(iterable)
+ n = len(pool)
+
+ if r is None or r == n:
+ r, c = n, factorial(n)
+ elif not 0 <= r < n:
+ raise ValueError
+ else:
+ c = factorial(n) // factorial(n - r)
+
+ if index < 0:
+ index += c
+
+ if not 0 <= index < c:
+ raise IndexError
+
+ if c == 0:
+ return tuple()
+
+ result = [0] * r
+ q = index * factorial(n) // c if r < n else index
+ for d in range(1, n + 1):
+ q, i = divmod(q, d)
+ if 0 <= n - d < r:
+ result[n - d] = i
+ if q == 0:
+ break
+
+ return tuple(map(pool.pop, result))
+
+
+def nth_combination_with_replacement(iterable, r, index):
+ """Equivalent to
+ ``list(combinations_with_replacement(iterable, r))[index]``.
+
+
+ The subsequences with repetition of *iterable* that are of length *r* can
+ be ordered lexicographically. :func:`nth_combination_with_replacement`
+ computes the subsequence at sort position *index* directly, without
+ computing the previous subsequences with replacement.
+
+ >>> nth_combination_with_replacement(range(5), 3, 5)
+ (0, 1, 1)
+
+ ``ValueError`` will be raised If *r* is negative or greater than the length
+ of *iterable*.
+ ``IndexError`` will be raised if the given *index* is invalid.
+ """
+ pool = tuple(iterable)
+ n = len(pool)
+ if (r < 0) or (r > n):
+ raise ValueError
+
+ c = factorial(n + r - 1) // (factorial(r) * factorial(n - 1))
+
+ if index < 0:
+ index += c
+
+ if (index < 0) or (index >= c):
+ raise IndexError
+
+ result = []
+ i = 0
+ while r:
+ r -= 1
+ while n >= 0:
+ num_combs = factorial(n + r - 1) // (
+ factorial(r) * factorial(n - 1)
+ )
+ if index < num_combs:
+ break
+ n -= 1
+ i += 1
+ index -= num_combs
+ result.append(pool[i])
+
+ return tuple(result)
+
+
+def value_chain(*args):
+ """Yield all arguments passed to the function in the same order in which
+ they were passed. If an argument itself is iterable then iterate over its
+ values.
+
+ >>> list(value_chain(1, 2, 3, [4, 5, 6]))
+ [1, 2, 3, 4, 5, 6]
+
+ Binary and text strings are not considered iterable and are emitted
+ as-is:
+
+ >>> list(value_chain('12', '34', ['56', '78']))
+ ['12', '34', '56', '78']
+
+
+ Multiple levels of nesting are not flattened.
+
+ """
+ for value in args:
+ if isinstance(value, (str, bytes)):
+ yield value
+ continue
+ try:
+ yield from value
+ except TypeError:
+ yield value
+
+
+def product_index(element, *args):
+ """Equivalent to ``list(product(*args)).index(element)``
+
+ The products of *args* can be ordered lexicographically.
+ :func:`product_index` computes the first index of *element* without
+ computing the previous products.
+
+ >>> product_index([8, 2], range(10), range(5))
+ 42
+
+ ``ValueError`` will be raised if the given *element* isn't in the product
+ of *args*.
+ """
+ index = 0
+
+ for x, pool in zip_longest(element, args, fillvalue=_marker):
+ if x is _marker or pool is _marker:
+ raise ValueError('element is not a product of args')
+
+ pool = tuple(pool)
+ index = index * len(pool) + pool.index(x)
+
+ return index
+
+
+def combination_index(element, iterable):
+ """Equivalent to ``list(combinations(iterable, r)).index(element)``
+
+ The subsequences of *iterable* that are of length *r* can be ordered
+ lexicographically. :func:`combination_index` computes the index of the
+ first *element*, without computing the previous combinations.
+
+ >>> combination_index('adf', 'abcdefg')
+ 10
+
+ ``ValueError`` will be raised if the given *element* isn't one of the
+ combinations of *iterable*.
