1013 lines
42 KiB
ReStructuredText
1013 lines
42 KiB
ReStructuredText
: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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--------------
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This module implements a number of :term:`iterator` building blocks inspired
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by constructs from APL, Haskell, and SML. Each has been recast in a form
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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. Together, they form an "iterator
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algebra" making it possible to construct specialized tools succinctly and
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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), ...``. The same 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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These tools and their built-in counterparts also work well with the high-speed
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functions in the :mod:`operator` module. For example, the multiplication
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operator can be mapped across two vectors to form an efficient dot-product:
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``sum(map(operator.mul, vector1, vector2))``.
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**Infinite iterators:**
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================== ================= ================================================= =========================================
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Iterator Arguments Results Example
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================== ================= ================================================= =========================================
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:func:`count` start, [step] start, start+step, start+2*step, ... ``count(10) --> 10 11 12 13 14 ...``
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:func:`cycle` p p0, p1, ... plast, p0, p1, ... ``cycle('ABCD') --> A B C D A B C D ...``
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:func:`repeat` elem [,n] elem, elem, elem, ... endlessly or up to n times ``repeat(10, 3) --> 10 10 10``
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================== ================= ================================================= =========================================
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**Iterators terminating on the shortest input sequence:**
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============================ ============================ ================================================= =============================================================
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Iterator Arguments Results Example
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============================ ============================ ================================================= =============================================================
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:func:`accumulate` p [,func] p0, p0+p1, p0+p1+p2, ... ``accumulate([1,2,3,4,5]) --> 1 3 6 10 15``
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:func:`chain` p, q, ... p0, p1, ... plast, q0, q1, ... ``chain('ABC', 'DEF') --> A B C D E F``
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:func:`chain.from_iterable` iterable p0, p1, ... plast, q0, q1, ... ``chain.from_iterable(['ABC', 'DEF']) --> A B C D E F``
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: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``
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: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``
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:func:`filterfalse` pred, seq elements of seq where pred(elem) is false ``filterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8``
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:func:`groupby` iterable[, key] sub-iterators grouped by value of key(v)
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:func:`islice` seq, [start,] stop [, step] elements from seq[start:stop:step] ``islice('ABCDEFG', 2, None) --> C D E F G``
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:func:`pairwise` iterable (p[0], p[1]), (p[1], p[2]) ``pairwise('ABCDEFG') --> AB BC CD DE EF FG``
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:func:`starmap` func, seq func(\*seq[0]), func(\*seq[1]), ... ``starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000``
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:func:`takewhile` pred, seq seq[0], seq[1], until pred fails ``takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4``
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:func:`tee` it, n it1, it2, ... itn splits one iterator into n
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:func:`zip_longest` p, q, ... (p[0], q[0]), (p[1], q[1]), ... ``zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-``
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============================ ============================ ================================================= =============================================================
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**Combinatoric iterators:**
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============================================== ==================== =============================================================
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Iterator Arguments Results
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============================================== ==================== =============================================================
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:func:`product` p, q, ... [repeat=1] cartesian product, equivalent to a nested for-loop
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:func:`permutations` p[, r] r-length tuples, all possible orderings, no repeated elements
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:func:`combinations` p, r r-length tuples, in sorted order, no repeated elements
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:func:`combinations_with_replacement` p, r r-length tuples, in sorted order, with repeated elements
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============================================== ==================== =============================================================
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============================================== =============================================================
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Examples Results
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============================================== =============================================================
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``product('ABCD', repeat=2)`` ``AA AB AC AD BA BB BC BD CA CB CC CD DA DB DC DD``
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``permutations('ABCD', 2)`` ``AB AC AD BA BC BD CA CB CD DA DB DC``
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``combinations('ABCD', 2)`` ``AB AC AD BC BD CD``
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``combinations_with_replacement('ABCD', 2)`` ``AA AB AC AD BB BC BD CC CD DD``
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============================================== =============================================================
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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:: accumulate(iterable[, func, *, initial=None])
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Make an iterator that returns accumulated sums, or accumulated
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results of other binary functions (specified via the optional
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*func* argument).
