842 lines
22 KiB
Python
842 lines
22 KiB
Python
"""Imported from the recipes section of the itertools documentation.
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All functions taken from the recipes section of the itertools library docs
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[1]_.
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Some backward-compatible usability improvements have been made.
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.. [1] http://docs.python.org/library/itertools.html#recipes
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"""
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import math
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import operator
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from collections import deque
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from collections.abc import Sized
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from functools import reduce
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from itertools import (
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chain,
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combinations,
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compress,
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count,
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cycle,
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groupby,
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islice,
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repeat,
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starmap,
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tee,
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zip_longest,
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)
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from random import randrange, sample, choice
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__all__ = [
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'all_equal',
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'batched',
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'before_and_after',
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'consume',
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'convolve',
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'dotproduct',
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'first_true',
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'flatten',
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'grouper',
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'iter_except',
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'ncycles',
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'nth',
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'nth_combination',
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'padnone',
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'pad_none',
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'pairwise',
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'partition',
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'polynomial_from_roots',
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'powerset',
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'prepend',
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'quantify',
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'random_combination_with_replacement',
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'random_combination',
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'random_permutation',
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'random_product',
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'repeatfunc',
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'roundrobin',
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'sieve',
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'sliding_window',
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'subslices',
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'tabulate',
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'tail',
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'take',
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'triplewise',
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'unique_everseen',
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'unique_justseen',
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]
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_marker = object()
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def take(n, iterable):
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"""Return first *n* items of the iterable as a list.
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>>> take(3, range(10))
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[0, 1, 2]
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If there are fewer than *n* items in the iterable, all of them are
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returned.
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>>> take(10, range(3))
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[0, 1, 2]
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"""
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return list(islice(iterable, n))
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def tabulate(function, start=0):
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"""Return an iterator over the results of ``func(start)``,
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``func(start + 1)``, ``func(start + 2)``...
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*func* should be a function that accepts one integer argument.
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If *start* is not specified it defaults to 0. It will be incremented each
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time the iterator is advanced.
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>>> square = lambda x: x ** 2
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>>> iterator = tabulate(square, -3)
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>>> take(4, iterator)
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[9, 4, 1, 0]
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"""
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return map(function, count(start))
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def tail(n, iterable):
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"""Return an iterator over the last *n* items of *iterable*.
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>>> t = tail(3, 'ABCDEFG')
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>>> list(t)
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['E', 'F', 'G']
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"""
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# If the given iterable has a length, then we can use islice to get its
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# final elements. Note that if the iterable is not actually Iterable,
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# either islice or deque will throw a TypeError. This is why we don't
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# check if it is Iterable.
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if isinstance(iterable, Sized):
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yield from islice(iterable, max(0, len(iterable) - n), None)
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else:
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yield from iter(deque(iterable, maxlen=n))
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def consume(iterator, n=None):
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"""Advance *iterable* by *n* steps. If *n* is ``None``, consume it
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entirely.
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Efficiently exhausts an iterator without returning values. Defaults to
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consuming the whole iterator, but an optional second argument may be
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provided to limit consumption.
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>>> i = (x for x in range(10))
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>>> next(i)
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0
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>>> consume(i, 3)
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>>> next(i)
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4
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>>> consume(i)
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>>> next(i)
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Traceback (most recent call last):
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File "<stdin>", line 1, in <module>
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StopIteration
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If the iterator has fewer items remaining than the provided limit, the
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whole iterator will be consumed.
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>>> i = (x for x in range(3))
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>>> consume(i, 5)
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>>> next(i)
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Traceback (most recent call last):
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File "<stdin>", line 1, in <module>
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StopIteration
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"""
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# Use functions that consume iterators at C speed.
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if n is None:
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# feed the entire iterator into a zero-length deque
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deque(iterator, maxlen=0)
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else:
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# advance to the empty slice starting at position n
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next(islice(iterator, n, n), None)
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def nth(iterable, n, default=None):
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"""Returns the nth item or a default value.