+ """
+ element = enumerate(element)
+ k, y = next(element, (None, None))
+ if k is None:
+ return 0
+
+ indexes = []
+ pool = enumerate(iterable)
+ for n, x in pool:
+ if x == y:
+ indexes.append(n)
+ tmp, y = next(element, (None, None))
+ if tmp is None:
+ break
+ else:
+ k = tmp
+ else:
+ raise ValueError('element is not a combination of iterable')
+
+ n, _ = last(pool, default=(n, None))
+
+ # Python versions below 3.8 don't have math.comb
+ index = 1
+ for i, j in enumerate(reversed(indexes), start=1):
+ j = n - j
+ if i <= j:
+ index += factorial(j) // (factorial(i) * factorial(j - i))
+
+ return factorial(n + 1) // (factorial(k + 1) * factorial(n - k)) - index
+
+
+def combination_with_replacement_index(element, iterable):
+ """Equivalent to
+ ``list(combinations_with_replacement(iterable, r)).index(element)``
+
+ The subsequences with repetition of *iterable* that are of length *r* can
+ be ordered lexicographically. :func:`combination_with_replacement_index`
+ computes the index of the first *element*, without computing the previous
+ combinations with replacement.
+
+ >>> combination_with_replacement_index('adf', 'abcdefg')
+ 20
+
+ ``ValueError`` will be raised if the given *element* isn't one of the
+ combinations with replacement of *iterable*.
+ """
+ element = tuple(element)
+ l = len(element)
+ element = enumerate(element)
+
+ k, y = next(element, (None, None))
+ if k is None:
+ return 0
+
+ indexes = []
+ pool = tuple(iterable)
+ for n, x in enumerate(pool):
+ while x == y:
+ indexes.append(n)
+ tmp, y = next(element, (None, None))
+ if tmp is None:
+ break
+ else:
+ k = tmp
+ if y is None:
+ break
+ else:
+ raise ValueError(
+ 'element is not a combination with replacment of iterable'
+ )
+
+ n = len(pool)
+ occupations = [0] * n
+ for p in indexes:
+ occupations[p] += 1
+
+ index = 0
+ for k in range(1, n):
+ j = l + n - 1 - k - sum(occupations[:k])
+ i = n - k
+ if i <= j:
+ index += factorial(j) // (factorial(i) * factorial(j - i))
+
+ return index
+
+
+def permutation_index(element, iterable):
+ """Equivalent to ``list(permutations(iterable, r)).index(element)```
+
+ The subsequences of *iterable* that are of length *r* where order is
+ important can be ordered lexicographically. :func:`permutation_index`
+ computes the index of the first *element* directly, without computing
+ the previous permutations.
+
+ >>> permutation_index([1, 3, 2], range(5))
+ 19
+
+ ``ValueError`` will be raised if the given *element* isn't one of the
+ permutations of *iterable*.
+ """
+ index = 0
+ pool = list(iterable)
+ for i, x in zip(range(len(pool), -1, -1), element):
+ r = pool.index(x)
+ index = index * i + r
+ del pool[r]
+
+ return index
+
+
+class countable:
+ """Wrap *iterable* and keep a count of how many items have been consumed.
+
+ The ``items_seen`` attribute starts at ``0`` and increments as the iterable
+ is consumed:
+
+ >>> iterable = map(str, range(10))
+ >>> it = countable(iterable)
+ >>> it.items_seen
+ 0
+ >>> next(it), next(it)
+ ('0', '1')
+ >>> list(it)
+ ['2', '3', '4', '5', '6', '7', '8', '9']
+ >>> it.items_seen
+ 10
+ """
+
+ def __init__(self, iterable):
+ self._it = iter(iterable)
+ self.items_seen = 0
+
+ def __iter__(self):
+ return self
+
+ def __next__(self):
+ item = next(self._it)
+ self.items_seen += 1
+
+ return item
+
+
+def chunked_even(iterable, n):
+ """Break *iterable* into lists of approximately length *n*.
+ Items are distributed such the lengths of the lists differ by at most
+ 1 item.
+
+ >>> iterable = [1, 2, 3, 4, 5, 6, 7]
+ >>> n = 3
+ >>> list(chunked_even(iterable, n)) # List lengths: 3, 2, 2
+ [[1, 2, 3], [4, 5], [6, 7]]
+ >>> list(chunked(iterable, n)) # List lengths: 3, 3, 1
+ [[1, 2, 3], [4, 5, 6], [7]]
+
+ """
+
+ len_method = getattr(iterable, '__len__', None)
+
+ if len_method is None:
+ return _chunked_even_online(iterable, n)
+ else:
+ return _chunked_even_finite(iterable, len_method(), n)
+
+
+def _chunked_even_online(iterable, n):
+ buffer = []
+ maxbuf = n + (n - 2) * (n - 1)
+ for x in iterable:
+ buffer.append(x)
+ if len(buffer) == maxbuf:
+ yield buffer[:n]
+ buffer = buffer[n:]
+ yield from _chunked_even_finite(buffer, len(buffer), n)
+
+
+def _chunked_even_finite(iterable, N, n):
+ if N < 1:
+ return
+
+ # Lists are either size `full_size <= n` or `partial_size = full_size - 1`
+ q, r = divmod(N, n)
+ num_lists = q + (1 if r > 0 else 0)
+ q, r = divmod(N, num_lists)
+ full_size = q + (1 if r > 0 else 0)
+ partial_size = full_size - 1
+ num_full = N - partial_size * num_lists
+ num_partial = num_lists - num_full
+
+ # Yield num_full lists of full_size
+ partial_start_idx = num_full * full_size
+ if full_size > 0:
+ for i in range(0, partial_start_idx, full_size):
+ yield list(islice(iterable, i, i + full_size))
+
+ # Yield num_partial lists of partial_size
+ if partial_size > 0:
+ for i in range(
+ partial_start_idx,
+ partial_start_idx + (num_partial * partial_size),
+ partial_size,
+ ):
+ yield list(islice(iterable, i, i + partial_size))
+
+
+def zip_broadcast(*objects, scalar_types=(str, bytes), strict=False):
+ """A version of :func:`zip` that "broadcasts" any scalar
+ (i.e., non-iterable) items into output tuples.
