:mod:`itertools` --- Functions creating iterators for efficient looping

.. module:: itertools
 :synopsis: Functions creating iterators for efficient looping.

.. moduleauthor:: Raymond Hettinger <python@rcn.com>

.. sectionauthor:: Raymond Hettinger <python@rcn.com>

.. testsetup::

 from itertools import *

This module implements a number of :term:`iterator` building blocks inspired by constructs from APL, Haskell, and SML. Each has been recast in a form suitable for Python.

The module standardizes a core set of fast, memory efficient tools that are useful by themselves or in combination. Together, they form an "iterator algebra" making it possible to construct specialized tools succinctly and efficiently in pure Python.

For instance, SML provides a tabulation tool: tabulate(f) which produces a sequence f(0), f(1), .... The same effect can be achieved in Python by combining :func:`map` and :func:`count` to form map(f, count()).

These tools and their built-in counterparts also work well with the high-speed functions in the :mod:`operator` module. For example, the multiplication operator can be mapped across two vectors to form an efficient dot-product: sum(map(operator.mul, vector1, vector2)).

Infinite iterators:

Iterators terminating on the shortest input sequence:

Combinatoric iterators:

Itertool functions

The following module functions all construct and return iterators. Some provide streams of infinite length, so they should only be accessed by functions or loops that truncate the stream.

.. function:: accumulate(iterable[, func])

 Make an iterator that returns accumulated sums, or accumulated
 results of other binary functions (specified via the optional
 *func* argument). If *func* is supplied, it should be a function
 of two arguments. Elements of the input *iterable* may be any type
 that can be accepted as arguments to *func*. (For example, with
 the default operation of addition, elements may be any addable
 type including :class:`~decimal.Decimal` or
 :class:`~fractions.Fraction`.) If the input iterable is empty, the
 output iterable will also be empty.

 Roughly equivalent to::

 def accumulate(iterable, func=operator.add):
 'Return running totals'
 # accumulate([1,2,3,4,5]) --> 1 3 6 10 15
 # accumulate([1,2,3,4,5], operator.mul) --> 1 2 6 24 120
 it = iter(iterable)
 try:
 total = next(it)
 except StopIteration:
 return
 yield total
 for element in it:
 total = func(total, element)
 yield total

 There are a number of uses for the *func* argument. It can be set to
 :func:`min` for a running minimum, :func:`max` for a running maximum, or
 :func:`operator.mul` for a running product. Amortization tables can be
 built by accumulating interest and applying payments. First-order
 `recurrence relations <https://en.wikipedia.org/wiki/Recurrence_relation>`_
 can be modeled by supplying the initial value in the iterable and using only
 the accumulated total in *func* argument::

 >>> data = [3, 4, 6, 2, 1, 9, 0, 7, 5, 8]
 >>> list(accumulate(data, operator.mul)) # running product
 [3, 12, 72, 144, 144, 1296, 0, 0, 0, 0]
 >>> list(accumulate(data, max)) # running maximum
 [3, 4, 6, 6, 6, 9, 9, 9, 9, 9]

 # Amortize a 5% loan of 1000 with 4 annual payments of 90
 >>> cashflows = [1000, -90, -90, -90, -90]
 >>> list(accumulate(cashflows, lambda bal, pmt: bal*1.05 + pmt))
 [1000, 960.0, 918.0, 873.9000000000001, 827.5950000000001]

 # Chaotic recurrence relation https://en.wikipedia.org/wiki/Logistic_map
 >>> logistic_map = lambda x, _: r * x * (1 - x)
 >>> r = 3.8
 >>> x0 = 0.4
 >>> inputs = repeat(x0, 36) # only the initial value is used
 >>> [format(x, '.2f') for x in accumulate(inputs, logistic_map)]
 ['0.40', '0.91', '0.30', '0.81', '0.60', '0.92', '0.29', '0.79', '0.63',
 '0.88', '0.39', '0.90', '0.33', '0.84', '0.52', '0.95', '0.18', '0.57',
 '0.93', '0.25', '0.71', '0.79', '0.63', '0.88', '0.39', '0.91', '0.32',
 '0.83', '0.54', '0.95', '0.20', '0.60', '0.91', '0.30', '0.80', '0.60']

 See :func:`functools.reduce` for a similar function that returns only the
 final accumulated value.

