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1
2:mod:`itertools` --- Functions creating iterators for efficient looping
3=======================================================================
4
5.. module:: itertools
6   :synopsis: Functions creating iterators for efficient looping.
7.. moduleauthor:: Raymond Hettinger <python@rcn.com>
8.. sectionauthor:: Raymond Hettinger <python@rcn.com>
9
10
11.. testsetup::
12
13   from itertools import *
14
15.. versionadded:: 2.3
16
17This module implements a number of :term:`iterator` building blocks inspired
18by constructs from APL, Haskell, and SML.  Each has been recast in a form
19suitable for Python.
20
21The module standardizes a core set of fast, memory efficient tools that are
22useful by themselves or in combination.  Together, they form an "iterator
23algebra" making it possible to construct specialized tools succinctly and
24efficiently in pure Python.
25
26For instance, SML provides a tabulation tool: ``tabulate(f)`` which produces a
27sequence ``f(0), f(1), ...``.  The same effect can be achieved in Python
28by combining :func:`imap` and :func:`count` to form ``imap(f, count())``.
29
30These tools and their built-in counterparts also work well with the high-speed
31functions in the :mod:`operator` module.  For example, the multiplication
32operator can be mapped across two vectors to form an efficient dot-product:
33``sum(imap(operator.mul, vector1, vector2))``.
34
35
36**Infinite Iterators:**
37
38==================  =================       =================================================               =========================================
39Iterator            Arguments               Results                                                         Example
40==================  =================       =================================================               =========================================
41:func:`count`       start, [step]           start, start+step, start+2*step, ...                            ``count(10) --> 10 11 12 13 14 ...``
42:func:`cycle`       p                       p0, p1, ... plast, p0, p1, ...                                  ``cycle('ABCD') --> A B C D A B C D ...``
43:func:`repeat`      elem [,n]               elem, elem, elem, ... endlessly or up to n times                ``repeat(10, 3) --> 10 10 10``
44==================  =================       =================================================               =========================================
45
46**Iterators terminating on the shortest input sequence:**
47
48====================    ============================    =================================================   =============================================================
49Iterator                Arguments                       Results                                             Example
50====================    ============================    =================================================   =============================================================
51:func:`chain`           p, q, ...                       p0, p1, ... plast, q0, q1, ...                      ``chain('ABC', 'DEF') --> A B C D E F``
52:func:`compress`        data, selectors                 (d[0] if s[0]), (d[1] if s[1]), ...                 ``compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F``
53:func:`dropwhile`       pred, seq                       seq[n], seq[n+1], starting when pred fails          ``dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1``
54:func:`groupby`         iterable[, keyfunc]             sub-iterators grouped by value of keyfunc(v)
55:func:`ifilter`         pred, seq                       elements of seq where pred(elem) is true            ``ifilter(lambda x: x%2, range(10)) --> 1 3 5 7 9``
56:func:`ifilterfalse`    pred, seq                       elements of seq where pred(elem) is false           ``ifilterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8``
57:func:`islice`          seq, [start,] stop [, step]     elements from seq[start:stop:step]                  ``islice('ABCDEFG', 2, None) --> C D E F G``
58:func:`imap`            func, p, q, ...                 func(p0, q0), func(p1, q1), ...                     ``imap(pow, (2,3,10), (5,2,3)) --> 32 9 1000``
59:func:`starmap`         func, seq                       func(\*seq[0]), func(\*seq[1]), ...                 ``starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000``
60:func:`tee`             it, n                           it1, it2, ... itn  splits one iterator into n
61:func:`takewhile`       pred, seq                       seq[0], seq[1], until pred fails                    ``takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4``
62:func:`izip`            p, q, ...                       (p[0], q[0]), (p[1], q[1]), ...                     ``izip('ABCD', 'xy') --> Ax By``
63:func:`izip_longest`    p, q, ...                       (p[0], q[0]), (p[1], q[1]), ...                     ``izip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-``
64====================    ============================    =================================================   =============================================================
65
66**Combinatoric generators:**
67
68==============================================   ====================       =============================================================
69Iterator                                         Arguments                  Results
70==============================================   ====================       =============================================================
71:func:`product`                                  p, q, ... [repeat=1]       cartesian product, equivalent to a nested for-loop
72:func:`permutations`                             p[, r]                     r-length tuples, all possible orderings, no repeated elements
73:func:`combinations`                             p, r                       r-length tuples, in sorted order, no repeated elements
74:func:`combinations_with_replacement`            p, r                       r-length tuples, in sorted order, with repeated elements
75``product('ABCD', repeat=2)``                                               ``AA AB AC AD BA BB BC BD CA CB CC CD DA DB DC DD``
76``permutations('ABCD', 2)``                                                 ``AB AC AD BA BC BD CA CB CD DA DB DC``
77``combinations('ABCD', 2)``                                                 ``AB AC AD BC BD CD``
78``combinations_with_replacement('ABCD', 2)``                                ``AA AB AC AD BB BC BD CC CD DD``
79==============================================   ====================       =============================================================
80
81
82.. _itertools-functions:
83
84Itertool functions
85------------------
86
87The following module functions all construct and return iterators. Some provide
88streams of infinite length, so they should only be accessed by functions or
89loops that truncate the stream.
