tests/test_recipes.py - master - niceSOFT/python3-more-itertools

tests/test_recipes.py
1 711 строк55 KB
darrenhuai
test: close the last coverage gaps, fix a no-op equality assertion
07 авг 2026, 22:52
07 авг 2026, 22:525c715d8
from collections import Counter
from decimal import Decimal
from doctest import DocTestSuite
from fractions import Fraction
from functools import reduce
from itertools import (
    combinations,
    count,
    groupby,
    permutations,
    islice,
)
from operator import mul, eq
from math import comb, prod, factorial
from statistics import mean
from unittest import TestCase
from unittest.mock import patch

import more_itertools as mi
import statistics
import random


def load_tests(loader, tests, ignore):
    # Add the doctests
    tests.addTests(DocTestSuite('more_itertools.recipes'))
    return tests


class TakeTests(TestCase):
    """Tests for ``take()``"""

    def test_simple_take(self):
        """Test basic usage"""
        t = mi.take(5, range(10))
        self.assertEqual(t, [0, 1, 2, 3, 4])

    def test_null_take(self):
        """Check the null case"""
        t = mi.take(0, range(10))
        self.assertEqual(t, [])

    def test_negative_take(self):
        """Make sure taking negative items results in a ValueError"""
        self.assertRaises(ValueError, lambda: mi.take(-3, range(10)))

    def test_take_too_much(self):
        """Taking more than an iterator has remaining should return what the
        iterator has remaining.

        """
        t = mi.take(10, range(5))
        self.assertEqual(t, [0, 1, 2, 3, 4])


class TabulateTests(TestCase):
    """Tests for ``tabulate()``"""

    def test_simple_tabulate(self):
        """Test the happy path"""
        t = mi.tabulate(lambda x: x)
        f = tuple([next(t) for _ in range(3)])
        self.assertEqual(f, (0, 1, 2))

    def test_count(self):
        """Ensure tabulate accepts specific count"""
        t = mi.tabulate(lambda x: 2 * x, -1)
        f = (next(t), next(t), next(t))
        self.assertEqual(f, (-2, 0, 2))


class TailTests(TestCase):
    """Tests for ``tail()``"""

    def test_iterator_greater(self):
        """Length of iterator is greater than requested tail"""
        self.assertEqual(list(mi.tail(3, iter('ABCDEFG'))), list('EFG'))

    def test_iterator_equal(self):
        """Length of iterator is equal to the requested tail"""
        self.assertEqual(list(mi.tail(7, iter('ABCDEFG'))), list('ABCDEFG'))

    def test_iterator_less(self):
        """Length of iterator is less than requested tail"""
        self.assertEqual(list(mi.tail(8, iter('ABCDEFG'))), list('ABCDEFG'))

    def test_iterator_negative(self):
        """Negative tail sizes should raise for non-sized iterables."""
        self.assertRaises(
            ValueError, lambda: list(mi.tail(-1, iter('ABCDEFG')))
        )

    def test_sized_greater(self):
        """Length of sized iterable is greater than requested tail"""
        self.assertEqual(list(mi.tail(3, 'ABCDEFG')), list('EFG'))

    def test_sized_equal(self):
        """Length of sized iterable is less than requested tail"""
        self.assertEqual(list(mi.tail(7, 'ABCDEFG')), list('ABCDEFG'))

    def test_sized_less(self):
        """Length of sized iterable is less than requested tail"""
        self.assertEqual(list(mi.tail(8, 'ABCDEFG')), list('ABCDEFG'))

    def test_sized_negative(self):
        """Negative tail sizes should raise for sized iterables."""
        self.assertRaises(ValueError, lambda: list(mi.tail(-1, 'ABCDEFG')))


class ConsumeTests(TestCase):
    """Tests for ``consume()``"""

    def test_sanity(self):
        """Test basic functionality"""
        r = (x for x in range(10))
        mi.consume(r, 3)
        self.assertEqual(3, next(r))

    def test_null_consume(self):
        """Check the null case"""
        r = (x for x in range(10))
        mi.consume(r, 0)
        self.assertEqual(0, next(r))

    def test_negative_consume(self):
        """Check that negative consumption throws an error"""
        r = (x for x in range(10))
        self.assertRaises(ValueError, lambda: mi.consume(r, -1))

    def test_total_consume(self):
        """Check that iterator is totally consumed by default"""
        r = (x for x in range(10))
        mi.consume(r)
        self.assertRaises(StopIteration, lambda: next(r))


class NthTests(TestCase):
    """Tests for ``nth()``"""

    def test_basic(self):
        """Make sure the nth item is returned"""
        l = range(10)
        for i, v in enumerate(l):
            self.assertEqual(mi.nth(l, i), v)

    def test_default(self):
        """Ensure a default value is returned when nth item not found"""
        l = range(3)
        self.assertEqual(mi.nth(l, 100, "zebra"), "zebra")

    def test_negative_item_raises(self):
        """Ensure asking for a negative item raises an exception"""
        self.assertRaises(ValueError, lambda: mi.nth(range(10), -3))


class AllEqualTests(TestCase):
    def test_true(self):
        self.assertTrue(mi.all_equal('aaaaaa'))
        self.assertTrue(mi.all_equal([0, 0, 0, 0]))

    def test_false(self):
        self.assertFalse(mi.all_equal('aaaaab'))
        self.assertFalse(mi.all_equal([0, 0, 0, 1]))

    def test_tricky(self):
        items = [1, complex(1, 0), 1.0]
        self.assertTrue(mi.all_equal(items))

    def test_empty(self):
        self.assertTrue(mi.all_equal(''))
        self.assertTrue(mi.all_equal([]))

    def test_one(self):
        self.assertTrue(mi.all_equal('0'))
        self.assertTrue(mi.all_equal([0]))

    def test_key(self):
        self.assertTrue(mi.all_equal('4٤໔４৪', key=int))
        self.assertFalse(mi.all_equal('Abc', key=str.casefold))

    @patch('more_itertools.recipes.groupby', autospec=True)
    def test_groupby_calls(self, mock_groupby):
        next_count = 0

        class _groupby(groupby):
            def __next__(true_self):
                nonlocal next_count
                next_count += 1
                return super().__next__()

        mock_groupby.side_effect = _groupby
        iterable = iter('aaaaa')
        self.assertTrue(mi.all_equal(iterable))
        self.assertEqual(list(iterable), [])
        self.assertEqual(next_count, 2)


class QuantifyTests(TestCase):
    """Tests for ``quantify()``"""

    def test_happy_path(self):
        """Make sure True count is returned"""
        q = [True, False, True]
        self.assertEqual(mi.quantify(q), 2)

    def test_custom_predicate(self):
        """Ensure non-default predicates return as expected"""
        q = range(10)
        self.assertEqual(mi.quantify(q, lambda x: x % 2 == 0), 5)


class PadnoneTests(TestCase):
    def test_basic(self):
        iterable = range(2)
        for func in (mi.pad_none, mi.padnone):
            with self.subTest(func=func):
                p = func(iterable)
                self.assertEqual(
                    [0, 1, None, None], [next(p) for _ in range(4)]
                )