 .. versionadded:: 3.2

 .. versionchanged:: 3.3
 Added the optional *func* parameter.

.. function:: chain(*iterables)

 Make an iterator that returns elements from the first iterable until it is
 exhausted, then proceeds to the next iterable, until all of the iterables are
 exhausted. Used for treating consecutive sequences as a single sequence.
 Roughly equivalent to::

 def chain(*iterables):
 # chain('ABC', 'DEF') --> A B C D E F
 for it in iterables:
 for element in it:
 yield element

.. classmethod:: chain.from_iterable(iterable)

 Alternate constructor for :func:`chain`. Gets chained inputs from a
 single iterable argument that is evaluated lazily. Roughly equivalent to::

 def from_iterable(iterables):
 # chain.from_iterable(['ABC', 'DEF']) --> A B C D E F
 for it in iterables:
 for element in it:
 yield element

.. function:: combinations(iterable, r)

 Return *r* length subsequences of elements from the input *iterable*.

 Combinations are emitted in lexicographic sort order. So, if the
 input *iterable* is sorted, the combination tuples will be produced
 in sorted order.

 Elements are treated as unique based on their position, not on their
 value. So if the input elements are unique, there will be no repeat
 values in each combination.

 Roughly equivalent to::

 def combinations(iterable, r):
 # combinations('ABCD', 2) --> AB AC AD BC BD CD
 # combinations(range(4), 3) --> 012 013 023 123
 pool = tuple(iterable)
 n = len(pool)
 if r > n:
 return
 indices = list(range(r))
 yield tuple(pool[i] for i in indices)
 while True:
 for i in reversed(range(r)):
 if indices[i] != i + n - r:
 break
 else:
 return
 indices[i] += 1
 for j in range(i+1, r):
 indices[j] = indices[j-1] + 1
 yield tuple(pool[i] for i in indices)

 The code for :func:`combinations` can be also expressed as a subsequence
 of :func:`permutations` after filtering entries where the elements are not
 in sorted order (according to their position in the input pool)::

 def combinations(iterable, r):
 pool = tuple(iterable)
 n = len(pool)
 for indices in permutations(range(n), r):
 if sorted(indices) == list(indices):
 yield tuple(pool[i] for i in indices)

 The number of items returned is ``n! / r! / (n-r)!`` when ``0 <= r <= n``
 or zero when ``r > n``.

.. function:: combinations_with_replacement(iterable, r)

 Return *r* length subsequences of elements from the input *iterable*
 allowing individual elements to be repeated more than once.

 Combinations are emitted in lexicographic sort order. So, if the
 input *iterable* is sorted, the combination tuples will be produced
 in sorted order.

 Elements are treated as unique based on their position, not on their
 value. So if the input elements are unique, the generated combinations
 will also be unique.

 Roughly equivalent to::

 def combinations_with_replacement(iterable, r):
 # combinations_with_replacement('ABC', 2) --> AA AB AC BB BC CC
 pool = tuple(iterable)
 n = len(pool)
 if not n and r:
 return
 indices = [0] * r
 yield tuple(pool[i] for i in indices)
 while True:
 for i in reversed(range(r)):
 if indices[i] != n - 1:
 break
 else:
 return
 indices[i:] = [indices[i] + 1] * (r - i)
 yield tuple(pool[i] for i in indices)

 The code for :func:`combinations_with_replacement` can be also expressed as
 a subsequence of :func:`product` after filtering entries where the elements
 are not in sorted order (according to their position in the input pool)::

 def combinations_with_replacement(iterable, r):
 pool = tuple(iterable)
 n = len(pool)
 for indices in product(range(n), repeat=r):
 if sorted(indices) == list(indices):
 yield tuple(pool[i] for i in indices)

 The number of items returned is ``(n+r-1)! / r! / (n-1)!`` when ``n > 0``.

