Lib/test/test_itertools.py

import unittest
from test import test_support
from itertools import *
from weakref import proxy
import sys
import operator
import random
maxsize = test_support.MAX_Py_ssize_t
minsize = -maxsize-1

def onearg(x):
    'Test function of one argument'
    return 2*x

def errfunc(*args):
    'Test function that raises an error'
    raise ValueError

def gen3():
    'Non-restartable source sequence'
    for i in (0, 1, 2):
        yield i

def isEven(x):
    'Test predicate'
    return x%2==0

def isOdd(x):
    'Test predicate'
    return x%2==1

class StopNow:
    'Class emulating an empty iterable.'
    def __iter__(self):
        return self
    def next(self):
        raise StopIteration

def take(n, seq):
    'Convenience function for partially consuming a long of infinite iterable'
    return list(islice(seq, n))

def prod(iterable):
    return reduce(operator.mul, iterable, 1)

def fact(n):
    'Factorial'
    return prod(range(1, n+1))

class TestBasicOps(unittest.TestCase):
    def test_chain(self):

        def chain2(*iterables):
            'Pure python version in the docs'
            for it in iterables:
                for element in it:
                    yield element

        for c in (chain, chain2):
            self.assertEqual(list(c('abc', 'def')), list('abcdef'))
            self.assertEqual(list(c('abc')), list('abc'))
            self.assertEqual(list(c('')), [])
            self.assertEqual(take(4, c('abc', 'def')), list('abcd'))
            self.assertRaises(TypeError, list,c(2, 3))

    def test_chain_from_iterable(self):
        self.assertEqual(list(chain.from_iterable(['abc', 'def'])), list('abcdef'))
        self.assertEqual(list(chain.from_iterable(['abc'])), list('abc'))
        self.assertEqual(list(chain.from_iterable([''])), [])
        self.assertEqual(take(4, chain.from_iterable(['abc', 'def'])), list('abcd'))
        self.assertRaises(TypeError, list, chain.from_iterable([2, 3]))

    def test_combinations(self):
        self.assertRaises(TypeError, combinations, 'abc')       # missing r argument
        self.assertRaises(TypeError, combinations, 'abc', 2, 1) # too many arguments
        self.assertRaises(TypeError, combinations, None)        # pool is not iterable
        self.assertRaises(ValueError, combinations, 'abc', -2)  # r is negative
        self.assertEqual(list(combinations('abc', 32)), [])     # r > n
        self.assertEqual(list(combinations(range(4), 3)),
                                           [(0,1,2), (0,1,3), (0,2,3), (1,2,3)])

        def combinations1(iterable, r):
            'Pure python version shown in the docs'
            pool = tuple(iterable)
            n = len(pool)
            if r > n:
                return
            indices = range(r)
            yield tuple(pool[i] for i in indices)
            while 1:
                for i in reversed(range(r)):
                    if indices[i] != i + n - r:
                        break
                else:
                    return
                indices[i] += 1
                for j in range(i+1, r):
                    indices[j] = indices[j-1] + 1
                yield tuple(pool[i] for i in indices)

        def combinations2(iterable, r):
            'Pure python version shown in the docs'
            pool = tuple(iterable)
            n = len(pool)
            for indices in permutations(range(n), r):
                if sorted(indices) == list(indices):
                    yield tuple(pool[i] for i in indices)

        for n in range(7):
            values = [5*x-12 for x in range(n)]
            for r in range(n+2):
                result = list(combinations(values, r))
                self.assertEqual(len(result), 0 if r>n else fact(n) / fact(r) / fact(n-r)) # right number of combs
                self.assertEqual(len(result), len(set(result)))         # no repeats
                self.assertEqual(result, sorted(result))                # lexicographic order
                for c in result:
                    self.assertEqual(len(c), r)                         # r-length combinations
                    self.assertEqual(len(set(c)), r)                    # no duplicate elements
                    self.assertEqual(list(c), sorted(c))                # keep original ordering
                    self.assert_(all(e in values for e in c))           # elements taken from input iterable
                    self.assertEqual(list(c),
                                     [e for e in values if e in c])      # comb is a subsequence of the input iterable
                self.assertEqual(result, list(combinations1(values, r))) # matches first pure python version
                self.assertEqual(result, list(combinations2(values, r))) # matches second pure python version

        # Test implementation detail:  tuple re-use
        self.assertEqual(len(set(map(id, combinations('abcde', 3)))), 1)
        self.assertNotEqual(len(set(map(id, list(combinations('abcde', 3))))), 1)

    def test_permutations(self):
        self.assertRaises(TypeError, permutations)              # too few arguments
        self.assertRaises(TypeError, permutations, 'abc', 2, 1) # too many arguments
        self.assertRaises(TypeError, permutations, None)        # pool is not iterable
        self.assertRaises(ValueError, permutations, 'abc', -2)  # r is negative
        self.assertEqual(list(permutations('abc', 32)), [])     # r > n
        self.assertRaises(TypeError, permutations, 'abc', 's')  # r is not an int or None
        self.assertEqual(list(permutations(range(3), 2)),
                                           [(0,1), (0,2), (1,0), (1,2), (2,0), (2,1)])

        def permutations1(iterable, r=None):
            'Pure python version shown in the docs'
            pool = tuple(iterable)
            n = len(pool)
            r = n if r is None else r
            if r > n:
                return
            indices = range(n)
            cycles = 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

        def permutations2(iterable, r=None):
            'Pure python version shown in the docs'
            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)

        for n in range(7):
            values = [5*x-12 for x in range(n)]
            for r in range(n+2):
                result = list(permutations(values, r))
                self.assertEqual(len(result), 0 if r>n else fact(n) / fact(n-r))      # right number of perms
                self.assertEqual(len(result), len(set(result)))         # no repeats
                self.assertEqual(result, sorted(result))                # lexicographic order
                for p in result:
                    self.assertEqual(len(p), r)                         # r-length permutations
                    self.assertEqual(len(set(p)), r)                    # no duplicate elements
                    self.assert_(all(e in values for e in p))           # elements taken from input iterable
                self.assertEqual(result, list(permutations1(values, r))) # matches first pure python version
                self.assertEqual(result, list(permutations2(values, r))) # matches second pure python version
                if r == n:
                    self.assertEqual(result, list(permutations(values, None))) # test r as None
                    self.assertEqual(result, list(permutations(values)))       # test default r