class NcyclesTests(TestCase):
    """Tests for ``nyclces()``"""

    def test_happy_path(self):
        """cycle a sequence three times"""
        r = ["a", "b", "c"]
        n = mi.ncycles(r, 3)
        self.assertEqual(
            ["a", "b", "c", "a", "b", "c", "a", "b", "c"], list(n)
        )

    def test_null_case(self):
        """asking for 0 cycles should return an empty iterator"""
        n = mi.ncycles(range(100), 0)
        self.assertRaises(StopIteration, lambda: next(n))

    def test_pathological_case(self):
        """asking for negative cycles should return an empty iterator"""
        n = mi.ncycles(range(100), -10)
        self.assertRaises(StopIteration, lambda: next(n))


class DotproductTests(TestCase):
    """Tests for ``dotproduct()``'"""

    def test_happy_path(self):
        """simple dotproduct example"""
        self.assertEqual(400, mi.dotproduct([10, 10], [20, 20]))


class FlattenTests(TestCase):
    """Tests for ``flatten()``"""

    def test_basic_usage(self):
        """ensure list of lists is flattened one level"""
        f = [[0, 1, 2], [3, 4, 5]]
        self.assertEqual(list(range(6)), list(mi.flatten(f)))

    def test_single_level(self):
        """ensure list of lists is flattened only one level"""
        f = [[0, [1, 2]], [[3, 4], 5]]
        self.assertEqual([0, [1, 2], [3, 4], 5], list(mi.flatten(f)))


class RepeatfuncTests(TestCase):
    """Tests for ``repeatfunc()``"""

    def test_simple_repeat(self):
        """test simple repeated functions"""
        r = mi.repeatfunc(lambda: 5)
        self.assertEqual([5, 5, 5, 5, 5], [next(r) for _ in range(5)])

    def test_finite_repeat(self):
        """ensure limited repeat when times is provided"""
        r = mi.repeatfunc(lambda: 5, times=5)
        self.assertEqual([5, 5, 5, 5, 5], list(r))

    def test_added_arguments(self):
        """ensure arguments are applied to the function"""
        r = mi.repeatfunc(lambda x: x, 2, 3)
        self.assertEqual([3, 3], list(r))

    def test_null_times(self):
        """repeat 0 should return an empty iterator"""
        r = mi.repeatfunc(range, 0, 3)
        self.assertRaises(StopIteration, lambda: next(r))


class GrouperTests(TestCase):
    def test_basic(self):
        seq = 'ABCDEF'
        for n, expected in [
            (3, [('A', 'B', 'C'), ('D', 'E', 'F')]),
            (4, [('A', 'B', 'C', 'D'), ('E', 'F', None, None)]),
            (5, [('A', 'B', 'C', 'D', 'E'), ('F', None, None, None, None)]),
            (6, [('A', 'B', 'C', 'D', 'E', 'F')]),
            (7, [('A', 'B', 'C', 'D', 'E', 'F', None)]),
        ]:
            with self.subTest(n=n):
                actual = list(mi.grouper(iter(seq), n))
                self.assertEqual(actual, expected)

    def test_fill(self):
        seq = 'ABCDEF'
        fillvalue = 'x'
        for n, expected in [
            (1, ['A', 'B', 'C', 'D', 'E', 'F']),
            (2, ['AB', 'CD', 'EF']),
            (3, ['ABC', 'DEF']),
            (4, ['ABCD', 'EFxx']),
            (5, ['ABCDE', 'Fxxxx']),
            (6, ['ABCDEF']),
            (7, ['ABCDEFx']),
        ]:
            with self.subTest(n=n):
                it = mi.grouper(
                    iter(seq), n, incomplete='fill', fillvalue=fillvalue
                )
                actual = [''.join(x) for x in it]
                self.assertEqual(actual, expected)

    def test_ignore(self):
        seq = 'ABCDEF'
        for n, expected in [
            (1, ['A', 'B', 'C', 'D', 'E', 'F']),
            (2, ['AB', 'CD', 'EF']),
            (3, ['ABC', 'DEF']),
            (4, ['ABCD']),
            (5, ['ABCDE']),
            (6, ['ABCDEF']),
            (7, []),
        ]:
            with self.subTest(n=n):
                it = mi.grouper(iter(seq), n, incomplete='ignore')
                actual = [''.join(x) for x in it]
                self.assertEqual(actual, expected)

    def test_strict(self):
        seq = 'ABCDEF'
        for n, expected in [
            (1, ['A', 'B', 'C', 'D', 'E', 'F']),
            (2, ['AB', 'CD', 'EF']),
            (3, ['ABC', 'DEF']),
            (6, ['ABCDEF']),
        ]:
            with self.subTest(n=n):
                it = mi.grouper(iter(seq), n, incomplete='strict')
                actual = [''.join(x) for x in it]
                self.assertEqual(actual, expected)

    def test_strict_fails(self):
        seq = 'ABCDEF'
        for n in [4, 5, 7]:
            with self.subTest(n=n):
                with self.assertRaises(ValueError):
                    list(mi.grouper(iter(seq), n, incomplete='strict'))

    def test_invalid_incomplete(self):
        with self.assertRaises(ValueError):
            list(mi.grouper('ABCD', 3, incomplete='bogus'))


class RoundrobinTests(TestCase):
    """Tests for ``roundrobin()``"""

    def test_even_groups(self):
        """Ensure ordered output from evenly populated iterables"""
        self.assertEqual(
            list(mi.roundrobin('ABC', [1, 2, 3], range(3))),
            ['A', 1, 0, 'B', 2, 1, 'C', 3, 2],
        )

    def test_uneven_groups(self):
        """Ensure ordered output from unevenly populated iterables"""
        self.assertEqual(
            list(mi.roundrobin('ABCD', [1, 2], range(0))),
            ['A', 1, 'B', 2, 'C', 'D'],
        )


class PartitionTests(TestCase):
    """Tests for ``partition()``"""

    def test_bool(self):
        lesser, greater = mi.partition(lambda x: x > 5, range(10))
        self.assertEqual(list(lesser), [0, 1, 2, 3, 4, 5])
        self.assertEqual(list(greater), [6, 7, 8, 9])

    def test_arbitrary(self):
        divisibles, remainders = mi.partition(lambda x: x % 3, range(10))
        self.assertEqual(list(divisibles), [0, 3, 6, 9])
        self.assertEqual(list(remainders), [1, 2, 4, 5, 7, 8])

    def test_pred_is_none(self):
        falses, trues = mi.partition(None, range(3))
        self.assertEqual(list(falses), [0])
        self.assertEqual(list(trues), [1, 2])


class PowersetTests(TestCase):
    """Tests for ``powerset()``"""

    def test_combinatorics(self):
        """Ensure a proper enumeration"""
        p = mi.powerset([1, 2, 3])
        self.assertEqual(
            list(p), [(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)]
        )