 .. versionadded:: 3.1

.. function:: compress(data, selectors)

 Make an iterator that filters elements from *data* returning only those that
 have a corresponding element in *selectors* that evaluates to ``True``.
 Stops when either the *data* or *selectors* iterables has been exhausted.
 Roughly equivalent to::

 def compress(data, selectors):
 # compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F
 return (d for d, s in zip(data, selectors) if s)

 .. versionadded:: 3.1

.. function:: count(start=0, step=1)

 Make an iterator that returns evenly spaced values starting with number *start*. Often
 used as an argument to :func:`map` to generate consecutive data points.
 Also, used with :func:`zip` to add sequence numbers. Roughly equivalent to::

 def count(start=0, step=1):
 # count(10) --> 10 11 12 13 14 ...
 # count(2.5, 0.5) -> 2.5 3.0 3.5 ...
 n = start
 while True:
 yield n
 n += step

 When counting with floating point numbers, better accuracy can sometimes be
 achieved by substituting multiplicative code such as: ``(start + step * i
 for i in count())``.

 .. versionchanged:: 3.1
 Added *step* argument and allowed non-integer arguments.

.. function:: cycle(iterable)

 Make an iterator returning elements from the iterable and saving a copy of each.
 When the iterable is exhausted, return elements from the saved copy. Repeats
 indefinitely. Roughly equivalent to::

 def cycle(iterable):
 # cycle('ABCD') --> A B C D A B C D A B C D ...
 saved = []
 for element in iterable:
 yield element
 saved.append(element)
 while saved:
 for element in saved:
 yield element

 Note, this member of the toolkit may require significant auxiliary storage
 (depending on the length of the iterable).

.. function:: dropwhile(predicate, iterable)

 Make an iterator that drops elements from the iterable as long as the predicate
 is true; afterwards, returns every element. Note, the iterator does not produce
 *any* output until the predicate first becomes false, so it may have a lengthy
 start-up time. Roughly equivalent to::

 def dropwhile(predicate, iterable):
 # dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1
 iterable = iter(iterable)
 for x in iterable:
 if not predicate(x):
 yield x
 break
 for x in iterable:
 yield x

.. function:: filterfalse(predicate, iterable)

 Make an iterator that filters elements from iterable returning only those for
 which the predicate is ``False``. If *predicate* is ``None``, return the items
 that are false. Roughly equivalent to::

 def filterfalse(predicate, iterable):
 # filterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8
 if predicate is None:
 predicate = bool
 for x in iterable:
 if not predicate(x):
 yield x

.. function:: groupby(iterable, key=None)

 Make an iterator that returns consecutive keys and groups from the *iterable*.
 The *key* is a function computing a key value for each element. If not
 specified or is ``None``, *key* defaults to an identity function and returns
 the element unchanged. Generally, the iterable needs to already be sorted on
 the same key function.

 The operation of :func:`groupby` is similar to the ``uniq`` filter in Unix. It
 generates a break or new group every time the value of the key function changes
 (which is why it is usually necessary to have sorted the data using the same key
 function). That behavior differs from SQL's GROUP BY which aggregates common
 elements regardless of their input order.

