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+"""Imported from the recipes section of the itertools documentation.
+
+All functions taken from the recipes section of the itertools library docs
+[1]_.
+Some backward-compatible usability improvements have been made.
+
+.. [1] http://docs.python.org/library/itertools.html#recipes
+
+"""
+import warnings
+from collections import deque
+from itertools import (
+ chain,
+ combinations,
+ count,
+ cycle,
+ groupby,
+ islice,
+ repeat,
+ starmap,
+ tee,
+ zip_longest,
+)
+import operator
+from random import randrange, sample, choice
+
+__all__ = [
+ 'all_equal',
+ 'consume',
+ 'convolve',
+ 'dotproduct',
+ 'first_true',
+ 'flatten',
+ 'grouper',
+ 'iter_except',
+ 'ncycles',
+ 'nth',
+ 'nth_combination',
+ 'padnone',
+ 'pad_none',
+ 'pairwise',
+ 'partition',
+ 'powerset',
+ 'prepend',
+ 'quantify',
+ 'random_combination_with_replacement',
+ 'random_combination',
+ 'random_permutation',
+ 'random_product',
+ 'repeatfunc',
+ 'roundrobin',
+ 'tabulate',
+ 'tail',
+ 'take',
+ 'unique_everseen',
+ 'unique_justseen',
+]
+
+
+def take(n, iterable):
+ """Return first *n* items of the iterable as a list.
+
+ >>> take(3, range(10))
+ [0, 1, 2]
+
+ If there are fewer than *n* items in the iterable, all of them are
+ returned.
+
+ >>> take(10, range(3))
+ [0, 1, 2]
+
+ """
+ return list(islice(iterable, n))
+
+
+def tabulate(function, start=0):
+ """Return an iterator over the results of ``func(start)``,
+ ``func(start + 1)``, ``func(start + 2)``...
+
+ *func* should be a function that accepts one integer argument.
+
+ If *start* is not specified it defaults to 0. It will be incremented each
+ time the iterator is advanced.
+
+ >>> square = lambda x: x ** 2
+ >>> iterator = tabulate(square, -3)
+ >>> take(4, iterator)
+ [9, 4, 1, 0]
+
+ """
+ return map(function, count(start))
+
+
+def tail(n, iterable):
+ """Return an iterator over the last *n* items of *iterable*.
+
+ >>> t = tail(3, 'ABCDEFG')
+ >>> list(t)
+ ['E', 'F', 'G']
+
+ """
+ return iter(deque(iterable, maxlen=n))
+
+
+def consume(iterator, n=None):
+ """Advance *iterable* by *n* steps. If *n* is ``None``, consume it
+ entirely.
+
+ Efficiently exhausts an iterator without returning values. Defaults to
+ consuming the whole iterator, but an optional second argument may be
+ provided to limit consumption.
+
+ >>> i = (x for x in range(10))
+ >>> next(i)
+ 0
+ >>> consume(i, 3)
+ >>> next(i)
+ 4
+ >>> consume(i)
+ >>> next(i)
+ Traceback (most recent call last):
+ File "<stdin>", line 1, in <module>
+ StopIteration
+
+ If the iterator has fewer items remaining than the provided limit, the
+ whole iterator will be consumed.
+
+ >>> i = (x for x in range(3))
+ >>> consume(i, 5)
+ >>> next(i)
+ Traceback (most recent call last):
+ File "<stdin>", line 1, in <module>
+ StopIteration
+
+ """
+ # Use functions that consume iterators at C speed.
+ if n is None:
+ # feed the entire iterator into a zero-length deque
+ deque(iterator, maxlen=0)
+ else:
+ # advance to the empty slice starting at position n
+ next(islice(iterator, n, n), None)
+
+
+def nth(iterable, n, default=None):
+ """Returns the nth item or a default value.
+
+ >>> l = range(10)
+ >>> nth(l, 3)
+ 3
+ >>> nth(l, 20, "zebra")
+ 'zebra'
+
+ """
+ return next(islice(iterable, n, None), default)
+
+
+def all_equal(iterable):
+ """
+ Returns ``True`` if all the elements are equal to each other.
+
+ >>> all_equal('aaaa')
+ True
+ >>> all_equal('aaab')
+ False
+
+ """
+ g = groupby(iterable)
+ return next(g, True) and not next(g, False)
+
+
+def quantify(iterable, pred=bool):
+ """Return the how many times the predicate is true.
+
+ >>> quantify([True, False, True])
+ 2
+
+ """
+ return sum(map(pred, iterable))
+
+
+def pad_none(iterable):
+ """Returns the sequence of elements and then returns ``None`` indefinitely.