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>>> l = range(10)
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>>> nth(l, 3)
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3
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>>> nth(l, 20, "zebra")
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'zebra'
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"""
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return next(islice(iterable, n, None), default)
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def all_equal(iterable):
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"""
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Returns ``True`` if all the elements are equal to each other.
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>>> all_equal('aaaa')
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True
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>>> all_equal('aaab')
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False
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"""
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g = groupby(iterable)
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return next(g, True) and not next(g, False)
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def quantify(iterable, pred=bool):
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"""Return the how many times the predicate is true.
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>>> quantify([True, False, True])
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2
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"""
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return sum(map(pred, iterable))
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def pad_none(iterable):
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"""Returns the sequence of elements and then returns ``None`` indefinitely.
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>>> take(5, pad_none(range(3)))
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[0, 1, 2, None, None]
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Useful for emulating the behavior of the built-in :func:`map` function.
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See also :func:`padded`.
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"""
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return chain(iterable, repeat(None))
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padnone = pad_none
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def ncycles(iterable, n):
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"""Returns the sequence elements *n* times
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>>> list(ncycles(["a", "b"], 3))
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['a', 'b', 'a', 'b', 'a', 'b']
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"""
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return chain.from_iterable(repeat(tuple(iterable), n))
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def dotproduct(vec1, vec2):
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"""Returns the dot product of the two iterables.
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>>> dotproduct([10, 10], [20, 20])
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400
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"""
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return sum(map(operator.mul, vec1, vec2))
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def flatten(listOfLists):
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"""Return an iterator flattening one level of nesting in a list of lists.
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>>> list(flatten([[0, 1], [2, 3]]))
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[0, 1, 2, 3]
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See also :func:`collapse`, which can flatten multiple levels of nesting.
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"""
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return chain.from_iterable(listOfLists)
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def repeatfunc(func, times=None, *args):
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"""Call *func* with *args* repeatedly, returning an iterable over the
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results.
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If *times* is specified, the iterable will terminate after that many
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repetitions:
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>>> from operator import add
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>>> times = 4
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>>> args = 3, 5
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>>> list(repeatfunc(add, times, *args))
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[8, 8, 8, 8]
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If *times* is ``None`` the iterable will not terminate:
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>>> from random import randrange
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>>> times = None
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>>> args = 1, 11
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>>> take(6, repeatfunc(randrange, times, *args)) # doctest:+SKIP
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[2, 4, 8, 1, 8, 4]
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"""
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if times is None:
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return starmap(func, repeat(args))
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return starmap(func, repeat(args, times))
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def _pairwise(iterable):
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"""Returns an iterator of paired items, overlapping, from the original
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>>> take(4, pairwise(count()))
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[(0, 1), (1, 2), (2, 3), (3, 4)]
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On Python 3.10 and above, this is an alias for :func:`itertools.pairwise`.
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"""
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a, b = tee(iterable)
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next(b, None)
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yield from zip(a, b)
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try:
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from itertools import pairwise as itertools_pairwise
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except ImportError:
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pairwise = _pairwise
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else:
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def pairwise(iterable):
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yield from itertools_pairwise(iterable)
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pairwise.__doc__ = _pairwise.__doc__
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class UnequalIterablesError(ValueError):
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def __init__(self, details=None):
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msg = 'Iterables have different lengths'
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if details is not None:
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msg += (': index 0 has length {}; index {} has length {}').format(
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*details
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)
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super().__init__(msg)
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def _zip_equal_generator(iterables):
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for combo in zip_longest(*iterables, fillvalue=_marker):
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for val in combo:
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if val is _marker:
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raise UnequalIterablesError()
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yield combo
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def _zip_equal(*iterables):
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# Check whether the iterables are all the same size.
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try:
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first_size = len(iterables[0])
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for i, it in enumerate(iterables[1:], 1):
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size = len(it)
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if size != first_size:
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break
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else:
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# If we didn't break out, we can use the built-in zip.
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return zip(*iterables)
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# If we did break out, there was a mismatch.