        # Test implementation detail:  tuple re-use
        self.assertEqual(len(set(map(id, permutations('abcde', 3)))), 1)
        self.assertNotEqual(len(set(map(id, list(permutations('abcde', 3))))), 1)

    def test_count(self):
        self.assertEqual(zip('abc',count()), [('a', 0), ('b', 1), ('c', 2)])
        self.assertEqual(zip('abc',count(3)), [('a', 3), ('b', 4), ('c', 5)])
        self.assertEqual(take(2, zip('abc',count(3))), [('a', 3), ('b', 4)])
        self.assertEqual(take(2, zip('abc',count(-1))), [('a', -1), ('b', 0)])
        self.assertEqual(take(2, zip('abc',count(-3))), [('a', -3), ('b', -2)])
        self.assertRaises(TypeError, count, 2, 3)
        self.assertRaises(TypeError, count, 'a')
        self.assertEqual(list(islice(count(maxsize-5), 10)), range(maxsize-5, maxsize+5))
        self.assertEqual(list(islice(count(-maxsize-5), 10)), range(-maxsize-5, -maxsize+5))
        c = count(3)
        self.assertEqual(repr(c), 'count(3)')
        c.next()
        self.assertEqual(repr(c), 'count(4)')
        c = count(-9)
        self.assertEqual(repr(c), 'count(-9)')
        c.next()
        self.assertEqual(c.next(), -8)
        for i in (-sys.maxint-5, -sys.maxint+5 ,-10, -1, 0, 10, sys.maxint-5, sys.maxint+5):
            # Test repr (ignoring the L in longs)
            r1 = repr(count(i)).replace('L', '')
            r2 = 'count(%r)'.__mod__(i).replace('L', '')
            self.assertEqual(r1, r2)

    def test_cycle(self):
        self.assertEqual(take(10, cycle('abc')), list('abcabcabca'))
        self.assertEqual(list(cycle('')), [])
        self.assertRaises(TypeError, cycle)
        self.assertRaises(TypeError, cycle, 5)
        self.assertEqual(list(islice(cycle(gen3()),10)), [0,1,2,0,1,2,0,1,2,0])

    def test_groupby(self):
        # Check whether it accepts arguments correctly
        self.assertEqual([], list(groupby([])))
        self.assertEqual([], list(groupby([], key=id)))
        self.assertRaises(TypeError, list, groupby('abc', []))
        self.assertRaises(TypeError, groupby, None)
        self.assertRaises(TypeError, groupby, 'abc', lambda x:x, 10)

        # Check normal input
        s = [(0, 10, 20), (0, 11,21), (0,12,21), (1,13,21), (1,14,22),
             (2,15,22), (3,16,23), (3,17,23)]
        dup = []
        for k, g in groupby(s, lambda r:r[0]):
            for elem in g:
                self.assertEqual(k, elem[0])
                dup.append(elem)
        self.assertEqual(s, dup)

        # Check nested case
        dup = []
        for k, g in groupby(s, lambda r:r[0]):
            for ik, ig in groupby(g, lambda r:r[2]):
                for elem in ig:
                    self.assertEqual(k, elem[0])
                    self.assertEqual(ik, elem[2])
                    dup.append(elem)
        self.assertEqual(s, dup)

        # Check case where inner iterator is not used
        keys = [k for k, g in groupby(s, lambda r:r[0])]
        expectedkeys = set([r[0] for r in s])
        self.assertEqual(set(keys), expectedkeys)
        self.assertEqual(len(keys), len(expectedkeys))

        # Exercise pipes and filters style
        s = 'abracadabra'
        # sort s | uniq
        r = [k for k, g in groupby(sorted(s))]
        self.assertEqual(r, ['a', 'b', 'c', 'd', 'r'])
        # sort s | uniq -d
        r = [k for k, g in groupby(sorted(s)) if list(islice(g,1,2))]
        self.assertEqual(r, ['a', 'b', 'r'])
        # sort s | uniq -c
        r = [(len(list(g)), k) for k, g in groupby(sorted(s))]
        self.assertEqual(r, [(5, 'a'), (2, 'b'), (1, 'c'), (1, 'd'), (2, 'r')])
        # sort s | uniq -c | sort -rn | head -3
        r = sorted([(len(list(g)) , k) for k, g in groupby(sorted(s))], reverse=True)[:3]
        self.assertEqual(r, [(5, 'a'), (2, 'r'), (2, 'b')])

        # iter.next failure
        class ExpectedError(Exception):
            pass
        def delayed_raise(n=0):
            for i in range(n):
                yield 'yo'
            raise ExpectedError
        def gulp(iterable, keyp=None, func=list):
            return [func(g) for k, g in groupby(iterable, keyp)]

        # iter.next failure on outer object
        self.assertRaises(ExpectedError, gulp, delayed_raise(0))
        # iter.next failure on inner object
        self.assertRaises(ExpectedError, gulp, delayed_raise(1))

        # __cmp__ failure
        class DummyCmp:
            def __cmp__(self, dst):
                raise ExpectedError
        s = [DummyCmp(), DummyCmp(), None]

        # __cmp__ failure on outer object
        self.assertRaises(ExpectedError, gulp, s, func=id)
        # __cmp__ failure on inner object
        self.assertRaises(ExpectedError, gulp, s)

        # keyfunc failure
        def keyfunc(obj):
            if keyfunc.skip > 0:
                keyfunc.skip -= 1
                return obj
            else:
                raise ExpectedError

        # keyfunc failure on outer object
        keyfunc.skip = 0
        self.assertRaises(ExpectedError, gulp, [None], keyfunc)
        keyfunc.skip = 1
        self.assertRaises(ExpectedError, gulp, [None, None], keyfunc)

    def test_ifilter(self):
        self.assertEqual(list(ifilter(isEven, range(6))), [0,2,4])
        self.assertEqual(list(ifilter(None, [0,1,0,2,0])), [1,2])
        self.assertEqual(list(ifilter(bool, [0,1,0,2,0])), [1,2])
        self.assertEqual(take(4, ifilter(isEven, count())), [0,2,4,6])
        self.assertRaises(TypeError, ifilter)
        self.assertRaises(TypeError, ifilter, lambda x:x)
        self.assertRaises(TypeError, ifilter, lambda x:x, range(6), 7)
        self.assertRaises(TypeError, ifilter, isEven, 3)
        self.assertRaises(TypeError, ifilter(range(6), range(6)).next)

    def test_ifilterfalse(self):
        self.assertEqual(list(ifilterfalse(isEven, range(6))), [1,3,5])
        self.assertEqual(list(ifilterfalse(None, [0,1,0,2,0])), [0,0,0])
        self.assertEqual(list(ifilterfalse(bool, [0,1,0,2,0])), [0,0,0])
        self.assertEqual(take(4, ifilterfalse(isEven, count())), [1,3,5,7])
        self.assertRaises(TypeError, ifilterfalse)
        self.assertRaises(TypeError, ifilterfalse, lambda x:x)
        self.assertRaises(TypeError, ifilterfalse, lambda x:x, range(6), 7)
        self.assertRaises(TypeError, ifilterfalse, isEven, 3)
        self.assertRaises(TypeError, ifilterfalse(range(6), range(6)).next)

    def test_izip(self):
        ans = [(x,y) for x, y in izip('abc',count())]
        self.assertEqual(ans, [('a', 0), ('b', 1), ('c', 2)])
        self.assertEqual(list(izip('abc', range(6))), zip('abc', range(6)))
        self.assertEqual(list(izip('abcdef', range(3))), zip('abcdef', range(3)))
        self.assertEqual(take(3,izip('abcdef', count())), zip('abcdef', range(3)))
        self.assertEqual(list(izip('abcdef')), zip('abcdef'))
        self.assertEqual(list(izip()), zip())
        self.assertRaises(TypeError, izip, 3)
        self.assertRaises(TypeError, izip, range(3), 3)
        # Check tuple re-use (implementation detail)
        self.assertEqual([tuple(list(pair)) for pair in izip('abc', 'def')],
                         zip('abc', 'def'))
        self.assertEqual([pair for pair in izip('abc', 'def')],
                         zip('abc', 'def'))
        ids = map(id, izip('abc', 'def'))
        self.assertEqual(min(ids), max(ids))
        ids = map(id, list(izip('abc', 'def')))
        self.assertEqual(len(dict.fromkeys(ids)), len(ids))