90
91
92.. function:: chain(*iterables)
93
94   Make an iterator that returns elements from the first iterable until it is
95   exhausted, then proceeds to the next iterable, until all of the iterables are
96   exhausted.  Used for treating consecutive sequences as a single sequence.
97   Roughly equivalent to::
98
99      def chain(*iterables):
100          # chain('ABC', 'DEF') --> A B C D E F
101          for it in iterables:
102              for element in it:
103                  yield element
104
105
106.. classmethod:: chain.from_iterable(iterable)
107
108   Alternate constructor for :func:`chain`.  Gets chained inputs from a
109   single iterable argument that is evaluated lazily.  Roughly equivalent to::
110
111      def from_iterable(iterables):
112          # chain.from_iterable(['ABC', 'DEF']) --> A B C D E F
113          for it in iterables:
114              for element in it:
115                  yield element
116
117   .. versionadded:: 2.6
118
119
120.. function:: combinations(iterable, r)
121
122   Return *r* length subsequences of elements from the input *iterable*.
123
124   Combinations are emitted in lexicographic sort order.  So, if the
125   input *iterable* is sorted, the combination tuples will be produced
126   in sorted order.
127
128   Elements are treated as unique based on their position, not on their
129   value.  So if the input elements are unique, there will be no repeat
130   values in each combination.
131
132   Roughly equivalent to::
133
134        def combinations(iterable, r):
135            # combinations('ABCD', 2) --> AB AC AD BC BD CD
136            # combinations(range(4), 3) --> 012 013 023 123
137            pool = tuple(iterable)
138            n = len(pool)
139            if r > n:
140                return
141            indices = range(r)
142            yield tuple(pool[i] for i in indices)
143            while True:
144                for i in reversed(range(r)):
145                    if indices[i] != i + n - r:
146                        break
147                else:
148                    return
149                indices[i] += 1
150                for j in range(i+1, r):
151                    indices[j] = indices[j-1] + 1
152                yield tuple(pool[i] for i in indices)
153
154   The code for :func:`combinations` can be also expressed as a subsequence
155   of :func:`permutations` after filtering entries where the elements are not
156   in sorted order (according to their position in the input pool)::
157
158        def combinations(iterable, r):
159            pool = tuple(iterable)
160            n = len(pool)
161            for indices in permutations(range(n), r):
162                if sorted(indices) == list(indices):
163                    yield tuple(pool[i] for i in indices)
164
165   The number of items returned is ``n! / r! / (n-r)!`` when ``0 <= r <= n``
166   or zero when ``r > n``.
167
168   .. versionadded:: 2.6
169
170.. function:: combinations_with_replacement(iterable, r)
171
172   Return *r* length subsequences of elements from the input *iterable*
173   allowing individual elements to be repeated more than once.
174
175   Combinations are emitted in lexicographic sort order.  So, if the
176   input *iterable* is sorted, the combination tuples will be produced
177   in sorted order.
178
179   Elements are treated as unique based on their position, not on their
180   value.  So if the input elements are unique, the generated combinations
181   will also be unique.
