: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 *

.. versionadded:: 2.3

This module implements a number of :term:`iterator` building blocks inspired by

constructs from the Haskell and SML programming languages.  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.  Standardization helps avoid the

readability and reliability problems which arise when many different individuals

create their own slightly varying implementations, each with their own quirks

and naming conventions.

The tools are designed to combine readily with one another.  This makes it easy

to construct more 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), ...``.  This toolbox provides :func:`imap` and

:func:`count` which can be combined to form ``imap(f, count())`` and produce an

equivalent result.

Likewise, the functional tools are designed to work well with the high-speed

functions provided by the :mod:`operator` module.

Whether cast in pure python form or compiled code, tools that use iterators are

more memory efficient (and often faster) than their list based counterparts. Adopting

the principles of just-in-time manufacturing, they create data when and where

needed instead of consuming memory with the computer equivalent of "inventory".

.. seealso::

   The Standard ML Basis Library, `The Standard ML Basis Library

   <http://www.standardml.org/Basis/>`_.

   Haskell, A Purely Functional Language, `Definition of Haskell and the Standard

   Libraries <http://www.haskell.org/definition/>`_.

.. _itertools-functions:

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:: 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.

   Equivalent to::

      def chain(*iterables):

          # chain('ABC', 'DEF') --> A B C D E F

          for it in iterables:

              for element in it:

                  yield element

.. function:: itertools.chain.from_iterable(iterable)

   Alternate constructor for :func:`chain`.  Gets chained inputs from a 

   single iterable argument that is evaluated lazily.  Equivalent to::

      @classmethod

      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

   .. versionadded:: 2.6

.. 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.

   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)

            indices = range(r)

            yield tuple(pool[i] for i in indices)

            while 1:

                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)

   .. versionadded:: 2.6

.. function:: count([n])

   Make an iterator that returns consecutive integers starting with *n*. If not

   specified *n* defaults to zero.   Often used as an argument to :func:`imap` to

   generate consecutive data points. Also, used with :func:`izip` to add sequence

   numbers.  Equivalent to::

      def count(n=0):

          # count(10) --> 10 11 12 13 14 ...

          while True:

              yield n

              n += 1

.. 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.  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.  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:: groupby(iterable[, key])

   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 equivalent to::

      class groupby(object):

          # [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):

              while self.currkey == self.tgtkey:

                  self.currvalue = self.it.next() # Exit on StopIteration

                  self.currkey = self.keyfunc(self.currvalue)

              self.tgtkey = self.currkey

              return (self.currkey, self._grouper(self.tgtkey))

          def _grouper(self, tgtkey):

              while self.currkey == tgtkey:

                  yield self.currvalue

                  self.currvalue = self.it.next() # Exit on StopIteration

                  self.currkey = self.keyfunc(self.currvalue)

   .. versionadded:: 2.4

.. function:: ifilter(predicate, iterable)

   Make an iterator that filters elements from iterable returning only those for

   which the predicate is ``True``. If *predicate* is ``None``, return the items

   that are true. Equivalent to::

      def ifilter(predicate, iterable):

          # ifilter(lambda x: x%2, range(10)) --> 1 3 5 7 9

          if predicate is None:

              predicate = bool

          for x in iterable:

              if predicate(x):

                  yield x

.. function:: ifilterfalse(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. Equivalent to::

      def ifilterfalse(predicate, iterable):

          # ifilterfalse(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:: imap(function, *iterables)

   Make an iterator that computes the function using arguments from each of the

   iterables.  If *function* is set to ``None``, then :func:`imap` returns the

   arguments as a tuple.  Like :func:`map` but stops when the shortest iterable is

   exhausted instead of filling in ``None`` for shorter iterables.  The reason for

   the difference is that infinite iterator arguments are typically an error for

   :func:`map` (because the output is fully evaluated) but represent a common and

   useful way of supplying arguments to :func:`imap`. Equivalent to::

      def imap(function, *iterables):

          # imap(pow, (2,3,10), (5,2,3)) --> 32 9 1000

          iterables = map(iter, iterables)

          while True:

              args = [it.next() for it in iterables]

              if function is None:

                  yield tuple(args)

              else:

                  yield function(*args)

.. function:: 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).  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)

          it = iter(xrange(s.start or 0, s.stop or sys.maxint, s.step or 1))

          nexti = it.next()

          for i, element in enumerate(iterable):

              if i == nexti:

                  yield element

                  nexti = it.next()          

   If *start* is ``None``, then iteration starts at zero. If *step* is ``None``,

   then the step defaults to one.