    def test_iziplongest(self):
        for args in [
                ['abc', range(6)],
                [range(6), 'abc'],
                [range(1000), range(2000,2100), range(3000,3050)],
                [range(1000), range(0), range(3000,3050), range(1200), range(1500)],
                [range(1000), range(0), range(3000,3050), range(1200), range(1500), range(0)],
            ]:
            target = map(None, *args)
            self.assertEqual(list(izip_longest(*args)), target)
            self.assertEqual(list(izip_longest(*args, **{})), target)
            target = [tuple((e is None and 'X' or e) for e in t) for t in target]   # Replace None fills with 'X'
            self.assertEqual(list(izip_longest(*args, **dict(fillvalue='X'))), target)

        self.assertEqual(take(3,izip_longest('abcdef', count())), zip('abcdef', range(3))) # take 3 from infinite input

        self.assertEqual(list(izip_longest()), zip())
        self.assertEqual(list(izip_longest([])), zip([]))
        self.assertEqual(list(izip_longest('abcdef')), zip('abcdef'))

        self.assertEqual(list(izip_longest('abc', 'defg', **{})), map(None, 'abc', 'defg')) # empty keyword dict
        self.assertRaises(TypeError, izip_longest, 3)
        self.assertRaises(TypeError, izip_longest, range(3), 3)

        for stmt in [
            "izip_longest('abc', fv=1)",
            "izip_longest('abc', fillvalue=1, bogus_keyword=None)",
        ]:
            try:
                eval(stmt, globals(), locals())
            except TypeError:
                pass
            else:
                self.fail('Did not raise Type in:  ' + stmt)

        # Check tuple re-use (implementation detail)
        self.assertEqual([tuple(list(pair)) for pair in izip_longest('abc', 'def')],
                         zip('abc', 'def'))
        self.assertEqual([pair for pair in izip_longest('abc', 'def')],
                         zip('abc', 'def'))
        ids = map(id, izip_longest('abc', 'def'))
        self.assertEqual(min(ids), max(ids))
        ids = map(id, list(izip_longest('abc', 'def')))
        self.assertEqual(len(dict.fromkeys(ids)), len(ids))

    def test_bug_7244(self):

        class Repeater(object):
            # this class is similar to itertools.repeat
            def __init__(self, o, t, e):
                self.o = o
                self.t = int(t)
                self.e = e
            def __iter__(self): # its iterator is itself
                return self
            def next(self):
                if self.t > 0:
                    self.t -= 1
                    return self.o
                else:
                    raise self.e

        # Formerly this code in would fail in debug mode
        # with Undetected Error and Stop Iteration
        r1 = Repeater(1, 3, StopIteration)
        r2 = Repeater(2, 4, StopIteration)
        def run(r1, r2):
            result = []
            for i, j in izip_longest(r1, r2, fillvalue=0):
                print(i, j)
                result.append((i, j))
            return result
        self.assertEqual(run(r1, r2), [(1,2), (1,2), (1,2), (0,2)])

        # Formerly, the RuntimeError would be lost
        # and StopIteration would stop as expected
        r1 = Repeater(1, 3, RuntimeError)
        r2 = Repeater(2, 4, StopIteration)
        mylist = lambda it: [v for v in it]
        self.assertRaises(RuntimeError, mylist, izip_longest(r1, r2, fillvalue=0))

    def test_product(self):
        for args, result in [
            ([], [()]),                     # zero iterables
            (['ab'], [('a',), ('b',)]),     # one iterable
            ([range(2), range(3)], [(0,0), (0,1), (0,2), (1,0), (1,1), (1,2)]),     # two iterables
            ([range(0), range(2), range(3)], []),           # first iterable with zero length
            ([range(2), range(0), range(3)], []),           # middle iterable with zero length
            ([range(2), range(3), range(0)], []),           # last iterable with zero length
            ]:
            self.assertEqual(list(product(*args)), result)
            for r in range(4):
                self.assertEqual(list(product(*(args*r))),
                                 list(product(*args, **dict(repeat=r))))
        self.assertEqual(len(list(product(*[range(7)]*6))), 7**6)
        self.assertRaises(TypeError, product, range(6), None)

        def product1(*args, **kwds):
            pools = map(tuple, args) * kwds.get('repeat', 1)
            n = len(pools)
            if n == 0:
                yield ()
                return
            if any(len(pool) == 0 for pool in pools):
                return
            indices = [0] * n
            yield tuple(pool[i] for pool, i in zip(pools, indices))
            while 1:
                for i in reversed(range(n)):  # right to left
                    if indices[i] == len(pools[i]) - 1:
                        continue
                    indices[i] += 1
                    for j in range(i+1, n):
                        indices[j] = 0
                    yield tuple(pool[i] for pool, i in zip(pools, indices))
                    break
                else:
                    return

        def product2(*args, **kwds):
            'Pure python version used in docs'
            pools = map(tuple, args) * kwds.get('repeat', 1)
            result = [[]]
            for pool in pools:
                result = [x+[y] for x in result for y in pool]
            for prod in result:
                yield tuple(prod)

        argtypes = ['', 'abc', '', xrange(0), xrange(4), dict(a=1, b=2, c=3),
                    set('abcdefg'), range(11), tuple(range(13))]
        for i in range(100):
            args = [random.choice(argtypes) for j in range(random.randrange(5))]
            expected_len = prod(map(len, args))
            self.assertEqual(len(list(product(*args))), expected_len)
            self.assertEqual(list(product(*args)), list(product1(*args)))
            self.assertEqual(list(product(*args)), list(product2(*args)))
            args = map(iter, args)
            self.assertEqual(len(list(product(*args))), expected_len)