class UniqueEverseenTests(TestCase):
    def test_everseen(self):
        u = mi.unique_everseen('AAAABBBBCCDAABBB')
        self.assertEqual(['A', 'B', 'C', 'D'], list(u))

    def test_custom_key(self):
        u = mi.unique_everseen('aAbACCc', key=str.lower)
        self.assertEqual(list('abC'), list(u))

    def test_unhashable_lists(self):
        data = [[10, 20], [30, 40], [10, 20]]

        with self.assertRaises(TypeError):
            list(mi.unique_everseen(data))

        self.assertEqual(
            list(mi.unique_everseen(data, key=tuple)), [[10, 20], [30, 40]]
        )

    def test_unhashable_sets(self):
        data = [{10, 20}, {30, 40}, {20, 10}]

        with self.assertRaises(TypeError):
            list(mi.unique_everseen(data))

        self.assertEqual(
            list(mi.unique_everseen(data, key=frozenset)), [{10, 20}, {30, 40}]
        )

    def test_unhashable_dicts(self):
        data = [{'a': 10}, {'b': 20}, {'a': 10}]

        with self.assertRaises(TypeError):
            list(mi.unique_everseen(data))

        self.assertEqual(
            list(mi.unique_everseen(data, key=frozenset)),
            [{'a': 10}, {'b': 20}],
        )


class UniqueJustseenTests(TestCase):
    def test_justseen(self):
        u = mi.unique_justseen('AAAABBBCCDABB')
        self.assertEqual(list('ABCDAB'), list(u))

    def test_custom_key(self):
        u = mi.unique_justseen('AABCcAD', str.lower)
        self.assertEqual(list('ABCAD'), list(u))


class UniqueTests(TestCase):
    def test_basic(self):
        iterable = [0, 1, 1, 8, 9, 9, 9, 8, 8, 1, 9, 9]
        actual = list(mi.unique(iterable))
        expected = [0, 1, 8, 9]
        self.assertEqual(actual, expected)

    def test_key(self):
        iterable = ['1', '1', '10', '10', '2', '2', '20', '20']
        actual = list(mi.unique(iterable, key=int))
        expected = ['1', '2', '10', '20']
        self.assertEqual(actual, expected)

    def test_reverse(self):
        iterable = ['1', '1', '10', '10', '2', '2', '20', '20']
        actual = list(mi.unique(iterable, key=int, reverse=True))
        expected = ['20', '10', '2', '1']
        self.assertEqual(actual, expected)


class IterExceptTests(TestCase):
    """Tests for ``iter_except()``"""

    def test_exact_exception(self):
        """ensure the exact specified exception is caught"""
        l = [1, 2, 3]
        i = mi.iter_except(l.pop, IndexError)
        self.assertEqual(list(i), [3, 2, 1])

    def test_generic_exception(self):
        """ensure the generic exception can be caught"""
        l = [1, 2]
        i = mi.iter_except(l.pop, Exception)
        self.assertEqual(list(i), [2, 1])

    def test_uncaught_exception_is_raised(self):
        """ensure a non-specified exception is raised"""
        l = [1, 2, 3]
        i = mi.iter_except(l.pop, KeyError)
        self.assertRaises(IndexError, lambda: list(i))

    def test_first(self):
        """ensure first is run before the function"""
        l = [1, 2, 3]
        f = lambda: 25
        i = mi.iter_except(l.pop, IndexError, f)
        self.assertEqual(list(i), [25, 3, 2, 1])

    def test_multiple(self):
        """ensure can catch multiple exceptions"""

        class Fiz(Exception):
            pass

        class Buzz(Exception):
            pass

        i = 0

        def fizbuzz():
            nonlocal i
            i += 1
            if i % 3 == 0:
                raise Fiz
            if i % 5 == 0:
                raise Buzz
            return i

        expected = ([1, 2], [4], [], [7, 8], [])
        for x in expected:
            self.assertEqual(list(mi.iter_except(fizbuzz, (Fiz, Buzz))), x)


class FirstTrueTests(TestCase):
    """Tests for ``first_true()``"""

    def test_something_true(self):
        """Test with no keywords"""
        self.assertEqual(mi.first_true(range(10)), 1)

    def test_nothing_true(self):
        """Test default return value."""
        self.assertIsNone(mi.first_true([0, 0, 0]))

    def test_default(self):
        """Test with a default keyword"""
        self.assertEqual(mi.first_true([0, 0, 0], default='!'), '!')

    def test_pred(self):
        """Test with a custom predicate"""
        self.assertEqual(
            mi.first_true([2, 4, 6], pred=lambda x: x % 3 == 0), 6
        )


class RandomProductTests(TestCase):
    """Tests for ``random_product()``

    Since random.choice() has different results with the same seed across
    python versions 2.x and 3.x, these tests use highly probably events to
    create predictable outcomes across platforms.
    """

    def test_simple_lists(self):
        """Ensure that one item is chosen from each list in each pair.
        Also ensure that each item from each list eventually appears in
        the chosen combinations.

        Odds are roughly 1 in 7.1 * 10e16 that one item from either list will
        not be chosen after 100 samplings of one item from each list. Just to
        be safe, better use a known random seed, too.

        """
        nums = [1, 2, 3]
        lets = ['a', 'b', 'c']
        n, m = zip(*[mi.random_product(nums, lets) for _ in range(100)])
        n, m = set(n), set(m)
        self.assertEqual(n, set(nums))
        self.assertEqual(m, set(lets))
        self.assertEqual(len(n), len(nums))
        self.assertEqual(len(m), len(lets))

    def test_list_with_repeat(self):
        """ensure multiple items are chosen, and that they appear to be chosen
        from one list then the next, in proper order.

        """
        nums = [1, 2, 3]
        lets = ['a', 'b', 'c']
        r = list(mi.random_product(nums, lets, repeat=100))
        self.assertEqual(2 * 100, len(r))
        n, m = set(r[::2]), set(r[1::2])
        self.assertEqual(n, set(nums))
        self.assertEqual(m, set(lets))
        self.assertEqual(len(n), len(nums))
        self.assertEqual(len(m), len(lets))

        r = list(mi.random_product(iter(nums), iter(lets), repeat=100))
        self.assertEqual(2 * 100, len(r))
        n, m = set(r[::2]), set(r[1::2])
        self.assertEqual(n, set(nums))
        self.assertEqual(m, set(lets))
        self.assertEqual(len(n), len(nums))
        self.assertEqual(len(m), len(lets))


class RandomPermutationTests(TestCase):
    """Tests for ``random_permutation()``"""

    def test_full_permutation(self):
        """ensure every item from the iterable is returned in a new ordering

        15 elements have a 1 in 1.3 * 10e12 of appearing in sorted order, so
        we fix a seed value just to be sure.

        """
        i = range(15)
        r = mi.random_permutation(i)
        self.assertEqual(set(i), set(r))
        if i == r:
            raise AssertionError("Values were not permuted")

    def test_partial_permutation(self):
        """ensure all returned items are from the iterable, that the returned
        permutation is of the desired length, and that all items eventually
        get returned.

