def multipartitions(x, count, incl_ones):
if not isinstance(x, int) or not isinstance(count, int)\
or not isinstance(incl_ones, int):
raise FunctionError('multipartitions: unsupported argument type')
if x <= 0 or count <= 0:
raise FunctionError('multipartitions: x and count must be positive')
primes, multiplicities = zip(*sympy.factorint(x).items())
mtp = sue.MultisetPartitionTraverser()
if incl_ones:
it = mtp.enum_small(multiplicities, count)
else:
it = mtp.enum_range(multiplicities, count - 1, count)
it = map(lambda x: sue.factoring_visitor(x, primes), it)
if incl_ones:
it = map(lambda x: tuple(list(x) + [1] * (count - len(x))), it)
it = toolz.concat(map(sui.multiset_permutations, it))
return it
def test_multiset_partitions():
A = [0, 1, 2, 3, 4]
assert list(multiset_partitions(A, 5)) == [[[0], [1], [2], [3], [4]]]
assert len(list(multiset_partitions(A, 4))) == 10
assert len(list(multiset_partitions(A, 3))) == 25
assert list(multiset_partitions([1, 1, 1, 2, 2],
2)) == [[[1, 1, 1, 2], [2]],
[[1, 1, 1], [2, 2]],
[[1, 1, 2, 2], [1]],
[[1, 1, 2], [1, 2]],
[[1, 1], [1, 2, 2]]]
assert list(multiset_partitions([1, 1, 2, 2], 2)) == [[[1, 1, 2], [2]],
[[1, 1], [2, 2]],
[[1, 2, 2], [1]],
[[1, 2], [1, 2]]]
assert list(multiset_partitions([1, 2, 3, 4], 2)) == [[[1, 2, 3], [4]],
[[1, 2, 4], [3]],
[[1, 2], [3, 4]],
[[1, 3, 4], [2]],
[[1, 3], [2, 4]],
[[1, 4], [2, 3]],
[[1], [2, 3, 4]]]
assert list(multiset_partitions([1, 2, 2], 2)) == [[[1, 2], [2]],
[[1], [2, 2]]]
assert list(multiset_partitions(3)) == [[[0, 1, 2]], [[0, 1], [2]],
[[0, 2], [1]], [[0], [1, 2]],
[[0], [1], [2]]]
assert list(multiset_partitions(3, 2)) == [[[0, 1], [2]], [[0, 2], [1]],
[[0], [1, 2]]]
assert list(multiset_partitions([1] * 3, 2)) == [[[1], [1, 1]]]
assert list(multiset_partitions([1] * 3)) == [[[1, 1, 1]], [[1], [1, 1]],
[[1], [1], [1]]]
a = [3, 2, 1]
assert list(multiset_partitions(a)) == \
list(multiset_partitions(sorted(a)))
assert list(multiset_partitions(a, 5)) == []
assert list(multiset_partitions(a, 1)) == [[[1, 2, 3]]]
assert list(multiset_partitions(a + [4], 5)) == []
assert list(multiset_partitions(a + [4], 1)) == [[[1, 2, 3, 4]]]
assert list(multiset_partitions(2, 5)) == []
assert list(multiset_partitions(2, 1)) == [[[0, 1]]]
assert list(multiset_partitions('a')) == [[['a']]]
assert list(multiset_partitions('a', 2)) == []
assert list(multiset_partitions('ab')) == [[['a', 'b']], [['a'], ['b']]]
assert list(multiset_partitions('ab', 1)) == [[['a', 'b']]]
assert list(multiset_partitions('aaa', 1)) == [['aaa']]
assert list(multiset_partitions([1, 1], 1)) == [[[1, 1]]]
ans = [('mpsyy', ), ('mpsy', 'y'), ('mps', 'yy'), ('mps', 'y', 'y'),
('mpyy', 's'), ('mpy', 'sy'), ('mpy', 's', 'y'), ('mp', 'syy'),
('mp', 'sy', 'y'), ('mp', 's', 'yy'), ('mp', 's', 'y', 'y'),
('msyy', 'p'), ('msy', 'py'), ('msy', 'p', 'y'), ('ms', 'pyy'),
('ms', 'py', 'y'), ('ms', 'p', 'yy'), ('ms', 'p', 'y', 'y'),
('myy', 'ps'), ('myy', 'p', 's'), ('my', 'psy'), ('my', 'ps', 'y'),
('my', 'py', 's'), ('my', 'p', 'sy'), ('my', 'p', 's', 'y'),
('m', 'psyy'), ('m', 'psy', 'y'), ('m', 'ps', 'yy'),