        # Test implementation detail:  tuple re-use
        self.assertEqual(len(set(map(id, product('abc', 'def')))), 1)
        self.assertNotEqual(len(set(map(id, list(product('abc', 'def'))))), 1)

    def test_repeat(self):
        self.assertEqual(zip(xrange(3),repeat('a')),
                         [(0, 'a'), (1, 'a'), (2, 'a')])
        self.assertEqual(list(repeat('a', 3)), ['a', 'a', 'a'])
        self.assertEqual(take(3, repeat('a')), ['a', 'a', 'a'])
        self.assertEqual(list(repeat('a', 0)), [])
        self.assertEqual(list(repeat('a', -3)), [])
        self.assertRaises(TypeError, repeat)
        self.assertRaises(TypeError, repeat, None, 3, 4)
        self.assertRaises(TypeError, repeat, None, 'a')
        r = repeat(1+0j)
        self.assertEqual(repr(r), 'repeat((1+0j))')
        r = repeat(1+0j, 5)
        self.assertEqual(repr(r), 'repeat((1+0j), 5)')
        list(r)
        self.assertEqual(repr(r), 'repeat((1+0j), 0)')

    def test_imap(self):
        self.assertEqual(list(imap(operator.pow, range(3), range(1,7))),
                         [0**1, 1**2, 2**3])
        self.assertEqual(list(imap(None, 'abc', range(5))),
                         [('a',0),('b',1),('c',2)])
        self.assertEqual(list(imap(None, 'abc', count())),
                         [('a',0),('b',1),('c',2)])
        self.assertEqual(take(2,imap(None, 'abc', count())),
                         [('a',0),('b',1)])
        self.assertEqual(list(imap(operator.pow, [])), [])
        self.assertRaises(TypeError, imap)
        self.assertRaises(TypeError, imap, operator.neg)
        self.assertRaises(TypeError, imap(10, range(5)).next)
        self.assertRaises(ValueError, imap(errfunc, [4], [5]).next)
        self.assertRaises(TypeError, imap(onearg, [4], [5]).next)

    def test_starmap(self):
        self.assertEqual(list(starmap(operator.pow, zip(range(3), range(1,7)))),
                         [0**1, 1**2, 2**3])
        self.assertEqual(take(3, starmap(operator.pow, izip(count(), count(1)))),
                         [0**1, 1**2, 2**3])
        self.assertEqual(list(starmap(operator.pow, [])), [])
        self.assertEqual(list(starmap(operator.pow, [iter([4,5])])), [4**5])
        self.assertRaises(TypeError, list, starmap(operator.pow, [None]))
        self.assertRaises(TypeError, starmap)
        self.assertRaises(TypeError, starmap, operator.pow, [(4,5)], 'extra')
        self.assertRaises(TypeError, starmap(10, [(4,5)]).next)
        self.assertRaises(ValueError, starmap(errfunc, [(4,5)]).next)
        self.assertRaises(TypeError, starmap(onearg, [(4,5)]).next)

    def test_islice(self):
        for args in [          # islice(args) should agree with range(args)
                (10, 20, 3),
                (10, 3, 20),
                (10, 20),
                (10, 3),
                (20,)
                ]:
            self.assertEqual(list(islice(xrange(100), *args)), range(*args))

        for args, tgtargs in [  # Stop when seqn is exhausted
                ((10, 110, 3), ((10, 100, 3))),
                ((10, 110), ((10, 100))),
                ((110,), (100,))
                ]:
            self.assertEqual(list(islice(xrange(100), *args)), range(*tgtargs))

        # Test stop=None
        self.assertEqual(list(islice(xrange(10), None)), range(10))
        self.assertEqual(list(islice(xrange(10), None, None)), range(10))
        self.assertEqual(list(islice(xrange(10), None, None, None)), range(10))
        self.assertEqual(list(islice(xrange(10), 2, None)), range(2, 10))
        self.assertEqual(list(islice(xrange(10), 1, None, 2)), range(1, 10, 2))

        # Test number of items consumed     SF #1171417
        it = iter(range(10))
        self.assertEqual(list(islice(it, 3)), range(3))
        self.assertEqual(list(it), range(3, 10))

        # Test invalid arguments
        self.assertRaises(TypeError, islice, xrange(10))
        self.assertRaises(TypeError, islice, xrange(10), 1, 2, 3, 4)
        self.assertRaises(ValueError, islice, xrange(10), -5, 10, 1)
        self.assertRaises(ValueError, islice, xrange(10), 1, -5, -1)
        self.assertRaises(ValueError, islice, xrange(10), 1, 10, -1)
        self.assertRaises(ValueError, islice, xrange(10), 1, 10, 0)
        self.assertRaises(ValueError, islice, xrange(10), 'a')
        self.assertRaises(ValueError, islice, xrange(10), 'a', 1)
        self.assertRaises(ValueError, islice, xrange(10), 1, 'a')
        self.assertRaises(ValueError, islice, xrange(10), 'a', 1, 1)
        self.assertRaises(ValueError, islice, xrange(10), 1, 'a', 1)
        self.assertEqual(len(list(islice(count(), 1, 10, maxsize))), 1)

    def test_takewhile(self):
        data = [1, 3, 5, 20, 2, 4, 6, 8]
        underten = lambda x: x<10
        self.assertEqual(list(takewhile(underten, data)), [1, 3, 5])
        self.assertEqual(list(takewhile(underten, [])), [])
        self.assertRaises(TypeError, takewhile)
        self.assertRaises(TypeError, takewhile, operator.pow)
        self.assertRaises(TypeError, takewhile, operator.pow, [(4,5)], 'extra')
        self.assertRaises(TypeError, takewhile(10, [(4,5)]).next)
        self.assertRaises(ValueError, takewhile(errfunc, [(4,5)]).next)
        t = takewhile(bool, [1, 1, 1, 0, 0, 0])
        self.assertEqual(list(t), [1, 1, 1])
        self.assertRaises(StopIteration, t.next)

    def test_dropwhile(self):
        data = [1, 3, 5, 20, 2, 4, 6, 8]
        underten = lambda x: x<10
        self.assertEqual(list(dropwhile(underten, data)), [20, 2, 4, 6, 8])
        self.assertEqual(list(dropwhile(underten, [])), [])
        self.assertRaises(TypeError, dropwhile)
        self.assertRaises(TypeError, dropwhile, operator.pow)
        self.assertRaises(TypeError, dropwhile, operator.pow, [(4,5)], 'extra')
        self.assertRaises(TypeError, dropwhile(10, [(4,5)]).next)
        self.assertRaises(ValueError, dropwhile(errfunc, [(4,5)]).next)

    def test_tee(self):
        n = 200
        def irange(n):
            for i in xrange(n):
                yield i

        a, b = tee([])        # test empty iterator
        self.assertEqual(list(a), [])
        self.assertEqual(list(b), [])

        a, b = tee(irange(n)) # test 100% interleaved
        self.assertEqual(zip(a,b), zip(range(n),range(n)))

        a, b = tee(irange(n)) # test 0% interleaved
        self.assertEqual(list(a), range(n))
        self.assertEqual(list(b), range(n))

        a, b = tee(irange(n)) # test dealloc of leading iterator
        for i in xrange(100):
            self.assertEqual(a.next(), i)
        del a
        self.assertEqual(list(b), range(n))

        a, b = tee(irange(n)) # test dealloc of trailing iterator
        for i in xrange(100):
            self.assertEqual(a.next(), i)
        del b
        self.assertEqual(list(a), range(100, n))

        for j in xrange(5):   # test randomly interleaved
            order = [0]*n + [1]*n
            random.shuffle(order)
            lists = ([], [])
            its = tee(irange(n))
            for i in order:
                value = its[i].next()
                lists[i].append(value)
            self.assertEqual(lists[0], range(n))
            self.assertEqual(lists[1], range(n))

        # test argument format checking
        self.assertRaises(TypeError, tee)
        self.assertRaises(TypeError, tee, 3)
        self.assertRaises(TypeError, tee, [1,2], 'x')
        self.assertRaises(TypeError, tee, [1,2], 3, 'x')