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If *func* is supplied, it should be a function
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of two arguments. Elements of the input *iterable* may be any type
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that can be accepted as arguments to *func*. (For example, with
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the default operation of addition, elements may be any addable
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type including :class:`~decimal.Decimal` or
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:class:`~fractions.Fraction`.)
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Usually, the number of elements output matches the input iterable.
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However, if the keyword argument *initial* is provided, the
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accumulation leads off with the *initial* value so that the output
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has one more element than the input iterable.
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Roughly equivalent to::
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def accumulate(iterable, func=operator.add, *, initial=None):
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'Return running totals'
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# accumulate([1,2,3,4,5]) --> 1 3 6 10 15
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# accumulate([1,2,3,4,5], initial=100) --> 100 101 103 106 110 115
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# accumulate([1,2,3,4,5], operator.mul) --> 1 2 6 24 120
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it = iter(iterable)
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total = initial
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if initial is None:
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try:
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total = next(it)
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except StopIteration:
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return
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yield total
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for element in it:
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total = func(total, element)
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yield total
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There are a number of uses for the *func* argument. It can be set to
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:func:`min` for a running minimum, :func:`max` for a running maximum, or
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:func:`operator.mul` for a running product. Amortization tables can be
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built by accumulating interest and applying payments. First-order
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`recurrence relations <https://en.wikipedia.org/wiki/Recurrence_relation>`_
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can be modeled by supplying the initial value in the iterable and using only
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the accumulated total in *func* argument::
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>>> data = [3, 4, 6, 2, 1, 9, 0, 7, 5, 8]
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>>> list(accumulate(data, operator.mul)) # running product
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[3, 12, 72, 144, 144, 1296, 0, 0, 0, 0]
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>>> list(accumulate(data, max)) # running maximum
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[3, 4, 6, 6, 6, 9, 9, 9, 9, 9]
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# Amortize a 5% loan of 1000 with 4 annual payments of 90
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>>> cashflows = [1000, -90, -90, -90, -90]
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>>> list(accumulate(cashflows, lambda bal, pmt: bal*1.05 + pmt))
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[1000, 960.0, 918.0, 873.9000000000001, 827.5950000000001]
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# Chaotic recurrence relation https://en.wikipedia.org/wiki/Logistic_map
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>>> logistic_map = lambda x, _: r * x * (1 - x)
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>>> r = 3.8
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>>> x0 = 0.4
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>>> inputs = repeat(x0, 36) # only the initial value is used
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>>> [format(x, '.2f') for x in accumulate(inputs, logistic_map)]
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['0.40', '0.91', '0.30', '0.81', '0.60', '0.92', '0.29', '0.79', '0.63',
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'0.88', '0.39', '0.90', '0.33', '0.84', '0.52', '0.95', '0.18', '0.57',
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'0.93', '0.25', '0.71', '0.79', '0.63', '0.88', '0.39', '0.91', '0.32',
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'0.83', '0.54', '0.95', '0.20', '0.60', '0.91', '0.30', '0.80', '0.60']
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See :func:`functools.reduce` for a similar function that returns only the
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final accumulated value.
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.. versionadded:: 3.2
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.. versionchanged:: 3.3
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Added the optional *func* parameter.
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.. versionchanged:: 3.8
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Added the optional *initial* parameter.
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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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Roughly 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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.. classmethod:: 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. Roughly equivalent to::
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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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The combination tuples are emitted in lexicographic ordering according to
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the order of the input *iterable*. So, if the input *iterable* is sorted,
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the combination tuples will be produced 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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Roughly 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 True:
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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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The combination tuples are emitted in lexicographic ordering according to
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the order of the input *iterable*. So, if the input *iterable* is sorted,
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the combination tuples will be produced 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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Roughly 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 True:
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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:: 3.1
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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 has been exhausted.