 The returned group is itself an iterator that shares the underlying iterable
 with :func:`groupby`. Because the source is shared, when the :func:`groupby`
 object is advanced, the previous group is no longer visible. So, if that data
 is needed later, it should be stored as a list::

 groups = []
 uniquekeys = []
 data = sorted(data, key=keyfunc)
 for k, g in groupby(data, keyfunc):
 groups.append(list(g)) # Store group iterator as a list
 uniquekeys.append(k)

 :func:`groupby` is roughly equivalent to::

 class groupby:
 # [k for k, g in groupby('AAAABBBCCDAABBB')] --> A B C D A B
 # [list(g) for k, g in groupby('AAAABBBCCD')] --> AAAA BBB CC D
 def __init__(self, iterable, key=None):
 if key is None:
 key = lambda x: x
 self.keyfunc = key
 self.it = iter(iterable)
 self.tgtkey = self.currkey = self.currvalue = object()
 def __iter__(self):
 return self
 def __next__(self):
 self.id = object()
 while self.currkey == self.tgtkey:
 self.currvalue = next(self.it) # Exit on StopIteration
 self.currkey = self.keyfunc(self.currvalue)
 self.tgtkey = self.currkey
 return (self.currkey, self._grouper(self.tgtkey, self.id))
 def _grouper(self, tgtkey, id):
 while self.id is id and self.currkey == tgtkey:
 yield self.currvalue
 try:
 self.currvalue = next(self.it)
 except StopIteration:
 return
 self.currkey = self.keyfunc(self.currvalue)

.. function:: islice(iterable, stop)
 islice(iterable, start, stop[, step])

 Make an iterator that returns selected elements from the iterable. If *start* is
 non-zero, then elements from the iterable are skipped until start is reached.
 Afterward, elements are returned consecutively unless *step* is set higher than
 one which results in items being skipped. If *stop* is ``None``, then iteration
 continues until the iterator is exhausted, if at all; otherwise, it stops at the
 specified position. Unlike regular slicing, :func:`islice` does not support
 negative values for *start*, *stop*, or *step*. Can be used to extract related
 fields from data where the internal structure has been flattened (for example, a
 multi-line report may list a name field on every third line). Roughly equivalent to::

 def islice(iterable, *args):
 # islice('ABCDEFG', 2) --> A B
 # islice('ABCDEFG', 2, 4) --> C D
 # islice('ABCDEFG', 2, None) --> C D E F G
 # islice('ABCDEFG', 0, None, 2) --> A C E G
 s = slice(*args)
 start, stop, step = s.start or 0, s.stop or sys.maxsize, s.step or 1
 it = iter(range(start, stop, step))
 try:
 nexti = next(it)
 except StopIteration:
 # Consume *iterable* up to the *start* position.
 for i, element in zip(range(start), iterable):
 pass
 return
 try:
 for i, element in enumerate(iterable):
 if i == nexti:
 yield element
 nexti = next(it)
 except StopIteration:
 # Consume to *stop*.
 for i, element in zip(range(i + 1, stop), iterable):
 pass

 If *start* is ``None``, then iteration starts at zero. If *step* is ``None``,
 then the step defaults to one.

.. function:: permutations(iterable, r=None)

 Return successive *r* length permutations of elements in the *iterable*.

 If *r* is not specified or is ``None``, then *r* defaults to the length
 of the *iterable* and all possible full-length permutations
 are generated.

 Permutations are emitted in lexicographic sort order. So, if the
 input *iterable* is sorted, the permutation tuples will be produced
 in sorted order.

 Elements are treated as unique based on their position, not on their
 value. So if the input elements are unique, there will be no repeat
 values in each permutation.

 Roughly equivalent to::

 def permutations(iterable, r=None):
 # permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC
 # permutations(range(3)) --> 012 021 102 120 201 210
 pool = tuple(iterable)
 n = len(pool)
 r = n if r is None else r
 if r > n:
 return
 indices = list(range(n))
 cycles = list(range(n, n-r, -1))
 yield tuple(pool[i] for i in indices[:r])
 while n:
 for i in reversed(range(r)):
 cycles[i] -= 1
 if cycles[i] == 0:
 indices[i:] = indices[i+1:] + indices[i:i+1]
 cycles[i] = n - i
 else:
 j = cycles[i]
 indices[i], indices[-j] = indices[-j], indices[i]
 yield tuple(pool[i] for i in indices[:r])
 break
 else:
 return

 The code for :func:`permutations` can be also expressed as a subsequence of
 :func:`product`, filtered to exclude entries with repeated elements (those
 from the same position in the input pool)::

 def permutations(iterable, r=None):
 pool = tuple(iterable)
 n = len(pool)
 r = n if r is None else r
 for indices in product(range(n), repeat=r):
 if len(set(indices)) == r:
 yield tuple(pool[i] for i in indices)

 The number of items returned is ``n! / (n-r)!`` when ``0 <= r <= n``
 or zero when ``r > n``.