        # tee object should be instantiable
        a, b = tee('abc')
        c = type(a)('def')
        self.assertEqual(list(c), list('def'))

        # test long-lagged and multi-way split
        a, b, c = tee(xrange(2000), 3)
        for i in xrange(100):
            self.assertEqual(a.next(), i)
        self.assertEqual(list(b), range(2000))
        self.assertEqual([c.next(), c.next()], range(2))
        self.assertEqual(list(a), range(100,2000))
        self.assertEqual(list(c), range(2,2000))

        # test values of n
        self.assertRaises(TypeError, tee, 'abc', 'invalid')
        self.assertRaises(ValueError, tee, [], -1)
        for n in xrange(5):
            result = tee('abc', n)
            self.assertEqual(type(result), tuple)
            self.assertEqual(len(result), n)
            self.assertEqual(map(list, result), [list('abc')]*n)

        # tee pass-through to copyable iterator
        a, b = tee('abc')
        c, d = tee(a)
        self.assert_(a is c)

        # test tee_new
        t1, t2 = tee('abc')
        tnew = type(t1)
        self.assertRaises(TypeError, tnew)
        self.assertRaises(TypeError, tnew, 10)
        t3 = tnew(t1)
        self.assert_(list(t1) == list(t2) == list(t3) == list('abc'))

        # test that tee objects are weak referencable
        a, b = tee(xrange(10))
        p = proxy(a)
        self.assertEqual(getattr(p, '__class__'), type(b))
        del a
        self.assertRaises(ReferenceError, getattr, p, '__class__')

    def test_StopIteration(self):
        self.assertRaises(StopIteration, izip().next)

        for f in (chain, cycle, izip, groupby):
            self.assertRaises(StopIteration, f([]).next)
            self.assertRaises(StopIteration, f(StopNow()).next)

        self.assertRaises(StopIteration, islice([], None).next)
        self.assertRaises(StopIteration, islice(StopNow(), None).next)

        p, q = tee([])
        self.assertRaises(StopIteration, p.next)
        self.assertRaises(StopIteration, q.next)
        p, q = tee(StopNow())
        self.assertRaises(StopIteration, p.next)
        self.assertRaises(StopIteration, q.next)

        self.assertRaises(StopIteration, repeat(None, 0).next)

        for f in (ifilter, ifilterfalse, imap, takewhile, dropwhile, starmap):
            self.assertRaises(StopIteration, f(lambda x:x, []).next)
            self.assertRaises(StopIteration, f(lambda x:x, StopNow()).next)


class TestExamples(unittest.TestCase):

    def test_chain(self):
        self.assertEqual(''.join(chain('ABC', 'DEF')), 'ABCDEF')

    def test_chain_from_iterable(self):
        self.assertEqual(''.join(chain.from_iterable(['ABC', 'DEF'])), 'ABCDEF')

    def test_combinations(self):
        self.assertEqual(list(combinations('ABCD', 2)),
                         [('A','B'), ('A','C'), ('A','D'), ('B','C'), ('B','D'), ('C','D')])
        self.assertEqual(list(combinations(range(4), 3)),
                         [(0,1,2), (0,1,3), (0,2,3), (1,2,3)])

    def test_count(self):
        self.assertEqual(list(islice(count(10), 5)), [10, 11, 12, 13, 14])

    def test_cycle(self):
        self.assertEqual(list(islice(cycle('ABCD'), 12)), list('ABCDABCDABCD'))

    def test_dropwhile(self):
        self.assertEqual(list(dropwhile(lambda x: x<5, [1,4,6,4,1])), [6,4,1])

    def test_groupby(self):
        self.assertEqual([k for k, g in groupby('AAAABBBCCDAABBB')],
                         list('ABCDAB'))
        self.assertEqual([(list(g)) for k, g in groupby('AAAABBBCCD')],
                         [list('AAAA'), list('BBB'), list('CC'), list('D')])

    def test_ifilter(self):
        self.assertEqual(list(ifilter(lambda x: x%2, range(10))), [1,3,5,7,9])

    def test_ifilterfalse(self):
        self.assertEqual(list(ifilterfalse(lambda x: x%2, range(10))), [0,2,4,6,8])

    def test_imap(self):
        self.assertEqual(list(imap(pow, (2,3,10), (5,2,3))), [32, 9, 1000])

    def test_islice(self):
        self.assertEqual(list(islice('ABCDEFG', 2)), list('AB'))
        self.assertEqual(list(islice('ABCDEFG', 2, 4)), list('CD'))
        self.assertEqual(list(islice('ABCDEFG', 2, None)), list('CDEFG'))
        self.assertEqual(list(islice('ABCDEFG', 0, None, 2)), list('ACEG'))

    def test_izip(self):
        self.assertEqual(list(izip('ABCD', 'xy')), [('A', 'x'), ('B', 'y')])

    def test_izip_longest(self):
        self.assertEqual(list(izip_longest('ABCD', 'xy', fillvalue='-')),
                         [('A', 'x'), ('B', 'y'), ('C', '-'), ('D', '-')])

    def test_permutations(self):
        self.assertEqual(list(permutations('ABCD', 2)),
                         map(tuple, 'AB AC AD BA BC BD CA CB CD DA DB DC'.split()))
        self.assertEqual(list(permutations(range(3))),
                         [(0,1,2), (0,2,1), (1,0,2), (1,2,0), (2,0,1), (2,1,0)])

    def test_product(self):
        self.assertEqual(list(product('ABCD', 'xy')),
                         map(tuple, 'Ax Ay Bx By Cx Cy Dx Dy'.split()))
        self.assertEqual(list(product(range(2), repeat=3)),
                        [(0,0,0), (0,0,1), (0,1,0), (0,1,1),
                         (1,0,0), (1,0,1), (1,1,0), (1,1,1)])

    def test_repeat(self):
        self.assertEqual(list(repeat(10, 3)), [10, 10, 10])

    def test_stapmap(self):
        self.assertEqual(list(starmap(pow, [(2,5), (3,2), (10,3)])),
                         [32, 9, 1000])

    def test_takewhile(self):
        self.assertEqual(list(takewhile(lambda x: x<5, [1,4,6,4,1])), [1,4])


class TestGC(unittest.TestCase):

    def makecycle(self, iterator, container):
        container.append(iterator)
        iterator.next()
        del container, iterator

    def test_chain(self):
        a = []
        self.makecycle(chain(a), a)

    def test_chain_from_iterable(self):
        a = []
        self.makecycle(chain.from_iterable([a]), a)

    def test_combinations(self):
        a = []
        self.makecycle(combinations([1,2,a,3], 3), a)

    def test_cycle(self):
        a = []
        self.makecycle(cycle([a]*2), a)

    def test_dropwhile(self):
        a = []
        self.makecycle(dropwhile(bool, [0, a, a]), a)

    def test_groupby(self):
        a = []
        self.makecycle(groupby([a]*2, lambda x:x), a)

    def test_issue2246(self):
        # Issue 2246 -- the _grouper iterator was not included in GC
        n = 10
        keyfunc = lambda x: x
        for i, j in groupby(xrange(n), key=keyfunc):
            keyfunc.__dict__.setdefault('x',[]).append(j)