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Roughly 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:: 3.1
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.. function:: count(start=0, step=1)
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Make an iterator that returns evenly spaced values starting with number *start*. Often
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used as an argument to :func:`map` to generate consecutive data points.
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Also, used with :func:`zip` to add sequence numbers. Roughly equivalent to::
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def count(start=0, step=1):
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# count(10) --> 10 11 12 13 14 ...
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# count(2.5, 0.5) -> 2.5 3.0 3.5 ...
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n = start
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while True:
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yield n
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n += step
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When counting with floating point numbers, better accuracy can sometimes be
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achieved by substituting multiplicative code such as: ``(start + step * i
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for i in count())``.
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.. versionchanged:: 3.1
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Added *step* argument and allowed non-integer arguments.
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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. Roughly 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. Roughly 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. Roughly 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=None)
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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 roughly equivalent to::
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class groupby:
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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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self.id = object()
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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, self.id))
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def _grouper(self, tgtkey, id):
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while self.id is id and self.currkey == tgtkey:
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yield self.currvalue
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try:
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self.currvalue = next(self.it)
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except StopIteration:
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return
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self.currkey = self.keyfunc(self.currvalue)
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.. function:: islice(iterable, stop)
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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). Roughly equivalent to::
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def islice(iterable, *args):
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# islice('ABCDEFG', 2) --> A B
|
||
# islice('ABCDEFG', 2, 4) --> C D
|
||
# islice('ABCDEFG', 2, None) --> C D E F G
|
||
# islice('ABCDEFG', 0, None, 2) --> A C E G
|
||
s = slice(*args)
|
||
start, stop, step = s.start or 0, s.stop or sys.maxsize, s.step or 1
|
||
it = iter(range(start, stop, step))
|
||
try:
|
||
nexti = next(it)
|
||
except StopIteration:
|
||
# Consume *iterable* up to the *start* position.
|
||
for i, element in zip(range(start), iterable):
|
||
pass
|
||
return
|
||
try:
|
||
for i, element in enumerate(iterable):
|
||
if i == nexti:
|
||
yield element
|
||
nexti = next(it)
|
||
except StopIteration:
|
||
# Consume to *stop*.
|
||
for i, element in zip(range(i + 1, stop), iterable):
|
||
pass
|
||
|
||
If *start* is ``None``, then iteration starts at zero. If *step* is ``None``,
|
||
then the step defaults to one.
|
||
|
||
.. function:: pairwise(iterable)
|
||
|
||
Return successive overlapping pairs taken from the input *iterable*.
|
||
|
||
The number of 2-tuples in the output iterator will be one fewer than the
|
||
number of inputs. It will be empty if the input iterable has fewer than
|
||
two values.
|
||
|
||
Roughly equivalent to::
|
||
|
||
def pairwise(iterable):
|
||
# pairwise('ABCDEFG') --> AB BC CD DE EF FG
|
||
a, b = tee(iterable)
|
||
next(b, None)
|
||
return zip(a, b)
|
||
|
||
.. versionadded:: 3.10
|
||
|
||
|
||
.. function:: permutations(iterable, r=None)
|
||
|
||
Return successive *r* length permutations of elements in the *iterable*.
|
||
|
||
If *r* is not specified or is ``None``, then *r* defaults to the length
|
||
of the *iterable* and all possible full-length permutations
|
||
are generated.
|
||
|
||
The permutation tuples are emitted in lexicographic ordering according to
|
||
the order of the input *iterable*. 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 permutation.