182
183   Roughly equivalent to::
184
185        def combinations_with_replacement(iterable, r):
186            # combinations_with_replacement('ABC', 2) --> AA AB AC BB BC CC
187            pool = tuple(iterable)
188            n = len(pool)
189            if not n and r:
190                return
191            indices = [0] * r
192            yield tuple(pool[i] for i in indices)
193            while True:
194                for i in reversed(range(r)):
195                    if indices[i] != n - 1:
196                        break
197                else:
198                    return
199                indices[i:] = [indices[i] + 1] * (r - i)
200                yield tuple(pool[i] for i in indices)
201
202   The code for :func:`combinations_with_replacement` can be also expressed as
203   a subsequence of :func:`product` after filtering entries where the elements
204   are not in sorted order (according to their position in the input pool)::
205
206        def combinations_with_replacement(iterable, r):
207            pool = tuple(iterable)
208            n = len(pool)
209            for indices in product(range(n), repeat=r):
210                if sorted(indices) == list(indices):
211                    yield tuple(pool[i] for i in indices)
212
213   The number of items returned is ``(n+r-1)! / r! / (n-1)!`` when ``n > 0``.
214
215   .. versionadded:: 2.7
216
217.. function:: compress(data, selectors)
218
219   Make an iterator that filters elements from *data* returning only those that
220   have a corresponding element in *selectors* that evaluates to ``True``.
221   Stops when either the *data* or *selectors* iterables has been exhausted.
222   Roughly equivalent to::
223
224       def compress(data, selectors):
225           # compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F
226           return (d for d, s in izip(data, selectors) if s)
227
228   .. versionadded:: 2.7
229
230
231.. function:: count(start=0, step=1)
232
233   Make an iterator that returns evenly spaced values starting with *n*. Often
234   used as an argument to :func:`imap` to generate consecutive data points.
235   Also, used with :func:`izip` to add sequence numbers.  Equivalent to::
236
237      def count(start=0, step=1):
238          # count(10) --> 10 11 12 13 14 ...
239          # count(2.5, 0.5) -> 2.5 3.0 3.5 ...
240          n = start
241          while True:
242              yield n
243              n += step
244
245   When counting with floating point numbers, better accuracy can sometimes be
246   achieved by substituting multiplicative code such as: ``(start + step * i
247   for i in count())``.
248
249   .. versionchanged:: 2.7
250      added *step* argument and allowed non-integer arguments.
251
252.. function:: cycle(iterable)
253
254   Make an iterator returning elements from the iterable and saving a copy of each.
255   When the iterable is exhausted, return elements from the saved copy.  Repeats
256   indefinitely.  Roughly equivalent to::
257
258      def cycle(iterable):
259          # cycle('ABCD') --> A B C D A B C D A B C D ...
260          saved = []
261          for element in iterable:
262              yield element
263              saved.append(element)
264          while saved:
265              for element in saved:
266                    yield element
267
268   Note, this member of the toolkit may require significant auxiliary storage
269   (depending on the length of the iterable).
270
271
272.. function:: dropwhile(predicate, iterable)
273
274   Make an iterator that drops elements from the iterable as long as the predicate
275   is true; afterwards, returns every element.  Note, the iterator does not produce
276   *any* output until the predicate first becomes false, so it may have a lengthy
277   start-up time.  Roughly equivalent to::
278
279      def dropwhile(predicate, iterable):
280          # dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1
281          iterable = iter(iterable)
282          for x in iterable:
283              if not predicate(x):
284                  yield x
285                  break
286          for x in iterable:
287              yield x
288
289
290.. function:: groupby(iterable[, key])
291
292   Make an iterator that returns consecutive keys and groups from the *iterable*.
293   The *key* is a function computing a key value for each element.  If not
294   specified or is ``None``, *key* defaults to an identity function and returns
295   the element unchanged.  Generally, the iterable needs to already be sorted on
296   the same key function.
297
298   The operation of :func:`groupby` is similar to the ``uniq`` filter in Unix.  It
299   generates a break or new group every time the value of the key function changes
300   (which is why it is usually necessary to have sorted the data using the same key
301   function).  That behavior differs from SQL's GROUP BY which aggregates common
302   elements regardless of their input order.