+
+ >>> take(5, pad_none(range(3)))
+ [0, 1, 2, None, None]
+
+ Useful for emulating the behavior of the built-in :func:`map` function.
+
+ See also :func:`padded`.
+
+ """
+ return chain(iterable, repeat(None))
+
+
+padnone = pad_none
+
+
+def ncycles(iterable, n):
+ """Returns the sequence elements *n* times
+
+ >>> list(ncycles(["a", "b"], 3))
+ ['a', 'b', 'a', 'b', 'a', 'b']
+
+ """
+ return chain.from_iterable(repeat(tuple(iterable), n))
+
+
+def dotproduct(vec1, vec2):
+ """Returns the dot product of the two iterables.
+
+ >>> dotproduct([10, 10], [20, 20])
+ 400
+
+ """
+ return sum(map(operator.mul, vec1, vec2))
+
+
+def flatten(listOfLists):
+ """Return an iterator flattening one level of nesting in a list of lists.
+
+ >>> list(flatten([[0, 1], [2, 3]]))
+ [0, 1, 2, 3]
+
+ See also :func:`collapse`, which can flatten multiple levels of nesting.
+
+ """
+ return chain.from_iterable(listOfLists)
+
+
+def repeatfunc(func, times=None, *args):
+ """Call *func* with *args* repeatedly, returning an iterable over the
+ results.
+
+ If *times* is specified, the iterable will terminate after that many
+ repetitions:
+
+ >>> from operator import add
+ >>> times = 4
+ >>> args = 3, 5
+ >>> list(repeatfunc(add, times, *args))
+ [8, 8, 8, 8]
+
+ If *times* is ``None`` the iterable will not terminate:
+
+ >>> from random import randrange
+ >>> times = None
+ >>> args = 1, 11
+ >>> take(6, repeatfunc(randrange, times, *args)) # doctest:+SKIP
+ [2, 4, 8, 1, 8, 4]
+
+ """
+ if times is None:
+ return starmap(func, repeat(args))
+ return starmap(func, repeat(args, times))
+
+
+def _pairwise(iterable):
+ """Returns an iterator of paired items, overlapping, from the original
+
+ >>> take(4, pairwise(count()))
+ [(0, 1), (1, 2), (2, 3), (3, 4)]
+
+ On Python 3.10 and above, this is an alias for :func:`itertools.pairwise`.
+
+ """
+ a, b = tee(iterable)
+ next(b, None)
+ yield from zip(a, b)
+
+
+try:
+ from itertools import pairwise as itertools_pairwise
+except ImportError:
+ pairwise = _pairwise
+else:
+
+ def pairwise(iterable):
+ yield from itertools_pairwise(iterable)
+
+ pairwise.__doc__ = _pairwise.__doc__
+
+
+def grouper(iterable, n, fillvalue=None):
+ """Collect data into fixed-length chunks or blocks.
+
+ >>> list(grouper('ABCDEFG', 3, 'x'))
+ [('A', 'B', 'C'), ('D', 'E', 'F'), ('G', 'x', 'x')]
+
+ """
+ if isinstance(iterable, int):
+ warnings.warn(
+ "grouper expects iterable as first parameter", DeprecationWarning
+ )
+ n, iterable = iterable, n
+ args = [iter(iterable)] * n
+ return zip_longest(fillvalue=fillvalue, *args)
+
+
+def roundrobin(*iterables):
+ """Yields an item from each iterable, alternating between them.
+
+ >>> list(roundrobin('ABC', 'D', 'EF'))
+ ['A', 'D', 'E', 'B', 'F', 'C']
+
+ This function produces the same output as :func:`interleave_longest`, but
+ may perform better for some inputs (in particular when the number of
+ iterables is small).
+
+ """
+ # Recipe credited to George Sakkis
+ pending = len(iterables)
+ nexts = cycle(iter(it).__next__ for it in iterables)
+ while pending:
+ try:
+ for next in nexts:
+ yield next()
+ except StopIteration:
+ pending -= 1
+ nexts = cycle(islice(nexts, pending))
+
+
+def partition(pred, iterable):
+ """
+ Returns a 2-tuple of iterables derived from the input iterable.
+ The first yields the items that have ``pred(item) == False``.
+ The second yields the items that have ``pred(item) == True``.
+
+ >>> is_odd = lambda x: x % 2 != 0
+ >>> iterable = range(10)
+ >>> even_items, odd_items = partition(is_odd, iterable)
+ >>> list(even_items), list(odd_items)
+ ([0, 2, 4, 6, 8], [1, 3, 5, 7, 9])
+
+ If *pred* is None, :func:`bool` is used.
