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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)