303
304   The returned group is itself an iterator that shares the underlying iterable
305   with :func:`groupby`.  Because the source is shared, when the :func:`groupby`
306   object is advanced, the previous group is no longer visible.  So, if that data
307   is needed later, it should be stored as a list::
308
309      groups = []
310      uniquekeys = []
311      data = sorted(data, key=keyfunc)
312      for k, g in groupby(data, keyfunc):
313          groups.append(list(g))      # Store group iterator as a list
314          uniquekeys.append(k)
315
316   :func:`groupby` is roughly equivalent to::
317
318      class groupby(object):
319          # [k for k, g in groupby('AAAABBBCCDAABBB')] --> A B C D A B
320          # [list(g) for k, g in groupby('AAAABBBCCD')] --> AAAA BBB CC D
321          def __init__(self, iterable, key=None):
322              if key is None:
323                  key = lambda x: x
324              self.keyfunc = key
325              self.it = iter(iterable)
326              self.tgtkey = self.currkey = self.currvalue = object()
327          def __iter__(self):
328              return self
329          def next(self):
330              while self.currkey == self.tgtkey:
331                  self.currvalue = next(self.it)    # Exit on StopIteration
332                  self.currkey = self.keyfunc(self.currvalue)
333              self.tgtkey = self.currkey
334              return (self.currkey, self._grouper(self.tgtkey))
335          def _grouper(self, tgtkey):
336              while self.currkey == tgtkey:
337                  yield self.currvalue
338                  self.currvalue = next(self.it)    # Exit on StopIteration
339                  self.currkey = self.keyfunc(self.currvalue)
340
341   .. versionadded:: 2.4
342
343
344.. function:: ifilter(predicate, iterable)
345
346   Make an iterator that filters elements from iterable returning only those for
347   which the predicate is ``True``. If *predicate* is ``None``, return the items
348   that are true. Roughly equivalent to::
349
350      def ifilter(predicate, iterable):
351          # ifilter(lambda x: x%2, range(10)) --> 1 3 5 7 9
352          if predicate is None:
353              predicate = bool
354          for x in iterable:
355              if predicate(x):
356                  yield x
357
358
359.. function:: ifilterfalse(predicate, iterable)
360
361   Make an iterator that filters elements from iterable returning only those for
362   which the predicate is ``False``. If *predicate* is ``None``, return the items
363   that are false. Roughly equivalent to::
364
365      def ifilterfalse(predicate, iterable):
366          # ifilterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8
367          if predicate is None:
368              predicate = bool
369          for x in iterable:
370              if not predicate(x):
371                  yield x
372
373
374.. function:: imap(function, *iterables)
375
376   Make an iterator that computes the function using arguments from each of the
377   iterables.  If *function* is set to ``None``, then :func:`imap` returns the
378   arguments as a tuple.  Like :func:`map` but stops when the shortest iterable is
379   exhausted instead of filling in ``None`` for shorter iterables.  The reason for
380   the difference is that infinite iterator arguments are typically an error for
381   :func:`map` (because the output is fully evaluated) but represent a common and
382   useful way of supplying arguments to :func:`imap`. Roughly equivalent to::
383
384      def imap(function, *iterables):
385          # imap(pow, (2,3,10), (5,2,3)) --> 32 9 1000
386          iterables = map(iter, iterables)
387          while True:
388              args = [next(it) for it in iterables]
389              if function is None:
390                  yield tuple(args)
391              else:
392                  yield function(*args)
393
394
395.. function:: islice(iterable, stop)
396              islice(iterable, start, stop[, step])
397
398   Make an iterator that returns selected elements from the iterable. If *start* is
399   non-zero, then elements from the iterable are skipped until start is reached.
