680 lines
25 KiB
ReStructuredText
680 lines
25 KiB
ReStructuredText
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:mod:`itertools` --- Functions creating iterators for efficient looping
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=======================================================================
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.. module:: itertools
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:synopsis: Functions creating iterators for efficient looping.
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.. moduleauthor:: Raymond Hettinger <python@rcn.com>
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.. sectionauthor:: Raymond Hettinger <python@rcn.com>
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.. testsetup::
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from itertools import *
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This module implements a number of :term:`iterator` building blocks inspired by
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constructs from the Haskell and SML programming languages. Each has been recast
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in a form suitable for Python.
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The module standardizes a core set of fast, memory efficient tools that are
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useful by themselves or in combination. Standardization helps avoid the
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readability and reliability problems which arise when many different individuals
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create their own slightly varying implementations, each with their own quirks
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and naming conventions.
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The tools are designed to combine readily with one another. This makes it easy
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to construct more specialized tools succinctly and efficiently in pure Python.
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For instance, SML provides a tabulation tool: ``tabulate(f)`` which produces a
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sequence ``f(0), f(1), ...``. But, this effect can be achieved in Python
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by combining :func:`map` and :func:`count` to form ``map(f, count())``.
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Likewise, the functional tools are designed to work well with the high-speed
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functions provided by the :mod:`operator` module.
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Whether cast in pure python form or compiled code, tools that use iterators are
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more memory efficient (and often faster) than their list based counterparts. Adopting
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the principles of just-in-time manufacturing, they create data when and where
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needed instead of consuming memory with the computer equivalent of "inventory".
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.. seealso::
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The Standard ML Basis Library, `The Standard ML Basis Library
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<http://www.standardml.org/Basis/>`_.
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Haskell, A Purely Functional Language, `Definition of Haskell and the Standard
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Libraries <http://www.haskell.org/definition/>`_.
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.. _itertools-functions:
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Itertool functions
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------------------
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The following module functions all construct and return iterators. Some provide
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streams of infinite length, so they should only be accessed by functions or
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loops that truncate the stream.
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.. function:: chain(*iterables)
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Make an iterator that returns elements from the first iterable until it is
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exhausted, then proceeds to the next iterable, until all of the iterables are
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exhausted. Used for treating consecutive sequences as a single sequence.
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Equivalent to::
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def chain(*iterables):
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# chain('ABC', 'DEF') --> A B C D E F
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for it in iterables:
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for element in it:
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yield element
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.. function:: itertools.chain.from_iterable(iterable)
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Alternate constructor for :func:`chain`. Gets chained inputs from a
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single iterable argument that is evaluated lazily. Equivalent to::
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@classmethod
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def from_iterable(iterables):
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# chain.from_iterable(['ABC', 'DEF']) --> A B C D E F
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for it in iterables:
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for element in it:
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yield element
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.. function:: combinations(iterable, r)
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Return *r* length subsequences of elements from the input *iterable*.
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Combinations are emitted in lexicographic sort order. So, if the
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input *iterable* is sorted, the combination tuples will be produced
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in sorted order.
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Elements are treated as unique based on their position, not on their
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value. So if the input elements are unique, there will be no repeat
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values in each combination.
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Equivalent to::
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def combinations(iterable, r):
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# combinations('ABCD', 2) --> AB AC AD BC BD CD
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# combinations(range(4), 3) --> 012 013 023 123
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pool = tuple(iterable)
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n = len(pool)
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if r > n:
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return
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indices = list(range(r))
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yield tuple(pool[i] for i in indices)
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while 1:
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for i in reversed(range(r)):
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if indices[i] != i + n - r:
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break
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else:
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return
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indices[i] += 1
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for j in range(i+1, r):
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indices[j] = indices[j-1] + 1
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yield tuple(pool[i] for i in indices)
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The code for :func:`combinations` can be also expressed as a subsequence
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of :func:`permutations` after filtering entries where the elements are not
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in sorted order (according to their position in the input pool)::
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def combinations(iterable, r):
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pool = tuple(iterable)
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n = len(pool)
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for indices in permutations(range(n), r):
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if sorted(indices) == list(indices):
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yield tuple(pool[i] for i in indices)
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The number of items returned is ``n! / r! / (n-r)!`` when ``0 <= r <= n``
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or zero when ``r > n``.
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.. function:: combinations_with_replacement(iterable, r)
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Return *r* length subsequences of elements from the input *iterable*
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allowing individual elements to be repeated more than once.
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Combinations are emitted in lexicographic sort order. So, if the
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input *iterable* is sorted, the combination tuples will be produced
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in sorted order.
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Elements are treated as unique based on their position, not on their
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value. So if the input elements are unique, the generated combinations
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will also be unique.