+
+ >>> iterable_1 = [1, 2, 3]
+ >>> iterable_2 = ['a', 'b', 'c']
+ >>> scalar = '_'
+ >>> list(zip_broadcast(iterable_1, iterable_2, scalar))
+ [(1, 'a', '_'), (2, 'b', '_'), (3, 'c', '_')]
+
+ The *scalar_types* keyword argument determines what types are considered
+ scalar. It is set to ``(str, bytes)`` by default. Set it to ``None`` to
+ treat strings and byte strings as iterable:
+
+ >>> list(zip_broadcast('abc', 0, 'xyz', scalar_types=None))
+ [('a', 0, 'x'), ('b', 0, 'y'), ('c', 0, 'z')]
+
+ If the *strict* keyword argument is ``True``, then
+ ``UnequalIterablesError`` will be raised if any of the iterables have
+ different lengths.
+ """
+
+ def is_scalar(obj):
+ if scalar_types and isinstance(obj, scalar_types):
+ return True
+ try:
+ iter(obj)
+ except TypeError:
+ return True
+ else:
+ return False
+
+ size = len(objects)
+ if not size:
+ return
+
+ new_item = [None] * size
+ iterables, iterable_positions = [], []
+ for i, obj in enumerate(objects):
+ if is_scalar(obj):
+ new_item[i] = obj
+ else:
+ iterables.append(iter(obj))
+ iterable_positions.append(i)
+
+ if not iterables:
+ yield tuple(objects)
+ return
+
+ zipper = _zip_equal if strict else zip
+ for item in zipper(*iterables):
+ for i, new_item[i] in zip(iterable_positions, item):
+ pass
+ yield tuple(new_item)
+
+
+def unique_in_window(iterable, n, key=None):
+ """Yield the items from *iterable* that haven't been seen recently.
+ *n* is the size of the lookback window.
+
+ >>> iterable = [0, 1, 0, 2, 3, 0]
+ >>> n = 3
+ >>> list(unique_in_window(iterable, n))
+ [0, 1, 2, 3, 0]
+
+ The *key* function, if provided, will be used to determine uniqueness:
+
+ >>> list(unique_in_window('abAcda', 3, key=lambda x: x.lower()))
+ ['a', 'b', 'c', 'd', 'a']
+
+ The items in *iterable* must be hashable.
+
+ """
+ if n <= 0:
+ raise ValueError('n must be greater than 0')
+
+ window = deque(maxlen=n)
+ counts = defaultdict(int)
+ use_key = key is not None
+
+ for item in iterable:
+ if len(window) == n:
+ to_discard = window[0]
+ if counts[to_discard] == 1:
+ del counts[to_discard]
+ else:
+ counts[to_discard] -= 1
+
+ k = key(item) if use_key else item
+ if k not in counts:
+ yield item
+ counts[k] += 1
+ window.append(k)
+
+
+def duplicates_everseen(iterable, key=None):
+ """Yield duplicate elements after their first appearance.
+
+ >>> list(duplicates_everseen('mississippi'))
+ ['s', 'i', 's', 's', 'i', 'p', 'i']
+ >>> list(duplicates_everseen('AaaBbbCccAaa', str.lower))
+ ['a', 'a', 'b', 'b', 'c', 'c', 'A', 'a', 'a']
+
+ This function is analagous to :func:`unique_everseen` and is subject to
+ the same performance considerations.
