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"""Imported from the recipes section of the itertools documentation. All functions taken from the recipes section of the itertools library docs [1]_. Some backward-compatible usability improvements have been made. .. [1] http://docs.python.org/library/itertools.html#recipes """ from collections import deque from itertools import ( chain, combinations, count, cycle, groupby, islice, repeat, starmap, tee ) import operator from random import randrange, sample, choice from six import PY2 from six.moves import filter, filterfalse, map, range, zip, zip_longest __all__ = [ 'accumulate', 'all_equal', 'consume', 'dotproduct', 'first_true', 'flatten', 'grouper', 'iter_except', 'ncycles', 'nth', 'nth_combination', 'padnone', 'pairwise', 'partition', 'powerset', 'prepend', 'quantify', 'random_combination_with_replacement', 'random_combination', 'random_permutation', 'random_product', 'repeatfunc', 'roundrobin', 'tabulate', 'tail', 'take', 'unique_everseen', 'unique_justseen', ] def accumulate(iterable, func=operator.add): """ Return an iterator whose items are the accumulated results of a function (specified by the optional *func* argument) that takes two arguments. By default, returns accumulated sums with :func:`operator.add`. >>> list(accumulate([1, 2, 3, 4, 5])) # Running sum [1, 3, 6, 10, 15] >>> list(accumulate([1, 2, 3], func=operator.mul)) # Running product [1, 2, 6] >>> list(accumulate([0, 1, -1, 2, 3, 2], func=max)) # Running maximum [0, 1, 1, 2, 3, 3] This function is available in the ``itertools`` module for Python 3.2 and greater. """ it = iter(iterable) try: total = next(it) except StopIteration: return else: yield total for element in it: total = func(total, element) yield total def take(n, iterable): """Return first *n* items of the iterable as a list. >>> take(3, range(10)) [0, 1, 2] >>> take(5, range(3)) [0, 1, 2] Effectively a short replacement for ``next`` based iterator consumption when you want more than one item, but less than the whole iterator. """ return list(islice(iterable, n)) def tabulate(function, start=0): """Return an iterator over the results of ``func(start)``, ``func(start + 1)``, ``func(start + 2)``... *func* should be a function that accepts one integer argument. If *start* is not specified it defaults to 0. It will be incremented each time the iterator is advanced. >>> square = lambda x: x ** 2 >>> iterator = tabulate(square, -3) >>> take(4, iterator) [9, 4, 1, 0] """ return map(function, count(start)) def tail(n, iterable): """Return an iterator over the last *n* items of *iterable*. >>> t = tail(3, 'ABCDEFG') >>> list(t) ['E', 'F', 'G'] """ return iter(deque(iterable, maxlen=n)) def consume(iterator, n=None): """Advance *iterable* by *n* steps. If *n* is ``None``, consume it entirely. Efficiently exhausts an iterator without returning values. Defaults to consuming the whole iterator, but an optional second argument may be provided to limit consumption. >>> i = (x for x in range(10)) >>> next(i) 0 >>> consume(i, 3) >>> next(i) 4 >>> consume(i) >>> next(i) Traceback (most recent call last): File "<stdin>", line 1, in <module> StopIteration If the iterator has fewer items remaining than the provided limit, the whole iterator will be consumed. >>> i = (x for x in range(3)) >>> consume(i, 5) >>> next(i) Traceback (most recent call last): File "<stdin>", line 1, in <module> StopIteration """ # Use functions that consume iterators at C speed. if n is None: # feed the entire iterator into a zero-length deque 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. >>> l = range(10) >>> nth(l, 3) 3 >>> nth(l, 20, "zebra") 'zebra' """ return next(islice(iterable, n, None), default) def all_equal(iterable): """ Returns ``True`` if all the elements are equal to each other. >>> all_equal('aaaa') True >>> all_equal('aaab') False """ g = groupby(iterable) return next(g, True) and not next(g, False) def quantify(iterable, pred=bool): """Return the how many times the predicate is true. >>> quantify([True, False, True]) 2 """ return sum(map(pred, iterable)) def padnone(iterable): """Returns the sequence of elements and then returns ``None`` indefinitely. >>> take(5, padnone(range(3))) [0, 1, 2, None, None] Useful for emulating the behavior of the built-in :func:`map` function. See also :func:`padded`. """ return chain(iterable, repeat(None)) def ncycles(iterable, n): """Returns the sequence elements *n* times >>> list(ncycles(["a", "b"], 3)) ['a', 'b', 'a', 'b', 'a', 'b'] """ return chain.from_iterable(repeat(tuple(iterable), n)) def dotproduct(vec1, vec2): """Returns the dot product of the two iterables. >>> dotproduct([10, 10], [20, 20]) 400 """ return sum(map(operator.mul, vec1, vec2)) def flatten(listOfLists): """Return an iterator flattening one level of nesting in a list of lists. >>> list(flatten([[0, 1], [2, 3]])) [0, 1, 2, 3] See also :func:`collapse`, which can flatten multiple levels of nesting. """ return chain.from_iterable(listOfLists) def repeatfunc(func, times=None, *args): """Call *func* with *args* repeatedly, returning an iterable over the results. If *times* is specified, the iterable will terminate after that many repetitions: >>> from operator import add >>> times = 4 >>> args = 3, 5 >>> list(repeatfunc(add, times, *args)) [8, 8, 8, 8] If *times* is ``None`` the iterable will not terminate: >>> from random import randrange >>> times = None >>> args = 1, 11 >>> take(6, repeatfunc(randrange, times, *args)) # doctest:+SKIP [2, 4, 8, 1, 8, 4] """ if times is None: return starmap(func, repeat(args)) return starmap(func, repeat(args, times)) def pairwise(iterable): """Returns an iterator of paired items, overlapping, from the original >>> take(4, pairwise(count())) [(0, 1), (1, 2), (2, 3), (3, 4)] """ a, b = tee(iterable) next(b, None) return zip(a, b) def grouper(n, iterable, fillvalue=None): """Collect data into fixed-length chunks or blocks. >>> list(grouper(3, 'ABCDEFG', 'x')) [('A', 'B', 'C'), ('D', 'E', 'F'), ('G', 'x', 'x')] """ args = [iter(iterable)] * n return zip_longest(fillvalue=fillvalue, *args) def roundrobin(*iterables): """Yields an item from each iterable, alternating between them. >>> list(roundrobin('ABC', 'D', 'EF')) ['A', 'D', 'E', 'B', 'F', 'C'] This function produces the same output as :func:`interleave_longest`, but may perform better for some inputs (in particular when the number of iterables is small). """ # Recipe credited to George Sakkis pending = len(iterables) if PY2: nexts = cycle(iter(it).next for it in iterables) else: nexts = cycle(iter(it).__next__ for it in iterables) while pending: try: for next in nexts: yield next() except StopIteration: pending -= 1 nexts = cycle(islice(nexts, pending)) def partition(pred, iterable): """ Returns a 2-tuple of iterables derived from the input iterable. The first yields the items that have ``pred(item) == False``. The second yields the items that have ``pred(item) == True``. >>> is_odd = lambda x: x % 2 != 0 >>> iterable = range(10) >>> even_items, odd_items = partition(is_odd, iterable) >>> list(even_items), list(odd_items) ([0, 2, 4, 6, 8], [1, 3, 5, 7, 9]) """ # 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 powerset(iterable): """Yields all possible subsets of the iterable. >>> list(powerset([1, 2, 3])) [(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)] :func:`powerset` will operate on iterables that aren't :class:`set` instances, so repeated elements in the input will produce repeated elements in the output. Use :func:`unique_everseen` on the input to avoid generating duplicates: >>> seq = [1, 1, 0] >>> list(powerset(seq)) [(), (1,), (1,), (0,), (1, 1), (1, 0), (1, 0), (1, 1, 0)] >>> from more_itertools import unique_everseen >>> list(powerset(unique_everseen(seq))) [(), (1,), (0,), (1, 0)] """ s = list(iterable) return chain.from_iterable(combinations(s, r) for r in range(len(s) + 1)) def unique_everseen(iterable, key=None): """ Yield unique elements, preserving order. >>> list(unique_everseen('AAAABBBCCDAABBB')) ['A', 'B', 'C', 'D'] >>> list(unique_everseen('ABBCcAD', str.lower)) ['A', 'B', 'C', 'D'] Sequences with a mix of hashable and unhashable items can be used. The function will be slower (i.e., `O(n^2)`) for unhashable items. """ seenset = set() seenset_add = seenset.add seenlist = [] seenlist_add = seenlist.append if key is None: for element in iterable: try: if element not in seenset: seenset_add(element) yield element except TypeError: if element not in seenlist: seenlist_add(element) yield element else: for element in iterable: k = key(element) try: if k not in seenset: seenset_add(k) yield element except TypeError: if k not in seenlist: seenlist_add(k) yield element def unique_justseen(iterable, key=None): """Yields elements in order, ignoring serial duplicates >>> list(unique_justseen('AAAABBBCCDAABBB')) ['A', 'B', 'C', 'D', 'A', 'B'] >>> list(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): """Yields results from a function repeatedly until an exception is raised. Converts a call-until-exception interface to an iterator interface. Like ``iter(func, sentinel)``, but uses an exception instead of a sentinel to end the loop. >>> l = [0, 1, 2] >>> list(iter_except(l.pop, IndexError)) [2, 1, 0] """ try: if first is not None: yield first() while 1: yield func() except exception: pass def first_true(iterable, default=None, 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) == True`` . >>> first_true(range(10)) 1 >>> first_true(range(10), pred=lambda x: x > 5) 6 >>> first_true(range(10), default='missing', pred=lambda x: x > 9) 'missing' """ return next(filter(pred, iterable), default) def random_product(*args, **kwds): """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] * kwds.get('repeat', 1) 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. """ 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`. """ return chain([value], iterator)