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Equivalent to::
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def combinations_with_replacement(iterable, r):
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# combinations_with_replacement('ABC', 2) --> AA AB AC BB BC CC
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pool = tuple(iterable)
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n = len(pool)
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if not n and r:
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return
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indices = [0] * r
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yield tuple(pool[i] for i in indices)
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while 1:
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for i in reversed(range(r)):
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if indices[i] != n - 1:
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break
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else:
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return
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indices[i:] = [indices[i] + 1] * (r - i)
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yield tuple(pool[i] for i in indices)
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The code for :func:`combinations_with_replacement` can be also expressed as
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a subsequence of :func:`product` after filtering entries where the elements
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are not in sorted order (according to their position in the input pool)::
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def combinations_with_replacement(iterable, r):
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pool = tuple(iterable)
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n = len(pool)
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for indices in product(range(n), repeat=r):
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if sorted(indices) == list(indices):
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yield tuple(pool[i] for i in indices)
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The number of items returned is ``(n+r-1)! / r! / (n-1)!`` when ``n > 0``.
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.. versionadded:: 2.7
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.. function:: compress(data, selectors)
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Make an iterator that filters elements from *data* returning only those that
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have a corresponding element in *selectors* that evaluates to ``True``.
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Stops when either the *data* or *selectors* iterables have been exhausted.
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Equivalent to::
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def compress(data, selectors):
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# compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F
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return (d for d, s in zip(data, selectors) if s)
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.. versionadded:: 2.7
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.. function:: count([n])
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Make an iterator that returns consecutive integers starting with *n*. If not
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specified *n* defaults to zero. Often used as an argument to :func:`map` to
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generate consecutive data points. Also, used with :func:`zip` to add sequence
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numbers. Equivalent to::
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def count(n=0):
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# count(10) --> 10 11 12 13 14 ...
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while True:
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yield n
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n += 1
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.. function:: cycle(iterable)
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Make an iterator returning elements from the iterable and saving a copy of each.
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When the iterable is exhausted, return elements from the saved copy. Repeats
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indefinitely. Equivalent to::
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def cycle(iterable):
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# cycle('ABCD') --> A B C D A B C D A B C D ...
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saved = []
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for element in iterable:
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yield element
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saved.append(element)
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while saved:
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for element in saved:
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yield element
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Note, this member of the toolkit may require significant auxiliary storage
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(depending on the length of the iterable).
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.. function:: dropwhile(predicate, iterable)
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Make an iterator that drops elements from the iterable as long as the predicate
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is true; afterwards, returns every element. Note, the iterator does not produce
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*any* output until the predicate first becomes false, so it may have a lengthy
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start-up time. Equivalent to::
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def dropwhile(predicate, iterable):
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# dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1
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iterable = iter(iterable)
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for x in iterable:
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if not predicate(x):
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yield x
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break
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for x in iterable:
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yield x
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.. function:: filterfalse(predicate, iterable)
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Make an iterator that filters elements from iterable returning only those for
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which the predicate is ``False``. If *predicate* is ``None``, return the items
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that are false. Equivalent to::
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def filterfalse(predicate, iterable):
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# filterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8
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if predicate is None:
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predicate = bool
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for x in iterable:
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if not predicate(x):
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yield x
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.. function:: groupby(iterable[, key])
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Make an iterator that returns consecutive keys and groups from the *iterable*.
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The *key* is a function computing a key value for each element. If not
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specified or is ``None``, *key* defaults to an identity function and returns
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the element unchanged. Generally, the iterable needs to already be sorted on
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the same key function.
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The operation of :func:`groupby` is similar to the ``uniq`` filter in Unix. It
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generates a break or new group every time the value of the key function changes
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(which is why it is usually necessary to have sorted the data using the same key
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function). That behavior differs from SQL's GROUP BY which aggregates common
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elements regardless of their input order.
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The returned group is itself an iterator that shares the underlying iterable
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with :func:`groupby`. Because the source is shared, when the :func:`groupby`
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object is advanced, the previous group is no longer visible. So, if that data
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is needed later, it should be stored as a list::
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groups = []
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uniquekeys = []
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data = sorted(data, key=keyfunc)
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for k, g in groupby(data, keyfunc):
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groups.append(list(g)) # Store group iterator as a list
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uniquekeys.append(k)
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:func:`groupby` is equivalent to::
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class groupby(object):
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# [k for k, g in groupby('AAAABBBCCDAABBB')] --> A B C D A B
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# [list(g) for k, g in groupby('AAAABBBCCD')] --> AAAA BBB CC D
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def __init__(self, iterable, key=None):
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if key is None:
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key = lambda x: x
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self.keyfunc = key
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self.it = iter(iterable)
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self.tgtkey = self.currkey = self.currvalue = object()
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def __iter__(self):
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return self
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def __next__(self):
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while self.currkey == self.tgtkey:
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self.currvalue = next(self.it) # Exit on StopIteration
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self.currkey = self.keyfunc(self.currvalue)
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self.tgtkey = self.currkey
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return (self.currkey, self._grouper(self.tgtkey))
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def _grouper(self, tgtkey):
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while self.currkey == tgtkey:
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yield self.currvalue
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self.currvalue = next(self.it) # Exit on StopIteration
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self.currkey = self.keyfunc(self.currvalue)
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.. function:: islice(iterable, [start,] stop [, step])
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Make an iterator that returns selected elements from the iterable. If *start* is
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non-zero, then elements from the iterable are skipped until start is reached.