('m', 'ps', 'y', 'y'), ('m', 'pyy', 's'), ('m', 'py', 'sy'),
('m', 'py', 's', 'y'), ('m', 'p', 'syy'), ('m', 'p', 'sy', 'y'),
('m', 'p', 's', 'yy'), ('m', 'p', 's', 'y', 'y')]
assert list(
tuple("".join(part) for part in p)
for p in multiset_partitions('sympy')) == ans
factorings = [[24], [8, 3], [12, 2], [4, 6], [4, 2, 3], [6, 2, 2],
[2, 2, 2, 3]]
assert list(
factoring_visitor(p, [2, 3])
for p in multiset_partitions_taocp([3, 1])) == factorings
def test_multiset_partitions():
A = [0, 1, 2, 3, 4]
assert list(multiset_partitions(A, 5)) == [[[0], [1], [2], [3], [4]]]
assert len(list(multiset_partitions(A, 4))) == 10
assert len(list(multiset_partitions(A, 3))) == 25
assert list(multiset_partitions([1, 1, 1, 2, 2], 2)) == [
[[1, 1, 1, 2], [2]], [[1, 1, 1], [2, 2]], [[1, 1, 2, 2], [1]],
[[1, 1, 2], [1, 2]], [[1, 1], [1, 2, 2]]]
assert list(multiset_partitions([1, 1, 2, 2], 2)) == [
[[1, 1, 2], [2]], [[1, 1], [2, 2]], [[1, 2, 2], [1]],
[[1, 2], [1, 2]]]
assert list(multiset_partitions([1, 2, 3, 4], 2)) == [
[[1, 2, 3], [4]], [[1, 2, 4], [3]], [[1, 2], [3, 4]],
[[1, 3, 4], [2]], [[1, 3], [2, 4]], [[1, 4], [2, 3]],
[[1], [2, 3, 4]]]
assert list(multiset_partitions([1, 2, 2], 2)) == [
[[1, 2], [2]], [[1], [2, 2]]]
assert list(multiset_partitions(3)) == [
[[0, 1, 2]], [[0, 1], [2]], [[0, 2], [1]], [[0], [1, 2]],
[[0], [1], [2]]]
assert list(multiset_partitions(3, 2)) == [
[[0, 1], [2]], [[0, 2], [1]], [[0], [1, 2]]]
assert list(multiset_partitions([1] * 3, 2)) == [[[1], [1, 1]]]
assert list(multiset_partitions([1] * 3)) == [
[[1, 1, 1]], [[1], [1, 1]], [[1], [1], [1]]]
a = [3, 2, 1]
assert list(multiset_partitions(a)) == \
list(multiset_partitions(sorted(a)))
assert list(multiset_partitions(a, 5)) == []
assert list(multiset_partitions(a, 1)) == [[[1, 2, 3]]]
assert list(multiset_partitions(a + [4], 5)) == []
assert list(multiset_partitions(a + [4], 1)) == [[[1, 2, 3, 4]]]
assert list(multiset_partitions(2, 5)) == []
assert list(multiset_partitions(2, 1)) == [[[0, 1]]]
assert list(multiset_partitions('a')) == [[['a']]]
assert list(multiset_partitions('a', 2)) == []
assert list(multiset_partitions('ab')) == [[['a', 'b']], [['a'], ['b']]]
assert list(multiset_partitions('ab', 1)) == [[['a', 'b']]]
assert list(multiset_partitions('aaa', 1)) == [['aaa']]
assert list(multiset_partitions([1, 1], 1)) == [[[1, 1]]]
ans = [('mpsyy',), ('mpsy', 'y'), ('mps', 'yy'), ('mps', 'y', 'y'),
('mpyy', 's'), ('mpy', 'sy'), ('mpy', 's', 'y'), ('mp', 'syy'),
('mp', 'sy', 'y'), ('mp', 's', 'yy'), ('mp', 's', 'y', 'y'),
('msyy', 'p'), ('msy', 'py'), ('msy', 'p', 'y'), ('ms', 'pyy'),
('ms', 'py', 'y'), ('ms', 'p', 'yy'), ('ms', 'p', 'y', 'y'),
('myy', 'ps'), ('myy', 'p', 's'), ('my', 'psy'), ('my', 'ps', 'y'),
('my', 'py', 's'), ('my', 'p', 'sy'), ('my', 'p', 's', 'y'),
('m', 'psyy'), ('m', 'psy', 'y'), ('m', 'ps', 'yy'),
('m', 'ps', 'y', 'y'), ('m', 'pyy', 's'), ('m', 'py', 'sy'),
('m', 'py', 's', 'y'), ('m', 'p', 'syy'),
('m', 'p', 'sy', 'y'), ('m', 'p', 's', 'yy'),
('m', 'p', 's', 'y', 'y')]
assert list(tuple("".join(part) for part in p)