.. function:: product(*iterables, repeat=1)

 Cartesian product of input iterables.

 Roughly equivalent to nested for-loops in a generator expression. For example,
 ``product(A, B)`` returns the same as ``((x,y) for x in A for y in B)``.

 The nested loops cycle like an odometer with the rightmost element advancing
 on every iteration. This pattern creates a lexicographic ordering so that if
 the input's iterables are sorted, the product tuples are emitted in sorted
 order.

 To compute the product of an iterable with itself, specify the number of
 repetitions with the optional *repeat* keyword argument. For example,
 ``product(A, repeat=4)`` means the same as ``product(A, A, A, A)``.

 This function is roughly equivalent to the following code, except that the
 actual implementation does not build up intermediate results in memory::

 def product(*args, repeat=1):
 # product('ABCD', 'xy') --> Ax Ay Bx By Cx Cy Dx Dy
 # product(range(2), repeat=3) --> 000 001 010 011 100 101 110 111
 pools = [tuple(pool) for pool in args] * repeat
 result = [[]]
 for pool in pools:
 result = [x+[y] for x in result for y in pool]
 for prod in result:
 yield tuple(prod)

.. function:: repeat(object[, times])

 Make an iterator that returns *object* over and over again. Runs indefinitely
 unless the *times* argument is specified. Used as argument to :func:`map` for
 invariant parameters to the called function. Also used with :func:`zip` to
 create an invariant part of a tuple record.

 Roughly equivalent to::

 def repeat(object, times=None):
 # repeat(10, 3) --> 10 10 10
 if times is None:
 while True:
 yield object
 else:
 for i in range(times):
 yield object

 A common use for *repeat* is to supply a stream of constant values to *map*
 or *zip*::

 >>> list(map(pow, range(10), repeat(2)))
 [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

.. function:: starmap(function, iterable)

 Make an iterator that computes the function using arguments obtained from
 the iterable. Used instead of :func:`map` when argument parameters are already
 grouped in tuples from a single iterable (the data has been "pre-zipped"). The
 difference between :func:`map` and :func:`starmap` parallels the distinction
 between ``function(a,b)`` and ``function(*c)``. Roughly equivalent to::

 def starmap(function, iterable):
 # starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000
 for args in iterable:
 yield function(*args)

.. function:: takewhile(predicate, iterable)

 Make an iterator that returns elements from the iterable as long as the
 predicate is true. Roughly equivalent to::

 def takewhile(predicate, iterable):
 # takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4
 for x in iterable:
 if predicate(x):
 yield x
 else:
 break

.. function:: tee(iterable, n=2)

 Return *n* independent iterators from a single iterable.

 The following Python code helps explain what *tee* does (although the actual
 implementation is more complex and uses only a single underlying
 :abbr:`FIFO (first-in, first-out)` queue).

 Roughly equivalent to::

 def tee(iterable, n=2):
 it = iter(iterable)
 deques = [collections.deque() for i in range(n)]
 def gen(mydeque):
 while True:
 if not mydeque: # when the local deque is empty
 try:
 newval = next(it) # fetch a new value and
 except StopIteration:
 return
 for d in deques: # load it to all the deques
 d.append(newval)
 yield mydeque.popleft()
 return tuple(gen(d) for d in deques)

 Once :func:`tee` has made a split, the original *iterable* should not be
 used anywhere else; otherwise, the *iterable* could get advanced without
 the tee objects being informed.