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Afterward, elements are returned consecutively unless *step* is set higher than
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one which results in items being skipped. If *stop* is ``None``, then iteration
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continues until the iterator is exhausted, if at all; otherwise, it stops at the
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specified position. Unlike regular slicing, :func:`islice` does not support
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negative values for *start*, *stop*, or *step*. Can be used to extract related
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fields from data where the internal structure has been flattened (for example, a
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multi-line report may list a name field on every third line). Equivalent to::
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def islice(iterable, *args):
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# islice('ABCDEFG', 2) --> A B
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# islice('ABCDEFG', 2, 4) --> C D
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# islice('ABCDEFG', 2, None) --> C D E F G
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# islice('ABCDEFG', 0, None, 2) --> A C E G
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s = slice(*args)
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it = range(s.start or 0, s.stop or sys.maxsize, s.step or 1)
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nexti = next(it)
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for i, element in enumerate(iterable):
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if i == nexti:
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yield element
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nexti = next(it)
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If *start* is ``None``, then iteration starts at zero. If *step* is ``None``,
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then the step defaults to one.
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.. function:: permutations(iterable[, r])
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Return successive *r* length permutations of elements in the *iterable*.
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If *r* is not specified or is ``None``, then *r* defaults to the length
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of the *iterable* and all possible full-length permutations
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are generated.
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Permutations are emitted in lexicographic sort order. So, if the
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input *iterable* is sorted, the permutation tuples will be produced
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in sorted order.
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Elements are treated as unique based on their position, not on their
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value. So if the input elements are unique, there will be no repeat
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values in each permutation.
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Equivalent to::
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def permutations(iterable, r=None):
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# permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC
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# permutations(range(3)) --> 012 021 102 120 201 210
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pool = tuple(iterable)
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n = len(pool)
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r = n if r is None else r
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if r > n:
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return
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indices = list(range(n))
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cycles = range(n, n-r, -1)
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yield tuple(pool[i] for i in indices[:r])
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while n:
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for i in reversed(range(r)):
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cycles[i] -= 1
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if cycles[i] == 0:
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indices[i:] = indices[i+1:] + indices[i:i+1]
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cycles[i] = n - i
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else:
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j = cycles[i]
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indices[i], indices[-j] = indices[-j], indices[i]
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yield tuple(pool[i] for i in indices[:r])
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break
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else:
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return
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The code for :func:`permutations` can be also expressed as a subsequence of
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:func:`product`, filtered to exclude entries with repeated elements (those
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from the same position in the input pool)::
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def permutations(iterable, r=None):
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pool = tuple(iterable)
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n = len(pool)
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r = n if r is None else r
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for indices in product(range(n), repeat=r):
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if len(set(indices)) == r:
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yield tuple(pool[i] for i in indices)
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The number of items returned is ``n! / (n-r)!`` when ``0 <= r <= n``
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or zero when ``r > n``.
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.. function:: product(*iterables[, repeat])
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Cartesian product of input iterables.
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Equivalent to nested for-loops in a generator expression. For example,
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``product(A, B)`` returns the same as ``((x,y) for x in A for y in B)``.
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The nested loops cycle like an odometer with the rightmost element advancing
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on every iteration. This pattern creates a lexicographic ordering so that if
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the input's iterables are sorted, the product tuples are emitted in sorted
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order.
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To compute the product of an iterable with itself, specify the number of
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repetitions with the optional *repeat* keyword argument. For example,
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``product(A, repeat=4)`` means the same as ``product(A, A, A, A)``.