+
+ """
+ seen_set = set()
+ seen_list = []
+ use_key = key is not None
+
+ for element in iterable:
+ k = key(element) if use_key else element
+ try:
+ if k not in seen_set:
+ seen_set.add(k)
+ else:
+ yield element
+ except TypeError:
+ if k not in seen_list:
+ seen_list.append(k)
+ else:
+ yield element
+
+
+def duplicates_justseen(iterable, key=None):
+ """Yields serially-duplicate elements after their first appearance.
+
+ >>> list(duplicates_justseen('mississippi'))
+ ['s', 's', 'p']
+ >>> list(duplicates_justseen('AaaBbbCccAaa', str.lower))
+ ['a', 'a', 'b', 'b', 'c', 'c', 'a', 'a']
+
+ This function is analagous to :func:`unique_justseen`.
+
+ """
+ return flatten(g for _, g in groupby(iterable, key) for _ in g)
+
+
+def minmax(iterable_or_value, *others, key=None, default=_marker):
+ """Returns both the smallest and largest items in an iterable
+ or the largest of two or more arguments.
+
+ >>> minmax([3, 1, 5])
+ (1, 5)
+
+ >>> minmax(4, 2, 6)
+ (2, 6)
+
+ If a *key* function is provided, it will be used to transform the input
+ items for comparison.
+
+ >>> minmax([5, 30], key=str) # '30' sorts before '5'
+ (30, 5)
+
+ If a *default* value is provided, it will be returned if there are no
+ input items.
+
+ >>> minmax([], default=(0, 0))
+ (0, 0)
+
+ Otherwise ``ValueError`` is raised.
+
+ This function is based on the
+ `recipe `__ by
+ Raymond Hettinger and takes care to minimize the number of comparisons
+ performed.
+ """
+ iterable = (iterable_or_value, *others) if others else iterable_or_value
+
+ it = iter(iterable)
+
+ try:
+ lo = hi = next(it)
+ except StopIteration as e:
+ if default is _marker:
+ raise ValueError(
+ '`minmax()` argument is an empty iterable. '
+ 'Provide a `default` value to suppress this error.'
+ ) from e
+ return default
+
+ # Different branches depending on the presence of key. This saves a lot
+ # of unimportant copies which would slow the "key=None" branch
+ # significantly down.
+ if key is None:
+ for x, y in zip_longest(it, it, fillvalue=lo):
+ if y < x:
+ x, y = y, x
+ if x < lo:
+ lo = x
+ if hi < y:
+ hi = y
+
+ else:
+ lo_key = hi_key = key(lo)
+
+ for x, y in zip_longest(it, it, fillvalue=lo):
+ x_key, y_key = key(x), key(y)
+
+ if y_key < x_key:
+ x, y, x_key, y_key = y, x, y_key, x_key
+ if x_key < lo_key:
+ lo, lo_key = x, x_key
+ if hi_key < y_key:
+ hi, hi_key = y, y_key
+
+ return lo, hi
+
+
+def constrained_batches(
+ iterable, max_size, max_count=None, get_len=len, strict=True
+):
+ """Yield batches of items from *iterable* with a combined size limited by
+ *max_size*.
+
+ >>> iterable = [b'12345', b'123', b'12345678', b'1', b'1', b'12', b'1']
+ >>> list(constrained_batches(iterable, 10))
+ [(b'12345', b'123'), (b'12345678', b'1', b'1'), (b'12', b'1')]
+
+ If a *max_count* is supplied, the number of items per batch is also
+ limited:
+
+ >>> iterable = [b'12345', b'123', b'12345678', b'1', b'1', b'12', b'1']
+ >>> list(constrained_batches(iterable, 10, max_count = 2))
+ [(b'12345', b'123'), (b'12345678', b'1'), (b'1', b'12'), (b'1',)]
+
+ If a *get_len* function is supplied, use that instead of :func:`len` to
+ determine item size.
+
+ If *strict* is ``True``, raise ``ValueError`` if any single item is bigger
+ than *max_size*. Otherwise, allow single items to exceed *max_size*.
+ """
+ if max_size <= 0:
+ raise ValueError('maximum size must be greater than zero')
+
+ batch = []
+ batch_size = 0
+ batch_count = 0
+ for item in iterable:
+ item_len = get_len(item)
+ if strict and item_len > max_size:
+ raise ValueError('item size exceeds maximum size')
+
+ reached_count = batch_count == max_count
+ reached_size = item_len + batch_size > max_size
+ if batch_count and (reached_size or reached_count):
+ yield tuple(batch)
+ batch.clear()
+ batch_size = 0
+ batch_count = 0
+
+ batch.append(item)
+ batch_size += item_len
+ batch_count += 1
+
+ if batch:
+ yield tuple(batch)
+
+
+def gray_product(*iterables):
+ """Like :func:`itertools.product`, but return tuples in an order such
+ that only one element in the generated tuple changes from one iteration
+ to the next.