400   Afterward, elements are returned consecutively unless *step* is set higher than
401   one which results in items being skipped.  If *stop* is ``None``, then iteration
402   continues until the iterator is exhausted, if at all; otherwise, it stops at the
403   specified position.  Unlike regular slicing, :func:`islice` does not support
404   negative values for *start*, *stop*, or *step*.  Can be used to extract related
405   fields from data where the internal structure has been flattened (for example, a
406   multi-line report may list a name field on every third line).  Roughly equivalent to::
407
408      def islice(iterable, *args):
409          # islice('ABCDEFG', 2) --> A B
410          # islice('ABCDEFG', 2, 4) --> C D
411          # islice('ABCDEFG', 2, None) --> C D E F G
412          # islice('ABCDEFG', 0, None, 2) --> A C E G
413          s = slice(*args)
414          start, stop, step = s.start or 0, s.stop or sys.maxint, s.step or 1
415          it = iter(xrange(start, stop, step)))
416          try:
417              nexti = next(it)
418          except StopIteration:
419              # Consume *iterable* up to the *start* position.
420              for i, element in izip(xrange(start), iterable):
421                  pass
422              return
423          try:
424              for i, element in enumerate(iterable):
425                  if i == nexti:
426                      yield element
427                      nexti = next(it)
428          except StopIteration:
429              # Consume to *stop*.
430              for i, element in izip(xrange(i + 1, stop), iterable):
431                  pass
432
433   If *start* is ``None``, then iteration starts at zero. If *step* is ``None``,
434   then the step defaults to one.
435
436   .. versionchanged:: 2.5
437      accept ``None`` values for default *start* and *step*.
438
439
440.. function:: izip(*iterables)
441
442   Make an iterator that aggregates elements from each of the iterables. Like
443   :func:`zip` except that it returns an iterator instead of a list.  Used for
444   lock-step iteration over several iterables at a time.  Roughly equivalent to::
445
446      def izip(*iterables):
447          # izip('ABCD', 'xy') --> Ax By
448          iterators = map(iter, iterables)
449          while iterators:
450              yield tuple(map(next, iterators))
451
452   .. versionchanged:: 2.4
453      When no iterables are specified, returns a zero length iterator instead of
454      raising a :exc:`TypeError` exception.
455
456   The left-to-right evaluation order of the iterables is guaranteed. This
457   makes possible an idiom for clustering a data series into n-length groups
458   using ``izip(*[iter(s)]*n)``.
459
460   :func:`izip` should only be used with unequal length inputs when you don't
461   care about trailing, unmatched values from the longer iterables.  If those
462   values are important, use :func:`izip_longest` instead.
463
464
465.. function:: izip_longest(*iterables[, fillvalue])
466
467   Make an iterator that aggregates elements from each of the iterables. If the
468   iterables are of uneven length, missing values are filled-in with *fillvalue*.
469   Iteration continues until the longest iterable is exhausted.  Roughly equivalent to::
470
471      class ZipExhausted(Exception):
472          pass
473
474      def izip_longest(*args, **kwds):
475          # izip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-
476          fillvalue = kwds.get('fillvalue')
477          counter = [len(args) - 1]
478          def sentinel():
479              if not counter[0]:
480                  raise ZipExhausted
481              counter[0] -= 1
482              yield fillvalue
483          fillers = repeat(fillvalue)
484          iterators = [chain(it, sentinel(), fillers) for it in args]
485          try:
486              while iterators:
487                  yield tuple(map(next, iterators))
488          except ZipExhausted:
489              pass
490
491   If one of the iterables is potentially infinite, then the
492   :func:`izip_longest` function should be wrapped with something that limits
493   the number of calls (for example :func:`islice` or :func:`takewhile`).  If
494   not specified, *fillvalue* defaults to ``None``.
495
496   .. versionadded:: 2.6
497
498.. function:: permutations(iterable[, r])
499
500   Return successive *r* length permutations of elements in the *iterable*.
501
502   If *r* is not specified or is ``None``, then *r* defaults to the length
503   of the *iterable* and all possible full-length permutations
504   are generated.
505
506   Permutations are emitted in lexicographic sort order.  So, if the
507   input *iterable* is sorted, the permutation tuples will be produced
508   in sorted order.
509
510   Elements are treated as unique based on their position, not on their
511   value.  So if the input elements are unique, there will be no repeat
512   values in each permutation.