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This function is equivalent to the following code, except that the
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actual implementation does not build up intermediate results in memory::
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def product(*args, repeat=1):
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# product('ABCD', 'xy') --> Ax Ay Bx By Cx Cy Dx Dy
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# product(range(2), repeat=3) --> 000 001 010 011 100 101 110 111
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pools = map(tuple, args) * repeat
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result = [[]]
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for pool in pools:
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result = [x+[y] for x in result for y in pool]
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for prod in result:
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yield tuple(prod)
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.. function:: repeat(object[, times])
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Make an iterator that returns *object* over and over again. Runs indefinitely
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unless the *times* argument is specified. Used as argument to :func:`map` for
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invariant parameters to the called function. Also used with :func:`zip` to
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create an invariant part of a tuple record. Equivalent to::
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def repeat(object, times=None):
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# repeat(10, 3) --> 10 10 10
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if times is None:
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while True:
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yield object
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else:
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for i in range(times):
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yield object
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.. function:: starmap(function, iterable)
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Make an iterator that computes the function using arguments obtained from
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the iterable. Used instead of :func:`map` when argument parameters are already
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grouped in tuples from a single iterable (the data has been "pre-zipped"). The
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difference between :func:`map` and :func:`starmap` parallels the distinction
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between ``function(a,b)`` and ``function(*c)``. Equivalent to::
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def starmap(function, iterable):
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# starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000
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for args in iterable:
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yield function(*args)
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.. function:: takewhile(predicate, iterable)
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Make an iterator that returns elements from the iterable as long as the
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predicate is true. Equivalent to::
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def takewhile(predicate, iterable):
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# takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4
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for x in iterable:
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if predicate(x):
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yield x
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else:
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break
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.. function:: tee(iterable[, n=2])
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Return *n* independent iterators from a single iterable. The case where ``n==2``
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is equivalent to::
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def tee(iterable):
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def gen(next, data={}):
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for i in count():
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if i in data:
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yield data.pop(i)
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else:
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data[i] = next()
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yield data[i]
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it = iter(iterable)
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return (gen(it.__next__), gen(it.__next__))
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Note, once :func:`tee` has made a split, the original *iterable* should not be
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used anywhere else; otherwise, the *iterable* could get advanced without the tee
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objects being informed.
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Note, this member of the toolkit may require significant auxiliary storage
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(depending on how much temporary data needs to be stored). In general, if one
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iterator is going to use most or all of the data before the other iterator, it
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is faster to use :func:`list` instead of :func:`tee`.
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.. function:: zip_longest(*iterables[, fillvalue])
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Make an iterator that aggregates elements from each of the iterables. If the
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iterables are of uneven length, missing values are filled-in with *fillvalue*.
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Iteration continues until the longest iterable is exhausted. Equivalent to::
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def zip_longest(*args, fillvalue=None):
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# zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-
|
|
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 zip(*iters):
|
|
yield tup
|
|
except IndexError:
|
|
pass
|
|
|
|
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-example:
|
|
|
|
Examples
|
|
--------
|
|
|
|
The following examples show common uses for each tool and demonstrate ways they
|
|
can be combined.
|
|
|
|
.. doctest::
|
|
|
|
>>> # Show a dictionary sorted and grouped by value
|
|
>>> from operator import itemgetter
|
|
>>> d = dict(a=1, b=2, c=1, d=2, e=1, f=2, g=3)
|
|
>>> di = sorted(d.items(), key=itemgetter(1))
|
|
>>> for k, g in groupby(di, key=itemgetter(1)):
|
|
... print(k, map(itemgetter(0), g))
|
|
...
|
|
1 ['a', 'c', 'e']
|
|
2 ['b', 'd', 'f']
|
|
3 ['g']
|
|
|
|
>>> # Find runs of consecutive numbers using groupby. The key to the solution
|
|
>>> # is differencing with a range so that consecutive numbers all appear in
|
|
>>> # same group.
|
|
>>> data = [ 1, 4,5,6, 10, 15,16,17,18, 22, 25,26,27,28]
|
|
>>> for k, g in groupby(enumerate(data), lambda t:t[0]-t[1]):
|
|
... print(map(operator.itemgetter(1), g))
|
|
...
|
|
[1]
|
|
[4, 5, 6]
|
|
[10]
|
|
[15, 16, 17, 18]
|
|
[22]
|
|
[25, 26, 27, 28]
|
|
|
|
|
|
|
|
.. _itertools-recipes:
|
|
|
|
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 enumerate(iterable, start=0):
|
|
return zip(count(start), iterable)
|
|
|
|
def tabulate(function, start=0):
|
|
"Return function(0), function(1), ..."
|
|
return map(function, count(start))
|
|
|
|
def nth(iterable, n):
|
|
"Returns the nth item or None"
|
|
return next(islice(iterable, n, None), None)
|
|
|
|
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(iterable, n))
|
|
|
|
def dotproduct(vec1, vec2):
|
|
return sum(map(operator.mul, vec1, vec2))
|
|
|
|
def flatten(listOfLists):
|
|
return list(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)
|
|
for elem in b:
|
|
break
|
|
return zip(a, b)
|
|
|
|
def grouper(n, iterable, fillvalue=None):
|
|
"grouper(3, 'ABCDEFG', '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
|
|
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 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 iterable:
|
|
if element not in seen:
|
|
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, imap(itemgetter(1), groupby(iterable, key)))
|