|
||
|
||
Roughly equivalent to::
|
||
|
||
def permutations(iterable, r=None):
|
||
# permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC
|
||
# permutations(range(3)) --> 012 021 102 120 201 210
|
||
pool = tuple(iterable)
|
||
n = len(pool)
|
||
r = n if r is None else r
|
||
if r > n:
|
||
return
|
||
indices = list(range(n))
|
||
cycles = list(range(n, n-r, -1))
|
||
yield tuple(pool[i] for i in indices[:r])
|
||
while n:
|
||
for i in reversed(range(r)):
|
||
cycles[i] -= 1
|
||
if cycles[i] == 0:
|
||
indices[i:] = indices[i+1:] + indices[i:i+1]
|
||
cycles[i] = n - i
|
||
else:
|
||
j = cycles[i]
|
||
indices[i], indices[-j] = indices[-j], indices[i]
|
||
yield tuple(pool[i] for i in indices[:r])
|
||
break
|
||
else:
|
||
return
|
||
|
||
The code for :func:`permutations` can be also expressed as a subsequence of
|
||
:func:`product`, filtered to exclude entries with repeated elements (those
|
||
from the same position in the input pool)::
|
||
|
||
def permutations(iterable, r=None):
|
||
pool = tuple(iterable)
|
||
n = len(pool)
|
||
r = n if r is None else r
|
||
for indices in product(range(n), repeat=r):
|
||
if len(set(indices)) == r:
|
||
yield tuple(pool[i] for i in indices)
|
||
|
||
The number of items returned is ``n! / (n-r)!`` when ``0 <= r <= n``
|
||
or zero when ``r > n``.
|
||
|
||
.. function:: product(*iterables, repeat=1)
|
||
|
||
Cartesian product of input iterables.
|
||
|
||
Roughly equivalent to nested for-loops in a generator expression. For example,
|
||
``product(A, B)`` returns the same as ``((x,y) for x in A for y in B)``.
|
||
|
||
The nested loops cycle like an odometer with the rightmost element advancing
|
||
on every iteration. This pattern creates a lexicographic ordering so that if
|
||
the input's iterables are sorted, the product tuples are emitted in sorted
|
||
order.
|
||
|
||
To compute the product of an iterable with itself, specify the number of
|
||
repetitions with the optional *repeat* keyword argument. For example,
|
||
``product(A, repeat=4)`` means the same as ``product(A, A, A, A)``.
|
||
|
||
This function is roughly equivalent to the following code, except that the
|
||
actual implementation does not build up intermediate results in memory::
|
||
|
||
def product(*args, repeat=1):
|
||
# product('ABCD', 'xy') --> Ax Ay Bx By Cx Cy Dx Dy
|
||
# product(range(2), repeat=3) --> 000 001 010 011 100 101 110 111
|
||
pools = [tuple(pool) for pool in args] * repeat
|
||
result = [[]]
|
||
for pool in pools:
|
||
result = [x+[y] for x in result for y in pool]
|
||
for prod in result:
|
||
yield tuple(prod)
|
||
|
||
Before :func:`product` runs, it completely consumes the input iterables,
|
||
keeping pools of values in memory to generate the products. Accordingly,
|
||
it is only useful with finite inputs.
|
||
|
||
.. function:: repeat(object[, times])
|
||
|
||
Make an iterator that returns *object* over and over again. Runs indefinitely
|
||
unless the *times* argument is specified. Used as argument to :func:`map` for
|
||
invariant parameters to the called function. Also used with :func:`zip` to
|
||
create an invariant part of a tuple record.
|
||
|
||
Roughly equivalent to::
|
||
|
||
def repeat(object, times=None):
|
||
# repeat(10, 3) --> 10 10 10
|
||
if times is None:
|
||
while True:
|
||
yield object
|
||
else:
|
||
for i in range(times):
|
||
yield object
|
||
|
||
A common use for *repeat* is to supply a stream of constant values to *map*
|
||
or *zip*::
|
||
|
||
>>> list(map(pow, range(10), repeat(2)))
|
||
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
|
||
|
||
.. function:: starmap(function, iterable)
|
||
|
||
Make an iterator that computes the function using arguments obtained from
|
||
the iterable. Used instead of :func:`map` when argument parameters are already
|
||
grouped in tuples from a single iterable (the data has been "pre-zipped"). The
|
||
difference between :func:`map` and :func:`starmap` parallels the distinction
|
||
between ``function(a,b)`` and ``function(*c)``. Roughly equivalent to::
|
||
|
||
def starmap(function, iterable):
|
||
# starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000
|
||
for args in iterable:
|
||
yield function(*args)
|
||
|
||
|
||
.. function:: takewhile(predicate, iterable)
|
||
|
||
Make an iterator that returns elements from the iterable as long as the
|
||
predicate is true. Roughly equivalent to::
|
||
|
||
def takewhile(predicate, iterable):
|
||
# takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4
|
||
for x in iterable:
|
||
if predicate(x):
|
||
yield x
|
||
else:
|
||
break
|
||
|
||
|
||
.. function:: tee(iterable, n=2)
|
||
|
||
Return *n* independent iterators from a single iterable.