   .. versionchanged:: 2.5

      accept ``None`` values for default *start* and *step*.

.. function:: izip(*iterables)

   Make an iterator that aggregates elements from each of the iterables. Like

   :func:`zip` except that it returns an iterator instead of a list.  Used for

   lock-step iteration over several iterables at a time.  Equivalent to::

      def izip(*iterables):

          # izip('ABCD', 'xy') --> Ax By

          iterables = map(iter, iterables)

          while iterables:

              result = [it.next() for it in iterables]

              yield tuple(result)

   .. versionchanged:: 2.4

      When no iterables are specified, returns a zero length iterator instead of

      raising a :exc:`TypeError` exception.

   The left-to-right evaluation order of the iterables is guaranteed. This

   makes possible an idiom for clustering a data series into n-length groups

   using ``izip(*[iter(s)]*n)``.

   :func:`izip` should only be used with unequal length inputs when you don't

   care about trailing, unmatched values from the longer iterables.  If those

   values are important, use :func:`izip_longest` instead.

.. function:: izip_longest(*iterables[, fillvalue])

   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.  Equivalent to::

      def izip_longest(*args, **kwds):

          # izip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-

          fillvalue = kwds.get('fillvalue')

          def sentinel(counter = ([fillvalue]*(len(args)-1)).pop):

              yield counter()         # yields the fillvalue, or raises IndexError

          fillers = repeat(fillvalue)

          iters = [chain(it, sentinel(), fillers) for it in args]

          try:

              for tup in izip(*iters):

                  yield tup

          except IndexError:

              pass

   If one of the iterables is potentially infinite, then the

   :func:`izip_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``.

   .. versionadded:: 2.6

.. function:: permutations(iterable[, r])

   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.

   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

            indices = range(n)

            cycles = 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)

   .. versionadded:: 2.6

.. function:: product(*iterables[, repeat])

   Cartesian product of input iterables.

   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 equivalent to the following code, except that the

   actual implementation does not build up intermediate results in memory::

       def product(*args, **kwds):

           # 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 = map(tuple, args) * kwds.get('repeat', 1)

           result = [[]]

           for pool in pools:

               result = [x+[y] for x in result for y in pool]

           for prod in result:

               yield tuple(prod)

   .. versionadded:: 2.6

.. 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:`imap` for

   invariant function parameters.  Also used with :func:`izip` to create constant

   fields in a tuple record.  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 xrange(times):

                  yield object

.. function:: starmap(function, iterable)

   Make an iterator that computes the function using arguments obtained from

   the iterable.  Used instead of :func:`imap` when argument parameters are already

   grouped in tuples from a single iterable (the data has been "pre-zipped").  The

   difference between :func:`imap` and :func:`starmap` parallels the distinction

   between ``function(a,b)`` and ``function(*c)``. Equivalent to::

      def starmap(function, iterable):

          # starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000

          for args in iterable:

              yield function(*args)

   .. versionchanged:: 2.6

      Previously, :func:`starmap` required the function arguments to be tuples.

      Now, any iterable is allowed.

.. function:: takewhile(predicate, iterable)

   Make an iterator that returns elements from the iterable as long as the

   predicate is true.  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 case where ``n==2``

   is equivalent to::

      def tee(iterable):

          def gen(next, data={}):

              for i in count():

                  if i in data:

                      yield data.pop(i)

                  else:

                      data[i] = next()

                      yield data[i]

          it = iter(iterable)

          return gen(it.next), gen(it.next)

   Note, once :func:`tee` has made a split, the original *iterable* should not be