        Sampling 100 permutations of length 5 from a set of 15 leaves a
        (2/3)^100 chance that an item will not be chosen. Multiplied by 15
        items, there is a 1 in 2.6e16 chance that at least 1 item will not
        show up in the resulting output. Using a random seed will fix that.

        """
        items = range(15)
        item_set = set(items)
        all_items = set()
        for _ in range(100):
            permutation = mi.random_permutation(items, 5)
            self.assertEqual(len(permutation), 5)
            permutation_set = set(permutation)
            self.assertLessEqual(permutation_set, item_set)
            all_items |= permutation_set
        self.assertEqual(all_items, item_set)


class RandomCombinationTests(TestCase):
    """Tests for ``random_combination()``"""

    def test_pseudorandomness(self):
        """ensure different subsets of the iterable get returned over many
        samplings of random combinations"""
        items = range(15)
        all_items = set()
        for _ in range(50):
            combination = mi.random_combination(items, 5)
            all_items |= set(combination)
        self.assertEqual(all_items, set(items))

    def test_no_replacement(self):
        """ensure that elements are sampled without replacement"""
        items = range(15)
        for _ in range(50):
            combination = mi.random_combination(items, len(items))
            self.assertEqual(len(combination), len(set(combination)))
        self.assertRaises(
            ValueError, lambda: mi.random_combination(items, len(items) + 1)
        )


class RandomCombinationWithReplacementTests(TestCase):
    """Tests for ``random_combination_with_replacement()``"""

    def test_replacement(self):
        """ensure that elements are sampled with replacement"""
        items = range(5)
        combo = mi.random_combination_with_replacement(items, len(items) * 2)
        self.assertEqual(2 * len(items), len(combo))
        if len(set(combo)) == len(combo):
            raise AssertionError("Combination contained no duplicates")

    def test_pseudorandomness(self):
        """ensure different subsets of the iterable get returned over many
        samplings of random combinations"""
        items = range(15)
        all_items = set()
        for _ in range(50):
            combination = mi.random_combination_with_replacement(items, 5)
            all_items |= set(combination)
        self.assertEqual(all_items, set(items))


class TestRandomDerangement(TestCase):
    def test_basics(self):
        word = tuple('love')
        for _ in range(20):
            d = mi.random_derangement(word)
            self.assertEqual(len(d), len(word))  # Same size
            self.assertEqual(set(d), set(word))  # Same values
            self.assertFalse(any(map(eq, d, word)))  # No fixed points

        c = Counter(mi.random_derangement(word) for _ in range(10_000))

        # Repeated calls generate exactly the set of valid derangements.
        self.assertEqual(set(c), set(mi.derangements(word)))

        # Check approximate equidistribution (all counts within eight
        # standard deviations of the expected mean).
        self.assertTrue(940 <= min(c.values()) and max(c.values()) <= 1280)

        # Corner case for empty input
        self.assertEqual(mi.random_derangement(''), ())

        # Error case
        with self.assertRaises(IndexError):
            mi.random_derangement('x')  # Not enough values


class NthCombinationTests(TestCase):
    def test_basic(self):
        iterable = 'abcdefg'
        r = 4
        for index, expected in enumerate(combinations(iterable, r)):
            actual = mi.nth_combination(iterable, r, index)
            self.assertEqual(actual, expected)

    def test_long(self):
        actual = mi.nth_combination(range(180), 4, 2000000)
        expected = (2, 12, 35, 126)
        self.assertEqual(actual, expected)

    def test_invalid_r(self):
        with self.assertRaises(ValueError):
            mi.nth_combination([], -1, 0)
        with self.assertRaises(IndexError):
            mi.nth_combination('abc', 5, 0)

    def test_invalid_index(self):
        with self.assertRaises(IndexError):
            mi.nth_combination('abcdefg', 3, -36)


class NthPermutationTests(TestCase):
    def test_r_less_than_n(self):
        iterable = 'abcde'
        r = 4
        for index, expected in enumerate(permutations(iterable, r)):
            actual = mi.nth_permutation(iterable, r, index)
            self.assertEqual(actual, expected)

    def test_r_equal_to_n(self):
        iterable = 'abcde'
        for index, expected in enumerate(permutations(iterable)):
            actual = mi.nth_permutation(iterable, None, index)
            self.assertEqual(actual, expected)

    def test_long(self):
        iterable = tuple(range(180))
        r = 4
        index = 1000000
        actual = mi.nth_permutation(iterable, r, index)
        expected = mi.nth(permutations(iterable, r), index)
        self.assertEqual(actual, expected)

    def test_null(self):
        actual = mi.nth_permutation([], 0, 0)
        expected = tuple()
        self.assertEqual(actual, expected)

    def test_negative_index(self):
        iterable = 'abcde'
        r = 4
        n = factorial(len(iterable)) // factorial(len(iterable) - r)
        for index, expected in enumerate(permutations(iterable, r)):
            actual = mi.nth_permutation(iterable, r, index - n)
            self.assertEqual(actual, expected)

    def test_invalid_index(self):
        iterable = 'abcde'
        r = 4
        n = factorial(len(iterable)) // factorial(len(iterable) - r)
        for index in [-1 - n, n + 1]:
            with self.assertRaises(IndexError):
                mi.nth_permutation(iterable, r, index)
        with self.assertRaises(IndexError):
            mi.nth_permutation('abc', 5, 0)

    def test_invalid_r(self):
        with self.assertRaises(ValueError):
            mi.nth_permutation('abcde', -1, 0)


class PrependTests(TestCase):
    def test_basic(self):
        value = 'a'
        iterator = iter('bcdefg')
        actual = list(mi.prepend(value, iterator))
        expected = list('abcdefg')
        self.assertEqual(actual, expected)

    def test_multiple(self):
        value = 'ab'
        iterator = iter('cdefg')
        actual = tuple(mi.prepend(value, iterator))
        expected = ('ab',) + tuple('cdefg')
        self.assertEqual(actual, expected)


class Convolvetests(TestCase):
    def test_moving_average(self):
        signal = iter([10, 20, 30, 40, 50])
        kernel = [0.5, 0.5]
        actual = list(mi.convolve(signal, kernel))
        expected = [
            (10 + 0) / 2,
            (20 + 10) / 2,
            (30 + 20) / 2,
            (40 + 30) / 2,
            (50 + 40) / 2,
            (0 + 50) / 2,
        ]
        self.assertEqual(actual, expected)

    def test_derivative(self):
        signal = iter([10, 20, 30, 40, 50])
        kernel = [1, -1]
        actual = list(mi.convolve(signal, kernel))
        expected = [10 - 0, 20 - 10, 30 - 20, 40 - 30, 50 - 40, 0 - 50]
        self.assertEqual(actual, expected)

    def test_infinite_signal(self):
        signal = count()
        kernel = [1, -1]
        actual = mi.take(5, mi.convolve(signal, kernel))
        expected = [0, 1, 1, 1, 1]
        self.assertEqual(actual, expected)


class BeforeAndAfterTests(TestCase):
    def test_empty(self):
        before, after = mi.before_and_after(bool, [])
        self.assertEqual(list(before), [])
        self.assertEqual(list(after), [])

    def test_never_true(self):
        before, after = mi.before_and_after(bool, [0, False, None, ''])
        self.assertEqual(list(before), [])
        self.assertEqual(list(after), [0, False, None, ''])

    def test_never_false(self):
        before, after = mi.before_and_after(bool, [1, True, Ellipsis, ' '])
        self.assertEqual(list(before), [1, True, Ellipsis, ' '])
        self.assertEqual(list(after), [])

    def test_some_true(self):
        before, after = mi.before_and_after(bool, [1, True, 0, False])
        self.assertEqual(list(before), [1, True])
        self.assertEqual(list(after), [0, False])