 This itertool may require significant auxiliary storage (depending on how
 much temporary data needs to be stored). In general, if one iterator uses
 most or all of the data before another iterator starts, it is faster to use
 :func:`list` instead of :func:`tee`.

.. function:: zip_longest(*iterables, fillvalue=None)

 Make an iterator that aggregates elements from each of the iterables. If the
 iterables are of uneven length, missing values are filled-in with *fillvalue*.
 Iteration continues until the longest iterable is exhausted. Roughly equivalent to::

 def zip_longest(*args, fillvalue=None):
 # zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-
 iterators = [iter(it) for it in args]
 num_active = len(iterators)
 if not num_active:
 return
 while True:
 values = []
 for i, it in enumerate(iterators):
 try:
 value = next(it)
 except StopIteration:
 num_active -= 1
 if not num_active:
 return
 iterators[i] = repeat(fillvalue)
 value = fillvalue
 values.append(value)
 yield tuple(values)

 If one of the iterables is potentially infinite, then the :func:`zip_longest`
 function should be wrapped with something that limits the number of calls
 (for example :func:`islice` or :func:`takewhile`). If not specified,
 *fillvalue* defaults to ``None``.

Itertools Recipes

This section shows recipes for creating an extended toolset using the existing itertools as building blocks.

The extended tools offer the same high performance as the underlying toolset. The superior memory performance is kept by processing elements one at a time rather than bringing the whole iterable into memory all at once. Code volume is kept small by linking the tools together in a functional style which helps eliminate temporary variables. High speed is retained by preferring "vectorized" building blocks over the use of for-loops and :term:`generator`s which incur interpreter overhead.

.. testcode::

 def take(n, iterable):
 "Return first n items of the iterable as a list"
 return list(islice(iterable, n))

 def prepend(value, iterator):
 "Prepend a single value in front of an iterator"
 # prepend(1, [2, 3, 4]) -> 1 2 3 4
 return chain([value], iterator)

 def tabulate(function, start=0):
 "Return function(0), function(1), ..."
 return map(function, count(start))

 def tail(n, iterable):
 "Return an iterator over the last n items"
 # tail(3, 'ABCDEFG') --> E F G
 return iter(collections.deque(iterable, maxlen=n))

 def consume(iterator, n=None):
 "Advance the iterator n-steps ahead. If n is None, consume entirely."
 # Use functions that consume iterators at C speed.
 if n is None:
 # feed the entire iterator into a zero-length deque
 collections.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"
 return next(islice(iterable, n, None), default)

 def all_equal(iterable):
 "Returns True if all the elements are equal to each other"
 g = groupby(iterable)
 return next(g, True) and not next(g, False)

 def quantify(iterable, pred=bool):
 "Count how many times the predicate is true"
 return sum(map(pred, iterable))

 def padnone(iterable):
 """Returns the sequence elements and then returns None indefinitely.

 Useful for emulating the behavior of the built-in map() function.
 """
 return chain(iterable, repeat(None))

 def ncycles(iterable, n):
 "Returns the sequence elements n times"
 return chain.from_iterable(repeat(tuple(iterable), n))

 def dotproduct(vec1, vec2):
 return sum(map(operator.mul, vec1, vec2))

 def flatten(listOfLists):
 "Flatten one level of nesting"
 return chain.from_iterable(listOfLists)

 def repeatfunc(func, times=None, *args):
 """Repeat calls to func with specified arguments.