|
||
|
||
The following Python code helps explain what *tee* does (although the actual
|
||
implementation is more complex and uses only a single underlying
|
||
:abbr:`FIFO (first-in, first-out)` queue).
|
||
|
||
Roughly equivalent to::
|
||
|
||
def tee(iterable, n=2):
|
||
it = iter(iterable)
|
||
deques = [collections.deque() for i in range(n)]
|
||
def gen(mydeque):
|
||
while True:
|
||
if not mydeque: # when the local deque is empty
|
||
try:
|
||
newval = next(it) # fetch a new value and
|
||
except StopIteration:
|
||
return
|
||
for d in deques: # load it to all the deques
|
||
d.append(newval)
|
||
yield mydeque.popleft()
|
||
return tuple(gen(d) for d in deques)
|
||
|
||
Once :func:`tee` has made a split, the original *iterable* should not be
|
||
used anywhere else; otherwise, the *iterable* could get advanced without
|
||
the tee objects being informed.
|
||
|
||
``tee`` iterators are not threadsafe. A :exc:`RuntimeError` may be
|
||
raised when using simultaneously iterators returned by the same :func:`tee`
|
||
call, even if the original *iterable* is threadsafe.
|
||
|
||
This itertool may require significant auxiliary storage (depending on how
|
||
much temporary data needs to be stored). In general, if one iterator uses
|
||
most or all of the data before another iterator starts, it is faster to use
|
||
:func:`list` instead of :func:`tee`.
|
||
|
||
|
||
.. function:: zip_longest(*iterables, fillvalue=None)
|
||
|
||
Make an iterator that aggregates elements from each of the iterables. If the
|
||
iterables are of uneven length, missing values are filled-in with *fillvalue*.
|
||
Iteration continues until the longest iterable is exhausted. Roughly equivalent to::
|
||
|
||
def zip_longest(*args, fillvalue=None):
|
||
# zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-
|
||
iterators = [iter(it) for it in args]
|
||
num_active = len(iterators)
|
||
if not num_active:
|
||
return
|
||
while True:
|
||
values = []
|
||
for i, it in enumerate(iterators):
|
||
try:
|
||
value = next(it)
|
||
except StopIteration:
|
||
num_active -= 1
|
||
if not num_active:
|
||
return
|
||
iterators[i] = repeat(fillvalue)
|
||
value = fillvalue
|
||
values.append(value)
|
||
yield tuple(values)
|
||
|
||
If one of the iterables is potentially infinite, then the :func:`zip_longest`
|
||
function should be wrapped with something that limits the number of calls
|
||
(for example :func:`islice` or :func:`takewhile`). If not specified,
|
||
*fillvalue* defaults to ``None``.
|
||
|
||
|
||
.. _itertools-recipes:
|
||
|
||
Itertools Recipes
|
||
-----------------
|
||
|
||
This section shows recipes for creating an extended toolset using the existing
|
||
itertools as building blocks.
|
||
|
||
Substantially all of these recipes and many, many others can be installed from
|
||
the `more-itertools project <https://pypi.org/project/more-itertools/>`_ found
|
||
on the Python Package Index::
|
||
|
||
pip install more-itertools
|
||
|
||
The extended tools offer the same high performance as the underlying toolset.