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raise UnequalIterablesError(details=(first_size, i, size))
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# If any one of the iterables didn't have a length, start reading
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# them until one runs out.
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except TypeError:
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return _zip_equal_generator(iterables)
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def grouper(iterable, n, incomplete='fill', fillvalue=None):
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"""Group elements from *iterable* into fixed-length groups of length *n*.
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>>> list(grouper('ABCDEF', 3))
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[('A', 'B', 'C'), ('D', 'E', 'F')]
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The keyword arguments *incomplete* and *fillvalue* control what happens for
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iterables whose length is not a multiple of *n*.
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When *incomplete* is `'fill'`, the last group will contain instances of
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*fillvalue*.
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>>> list(grouper('ABCDEFG', 3, incomplete='fill', fillvalue='x'))
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[('A', 'B', 'C'), ('D', 'E', 'F'), ('G', 'x', 'x')]
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When *incomplete* is `'ignore'`, the last group will not be emitted.
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>>> list(grouper('ABCDEFG', 3, incomplete='ignore', fillvalue='x'))
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[('A', 'B', 'C'), ('D', 'E', 'F')]
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When *incomplete* is `'strict'`, a subclass of `ValueError` will be raised.
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>>> it = grouper('ABCDEFG', 3, incomplete='strict')
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>>> list(it) # doctest: +IGNORE_EXCEPTION_DETAIL
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Traceback (most recent call last):
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...
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UnequalIterablesError
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"""
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args = [iter(iterable)] * n
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if incomplete == 'fill':
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return zip_longest(*args, fillvalue=fillvalue)
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if incomplete == 'strict':
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return _zip_equal(*args)
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if incomplete == 'ignore':
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return zip(*args)
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else:
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raise ValueError('Expected fill, strict, or ignore')
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def roundrobin(*iterables):
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"""Yields an item from each iterable, alternating between them.
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>>> list(roundrobin('ABC', 'D', 'EF'))
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['A', 'D', 'E', 'B', 'F', 'C']
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This function produces the same output as :func:`interleave_longest`, but
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may perform better for some inputs (in particular when the number of
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iterables is small).
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"""
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# Recipe credited to George Sakkis
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pending = len(iterables)
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nexts = cycle(iter(it).__next__ for it in iterables)
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while pending:
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try:
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for next in nexts:
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yield next()
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except StopIteration:
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pending -= 1
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nexts = cycle(islice(nexts, pending))
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def partition(pred, iterable):
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"""
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Returns a 2-tuple of iterables derived from the input iterable.
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The first yields the items that have ``pred(item) == False``.
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The second yields the items that have ``pred(item) == True``.
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>>> is_odd = lambda x: x % 2 != 0
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>>> iterable = range(10)
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>>> even_items, odd_items = partition(is_odd, iterable)
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>>> list(even_items), list(odd_items)
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([0, 2, 4, 6, 8], [1, 3, 5, 7, 9])
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If *pred* is None, :func:`bool` is used.
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>>> iterable = [0, 1, False, True, '', ' ']
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>>> false_items, true_items = partition(None, iterable)
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>>> list(false_items), list(true_items)
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([0, False, ''], [1, True, ' '])
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"""
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if pred is None:
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pred = bool
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evaluations = ((pred(x), x) for x in iterable)
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t1, t2 = tee(evaluations)
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return (
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(x for (cond, x) in t1 if not cond),
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(x for (cond, x) in t2 if cond),
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)
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def powerset(iterable):
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"""Yields all possible subsets of the iterable.
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>>> list(powerset([1, 2, 3]))
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[(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)]
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:func:`powerset` will operate on iterables that aren't :class:`set`
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instances, so repeated elements in the input will produce repeated elements
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in the output. Use :func:`unique_everseen` on the input to avoid generating
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duplicates:
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>>> seq = [1, 1, 0]
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>>> list(powerset(seq))
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[(), (1,), (1,), (0,), (1, 1), (1, 0), (1, 0), (1, 1, 0)]
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>>> from more_itertools import unique_everseen
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>>> list(powerset(unique_everseen(seq)))
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[(), (1,), (0,), (1, 0)]
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"""
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s = list(iterable)
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return chain.from_iterable(combinations(s, r) for r in range(len(s) + 1))
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def unique_everseen(iterable, key=None):
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"""
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Yield unique elements, preserving order.