    @staticmethod
    def _group_events(events):
        events = iter(events)

        while True:
            try:
                operation = next(events)
            except StopIteration:
                break
            assert operation in ["SUM", "MULTIPLY"]

            # Here, the remainder `events` is passed into `before_and_after`
            # again, which would be problematic if the remainder is a
            # generator function (as in Python 3.10 itertools recipes), since
            # that creates recursion. `itertools.chain` solves this problem.
            numbers, events = mi.before_and_after(
                lambda e: isinstance(e, int), events
            )

            yield (operation, numbers)

    def test_nested_remainder(self):
        events = ["SUM", 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] * 1000
        events += ["MULTIPLY", 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] * 1000

        for operation, numbers in self._group_events(events):
            if operation == "SUM":
                res = sum(numbers)
                self.assertEqual(res, 55)
            elif operation == "MULTIPLY":
                res = reduce(lambda a, b: a * b, numbers)
                self.assertEqual(res, 3628800)


class TriplewiseTests(TestCase):
    def test_basic(self):
        for iterable, expected in [
            ([0], []),
            ([0, 1], []),
            ([0, 1, 2], [(0, 1, 2)]),
            ([0, 1, 2, 3], [(0, 1, 2), (1, 2, 3)]),
            ([0, 1, 2, 3, 4], [(0, 1, 2), (1, 2, 3), (2, 3, 4)]),
        ]:
            with self.subTest(expected=expected):
                actual = list(mi.triplewise(iterable))
                self.assertEqual(actual, expected)


class SlidingWindowTests(TestCase):
    def test_islice_version(self):
        for iterable, n, expected in [
            ([], 1, []),
            ([0], 1, [(0,)]),
            ([0, 1], 1, [(0,), (1,)]),
            ([0, 1, 2], 2, [(0, 1), (1, 2)]),
            ([0, 1, 2], 3, [(0, 1, 2)]),
            ([0, 1, 2], 4, []),
            ([0, 1, 2, 3], 4, [(0, 1, 2, 3)]),
            ([0, 1, 2, 3, 4], 4, [(0, 1, 2, 3), (1, 2, 3, 4)]),
        ]:
            with self.subTest(expected=expected):
                actual = list(mi.sliding_window(iterable, n))
                self.assertEqual(actual, expected)

    def test_deque_version(self):
        iterable = map(str, range(100))
        all_windows = list(mi.sliding_window(iterable, 95))
        self.assertEqual(all_windows[0], tuple(map(str, range(95))))
        self.assertEqual(all_windows[-1], tuple(map(str, range(5, 100))))

    def test_zero(self):
        iterable = map(str, range(100))
        with self.assertRaises(ValueError):
            list(mi.sliding_window(iterable, 0))


class SubslicesTests(TestCase):
    def test_basic(self):
        for iterable, expected in [
            ([], []),
            ([1], [[1]]),
            ([1, 2], [[1], [1, 2], [2]]),
            (iter([1, 2]), [[1], [1, 2], [2]]),
            ([2, 1], [[2], [2, 1], [1]]),
            (
                'ABCD',
                [
                    ['A'],
                    ['A', 'B'],
                    ['A', 'B', 'C'],
                    ['A', 'B', 'C', 'D'],
                    ['B'],
                    ['B', 'C'],
                    ['B', 'C', 'D'],
                    ['C'],
                    ['C', 'D'],
                    ['D'],
                ],
            ),
        ]:
            with self.subTest(expected=expected):
                actual = list(mi.subslices(iterable))
                self.assertEqual(actual, expected)


class PolynomialFromRootsTests(TestCase):
    def test_basic(self):
        for roots, expected in [
            ((2, 1, -1), [1, -2, -1, 2]),
            ((2, 3), [1, -5, 6]),
            ((1, 2, 3), [1, -6, 11, -6]),
            ((2, 4, 1), [1, -7, 14, -8]),
        ]:
            with self.subTest(roots=roots):
                actual = mi.polynomial_from_roots(roots)
                self.assertEqual(actual, expected)

    def test_large(self):
        n = 1_500
        actual = mi.polynomial_from_roots([-1] * n)
        expected = [comb(n, k) for k in range(n + 1)]
        self.assertEqual(actual, expected)


class PolynomialEvalTests(TestCase):
    def test_basic(self):
        for coefficients, x, expected in [
            ([1, -4, -17, 60], 2, 18),
            ([1, -4, -17, 60], 2.5, 8.125),
            ([1, -4, -17, 60], Fraction(2, 3), Fraction(1274, 27)),
            ([1, -4, -17, 60], Decimal('1.75'), Decimal('23.359375')),
            ([], 2, 0),
            ([], 2.5, 0.0),
            ([], Fraction(2, 3), Fraction(0, 1)),
            ([], Decimal('1.75'), Decimal('0.00')),
            ([11], 7, 11),
            ([11, 2], 7, 79),
        ]:
            with self.subTest(x=x):
                actual = mi.polynomial_eval(coefficients, x)
                self.assertEqual(actual, expected)
                self.assertEqual(type(actual), type(x))


class IterIndexTests(TestCase):
    def test_basic(self):
        iterable = 'AABCADEAF'
        for wrapper in (list, iter):
            with self.subTest(wrapper=wrapper):
                actual = list(mi.iter_index(wrapper(iterable), 'A'))
                expected = [0, 1, 4, 7]
                self.assertEqual(actual, expected)

    def test_start(self):
        for wrapper in (list, iter):
            with self.subTest(wrapper=wrapper):
                iterable = 'AABCADEAF'
                i = -1
                actual = []
                while True:
                    try:
                        i = next(
                            mi.iter_index(wrapper(iterable), 'A', start=i + 1)
                        )
                    except StopIteration:
                        break
                    else:
                        actual.append(i)

                expected = [0, 1, 4, 7]
                self.assertEqual(actual, expected)

    def test_stop(self):
        actual = list(mi.iter_index('AABCADEAF', 'A', stop=7))
        expected = [0, 1, 4]
        self.assertEqual(actual, expected)