+
+ >>> list(gray_product('AB','CD'))
+ [('A', 'C'), ('B', 'C'), ('B', 'D'), ('A', 'D')]
+
+ This function consumes all of the input iterables before producing output.
+ If any of the input iterables have fewer than two items, ``ValueError``
+ is raised.
+
+ For information on the algorithm, see
+ `this section `__
+ of Donald Knuth's *The Art of Computer Programming*.
+ """
+ all_iterables = tuple(tuple(x) for x in iterables)
+ iterable_count = len(all_iterables)
+ for iterable in all_iterables:
+ if len(iterable) < 2:
+ raise ValueError("each iterable must have two or more items")
+
+ # This is based on "Algorithm H" from section 7.2.1.1, page 20.
+ # a holds the indexes of the source iterables for the n-tuple to be yielded
+ # f is the array of "focus pointers"
+ # o is the array of "directions"
+ a = [0] * iterable_count
+ f = list(range(iterable_count + 1))
+ o = [1] * iterable_count
+ while True:
+ yield tuple(all_iterables[i][a[i]] for i in range(iterable_count))
+ j = f[0]
+ f[0] = 0
+ if j == iterable_count:
+ break
+ a[j] = a[j] + o[j]
+ if a[j] == 0 or a[j] == len(all_iterables[j]) - 1:
+ o[j] = -o[j]
+ f[j] = f[j + 1]
+ f[j + 1] = j + 1
+
+
+def partial_product(*iterables):
+ """Yields tuples containing one item from each iterator, with subsequent
+ tuples changing a single item at a time by advancing each iterator until it
+ is exhausted. This sequence guarantees every value in each iterable is
+ output at least once without generating all possible combinations.
+
+ This may be useful, for example, when testing an expensive function.
+
+ >>> list(partial_product('AB', 'C', 'DEF'))
+ [('A', 'C', 'D'), ('B', 'C', 'D'), ('B', 'C', 'E'), ('B', 'C', 'F')]
+ """
+
+ iterators = list(map(iter, iterables))
+
+ try:
+ prod = [next(it) for it in iterators]
+ except StopIteration:
+ return
+ yield tuple(prod)
+
+ for i, it in enumerate(iterators):
+ for prod[i] in it:
+ yield tuple(prod)
+
+
+def takewhile_inclusive(predicate, iterable):
+ """A variant of :func:`takewhile` that yields one additional element.
+
+ >>> list(takewhile_inclusive(lambda x: x < 5, [1, 4, 6, 4, 1]))
+ [1, 4, 6]
+
+ :func:`takewhile` would return ``[1, 4]``.
+ """
+ for x in iterable:
+ if predicate(x):
+ yield x
+ else:
+ yield x
+ break
+
+
+def outer_product(func, xs, ys, *args, **kwargs):
+ """A generalized outer product that applies a binary function to all
+ pairs of items. Returns a 2D matrix with ``len(xs)`` rows and ``len(ys)``
+ columns.
+ Also accepts ``*args`` and ``**kwargs`` that are passed to ``func``.
+
+ Multiplication table:
+
+ >>> list(outer_product(mul, range(1, 4), range(1, 6)))
+ [(1, 2, 3, 4, 5), (2, 4, 6, 8, 10), (3, 6, 9, 12, 15)]
+
+ Cross tabulation:
+
+ >>> xs = ['A', 'B', 'A', 'A', 'B', 'B', 'A', 'A', 'B', 'B']
+ >>> ys = ['X', 'X', 'X', 'Y', 'Z', 'Z', 'Y', 'Y', 'Z', 'Z']
+ >>> rows = list(zip(xs, ys))
+ >>> count_rows = lambda x, y: rows.count((x, y))
+ >>> list(outer_product(count_rows, sorted(set(xs)), sorted(set(ys))))
+ [(2, 3, 0), (1, 0, 4)]
+
+ Usage with ``*args`` and ``**kwargs``:
+
+ >>> animals = ['cat', 'wolf', 'mouse']
+ >>> list(outer_product(min, animals, animals, key=len))
+ [('cat', 'cat', 'cat'), ('cat', 'wolf', 'wolf'), ('cat', 'wolf', 'mouse')]
+ """
+ ys = tuple(ys)
+ return batched(
+ starmap(lambda x, y: func(x, y, *args, **kwargs), product(xs, ys)),
+ n=len(ys),
+ )