 Example: repeatfunc(random.random)
 """
 if times is None:
 return starmap(func, repeat(args))
 return starmap(func, repeat(args, times))

 def pairwise(iterable):
 "s -> (s0,s1), (s1,s2), (s2, s3), ..."
 a, b = tee(iterable)
 next(b, None)
 return zip(a, b)

 def grouper(iterable, n, fillvalue=None):
 "Collect data into fixed-length chunks or blocks"
 # grouper('ABCDEFG', 3, 'x') --> ABC DEF Gxx"
 args = [iter(iterable)] * n
 return zip_longest(*args, fillvalue=fillvalue)

 def roundrobin(*iterables):
 "roundrobin('ABC', 'D', 'EF') --> A D E B F C"
 # Recipe credited to George Sakkis
 num_active = len(iterables)
 nexts = cycle(iter(it).__next__ for it in iterables)
 while num_active:
 try:
 for next in nexts:
 yield next()
 except StopIteration:
 # Remove the iterator we just exhausted from the cycle.
 num_active -= 1
 nexts = cycle(islice(nexts, num_active))

 def partition(pred, iterable):
 'Use a predicate to partition entries into false entries and true entries'
 # partition(is_odd, range(10)) --> 0 2 4 6 8 and 1 3 5 7 9
 t1, t2 = tee(iterable)
 return filterfalse(pred, t1), filter(pred, t2)

 def powerset(iterable):
 "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
 s = list(iterable)
 return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))

 def unique_everseen(iterable, key=None):
 "List unique elements, preserving order. Remember all elements ever seen."
 # unique_everseen('AAAABBBCCDAABBB') --> A B C D
 # unique_everseen('ABBCcAD', str.lower) --> A B C D
 seen = set()
 seen_add = seen.add
 if key is None:
 for element in filterfalse(seen.__contains__, iterable):
 seen_add(element)
 yield element
 else:
 for element in iterable:
 k = key(element)
 if k not in seen:
 seen_add(k)
 yield element

 def unique_justseen(iterable, key=None):
 "List unique elements, preserving order. Remember only the element just seen."
 # unique_justseen('AAAABBBCCDAABBB') --> A B C D A B
 # unique_justseen('ABBCcAD', str.lower) --> A B C A D
 return map(next, map(itemgetter(1), groupby(iterable, key)))

 def iter_except(func, exception, first=None):
 """ Call a function repeatedly until an exception is raised.

 Converts a call-until-exception interface to an iterator interface.
 Like builtins.iter(func, sentinel) but uses an exception instead
 of a sentinel to end the loop.

 Examples:
 iter_except(functools.partial(heappop, h), IndexError) # priority queue iterator
 iter_except(d.popitem, KeyError) # non-blocking dict iterator
 iter_except(d.popleft, IndexError) # non-blocking deque iterator
 iter_except(q.get_nowait, Queue.Empty) # loop over a producer Queue
 iter_except(s.pop, KeyError) # non-blocking set iterator

 """
 try:
 if first is not None:
 yield first() # For database APIs needing an initial cast to db.first()
 while True:
 yield func()
 except exception:
 pass

 def first_true(iterable, default=False, 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) is true.

 """
 # first_true([a,b,c], x) --> a or b or c or x
 # first_true([a,b], x, f) --> a if f(a) else b if f(b) else x
 return next(filter(pred, iterable), default)

 def random_product(*args, repeat=1):
 "Random selection from itertools.product(*args, **kwds)"
 pools = [tuple(pool) for pool in args] * repeat
 return tuple(random.choice(pool) for pool in pools)

 def random_permutation(iterable, r=None):
 "Random selection from itertools.permutations(iterable, r)"
 pool = tuple(iterable)
 r = len(pool) if r is None else r
 return tuple(random.sample(pool, r))

 def random_combination(iterable, r):
 "Random selection from itertools.combinations(iterable, r)"
 pool = tuple(iterable)
 n = len(pool)
 indices = sorted(random.sample(range(n), r))
 return tuple(pool[i] for i in indices)

 def random_combination_with_replacement(iterable, r):
 "Random selection from itertools.combinations_with_replacement(iterable, r)"
 pool = tuple(iterable)
 n = len(pool)
 indices = sorted(random.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]'
 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)

Note, many of the above recipes can be optimized by replacing global lookups with local variables defined as default values. For example, the dotproduct recipe can be written as:

def dotproduct(vec1, vec2, sum=sum, map=map, mul=operator.mul):
 return sum(map(mul, vec1, vec2))

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