513
514   Roughly equivalent to::
515
516        def permutations(iterable, r=None):
517            # permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC
518            # permutations(range(3)) --> 012 021 102 120 201 210
519            pool = tuple(iterable)
520            n = len(pool)
521            r = n if r is None else r
522            if r > n:
523                return
524            indices = range(n)
525            cycles = range(n, n-r, -1)
526            yield tuple(pool[i] for i in indices[:r])
527            while n:
528                for i in reversed(range(r)):
529                    cycles[i] -= 1
530                    if cycles[i] == 0:
531                        indices[i:] = indices[i+1:] + indices[i:i+1]
532                        cycles[i] = n - i
533                    else:
534                        j = cycles[i]
535                        indices[i], indices[-j] = indices[-j], indices[i]
536                        yield tuple(pool[i] for i in indices[:r])
537                        break
538                else:
539                    return
540
541   The code for :func:`permutations` can be also expressed as a subsequence of
542   :func:`product`, filtered to exclude entries with repeated elements (those
543   from the same position in the input pool)::
544
545        def permutations(iterable, r=None):
546            pool = tuple(iterable)
547            n = len(pool)
548            r = n if r is None else r
549            for indices in product(range(n), repeat=r):
550                if len(set(indices)) == r:
551                    yield tuple(pool[i] for i in indices)
552
553   The number of items returned is ``n! / (n-r)!`` when ``0 <= r <= n``
554   or zero when ``r > n``.
555
556   .. versionadded:: 2.6
557
558.. function:: product(*iterables[, repeat])
559
560   Cartesian product of input iterables.
561
562   Roughly equivalent to nested for-loops in a generator expression. For example,
563   ``product(A, B)`` returns the same as ``((x,y) for x in A for y in B)``.
564
565   The nested loops cycle like an odometer with the rightmost element advancing
566   on every iteration.  This pattern creates a lexicographic ordering so that if
567   the input's iterables are sorted, the product tuples are emitted in sorted
568   order.
569
570   To compute the product of an iterable with itself, specify the number of
571   repetitions with the optional *repeat* keyword argument.  For example,
572   ``product(A, repeat=4)`` means the same as ``product(A, A, A, A)``.
573
574   This function is roughly equivalent to the following code, except that the
575   actual implementation does not build up intermediate results in memory::
576
577       def product(*args, **kwds):
578           # product('ABCD', 'xy') --> Ax Ay Bx By Cx Cy Dx Dy
579           # product(range(2), repeat=3) --> 000 001 010 011 100 101 110 111
580           pools = map(tuple, args) * kwds.get('repeat', 1)
581           result = [[]]
582           for pool in pools:
583               result = [x+[y] for x in result for y in pool]
584           for prod in result:
585               yield tuple(prod)
586
587   .. versionadded:: 2.6
588
589.. function:: repeat(object[, times])
590
591   Make an iterator that returns *object* over and over again. Runs indefinitely
592   unless the *times* argument is specified. Used as argument to :func:`imap` for
593   invariant function parameters.  Also used with :func:`izip` to create constant
594   fields in a tuple record.  Roughly equivalent to::
595
596      def repeat(object, times=None):
597          # repeat(10, 3) --> 10 10 10
598          if times is None:
599              while True:
600                  yield object
601          else:
602              for i in xrange(times):
603                  yield object
604
605   A common use for *repeat* is to supply a stream of constant values to *imap*
606   or *zip*::
607
608      >>> list(imap(pow, xrange(10), repeat(2)))
609      [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
610
611.. function:: starmap(function, iterable)
612
613   Make an iterator that computes the function using arguments obtained from
614   the iterable.  Used instead of :func:`imap` when argument parameters are already
615   grouped in tuples from a single iterable (the data has been "pre-zipped").  The
616   difference between :func:`imap` and :func:`starmap` parallels the distinction
617   between ``function(a,b)`` and ``function(*c)``. Roughly equivalent to::
618
619      def starmap(function, iterable):
620          # starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000
621          for args in iterable:
622              yield function(*args)