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>>> list(unique_everseen('AAAABBBCCDAABBB'))
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['A', 'B', 'C', 'D']
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>>> list(unique_everseen('ABBCcAD', str.lower))
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['A', 'B', 'C', 'D']
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Sequences with a mix of hashable and unhashable items can be used.
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The function will be slower (i.e., `O(n^2)`) for unhashable items.
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Remember that ``list`` objects are unhashable - you can use the *key*
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parameter to transform the list to a tuple (which is hashable) to
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avoid a slowdown.
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>>> iterable = ([1, 2], [2, 3], [1, 2])
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>>> list(unique_everseen(iterable)) # Slow
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[[1, 2], [2, 3]]
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>>> list(unique_everseen(iterable, key=tuple)) # Faster
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[[1, 2], [2, 3]]
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Similary, you may want to convert unhashable ``set`` objects with
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``key=frozenset``. For ``dict`` objects,
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``key=lambda x: frozenset(x.items())`` can be used.
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"""
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seenset = set()
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seenset_add = seenset.add
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seenlist = []
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seenlist_add = seenlist.append
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use_key = key is not None
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for element in iterable:
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k = key(element) if use_key else element
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try:
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if k not in seenset:
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seenset_add(k)
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yield element
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except TypeError:
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if k not in seenlist:
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seenlist_add(k)
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yield element
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def unique_justseen(iterable, key=None):
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"""Yields elements in order, ignoring serial duplicates
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>>> list(unique_justseen('AAAABBBCCDAABBB'))
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['A', 'B', 'C', 'D', 'A', 'B']
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>>> list(unique_justseen('ABBCcAD', str.lower))
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['A', 'B', 'C', 'A', 'D']
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"""
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return map(next, map(operator.itemgetter(1), groupby(iterable, key)))
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def iter_except(func, exception, first=None):
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"""Yields results from a function repeatedly until an exception is raised.
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Converts a call-until-exception interface to an iterator interface.
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Like ``iter(func, sentinel)``, but uses an exception instead of a sentinel
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to end the loop.
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>>> l = [0, 1, 2]
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>>> list(iter_except(l.pop, IndexError))
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[2, 1, 0]
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Multiple exceptions can be specified as a stopping condition:
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>>> l = [1, 2, 3, '...', 4, 5, 6]
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>>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError)))
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[7, 6, 5]
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>>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError)))
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[4, 3, 2]
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>>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError)))
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[]
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"""
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try:
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if first is not None:
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yield first()
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while 1:
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yield func()
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except exception:
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pass
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def first_true(iterable, default=None, pred=None):
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"""
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Returns the first true value in the iterable.
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If no true value is found, returns *default*
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If *pred* is not None, returns the first item for which
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``pred(item) == True`` .
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>>> first_true(range(10))
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1
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>>> first_true(range(10), pred=lambda x: x > 5)
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6
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>>> first_true(range(10), default='missing', pred=lambda x: x > 9)
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'missing'
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"""
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return next(filter(pred, iterable), default)
|
|
|
|
|
|
def random_product(*args, repeat=1):
|
|
"""Draw an item at random from each of the input iterables.
|
|
|
|
>>> random_product('abc', range(4), 'XYZ') # doctest:+SKIP
|
|
('c', 3, 'Z')
|
|
|
|
If *repeat* is provided as a keyword argument, that many items will be
|
|
drawn from each iterable.
|
|
|
|
>>> random_product('abcd', range(4), repeat=2) # doctest:+SKIP
|
|
('a', 2, 'd', 3)
|
|
|
|
This equivalent to taking a random selection from
|
|
``itertools.product(*args, **kwarg)``.