for p in multiset_partitions('sympy')) == ans
factorings = [[24], [8, 3], [12, 2], [4, 6], [4, 2, 3],
[6, 2, 2], [2, 2, 2, 3]]
assert list(factoring_visitor(p, [2,3]) for
p in multiset_partitions_taocp([3, 1])) == factorings
def test_multiset_partitions():
A = [0, 1, 2, 3, 4]
assert list(multiset_partitions(A, 5)) == [[[0], [1], [2], [3], [4]]]
assert len(list(multiset_partitions(A, 4))) == 10
assert len(list(multiset_partitions(A, 3))) == 25
assert list(multiset_partitions([1, 1, 1, 2, 2], 2)) == [
[[1, 1, 1, 2], [2]],
[[1, 1, 1], [2, 2]],
[[1, 1, 2, 2], [1]],
[[1, 1, 2], [1, 2]],
[[1, 1], [1, 2, 2]],
]
assert list(multiset_partitions([1, 1, 2, 2], 2)) == [
[[1, 1, 2], [2]],
[[1, 1], [2, 2]],
[[1, 2, 2], [1]],
[[1, 2], [1, 2]],
]
assert list(multiset_partitions([1, 2, 3, 4], 2)) == [
[[1, 2, 3], [4]],
[[1, 2, 4], [3]],
[[1, 2], [3, 4]],
[[1, 3, 4], [2]],
[[1, 3], [2, 4]],
[[1, 4], [2, 3]],
[[1], [2, 3, 4]],
]
assert list(multiset_partitions([1, 2, 2], 2)) == [[[1, 2], [2]], [[1], [2, 2]]]
assert list(multiset_partitions(3)) == [
[[0, 1, 2]],
[[0, 1], [2]],
[[0, 2], [1]],
[[0], [1, 2]],
[[0], [1], [2]],
]
assert list(multiset_partitions(3, 2)) == [
[[0, 1], [2]],
[[0, 2], [1]],
[[0], [1, 2]],
]
assert list(multiset_partitions([1] * 3, 2)) == [[[1], [1, 1]]]
assert list(multiset_partitions([1] * 3)) == [
[[1, 1, 1]],
[[1], [1, 1]],
[[1], [1], [1]],
]
a = [3, 2, 1]
assert list(multiset_partitions(a)) == list(multiset_partitions(sorted(a)))
assert list(multiset_partitions(a, 5)) == []
assert list(multiset_partitions(a, 1)) == [[[1, 2, 3]]]
assert list(multiset_partitions(a + [4], 5)) == []
assert list(multiset_partitions(a + [4], 1)) == [[[1, 2, 3, 4]]]
assert list(multiset_partitions(2, 5)) == []
assert list(multiset_partitions(2, 1)) == [[[0, 1]]]
assert list(multiset_partitions("a")) == [[["a"]]]
assert list(multiset_partitions("a", 2)) == []
assert list(multiset_partitions("ab")) == [[["a", "b"]], [["a"], ["b"]]]
assert list(multiset_partitions("ab", 1)) == [[["a", "b"]]]
assert list(multiset_partitions("aaa", 1)) == [["aaa"]]
assert list(multiset_partitions([1, 1], 1)) == [[[1, 1]]]
ans = [
("mpsyy",),
("mpsy", "y"),
("mps", "yy"),
("mps", "y", "y"),
("mpyy", "s"),
("mpy", "sy"),
("mpy", "s", "y"),
("mp", "syy"),
("mp", "sy", "y"),
("mp", "s", "yy"),
("mp", "s", "y", "y"),
("msyy", "p"),
("msy", "py"),
("msy", "p", "y"),
("ms", "pyy"),
("ms", "py", "y"),
("ms", "p", "yy"),
("ms", "p", "y", "y"),
("myy", "ps"),
("myy", "p", "s"),
("my", "psy"),
("my", "ps", "y"),
("my", "py", "s"),
("my", "p", "sy"),
("my", "p", "s", "y"),
("m", "psyy"),
("m", "psy", "y"),
("m", "ps", "yy"),
("m", "ps", "y", "y"),
("m", "pyy", "s"),
("m", "py", "sy"),
("m", "py", "s", "y"),
("m", "p", "syy"),
("m", "p", "sy", "y"),
("m", "p", "s", "yy"),
("m", "p", "s", "y", "y"),
]
assert (
list(tuple("".join(part) for part in p) for p in multiset_partitions("sympy"))
== ans
)
factorings = [[24], [8, 3], [12, 2], [4, 6], [4, 2, 3], [6, 2, 2], [2, 2, 2, 3]]
assert (
list(factoring_visitor(p, [2, 3]) for p in multiset_partitions_taocp([3, 1]))
== factorings
)