623
624   .. versionchanged:: 2.6
625      Previously, :func:`starmap` required the function arguments to be tuples.
626      Now, any iterable is allowed.
627
628.. function:: takewhile(predicate, iterable)
629
630   Make an iterator that returns elements from the iterable as long as the
631   predicate is true.  Roughly equivalent to::
632
633      def takewhile(predicate, iterable):
634          # takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4
635          for x in iterable:
636              if predicate(x):
637                  yield x
638              else:
639                  break
640
641
642.. function:: tee(iterable[, n=2])
643
644   Return *n* independent iterators from a single iterable.  Roughly equivalent to::
645
646        def tee(iterable, n=2):
647            it = iter(iterable)
648            deques = [collections.deque() for i in range(n)]
649            def gen(mydeque):
650                while True:
651                    if not mydeque:             # when the local deque is empty
652                        newval = next(it)       # fetch a new value and
653                        for d in deques:        # load it to all the deques
654                            d.append(newval)
655                    yield mydeque.popleft()
656            return tuple(gen(d) for d in deques)
657
658   Once :func:`tee` has made a split, the original *iterable* should not be
659   used anywhere else; otherwise, the *iterable* could get advanced without
660   the tee objects being informed.
661
662   This itertool may require significant auxiliary storage (depending on how
663   much temporary data needs to be stored). In general, if one iterator uses
664   most or all of the data before another iterator starts, it is faster to use
665   :func:`list` instead of :func:`tee`.
666
667   .. versionadded:: 2.4
668
669
670.. _itertools-recipes:
671
672Recipes
673-------
674
675This section shows recipes for creating an extended toolset using the existing
676itertools as building blocks.
677
678The extended tools offer the same high performance as the underlying toolset.
679The superior memory performance is kept by processing elements one at a time
680rather than bringing the whole iterable into memory all at once. Code volume is
681kept small by linking the tools together in a functional style which helps
682eliminate temporary variables.  High speed is retained by preferring
683"vectorized" building blocks over the use of for-loops and :term:`generator`\s
684which incur interpreter overhead.
685
686.. testcode::
687
688   def take(n, iterable):
689       "Return first n items of the iterable as a list"
690       return list(islice(iterable, n))
691
692   def tabulate(function, start=0):
693       "Return function(0), function(1), ..."
694       return imap(function, count(start))
695
696   def consume(iterator, n=None):
697       "Advance the iterator n-steps ahead. If n is None, consume entirely."
698       # Use functions that consume iterators at C speed.
699       if n is None:
700           # feed the entire iterator into a zero-length deque
701           collections.deque(iterator, maxlen=0)
702       else:
703           # advance to the empty slice starting at position n
704           next(islice(iterator, n, n), None)
705
706   def nth(iterable, n, default=None):
707       "Returns the nth item or a default value"
708       return next(islice(iterable, n, None), default)
709
710   def all_equal(iterable):
711       "Returns True if all the elements are equal to each other"
712       g = groupby(iterable)
713       return next(g, True) and not next(g, False)
714
715   def quantify(iterable, pred=bool):
716       "Count how many times the predicate is true"
717       return sum(imap(pred, iterable))
718
719   def padnone(iterable):
720       """Returns the sequence elements and then returns None indefinitely.
721
722       Useful for emulating the behavior of the built-in map() function.
723       """
724       return chain(iterable, repeat(None))
725
726   def ncycles(iterable, n):
727       "Returns the sequence elements n times"
728       return chain.from_iterable(repeat(tuple(iterable), n))
729
730   def dotproduct(vec1, vec2):
731       return sum(imap(operator.mul, vec1, vec2))
732
733   def flatten(listOfLists):
734       "Flatten one level of nesting"
735       return chain.from_iterable(listOfLists)
736
737   def repeatfunc(func, times=None, *args):
738       """Repeat calls to func with specified arguments.
739
740       Example:  repeatfunc(random.random)
741       """
742       if times is None:
743           return starmap(func, repeat(args))
744       return starmap(func, repeat(args, times))
745
746   def pairwise(iterable):
747       "s -> (s0,s1), (s1,s2), (s2, s3), ..."