|
|
|
|
"""
|
|
pools = [tuple(pool) for pool in args] * repeat
|
|
return tuple(choice(pool) for pool in pools)
|
|
|
|
|
|
def random_permutation(iterable, r=None):
|
|
"""Return a random *r* length permutation of the elements in *iterable*.
|
|
|
|
If *r* is not specified or is ``None``, then *r* defaults to the length of
|
|
*iterable*.
|
|
|
|
>>> random_permutation(range(5)) # doctest:+SKIP
|
|
(3, 4, 0, 1, 2)
|
|
|
|
This equivalent to taking a random selection from
|
|
``itertools.permutations(iterable, r)``.
|
|
|
|
"""
|
|
pool = tuple(iterable)
|
|
r = len(pool) if r is None else r
|
|
return tuple(sample(pool, r))
|
|
|
|
|
|
def random_combination(iterable, r):
|
|
"""Return a random *r* length subsequence of the elements in *iterable*.
|
|
|
|
>>> random_combination(range(5), 3) # doctest:+SKIP
|
|
(2, 3, 4)
|
|
|
|
This equivalent to taking a random selection from
|
|
``itertools.combinations(iterable, r)``.
|
|
|
|
"""
|
|
pool = tuple(iterable)
|
|
n = len(pool)
|
|
indices = sorted(sample(range(n), r))
|
|
return tuple(pool[i] for i in indices)
|
|
|
|
|
|
def random_combination_with_replacement(iterable, r):
|
|
"""Return a random *r* length subsequence of elements in *iterable*,
|
|
allowing individual elements to be repeated.
|
|
|
|
>>> random_combination_with_replacement(range(3), 5) # doctest:+SKIP
|
|
(0, 0, 1, 2, 2)
|
|
|
|
This equivalent to taking a random selection from
|
|
``itertools.combinations_with_replacement(iterable, r)``.
|
|
|
|
"""
|
|
pool = tuple(iterable)
|
|
n = len(pool)
|
|
indices = sorted(randrange(n) for i in range(r))
|
|
return tuple(pool[i] for i in indices)
|
|
|
|
|
|
def nth_combination(iterable, r, index):
|
|
"""Equivalent to ``list(combinations(iterable, r))[index]``.
|
|
|
|
The subsequences of *iterable* that are of length *r* can be ordered
|
|
lexicographically. :func:`nth_combination` computes the subsequence at
|
|
sort position *index* directly, without computing the previous
|
|
subsequences.
|
|
|
|
>>> nth_combination(range(5), 3, 5)
|
|
(0, 3, 4)
|
|
|
|
``ValueError`` will be raised If *r* is negative or greater than the length
|
|
of *iterable*.
|
|
``IndexError`` will be raised if the given *index* is invalid.
|
|
"""
|
|
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)
|
|
|
|
|
|
def prepend(value, iterator):
|
|
"""Yield *value*, followed by the elements in *iterator*.
|
|
|
|
>>> value = '0'
|
|
>>> iterator = ['1', '2', '3']
|
|
>>> list(prepend(value, iterator))
|
|
['0', '1', '2', '3']
|
|
|
|
To prepend multiple values, see :func:`itertools.chain`
|
|
or :func:`value_chain`.
|
|
|
|
"""
|
|
return chain([value], iterator)
|
|
|
|
|
|
def convolve(signal, kernel):
|
|
"""Convolve the iterable *signal* with the iterable *kernel*.
|
|
|
|
>>> signal = (1, 2, 3, 4, 5)
|
|
>>> kernel = [3, 2, 1]
|
|
>>> list(convolve(signal, kernel))
|
|
[3, 8, 14, 20, 26, 14, 5]
|
|
|
|
Note: the input arguments are not interchangeable, as the *kernel*
|
|
is immediately consumed and stored.