+
+ >>> iterable = [0, 1, False, True, '', ' ']
+ >>> false_items, true_items = partition(None, iterable)
+ >>> list(false_items), list(true_items)
+ ([0, False, ''], [1, True, ' '])
+
+ """
+ if pred is None:
+ pred = bool
+
+ evaluations = ((pred(x), x) for x in iterable)
+ t1, t2 = tee(evaluations)
+ return (
+ (x for (cond, x) in t1 if not cond),
+ (x for (cond, x) in t2 if cond),
+ )
+
+
+def powerset(iterable):
+ """Yields all possible subsets of the iterable.
+
+ >>> list(powerset([1, 2, 3]))
+ [(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)]
+
+ :func:`powerset` will operate on iterables that aren't :class:`set`
+ instances, so repeated elements in the input will produce repeated elements
+ in the output. Use :func:`unique_everseen` on the input to avoid generating
+ duplicates:
+
+ >>> seq = [1, 1, 0]
+ >>> list(powerset(seq))
+ [(), (1,), (1,), (0,), (1, 1), (1, 0), (1, 0), (1, 1, 0)]
+ >>> from more_itertools import unique_everseen
+ >>> list(powerset(unique_everseen(seq)))
+ [(), (1,), (0,), (1, 0)]
+
+ """
+ s = list(iterable)
+ return chain.from_iterable(combinations(s, r) for r in range(len(s) + 1))
+
+
+def unique_everseen(iterable, key=None):
+ """
+ Yield unique elements, preserving order.
+
+ >>> list(unique_everseen('AAAABBBCCDAABBB'))
+ ['A', 'B', 'C', 'D']
+ >>> list(unique_everseen('ABBCcAD', str.lower))
+ ['A', 'B', 'C', 'D']
+
+ Sequences with a mix of hashable and unhashable items can be used.
+ The function will be slower (i.e., `O(n^2)`) for unhashable items.
+
+ Remember that ``list`` objects are unhashable - you can use the *key*
+ parameter to transform the list to a tuple (which is hashable) to
+ avoid a slowdown.
+
+ >>> iterable = ([1, 2], [2, 3], [1, 2])
+ >>> list(unique_everseen(iterable)) # Slow
+ [[1, 2], [2, 3]]
+ >>> list(unique_everseen(iterable, key=tuple)) # Faster
+ [[1, 2], [2, 3]]
+
+ Similary, you may want to convert unhashable ``set`` objects with
+ ``key=frozenset``. For ``dict`` objects,
+ ``key=lambda x: frozenset(x.items())`` can be used.
+
+ """
+ seenset = set()
+ seenset_add = seenset.add
+ seenlist = []
+ seenlist_add = seenlist.append
+ use_key = key is not None
+
+ for element in iterable:
+ k = key(element) if use_key else element
+ try:
+ if k not in seenset:
+ seenset_add(k)
+ yield element
+ except TypeError:
+ if k not in seenlist:
+ seenlist_add(k)
+ yield element
+
+
+def unique_justseen(iterable, key=None):
+ """Yields elements in order, ignoring serial duplicates
+
+ >>> list(unique_justseen('AAAABBBCCDAABBB'))
+ ['A', 'B', 'C', 'D', 'A', 'B']
+ >>> list(unique_justseen('ABBCcAD', str.lower))
+ ['A', 'B', 'C', 'A', 'D']
+
+ """
+ return map(next, map(operator.itemgetter(1), groupby(iterable, key)))
+
+
+def iter_except(func, exception, first=None):
+ """Yields results from a function repeatedly until an exception is raised.
+
+ Converts a call-until-exception interface to an iterator interface.
+ Like ``iter(func, sentinel)``, but uses an exception instead of a sentinel
+ to end the loop.
+
+ >>> l = [0, 1, 2]
+ >>> list(iter_except(l.pop, IndexError))
+ [2, 1, 0]
+
+ """
+ try:
+ if first is not None:
+ yield first()
+ while 1:
+ yield func()
+ except exception:
+ pass
+
+
+def first_true(iterable, default=None, pred=None):
+ """
+ Returns the first true value in the iterable.
+
+ If no true value is found, returns *default*
+
+ If *pred* is not None, returns the first item for which
+ ``pred(item) == True`` .