|
||
The superior memory performance is kept by processing elements one at a time
|
||
rather than bringing the whole iterable into memory all at once. Code volume is
|
||
kept small by linking the tools together in a functional style which helps
|
||
eliminate temporary variables. High speed is retained by preferring
|
||
"vectorized" building blocks over the use of for-loops and :term:`generator`\s
|
||
which incur interpreter overhead.
|
||
|
||
.. testcode::
|
||
|
||
def take(n, iterable):
|
||
"Return first n items of the iterable as a list"
|
||
return list(islice(iterable, n))
|
||
|
||
def prepend(value, iterator):
|
||
"Prepend a single value in front of an iterator"
|
||
# prepend(1, [2, 3, 4]) -> 1 2 3 4
|
||
return chain([value], iterator)
|
||
|
||
def tabulate(function, start=0):
|
||
"Return function(0), function(1), ..."
|
||
return map(function, count(start))
|
||
|
||
def tail(n, iterable):
|
||
"Return an iterator over the last n items"
|
||
# tail(3, 'ABCDEFG') --> E F G
|
||
return iter(collections.deque(iterable, maxlen=n))
|
||
|
||
def consume(iterator, n=None):
|
||
"Advance the iterator n-steps ahead. If n is None, consume entirely."
|
||
# Use functions that consume iterators at C speed.
|
||
if n is None:
|
||
# feed the entire iterator into a zero-length deque
|
||
collections.deque(iterator, maxlen=0)
|
||
else:
|
||
# advance to the empty slice starting at position n
|
||
next(islice(iterator, n, n), None)
|
||
|
||
def nth(iterable, n, default=None):
|
||
"Returns the nth item or a default value"
|
||
return next(islice(iterable, n, None), default)
|
||
|
||
def all_equal(iterable):
|
||
"Returns True if all the elements are equal to each other"
|
||
g = groupby(iterable)
|
||
return next(g, True) and not next(g, False)
|
||
|
||
def quantify(iterable, pred=bool):
|
||
"Count how many times the predicate is true"
|
||
return sum(map(pred, iterable))
|
||
|
||
def pad_none(iterable):
|
||
"""Returns the sequence elements and then returns None indefinitely.
|
||
|
||
Useful for emulating the behavior of the built-in map() function.
|
||
"""
|
||
return chain(iterable, repeat(None))
|
||
|
||
def ncycles(iterable, n):
|
||
"Returns the sequence elements n times"
|
||
return chain.from_iterable(repeat(tuple(iterable), n))
|
||
|
||
def dotproduct(vec1, vec2):
|
||
return sum(map(operator.mul, vec1, vec2))
|
||
|
||
def convolve(signal, kernel):
|
||
# See: https://betterexplained.com/articles/intuitive-convolution/
|
||
# convolve(data, [0.25, 0.25, 0.25, 0.25]) --> Moving average (blur)
|
||
# convolve(data, [1, -1]) --> 1st finite difference (1st derivative)
|
||
# convolve(data, [1, -2, 1]) --> 2nd finite difference (2nd derivative)
|
||
kernel = tuple(kernel)[::-1]
|
||
n = len(kernel)
|
||
window = collections.deque([0], maxlen=n) * n
|
||
for x in chain(signal, repeat(0, n-1)):
|
||
window.append(x)
|
||
yield sum(map(operator.mul, kernel, window))
|
||
|
||
def flatten(list_of_lists):
|
||
"Flatten one level of nesting"
|
||
return chain.from_iterable(list_of_lists)
|
||
|
||
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 grouper(iterable, n, *, incomplete='fill', fillvalue=None):
|
||
"Collect data into non-overlapping fixed-length chunks or blocks"
|
||
# grouper('ABCDEFG', 3, fillvalue='x') --> ABC DEF Gxx
|
||
# grouper('ABCDEFG', 3, incomplete='strict') --> ABC DEF ValueError
|
||
# grouper('ABCDEFG', 3, incomplete='ignore') --> ABC DEF
|
||