    def test_ifilter(self):
        a = []
        self.makecycle(ifilter(lambda x:True, [a]*2), a)

    def test_ifilterfalse(self):
        a = []
        self.makecycle(ifilterfalse(lambda x:False, a), a)

    def test_izip(self):
        a = []
        self.makecycle(izip([a]*2, [a]*3), a)

    def test_izip_longest(self):
        a = []
        self.makecycle(izip_longest([a]*2, [a]*3), a)
        b = [a, None]
        self.makecycle(izip_longest([a]*2, [a]*3, fillvalue=b), a)

    def test_imap(self):
        a = []
        self.makecycle(imap(lambda x:x, [a]*2), a)

    def test_islice(self):
        a = []
        self.makecycle(islice([a]*2, None), a)

    def test_permutations(self):
        a = []
        self.makecycle(permutations([1,2,a,3], 3), a)

    def test_product(self):
        a = []
        self.makecycle(product([1,2,a,3], repeat=3), a)

    def test_repeat(self):
        a = []
        self.makecycle(repeat(a), a)

    def test_starmap(self):
        a = []
        self.makecycle(starmap(lambda *t: t, [(a,a)]*2), a)

    def test_takewhile(self):
        a = []
        self.makecycle(takewhile(bool, [1, 0, a, a]), a)

def R(seqn):
    'Regular generator'
    for i in seqn:
        yield i

class G:
    'Sequence using __getitem__'
    def __init__(self, seqn):
        self.seqn = seqn
    def __getitem__(self, i):
        return self.seqn[i]

class I:
    'Sequence using iterator protocol'
    def __init__(self, seqn):
        self.seqn = seqn
        self.i = 0
    def __iter__(self):
        return self
    def next(self):
        if self.i >= len(self.seqn): raise StopIteration
        v = self.seqn[self.i]
        self.i += 1
        return v

class Ig:
    'Sequence using iterator protocol defined with a generator'
    def __init__(self, seqn):
        self.seqn = seqn
        self.i = 0
    def __iter__(self):
        for val in self.seqn:
            yield val

class X:
    'Missing __getitem__ and __iter__'
    def __init__(self, seqn):
        self.seqn = seqn
        self.i = 0
    def next(self):
        if self.i >= len(self.seqn): raise StopIteration
        v = self.seqn[self.i]
        self.i += 1
        return v

class N:
    'Iterator missing next()'
    def __init__(self, seqn):
        self.seqn = seqn
        self.i = 0
    def __iter__(self):
        return self

class E:
    'Test propagation of exceptions'
    def __init__(self, seqn):
        self.seqn = seqn
        self.i = 0
    def __iter__(self):
        return self
    def next(self):
        3 // 0

class S:
    'Test immediate stop'
    def __init__(self, seqn):
        pass
    def __iter__(self):
        return self
    def next(self):
        raise StopIteration

def L(seqn):
    'Test multiple tiers of iterators'
    return chain(imap(lambda x:x, R(Ig(G(seqn)))))


class TestVariousIteratorArgs(unittest.TestCase):

    def test_chain(self):
        for s in ("123", "", range(1000), ('do', 1.2), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                self.assertEqual(list(chain(g(s))), list(g(s)))
                self.assertEqual(list(chain(g(s), g(s))), list(g(s))+list(g(s)))
            self.assertRaises(TypeError, list, chain(X(s)))
            self.assertRaises(TypeError, list, chain(N(s)))
            self.assertRaises(ZeroDivisionError, list, chain(E(s)))

    def test_product(self):
        for s in ("123", "", range(1000), ('do', 1.2), xrange(2000,2200,5)):
            self.assertRaises(TypeError, product, X(s))
            self.assertRaises(TypeError, product, N(s))
            self.assertRaises(ZeroDivisionError, product, E(s))

    def test_cycle(self):
        for s in ("123", "", range(1000), ('do', 1.2), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                tgtlen = len(s) * 3
                expected = list(g(s))*3
                actual = list(islice(cycle(g(s)), tgtlen))
                self.assertEqual(actual, expected)
            self.assertRaises(TypeError, cycle, X(s))
            self.assertRaises(TypeError, list, cycle(N(s)))
            self.assertRaises(ZeroDivisionError, list, cycle(E(s)))

    def test_groupby(self):
        for s in (range(10), range(0), range(1000), (7,11), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                self.assertEqual([k for k, sb in groupby(g(s))], list(g(s)))
            self.assertRaises(TypeError, groupby, X(s))
            self.assertRaises(TypeError, list, groupby(N(s)))
            self.assertRaises(ZeroDivisionError, list, groupby(E(s)))

    def test_ifilter(self):
        for s in (range(10), range(0), range(1000), (7,11), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                self.assertEqual(list(ifilter(isEven, g(s))), filter(isEven, g(s)))
            self.assertRaises(TypeError, ifilter, isEven, X(s))
            self.assertRaises(TypeError, list, ifilter(isEven, N(s)))
            self.assertRaises(ZeroDivisionError, list, ifilter(isEven, E(s)))

    def test_ifilterfalse(self):
        for s in (range(10), range(0), range(1000), (7,11), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                self.assertEqual(list(ifilterfalse(isEven, g(s))), filter(isOdd, g(s)))
            self.assertRaises(TypeError, ifilterfalse, isEven, X(s))
            self.assertRaises(TypeError, list, ifilterfalse(isEven, N(s)))
            self.assertRaises(ZeroDivisionError, list, ifilterfalse(isEven, E(s)))

    def test_izip(self):
        for s in ("123", "", range(1000), ('do', 1.2), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                self.assertEqual(list(izip(g(s))), zip(g(s)))
                self.assertEqual(list(izip(g(s), g(s))), zip(g(s), g(s)))
            self.assertRaises(TypeError, izip, X(s))
            self.assertRaises(TypeError, list, izip(N(s)))
            self.assertRaises(ZeroDivisionError, list, izip(E(s)))

    def test_iziplongest(self):
        for s in ("123", "", range(1000), ('do', 1.2), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                self.assertEqual(list(izip_longest(g(s))), zip(g(s)))
                self.assertEqual(list(izip_longest(g(s), g(s))), zip(g(s), g(s)))
            self.assertRaises(TypeError, izip_longest, X(s))
            self.assertRaises(TypeError, list, izip_longest(N(s)))
            self.assertRaises(ZeroDivisionError, list, izip_longest(E(s)))

    def test_imap(self):
        for s in (range(10), range(0), range(100), (7,11), xrange(20,50,5)):
            for g in (G, I, Ig, S, L, R):
                self.assertEqual(list(imap(onearg, g(s))), map(onearg, g(s)))
                self.assertEqual(list(imap(operator.pow, g(s), g(s))), map(operator.pow, g(s), g(s)))
            self.assertRaises(TypeError, imap, onearg, X(s))
            self.assertRaises(TypeError, list, imap(onearg, N(s)))
            self.assertRaises(ZeroDivisionError, list, imap(onearg, E(s)))