+
+ >>> first_true(range(10))
+ 1
+ >>> first_true(range(10), pred=lambda x: x > 5)
+ 6
+ >>> first_true(range(10), default='missing', pred=lambda x: x > 9)
+ 'missing'
+
+ """
+ return next(filter(pred, iterable), default)
+
+
+def random_product(*args, repeat=1):
+ """Draw an item at random from each of the input iterables.
+
+ >>> random_product('abc', range(4), 'XYZ') # doctest:+SKIP
+ ('c', 3, 'Z')
+
+ If *repeat* is provided as a keyword argument, that many items will be
+ drawn from each iterable.
+
+ >>> random_product('abcd', range(4), repeat=2) # doctest:+SKIP
+ ('a', 2, 'd', 3)
+
+ This equivalent to taking a random selection from
+ ``itertools.product(*args, **kwarg)``.
+
+ """
+ pools = [tuple(pool) for pool in args] * repeat
+ return tuple(choice(pool) for pool in pools)
+
+
+def random_permutation(iterable, r=None):
+ """Return a random *r* length permutation of the elements in *iterable*.
+
+ If *r* is not specified or is ``None``, then *r* defaults to the length of
+ *iterable*.
+
+ >>> random_permutation(range(5)) # doctest:+SKIP
+ (3, 4, 0, 1, 2)
+
+ This equivalent to taking a random selection from
+ ``itertools.permutations(iterable, r)``.
+
+ """
+ pool = tuple(iterable)
+ r = len(pool) if r is None else r
+ return tuple(sample(pool, r))
+
+
+def random_combination(iterable, r):
+ """Return a random *r* length subsequence of the elements in *iterable*.
+
+ >>> random_combination(range(5), 3) # doctest:+SKIP
+ (2, 3, 4)
+
+ This equivalent to taking a random selection from
+ ``itertools.combinations(iterable, r)``.
+
+ """
+ pool = tuple(iterable)
+ n = len(pool)
+ indices = sorted(sample(range(n), r))
+ return tuple(pool[i] for i in indices)
+
+
+def random_combination_with_replacement(iterable, r):
+ """Return a random *r* length subsequence of elements in *iterable*,
+ allowing individual elements to be repeated.
+
+ >>> random_combination_with_replacement(range(3), 5) # doctest:+SKIP
+ (0, 0, 1, 2, 2)
+
+ This equivalent to taking a random selection from
+ ``itertools.combinations_with_replacement(iterable, r)``.
+
+ """
+ pool = tuple(iterable)
+ n = len(pool)
+ indices = sorted(randrange(n) for i in range(r))
+ return tuple(pool[i] for i in indices)
+
+
+def nth_combination(iterable, r, index):
+ """Equivalent to ``list(combinations(iterable, r))[index]``.
+
+ The subsequences of *iterable* that are of length *r* can be ordered
+ lexicographically. :func:`nth_combination` computes the subsequence at
+ sort position *index* directly, without computing the previous
+ subsequences.
+
+ >>> nth_combination(range(5), 3, 5)
+ (0, 3, 4)
+
+ ``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 = 1
+ k = min(r, n - r)
+ for i in range(1, k + 1):
+ c = c * (n - k + i) // i
+
+ if index < 0:
+ index += c
+
+ if (index < 0) or (index >= c):
+ raise IndexError
+
+ result = []
+ while r:
+ c, n, r = c * r // n, n - 1, r - 1
+ while index >= c:
+ index -= c
+ c, n = c * (n - r) // n, n - 1
+ result.append(pool[-1 - n])
+
+ return tuple(result)
+
+
+def prepend(value, iterator):
+ """Yield *value*, followed by the elements in *iterator*.
+
+ >>> value = '0'
+ >>> iterator = ['1', '2', '3']
+ >>> list(prepend(value, iterator))
+ ['0', '1', '2', '3']
+
+ To prepend multiple values, see :func:`itertools.chain`
+ or :func:`value_chain`.
+
+ """
+ return chain([value], iterator)
+
+
+def convolve(signal, kernel):
+ """Convolve the iterable *signal* with the iterable *kernel*.
+
+ >>> signal = (1, 2, 3, 4, 5)
+ >>> kernel = [3, 2, 1]
+ >>> list(convolve(signal, kernel))
+ [3, 8, 14, 20, 26, 14, 5]
+
+ Note: the input arguments are not interchangeable, as the *kernel*
+ is immediately consumed and stored.
+
+ """
+ kernel = tuple(kernel)[::-1]
+ n = len(kernel)
+ window = deque([0], maxlen=n) * n
+ for x in chain(signal, repeat(0, n - 1)):
+ window.append(x)
+ yield sum(map(operator.mul, kernel, window))