args = [iter(iterable)] * n
|
||
if incomplete == 'fill':
|
||
return zip_longest(*args, fillvalue=fillvalue)
|
||
if incomplete == 'strict':
|
||
return zip(*args, strict=True)
|
||
if incomplete == 'ignore':
|
||
return zip(*args)
|
||
else:
|
||
raise ValueError('Expected fill, strict, or ignore')
|
||
|
||
def triplewise(iterable):
|
||
"Return overlapping triplets from an iterable"
|
||
# triplewise('ABCDEFG') -> ABC BCD CDE DEF EFG
|
||
for (a, _), (b, c) in pairwise(pairwise(iterable)):
|
||
yield a, b, c
|
||
|
||
def sliding_window(iterable, n):
|
||
# sliding_window('ABCDEFG', 4) -> ABCD BCDE CDEF DEFG
|
||
it = iter(iterable)
|
||
window = collections.deque(islice(it, n), maxlen=n)
|
||
if len(window) == n:
|
||
yield tuple(window)
|
||
for x in it:
|
||
window.append(x)
|
||
yield tuple(window)
|
||
|
||
def roundrobin(*iterables):
|
||
"roundrobin('ABC', 'D', 'EF') --> A D E B F C"
|
||
# Recipe credited to George Sakkis
|
||
num_active = len(iterables)
|
||
nexts = cycle(iter(it).__next__ for it in iterables)
|
||
while num_active:
|
||
try:
|
||
for next in nexts:
|
||
yield next()
|
||
except StopIteration:
|
||
# Remove the iterator we just exhausted from the cycle.
|
||
num_active -= 1
|
||
nexts = cycle(islice(nexts, num_active))
|
||
|
||
def partition(pred, iterable):
|
||
"Use a predicate to partition entries into false entries and true entries"
|
||
# partition(is_odd, range(10)) --> 0 2 4 6 8 and 1 3 5 7 9
|
||
t1, t2 = tee(iterable)
|
||
return filterfalse(pred, t1), filter(pred, t2)
|
||
|
||
def before_and_after(predicate, it):
|
||
""" Variant of takewhile() that allows complete
|
||
access to the remainder of the iterator.
|
||
|
||
>>> it = iter('ABCdEfGhI')
|
||
>>> all_upper, remainder = before_and_after(str.isupper, it)
|
||
>>> ''.join(all_upper)
|
||
'ABC'
|
||
>>> ''.join(remainder) # takewhile() would lose the 'd'
|
||
'dEfGhI'
|
||
|
||
Note that the first iterator must be fully
|
||
consumed before the second iterator can
|
||
generate valid results.
|
||
"""
|
||
it = iter(it)
|
||
transition = []
|
||
def true_iterator():
|
||
for elem in it:
|
||
if predicate(elem):
|
||
yield elem
|
||
else:
|
||
transition.append(elem)
|
||
return
|
||
def remainder_iterator():
|
||
yield from transition
|
||
yield from it
|
||
return true_iterator(), remainder_iterator()
|
||
|
||
def subslices(seq):
|
||
"Return all contiguous non-empty subslices of a sequence"
|
||
# subslices('ABCD') --> A AB ABC ABCD B BC BCD C CD D
|
||
slices = starmap(slice, combinations(range(len(seq) + 1), 2))
|
||
return map(operator.getitem, repeat(seq), slices)
|
||
|
||
def powerset(iterable):
|
||
"powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
|
||
s = list(iterable)
|
||
return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
|
||
|
||
def unique_everseen(iterable, key=None):
|
||
"List unique elements, preserving order. Remember all elements ever seen."
|
||
# unique_everseen('AAAABBBCCDAABBB') --> A B C D
|
||
# unique_everseen('ABBCcAD', str.lower) --> A B C D
|
||
seen = set()
|
||
seen_add = seen.add
|
||
if key is None:
|
||
for element in filterfalse(seen.__contains__, iterable):
|
||
seen_add(element)
|
||
yield element
|
||
else:
|
||
for element in iterable:
|
||
k = key(element)
|
||
if k not in seen:
|
||
seen_add(k)
|
||
yield element
|
||
|
||
def unique_justseen(iterable, key=None):
|
||
"List unique elements, preserving order. Remember only the element just seen."