    def test_islice(self):
        for s in ("12345", "", range(1000), ('do', 1.2), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                self.assertEqual(list(islice(g(s),1,None,2)), list(g(s))[1::2])
            self.assertRaises(TypeError, islice, X(s), 10)
            self.assertRaises(TypeError, list, islice(N(s), 10))
            self.assertRaises(ZeroDivisionError, list, islice(E(s), 10))

    def test_starmap(self):
        for s in (range(10), range(0), range(100), (7,11), xrange(20,50,5)):
            for g in (G, I, Ig, S, L, R):
                ss = zip(s, s)
                self.assertEqual(list(starmap(operator.pow, g(ss))), map(operator.pow, g(s), g(s)))
            self.assertRaises(TypeError, starmap, operator.pow, X(ss))
            self.assertRaises(TypeError, list, starmap(operator.pow, N(ss)))
            self.assertRaises(ZeroDivisionError, list, starmap(operator.pow, E(ss)))

    def test_takewhile(self):
        for s in (range(10), range(0), range(1000), (7,11), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                tgt = []
                for elem in g(s):
                    if not isEven(elem): break
                    tgt.append(elem)
                self.assertEqual(list(takewhile(isEven, g(s))), tgt)
            self.assertRaises(TypeError, takewhile, isEven, X(s))
            self.assertRaises(TypeError, list, takewhile(isEven, N(s)))
            self.assertRaises(ZeroDivisionError, list, takewhile(isEven, E(s)))

    def test_dropwhile(self):
        for s in (range(10), range(0), range(1000), (7,11), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                tgt = []
                for elem in g(s):
                    if not tgt and isOdd(elem): continue
                    tgt.append(elem)
                self.assertEqual(list(dropwhile(isOdd, g(s))), tgt)
            self.assertRaises(TypeError, dropwhile, isOdd, X(s))
            self.assertRaises(TypeError, list, dropwhile(isOdd, N(s)))
            self.assertRaises(ZeroDivisionError, list, dropwhile(isOdd, E(s)))

    def test_tee(self):
        for s in ("123", "", range(1000), ('do', 1.2), xrange(2000,2200,5)):
            for g in (G, I, Ig, S, L, R):
                it1, it2 = tee(g(s))
                self.assertEqual(list(it1), list(g(s)))
                self.assertEqual(list(it2), list(g(s)))
            self.assertRaises(TypeError, tee, X(s))
            self.assertRaises(TypeError, list, tee(N(s))[0])
            self.assertRaises(ZeroDivisionError, list, tee(E(s))[0])

class LengthTransparency(unittest.TestCase):

    def test_repeat(self):
        from test.test_iterlen import len
        self.assertEqual(len(repeat(None, 50)), 50)
        self.assertRaises(TypeError, len, repeat(None))

class RegressionTests(unittest.TestCase):

    def test_sf_793826(self):
        # Fix Armin Rigo's successful efforts to wreak havoc

        def mutatingtuple(tuple1, f, tuple2):
            # this builds a tuple t which is a copy of tuple1,
            # then calls f(t), then mutates t to be equal to tuple2
            # (needs len(tuple1) == len(tuple2)).
            def g(value, first=[1]):
                if first:
                    del first[:]
                    f(z.next())
                return value
            items = list(tuple2)
            items[1:1] = list(tuple1)
            gen = imap(g, items)
            z = izip(*[gen]*len(tuple1))
            z.next()

        def f(t):
            global T
            T = t
            first[:] = list(T)

        first = []
        mutatingtuple((1,2,3), f, (4,5,6))
        second = list(T)
        self.assertEqual(first, second)


    def test_sf_950057(self):
        # Make sure that chain() and cycle() catch exceptions immediately
        # rather than when shifting between input sources

        def gen1():
            hist.append(0)
            yield 1
            hist.append(1)
            raise AssertionError
            hist.append(2)

        def gen2(x):
            hist.append(3)
            yield 2
            hist.append(4)
            if x:
                raise StopIteration

        hist = []
        self.assertRaises(AssertionError, list, chain(gen1(), gen2(False)))
        self.assertEqual(hist, [0,1])

        hist = []
        self.assertRaises(AssertionError, list, chain(gen1(), gen2(True)))
        self.assertEqual(hist, [0,1])

        hist = []
        self.assertRaises(AssertionError, list, cycle(gen1()))
        self.assertEqual(hist, [0,1])

class SubclassWithKwargsTest(unittest.TestCase):
    def test_keywords_in_subclass(self):
        # count is not subclassable...
        for cls in (repeat, izip, ifilter, ifilterfalse, chain, imap,
                    starmap, islice, takewhile, dropwhile, cycle):
            class Subclass(cls):
                def __init__(self, newarg=None, *args):
                    cls.__init__(self, *args)
            try:
                Subclass(newarg=1)
            except TypeError, err:
                # we expect type errors because of wrong argument count
                self.failIf("does not take keyword arguments" in err.args[0])


libreftest = """ Doctest for examples in the library reference: libitertools.tex


>>> amounts = [120.15, 764.05, 823.14]
>>> for checknum, amount in izip(count(1200), amounts):
...     print 'Check %d is for $%.2f' % (checknum, amount)
...
Check 1200 is for $120.15
Check 1201 is for $764.05
Check 1202 is for $823.14

>>> import operator
>>> for cube in imap(operator.pow, xrange(1,4), repeat(3)):
...    print cube
...
1
8
27

>>> reportlines = ['EuroPython', 'Roster', '', 'alex', '', 'laura', '', 'martin', '', 'walter', '', 'samuele']
>>> for name in islice(reportlines, 3, None, 2):
...    print name.title()
...
Alex
Laura
Martin
Walter
Samuele

>>> from operator import itemgetter
>>> d = dict(a=1, b=2, c=1, d=2, e=1, f=2, g=3)
>>> di = sorted(sorted(d.iteritems()), key=itemgetter(1))
>>> for k, g in groupby(di, itemgetter(1)):
...     print k, map(itemgetter(0), g)
...
1 ['a', 'c', 'e']
2 ['b', 'd', 'f']
3 ['g']

# Find runs of consecutive numbers using groupby.  The key to the solution
# is differencing with a range so that consecutive numbers all appear in
# same group.
>>> data = [ 1,  4,5,6, 10, 15,16,17,18, 22, 25,26,27,28]
>>> for k, g in groupby(enumerate(data), lambda (i,x):i-x):
...     print map(operator.itemgetter(1), g)
...
[1]
[4, 5, 6]
[10]
[15, 16, 17, 18]
[22]
[25, 26, 27, 28]

>>> def take(n, iterable):
...     "Return first n items of the iterable as a list"
...     return list(islice(iterable, n))

>>> def enumerate(iterable, start=0):
...     return izip(count(start), iterable)

>>> def tabulate(function, start=0):
...     "Return function(0), function(1), ..."
...     return imap(function, count(start))

>>> def nth(iterable, n, default=None):
...     "Returns the nth item or a default value"
...     return next(islice(iterable, n, None), default)

>>> def quantify(iterable, pred=bool):
...     "Count how many times the predicate is true"
...     return sum(imap(pred, iterable))