|
|
|
|
"""
|
|
kernel = tuple(kernel)[::-1]
|
|
n = len(kernel)
|
|
window = 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 before_and_after(predicate, it):
|
|
"""A variant of :func:`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
|
|
|
|
# Note: this is different from itertools recipes to allow nesting
|
|
# before_and_after remainders into before_and_after again. See tests
|
|
# for an example.
|
|
remainder_iterator = chain(transition, it)
|
|
|
|
return true_iterator(), remainder_iterator
|
|
|
|
|
|
def triplewise(iterable):
|
|
"""Return overlapping triplets from *iterable*.
|
|
|
|
>>> list(triplewise('ABCDE'))
|
|
[('A', 'B', 'C'), ('B', 'C', 'D'), ('C', 'D', 'E')]
|
|
|
|
"""
|
|
for (a, _), (b, c) in pairwise(pairwise(iterable)):
|
|
yield a, b, c
|
|
|
|
|
|
def sliding_window(iterable, n):
|
|
"""Return a sliding window of width *n* over *iterable*.
|
|
|
|
>>> list(sliding_window(range(6), 4))
|
|
[(0, 1, 2, 3), (1, 2, 3, 4), (2, 3, 4, 5)]
|
|
|
|
If *iterable* has fewer than *n* items, then nothing is yielded:
|
|
|
|
>>> list(sliding_window(range(3), 4))
|
|
[]
|
|
|
|
For a variant with more features, see :func:`windowed`.
|
|
"""
|
|
it = iter(iterable)
|
|
window = deque(islice(it, n), maxlen=n)
|
|
if len(window) == n:
|
|
yield tuple(window)
|
|
for x in it:
|
|
window.append(x)
|
|
yield tuple(window)
|
|
|
|
|
|
def subslices(iterable):
|
|
"""Return all contiguous non-empty subslices of *iterable*.
|
|
|
|
>>> list(subslices('ABC'))
|
|
[['A'], ['A', 'B'], ['A', 'B', 'C'], ['B'], ['B', 'C'], ['C']]
|
|
|
|
This is similar to :func:`substrings`, but emits items in a different
|
|
order.
|
|
"""
|
|
seq = list(iterable)
|
|
slices = starmap(slice, combinations(range(len(seq) + 1), 2))
|
|
return map(operator.getitem, repeat(seq), slices)
|
|
|
|
|
|
def polynomial_from_roots(roots):
|
|
"""Compute a polynomial's coefficients from its roots.
|
|
|
|
>>> roots = [5, -4, 3] # (x - 5) * (x + 4) * (x - 3)
|
|
>>> polynomial_from_roots(roots) # x^3 - 4 * x^2 - 17 * x + 60
|
|
[1, -4, -17, 60]
|
|
"""
|
|
# Use math.prod for Python 3.8+,
|
|
prod = getattr(math, 'prod', lambda x: reduce(operator.mul, x, 1))
|
|
roots = list(map(operator.neg, roots))
|
|
return [
|
|
sum(map(prod, combinations(roots, k))) for k in range(len(roots) + 1)
|
|
]
|
|
|
|
|
|
def sieve(n):
|
|
"""Yield the primes less than n.
|
|
|
|
>>> list(sieve(30))
|
|
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
|
|
"""
|
|
isqrt = getattr(math, 'isqrt', lambda x: int(math.sqrt(x)))
|
|
limit = isqrt(n) + 1
|
|
data = bytearray([1]) * n
|
|
data[:2] = 0, 0
|
|
for p in compress(range(limit), data):
|
|
data[p + p : n : p] = bytearray(len(range(p + p, n, p)))
|
|
|
|
return compress(count(), data)
|
|
|
|
|
|
def batched(iterable, n):
|
|
"""Batch data into lists of length *n*. The last batch may be shorter.
|
|
|
|
>>> list(batched('ABCDEFG', 3))
|
|
[['A', 'B', 'C'], ['D', 'E', 'F'], ['G']]
|
|
|
|
This recipe is from the ``itertools`` docs. This library also provides
|
|
:func:`chunked`, which has a different implementation.
|
|
"""
|
|
it = iter(iterable)
|
|
while True:
|
|
batch = list(islice(it, n))
|
|
if not batch:
|
|
break
|
|
yield batch
|