748       a, b = tee(iterable)
749       next(b, None)
750       return izip(a, b)
751
752   def grouper(iterable, n, fillvalue=None):
753       "Collect data into fixed-length chunks or blocks"
754       # grouper('ABCDEFG', 3, 'x') --> ABC DEF Gxx
755       args = [iter(iterable)] * n
756       return izip_longest(fillvalue=fillvalue, *args)
757
758   def roundrobin(*iterables):
759       "roundrobin('ABC', 'D', 'EF') --> A D E B F C"
760       # Recipe credited to George Sakkis
761       pending = len(iterables)
762       nexts = cycle(iter(it).next for it in iterables)
763       while pending:
764           try:
765               for next in nexts:
766                   yield next()
767           except StopIteration:
768               pending -= 1
769               nexts = cycle(islice(nexts, pending))
770
771   def powerset(iterable):
772       "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
773       s = list(iterable)
774       return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
775
776   def unique_everseen(iterable, key=None):
777       "List unique elements, preserving order. Remember all elements ever seen."
778       # unique_everseen('AAAABBBCCDAABBB') --> A B C D
779       # unique_everseen('ABBCcAD', str.lower) --> A B C D
780       seen = set()
781       seen_add = seen.add
782       if key is None:
783           for element in ifilterfalse(seen.__contains__, iterable):
784               seen_add(element)
785               yield element
786       else:
787           for element in iterable:
788               k = key(element)
789               if k not in seen:
790                   seen_add(k)
791                   yield element
792
793   def unique_justseen(iterable, key=None):
794       "List unique elements, preserving order. Remember only the element just seen."
795       # unique_justseen('AAAABBBCCDAABBB') --> A B C D A B
796       # unique_justseen('ABBCcAD', str.lower) --> A B C A D
797       return imap(next, imap(itemgetter(1), groupby(iterable, key)))
798
799   def iter_except(func, exception, first=None):
800       """ Call a function repeatedly until an exception is raised.
801
802       Converts a call-until-exception interface to an iterator interface.
803       Like __builtin__.iter(func, sentinel) but uses an exception instead
804       of a sentinel to end the loop.
805
806       Examples:
807           bsddbiter = iter_except(db.next, bsddb.error, db.first)
808           heapiter = iter_except(functools.partial(heappop, h), IndexError)
809           dictiter = iter_except(d.popitem, KeyError)
810           dequeiter = iter_except(d.popleft, IndexError)
811           queueiter = iter_except(q.get_nowait, Queue.Empty)
812           setiter = iter_except(s.pop, KeyError)
813
814       """
815       try:
816           if first is not None:
817               yield first()
818           while 1:
819               yield func()
820       except exception:
821           pass
822
823   def random_product(*args, **kwds):
824       "Random selection from itertools.product(*args, **kwds)"
825       pools = map(tuple, args) * kwds.get('repeat', 1)
826       return tuple(random.choice(pool) for pool in pools)
827
828   def random_permutation(iterable, r=None):
829       "Random selection from itertools.permutations(iterable, r)"
830       pool = tuple(iterable)
831       r = len(pool) if r is None else r
832       return tuple(random.sample(pool, r))
833
834   def random_combination(iterable, r):
835       "Random selection from itertools.combinations(iterable, r)"
836       pool = tuple(iterable)
837       n = len(pool)
838       indices = sorted(random.sample(xrange(n), r))
839       return tuple(pool[i] for i in indices)
840
841   def random_combination_with_replacement(iterable, r):
842       "Random selection from itertools.combinations_with_replacement(iterable, r)"
843       pool = tuple(iterable)
844       n = len(pool)
845       indices = sorted(random.randrange(n) for i in xrange(r))
846       return tuple(pool[i] for i in indices)
847
848   def tee_lookahead(t, i):
849       """Inspect the i-th upcomping value from a tee object
850          while leaving the tee object at its current position.
851
852          Raise an IndexError if the underlying iterator doesn't
853          have enough values.
854
855       """
856       for value in islice(t.__copy__(), i, None):
857           return value
858       raise IndexError(i)
859
860Note, many of the above recipes can be optimized by replacing global lookups
861with local variables defined as default values.  For example, the
862*dotproduct* recipe can be written as::
863
864   def dotproduct(vec1, vec2, sum=sum, imap=imap, mul=operator.mul):
865       return sum(imap(mul, vec1, vec2))
866