>>> def padnone(iterable):
...     "Returns the sequence elements and then returns None indefinitely"
...     return chain(iterable, repeat(None))

>>> def ncycles(iterable, n):
...     "Returns the seqeuence elements n times"
...     return chain(*repeat(iterable, n))

>>> def dotproduct(vec1, vec2):
...     return sum(imap(operator.mul, vec1, vec2))

>>> def flatten(listOfLists):
...     return list(chain.from_iterable(listOfLists))

>>> def repeatfunc(func, times=None, *args):
...     "Repeat calls to func with specified arguments."
...     "   Example:  repeatfunc(random.random)"
...     if times is None:
...         return starmap(func, repeat(args))
...     else:
...         return starmap(func, repeat(args, times))

>>> def pairwise(iterable):
...     "s -> (s0,s1), (s1,s2), (s2, s3), ..."
...     a, b = tee(iterable)
...     for elem in b:
...         break
...     return izip(a, b)

>>> def grouper(n, iterable, fillvalue=None):
...     "grouper(3, 'ABCDEFG', 'x') --> ABC DEF Gxx"
...     args = [iter(iterable)] * n
...     return izip_longest(fillvalue=fillvalue, *args)

>>> def roundrobin(*iterables):
...     "roundrobin('ABC', 'D', 'EF') --> A D E B F C"
...     # Recipe credited to George Sakkis
...     pending = len(iterables)
...     nexts = cycle(iter(it).next for it in iterables)
...     while pending:
...         try:
...             for next in nexts:
...                 yield next()
...         except StopIteration:
...             pending -= 1
...             nexts = cycle(islice(nexts, pending))

>>> def powerset(iterable):
...     "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
...     s = list(iterable)
...     return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))

>>> def compress(data, selectors):
...     "compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F"
...     return (d for d, s in izip(data, selectors) if s)

>>> def combinations_with_replacement(iterable, r):
...     "combinations_with_replacement('ABC', 3) --> AA AB AC BB BC CC"
...     pool = tuple(iterable)
...     n = len(pool)
...     if not n and r:
...         return
...     indices = [0] * r
...     yield tuple(pool[i] for i in indices)
...     while 1:
...         for i in reversed(range(r)):
...             if indices[i] != n - 1:
...                 break
...         else:
...             return
...         indices[i:] = [indices[i] + 1] * (r - i)
...         yield tuple(pool[i] for i in indices)

>>> def unique_everseen(iterable, key=None):
...     "List unique elements, preserving order. Remember all elements ever seen."
...     # unique_everseen('AAAABBBCCDAABBB') --> A B C D
...     # unique_everseen('ABBCcAD', str.lower) --> A B C D
...     seen = set()
...     seen_add = seen.add
...     if key is None:
...         for element in iterable:
...             if element not in seen:
...                 seen_add(element)
...                 yield element
...     else:
...         for element in iterable:
...             k = key(element)
...             if k not in seen:
...                 seen_add(k)
...                 yield element

>>> def unique_justseen(iterable, key=None):
...     "List unique elements, preserving order. Remember only the element just seen."
...     # unique_justseen('AAAABBBCCDAABBB') --> A B C D A B
...     # unique_justseen('ABBCcAD', str.lower) --> A B C A D
...     return imap(next, imap(itemgetter(1), groupby(iterable, key)))

This is not part of the examples but it tests to make sure the definitions
perform as purported.

>>> take(10, count())
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

>>> list(enumerate('abc'))
[(0, 'a'), (1, 'b'), (2, 'c')]

>>> list(islice(tabulate(lambda x: 2*x), 4))
[0, 2, 4, 6]

>>> nth('abcde', 3)
'd'

>>> nth('abcde', 9) is None
True

>>> quantify(xrange(99), lambda x: x%2==0)
50

>>> a = [[1, 2, 3], [4, 5, 6]]
>>> flatten(a)
[1, 2, 3, 4, 5, 6]

>>> list(repeatfunc(pow, 5, 2, 3))
[8, 8, 8, 8, 8]

>>> import random
>>> take(5, imap(int, repeatfunc(random.random)))
[0, 0, 0, 0, 0]

>>> list(pairwise('abcd'))
[('a', 'b'), ('b', 'c'), ('c', 'd')]

>>> list(pairwise([]))
[]

>>> list(pairwise('a'))
[]

>>> list(islice(padnone('abc'), 0, 6))
['a', 'b', 'c', None, None, None]

>>> list(ncycles('abc', 3))
['a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c']

>>> dotproduct([1,2,3], [4,5,6])
32

>>> list(grouper(3, 'abcdefg', 'x'))
[('a', 'b', 'c'), ('d', 'e', 'f'), ('g', 'x', 'x')]

>>> list(roundrobin('abc', 'd', 'ef'))
['a', 'd', 'e', 'b', 'f', 'c']

>>> list(powerset([1,2,3]))
[(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)]

>>> list(compress('abcdef', [1,0,1,0,1,1]))
['a', 'c', 'e', 'f']

>>> list(combinations_with_replacement('abc', 2))
[('a', 'a'), ('a', 'b'), ('a', 'c'), ('b', 'b'), ('b', 'c'), ('c', 'c')]

>>> list(combinations_with_replacement('01', 3))
[('0', '0', '0'), ('0', '0', '1'), ('0', '1', '1'), ('1', '1', '1')]

>>> def combinations_with_replacement2(iterable, r):
...     'Alternate version that filters from product()'
...     pool = tuple(iterable)
...     n = len(pool)
...     for indices in product(range(n), repeat=r):
...         if sorted(indices) == list(indices):
...             yield tuple(pool[i] for i in indices)

>>> list(combinations_with_replacement('abc', 2)) == list(combinations_with_replacement2('abc', 2))
True

>>> list(combinations_with_replacement('01', 3)) == list(combinations_with_replacement2('01', 3))
True

>>> list(combinations_with_replacement('2310', 6)) == list(combinations_with_replacement2('2310', 6))
True

>>> list(unique_everseen('AAAABBBCCDAABBB'))
['A', 'B', 'C', 'D']

>>> list(unique_everseen('ABBCcAD', str.lower))
['A', 'B', 'C', 'D']

>>> list(unique_justseen('AAAABBBCCDAABBB'))
['A', 'B', 'C', 'D', 'A', 'B']

>>> list(unique_justseen('ABBCcAD', str.lower))
['A', 'B', 'C', 'A', 'D']

"""

__test__ = {'libreftest' : libreftest}

def test_main(verbose=None):
    test_classes = (TestBasicOps, TestVariousIteratorArgs, TestGC,
                    RegressionTests, LengthTransparency,
                    SubclassWithKwargsTest, TestExamples)
    test_support.run_unittest(*test_classes)

    # verify reference counting
    if verbose and hasattr(sys, "gettotalrefcount"):
        import gc
        counts = [None] * 5
        for i in xrange(len(counts)):
            test_support.run_unittest(*test_classes)
            gc.collect()
            counts[i] = sys.gettotalrefcount()
        print counts

    # doctest the examples in the library reference
    test_support.run_doctest(sys.modules[__name__], verbose)

if __name__ == "__main__":
    test_main(verbose=True)