    def test_negative_start_and_stop(self):
        # Negative *start* / *stop* should behave like the built-in
        # ``str.index`` / ``list.index`` and produce identical results for the
        # fast (sequence) and slow (general-iterable) code paths.
        iterable = 'AABCADEAF'  # 'A' occurs at indexes 0, 1, 4, 7
        cases = [
            (dict(start=-3), [7]),
            (dict(start=-9), [0, 1, 4, 7]),
            (dict(stop=-2), [0, 1, 4]),
            (dict(start=-5, stop=-1), [4, 7]),
        ]
        for kwargs, expected in cases:
            for wrapper in (list, iter):
                with self.subTest(kwargs=kwargs, wrapper=wrapper):
                    actual = list(
                        mi.iter_index(wrapper(iterable), 'A', **kwargs)
                    )
                    self.assertEqual(actual, expected)


class SieveTests(TestCase):
    def test_basic(self):
        self.assertEqual(
            list(mi.sieve(67)),
            [
                2,
                3,
                5,
                7,
                11,
                13,
                17,
                19,
                23,
                29,
                31,
                37,
                41,
                43,
                47,
                53,
                59,
                61,
            ],
        )
        self.assertEqual(list(mi.sieve(68))[-1], 67)

    def test_prime_counts(self):
        for n, expected in (
            (100, 25),
            (1_000, 168),
            (10_000, 1229),
            (100_000, 9592),
            (1_000_000, 78498),
        ):
            with self.subTest(n=n):
                self.assertEqual(mi.ilen(mi.sieve(n)), expected)

    def test_small_numbers(self):
        with self.assertRaises(ValueError):
            list(mi.sieve(-1))

        for n in (0, 1, 2):
            with self.subTest(n=n):
                self.assertEqual(list(mi.sieve(n)), [])


class BatchedTests(TestCase):
    def test_basic(self):
        iterable = range(1, 5 + 1)
        for n, expected in (
            (1, [(1,), (2,), (3,), (4,), (5,)]),
            (2, [(1, 2), (3, 4), (5,)]),
            (3, [(1, 2, 3), (4, 5)]),
            (4, [(1, 2, 3, 4), (5,)]),
            (5, [(1, 2, 3, 4, 5)]),
            (6, [(1, 2, 3, 4, 5)]),
        ):
            with self.subTest(n=n):
                actual = list(mi.batched(iterable, n))
                self.assertEqual(actual, expected)

    def test_strict(self):
        with self.assertRaises(ValueError):
            list(mi.batched('ABCDEFG', 3, strict=True))

        self.assertEqual(
            list(mi.batched('ABCDEF', 3, strict=True)),
            [('A', 'B', 'C'), ('D', 'E', 'F')],
        )


class TransposeTests(TestCase):
    def test_empty(self):
        it = []
        actual = list(mi.transpose(it))
        expected = []
        self.assertEqual(actual, expected)

    def test_basic(self):
        it = [(10, 11, 12), (20, 21, 22), (30, 31, 32)]
        actual = list(mi.transpose(it))
        expected = [(10, 20, 30), (11, 21, 31), (12, 22, 32)]
        self.assertEqual(actual, expected)

    def test_incompatible_error(self):
        it = [(10, 11, 12, 13), (20, 21, 22), (30, 31, 32)]
        with self.assertRaises(ValueError):
            list(mi.transpose(it))


class ReshapeTests(TestCase):
    def test_empty(self):
        actual = list(mi.reshape([], 3))
        self.assertEqual(actual, [])

    def test_zero(self):
        matrix = [(0, 1, 2, 3), (4, 5, 6, 7), (8, 9, 10, 11)]
        with self.assertRaises(ValueError):
            list(mi.reshape(matrix, 0))

    def test_basic(self):
        matrix = [(0, 1, 2, 3), (4, 5, 6, 7), (8, 9, 10, 11)]
        for cols, expected in (
            (
                1,
                [
                    (0,),
                    (1,),
                    (2,),
                    (3,),
                    (4,),
                    (5,),
                    (6,),
                    (7,),
                    (8,),
                    (9,),
                    (10,),
                    (11,),
                ],
            ),
            (2, [(0, 1), (2, 3), (4, 5), (6, 7), (8, 9), (10, 11)]),
            (3, [(0, 1, 2), (3, 4, 5), (6, 7, 8), (9, 10, 11)]),
            (4, [(0, 1, 2, 3), (4, 5, 6, 7), (8, 9, 10, 11)]),
            (6, [(0, 1, 2, 3, 4, 5), (6, 7, 8, 9, 10, 11)]),
            (12, [(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11)]),
        ):
            with self.subTest(cols=cols):
                actual = list(mi.reshape(matrix, cols))
                self.assertEqual(actual, expected)

    def test_multidimensional(self):
        reshape = mi.reshape

        def shape(tensor):
            if not hasattr(tensor, '__iter__'):
                return ()
            seq = list(tensor)
            return (len(seq),) + shape(seq[0])

        matrix = [(0, 1), (2, 3), (4, 5)]
        self.assertEqual(shape(matrix), (3, 2))

        for new_shape in [
            (2, 3),
            (6,),
            (6, 1),
            (1, 6),
            (2, 1, 3, 1),
            (1, 1, 3, 1, 2),
        ]:
            with self.subTest(new_shape=new_shape):
                new_matrix = reshape(matrix, new_shape)
                self.assertEqual(shape(new_matrix), new_shape)

        # Truncation:  Input larger than the requested shape
        self.assertEqual(list(reshape(matrix, [3])), [0, 1, 2])

        # Incomplete structure: Input smaller than the requested shape
        self.assertEqual(list(reshape(matrix, [8])), [0, 1, 2, 3, 4, 5])

        # Str and bytes treated as scalars
        word_matrix = [[['ab', b'de', 'gh', b'jk']]]  # Shape: 1 x 1 x 4
        self.assertEqual(
            list(reshape(word_matrix, (2, 2))),
            [('ab', b'de'), ('gh', b'jk')],
        )

        # Empty input
        self.assertEqual(list(reshape([[]], shape=(1,))), [])

        # Non-uniform input: scalar where a tensor is expected
        with self.assertRaises(TypeError):
            list(mi.reshape([[10, 20, 30], 40], shape=(4,)))

        # Non-integer indices
        with self.assertRaises((TypeError, ValueError)):
            matrix = [(0, 1), (2, 3), (4, 5)]
            list(reshape(matrix, ('a', 'b', 'c')))