|
||
# unique_justseen('AAAABBBCCDAABBB') --> A B C D A B
|
||
# unique_justseen('ABBCcAD', str.lower) --> A B C A D
|
||
return map(next, map(operator.itemgetter(1), groupby(iterable, key)))
|
||
|
||
def iter_except(func, exception, first=None):
|
||
""" Call a function repeatedly until an exception is raised.
|
||
|
||
Converts a call-until-exception interface to an iterator interface.
|
||
Like builtins.iter(func, sentinel) but uses an exception instead
|
||
of a sentinel to end the loop.
|
||
|
||
Examples:
|
||
iter_except(functools.partial(heappop, h), IndexError) # priority queue iterator
|
||
iter_except(d.popitem, KeyError) # non-blocking dict iterator
|
||
iter_except(d.popleft, IndexError) # non-blocking deque iterator
|
||
iter_except(q.get_nowait, Queue.Empty) # loop over a producer Queue
|
||
iter_except(s.pop, KeyError) # non-blocking set iterator
|
||
|
||
"""
|
||
try:
|
||
if first is not None:
|
||
yield first() # For database APIs needing an initial cast to db.first()
|
||
while True:
|
||
yield func()
|
||
except exception:
|
||
pass
|
||
|
||
def first_true(iterable, default=False, pred=None):
|
||
"""Returns the first true value in the iterable.
|
||
|
||
If no true value is found, returns *default*
|
||
|
||
If *pred* is not None, returns the first item
|
||
for which pred(item) is true.
|
||
|
||
"""
|
||
# first_true([a,b,c], x) --> a or b or c or x
|
||
# first_true([a,b], x, f) --> a if f(a) else b if f(b) else x
|
||
return next(filter(pred, iterable), default)
|
||
|
||
def random_product(*args, repeat=1):
|
||
"Random selection from itertools.product(*args, **kwds)"
|
||
pools = [tuple(pool) for pool in args] * repeat
|
||
return tuple(map(random.choice, pools))
|
||
|
||
def random_permutation(iterable, r=None):
|
||
"Random selection from itertools.permutations(iterable, r)"
|
||
pool = tuple(iterable)
|
||
r = len(pool) if r is None else r
|
||
return tuple(random.sample(pool, r))
|
||
|
||
def random_combination(iterable, r):
|
||
"Random selection from itertools.combinations(iterable, r)"
|
||
pool = tuple(iterable)
|
||
n = len(pool)
|
||
indices = sorted(random.sample(range(n), r))
|
||
return tuple(pool[i] for i in indices)
|
||
|
||
def random_combination_with_replacement(iterable, r):
|
||
"Random selection from itertools.combinations_with_replacement(iterable, r)"
|
||
pool = tuple(iterable)
|
||
n = len(pool)
|
||
indices = sorted(random.choices(range(n), k=r))
|
||
return tuple(pool[i] for i in indices)
|
||
|
||
def nth_combination(iterable, r, index):
|
||
"Equivalent to list(combinations(iterable, r))[index]"
|
||
pool = tuple(iterable)
|
||
n = len(pool)
|
||
if r < 0 or r > n:
|
||
raise ValueError
|
||
c = 1
|
||
k = min(r, n-r)
|
||
for i in range(1, k+1):
|
||
c = c * (n - k + i) // i
|
||
if index < 0:
|
||
index += c
|
||
if index < 0 or index >= c:
|
||
raise IndexError
|
||
result = []
|
||
while r:
|
||
c, n, r = c*r//n, n-1, r-1
|
||
while index >= c:
|
||
index -= c
|
||
c, n = c*(n-r)//n, n-1
|
||
result.append(pool[-1-n])
|
||
return tuple(result)
|