        # Indices smaller than one
        with self.assertRaises(ValueError):
            list(reshape(matrix, (6, 0, 1)))


class MatMulTests(TestCase):
    def test_n_by_n(self):
        actual = list(mi.matmul([(7, 5), (3, 5)], [[2, 5], [7, 9]]))
        expected = [(49, 80), (41, 60)]
        self.assertEqual(actual, expected)

    def test_m_by_n(self):
        m1 = [[2, 5], [7, 9], [3, 4]]
        m2 = [[7, 11, 5, 4, 9], [3, 5, 2, 6, 3]]
        actual = list(mi.matmul(m1, m2))
        expected = [
            (29, 47, 20, 38, 33),
            (76, 122, 53, 82, 90),
            (33, 53, 23, 36, 39),
        ]
        self.assertEqual(actual, expected)


class FactorTests(TestCase):
    def test_basic(self):
        for n, expected in (
            (0, []),
            (1, []),
            (2, [2]),
            (3, [3]),
            (4, [2, 2]),
            (6, [2, 3]),
            (360, [2, 2, 2, 3, 3, 5]),
            (128_884_753_939, [128_884_753_939]),
            (999_953 * 999_983, [999_953, 999_983]),
            (909_909_090_909, [3, 3, 7, 13, 13, 751, 1_137_97]),
            (
                1_647_403_876_764_101_672_307_088,
                [2, 2, 2, 2, 19, 23, 109471, 13571009, 158594251],
            ),
        ):
            with self.subTest(n=n):
                actual = list(mi.factor(n))
                self.assertEqual(actual, expected)

    def test_cross_check(self):
        prod = lambda x: reduce(mul, x, 1)
        self.assertTrue(all(prod(mi.factor(n)) == n for n in range(1, 2000)))
        self.assertTrue(
            all(set(mi.factor(n)) <= set(mi.sieve(n + 1)) for n in range(2000))
        )
        self.assertTrue(
            all(
                list(mi.factor(n)) == sorted(mi.factor(n)) for n in range(2000)
            )
        )


class SumOfSquaresTests(TestCase):
    def test_basic(self):
        for it, expected in (
            ([], 0),
            ([1, 2, 3], 1 + 4 + 9),
            ([2, 4, 6, 8], 4 + 16 + 36 + 64),
        ):
            with self.subTest(it=it):
                actual = mi.sum_of_squares(it)
                self.assertEqual(actual, expected)


class PolynomialDerivativeTests(TestCase):
    def test_basic(self):
        for coefficients, expected in [
            ([], []),
            ([1], []),
            ([1, 2], [1]),
            ([1, 2, 3], [2, 2]),
            ([1, 2, 3, 4], [3, 4, 3]),
            ([1.1, 2, 3, 4], [(1.1 * 3), 4, 3]),
        ]:
            with self.subTest(coefficients=coefficients):
                actual = mi.polynomial_derivative(coefficients)
                self.assertEqual(actual, expected)


class TotientTests(TestCase):
    def test_basic(self):
        for n, expected in (
            (1, 1),
            (2, 1),
            (3, 2),
            (4, 2),
            (9, 6),
            (12, 4),
            (128_884_753_939, 128_884_753_938),
            (999953 * 999983, 999952 * 999982),
            (6**20, 1 * 2**19 * 2 * 3**19),
        ):
            with self.subTest(n=n):
                self.assertEqual(mi.totient(n), expected)


class PrimeFunctionTests(TestCase):
    def test_is_prime_pseudoprimes(self):
        # Carmichael number that strong pseudoprime to prime bases < 307
        # https://doi.org/10.1006/jsco.1995.1042
        p = 29674495668685510550154174642905332730771991799853043350995075531276838753171770199594238596428121188033664754218345562493168782883  # noqa:E501
        gnarly_carmichael = (313 * (p - 1) + 1) * (353 * (p - 1) + 1)

        for n in (
            # Least Carmichael number with n prime factors:
            # https://oeis.org/A006931
            561,
            41041,
            825265,
            321197185,
            5394826801,
            232250619601,
            9746347772161,
            1436697831295441,
            60977817398996785,
            7156857700403137441,
            1791562810662585767521,
            87674969936234821377601,
            6553130926752006031481761,
            1590231231043178376951698401,
            # Carmichael numbers with exactly 4 prime factors:
            # https://oeis.org/A074379
            41041,
            62745,
            63973,
            75361,
            101101,
            126217,
            172081,
            188461,
            278545,
            340561,
            449065,
            552721,
            656601,
            658801,
            670033,
            748657,
            838201,
            852841,
            997633,
            1033669,
            1082809,
            1569457,
            1773289,
            2100901,
            2113921,
            2433601,
            2455921,
            # Lucas-Carmichael numbers:
            # https://oeis.org/A006972
            399,
            935,
            2015,
            2915,
            4991,
            5719,
            7055,
            8855,
            12719,
            18095,
            20705,
            20999,
            22847,
            29315,
            31535,
            46079,
            51359,
            60059,
            63503,
            67199,
            73535,
            76751,
            80189,
            81719,
            88559,
            90287,
            # Strong pseudoprimes to bases 2, 3 and 5:
            # https://oeis.org/A056915
            25326001,
            161304001,
            960946321,
            1157839381,
            3215031751,
            3697278427,
            5764643587,
            6770862367,
            14386156093,
            15579919981,
            18459366157,
            19887974881,
            21276028621,
            27716349961,
            29118033181,
            37131467521,
            41752650241,
            42550716781,
            43536545821,
            # Strong pseudoprimes to bases 2, 3, 5, and 7:
            # https://oeis.org/A211112
            39365185894561,
            52657210792621,
            11377272352951,
            15070413782971,
            3343433905957,
            16603327018981,
            3461715915661,
            52384617784801,
            3477707481751,
            18996486073489,
            55712149574381,
            gnarly_carmichael,
        ):
            with self.subTest(n=n):
                self.assertFalse(mi.is_prime(n))

    def test_primes(self):
        for i, n in enumerate(mi.sieve(10**5)):
            with self.subTest(n=n):
                self.assertTrue(mi.is_prime(n))
                self.assertEqual(mi.nth_prime(i), n)

        self.assertFalse(mi.is_prime(-1))
        with self.assertRaises(ValueError):
            mi.nth_prime(-1)

    def test_nth_prime_tightened_bound(self):
        # nth_prime() counts from 0 and asks for bounds on n + 1, so 688_382
        # is the first argument that gets the tightened upper bound and
        # 688_381 is the last that doesn't. The exact path sieves up to that
        # bound, so tightening it too far would leave the sieve short and
        # nth() would return None. At the threshold the bound clears the
        # prime it has to reach by 3.
        self.assertEqual(mi.nth_prime(688_381), 10_384_259)
        self.assertEqual(mi.nth_prime(688_382), 10_384_261)

    def test_nth_prime_approximate(self):
        # approximate=True is ignored at or below 1,000,000
        self.assertEqual(
            mi.nth_prime(1_000_000, approximate=True),
            mi.nth_prime(1_000_000),
        )

        # Above it, the result is some nearby prime rather than the exact one
        for n in (1_000_001, 2_000_000):
            with self.subTest(n=n):
                approximate = mi.nth_prime(n, approximate=True)
                exact = mi.nth_prime(n)
                self.assertTrue(mi.is_prime(approximate))
                self.assertLess(abs(approximate - exact) / exact, 0.01)

    def test_special_primes(self):
        for n in (
            # Mersenee primes:
            # https://oeis.org/A211112
            3,
            7,
            31,
            127,
            8191,
            131071,
            524287,
            2147483647,
            2305843009213693951,
            618970019642690137449562111,
            162259276829213363391578010288127,
            170141183460469231731687303715884105727,
            # Various big primes:
            # https://bigprimes.org/
            7990614013,
            80358337843874809987,
            814847562949580526031364519741,
            1982427225022428178169740526258124929077,
            91828213828508622559862344537590739566883686537727,
            406414746815201693481517584049440077164779143248351060891669,
        ):
            with self.subTest(n=n):
                self.assertTrue(mi.is_prime(n))


class LoopsTests(TestCase):
    def test_basic(self):
        self.assertTrue(
            all(list(mi.loops(n)) == [None] * n for n in range(-10, 10))
        )


class MultinomialTests(TestCase):
    def test_basic(self):
        multinomial = mi.multinomial

        # Case M(11; 5, 2, 1, 1, 2) = 83160
        # https://www.wolframalpha.com/input?i=Multinomia%285%2C+2%2C+1%2C+1%2C+2%29
        self.assertEqual(multinomial(5, 2, 1, 1, 2), 83160)

        # Commutative
        self.assertEqual(multinomial(2, 1, 1, 2, 5), 83160)

        # Unaffected by zero-sized bins
        self.assertEqual(multinomial(2, 0, 1, 0, 1, 2, 5, 0), 83160)

        # Matches definition
        self.assertEqual(
            multinomial(5, 2, 1, 1, 2),
            (
                factorial(sum([5, 2, 1, 1, 2]))
                // prod(map(factorial, [5, 2, 1, 1, 2]))
            ),
        )

        # Corner cases and identities
        self.assertEqual(multinomial(), 1)
        self.assertEqual(multinomial(5), 1)
        self.assertEqual(multinomial(5, 7), comb(12, 5))
        self.assertEqual(multinomial(1, 1, 1, 1, 1, 1, 1), factorial(7))

        # Relationship to distinct_permuations() and permutations()
        for word in ['plain', 'pizza', 'coffee', 'honolulu', 'assists']:
            with self.subTest(word=word):
                self.assertEqual(
                    multinomial(*Counter(word).values()),
                    mi.ilen(mi.distinct_permutations(word)),
                )
                self.assertEqual(
                    multinomial(*Counter(word).values()),
                    len(set(permutations(word))),
                )

        # Error cases
        with self.assertRaises(ValueError):
            multinomial(-5, 7)  # No negative inputs
        with self.assertRaises(TypeError):
            multinomial(5, 7.25)  # No float inputs
        with self.assertRaises(TypeError):
            multinomial(5, 'x')  # No non-numeric inputs
        with self.assertRaises(TypeError):
            multinomial([5, 7])  # No sequence inputs


def grow_to_window(data, maxlen):
    "Return growing window views upto maxlen."
    for j in range(1, len(data) + 1):
        i = max(j - maxlen, 0)
        yield data[i:j]


class RunningMeanTests(TestCase):
    def test_basic(self):
        for i, (iterable, expected) in enumerate(
            [
                ([], []),
                ([1], [1.0]),
                ([1, 2], [1.0, 1.5]),
                (
                    [Fraction(1, 1), Fraction(2, 1)],
                    [Fraction(1, 1), Fraction(3, 2)],
                ),
                (
                    [Decimal('1.0'), Decimal('2.0')],
                    [Decimal('1.0'), Decimal('1.5')],
                ),
                ([8.5, 9.5, 7.5, 6.5], [8.5, 9.0, 8.5, 8.0]),
                ([3 + 4j, 5 - 1j, 4 + 3j], [(3 + 4j), (4 + 1.5j), (4 + 2j)]),
            ]
        ):
            with self.subTest(i=i):
                actual = list(mi.running_mean(iterable))
                self.assertEqual(actual, expected)

    def test_maxlen(self):
        data = random.choices(range(20), k=1000)

        # Window size must be positive
        with self.assertRaises(ValueError):
            list(mi.running_mean(iter(data), maxlen=0))

        # Window size of 1 should return the original dataset unchanged
        self.assertEqual(list(mi.running_mean(iter(data), maxlen=1)), data)

        # Window size normal cases
        for maxlen in range(2, 6):
            with self.subTest(maxlen=maxlen):
                actual = list(mi.running_mean(iter(data), maxlen=maxlen))
                expected = list(map(mean, grow_to_window(data, maxlen)))
                self.assertEqual(actual, expected)

        # Window size larger than the data same as the unbounded case
        self.assertEqual(
            list(mi.running_mean(iter(data), maxlen=len(data) * 2)),
            list(mi.running_mean(iter(data))),
        )


class RunningMedianTests(TestCase):
    def test_vs_statistics_median(self):
        running_median = mi.running_median

        for data in [
            random.choices(range(-500, 500), k=500),
            # Apply unary plus to force context rounding.
            [+Decimal(random.uniform(-500, 500)) for _ in range(500)],
            [
                Fraction(random.randrange(-500, 500), random.randrange(1, 500))
                for _ in range(500)
            ],
        ]:
            with self.subTest(data=data):
                for k, rm in enumerate(running_median(iter(data)), start=1):
                    expected = statistics.median(data[:k])
                    self.assertEqual(rm, expected)
                    self.assertEqual(type(rm), type(expected))

        self.assertEqual(list(running_median([])), [])  # Empty input

    def test_vs_statistics_median_windowed(self):
        running_median = mi.running_median
        size = 10

        for data in [
            random.choices(range(-500, 500), k=500),
            # Apply unary plus to force context rounding.
            [+Decimal(random.uniform(-500, 500)) for _ in range(500)],
            [
                Fraction(random.randrange(-500, 500), random.randrange(1, 500))
                for _ in range(500)
            ],
        ]:
            with self.subTest(data=data):
                iterator = running_median(iter(data), maxlen=size)
                for k, rm in enumerate(iterator, start=1):
                    expected = statistics.median(data[max(0, k - size) : k])
                    self.assertEqual(rm, expected)
                    self.assertEqual(type(rm), type(expected))

        self.assertEqual(list(running_median([], maxlen=1)), [])  # Empty input

        # Window size of 1 should return the original dataset unchanged
        data = random.choices(range(-500, 500), k=500)
        self.assertEqual(list(running_median(data, maxlen=1)), data)

        # Window size of 2 is a moving average of pairs
        data = random.choices(range(-500, 500), k=500)
        expected = list(map(mean, mi.pairwise(data)))
        actual = list(islice(running_median(data, maxlen=2), 1, None))
        self.assertEqual(actual, expected)

        # A window larger than the dataset should give the same
        # result as an unbounded running median.
        data = random.choices(range(-500, 500), k=500)
        self.assertEqual(
            list(running_median(data, maxlen=600)), list(running_median(data))
        )

    def test_error_cases(self):
        running_median = mi.running_median
        with self.assertRaises(TypeError):
            running_median(1234)  # Non-iterable input
        with self.assertRaises(TypeError):
            running_median([], maxlen=3.0)  # Non-integer type for window size
        with self.assertRaises(ValueError):
            running_median([], maxlen=0)  # Invalid window size
        with self.assertRaises(TypeError):
            list(running_median([3 + 4j, 5 - 7j]))  # Unorderable input type
        with self.assertRaises(TypeError):
            list(
                running_median(['abc', 'def', 'ghi'])
            )  # Input type that doesn't support division