本文整理汇总了Python中sympy.utilities.iterables.multiset_partitions函数的典型用法代码示例。如果您正苦于以下问题：Python multiset_partitions函数的具体用法？Python multiset_partitions怎么用？Python multiset_partitions使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了multiset_partitions函数的8个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于我们的系统推荐出更棒的Python代码示例。
示例1: test_multiset_partitions
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, 2], [1, 2]], [[1, 1], [1, 2, 2]], [[1], [1, 1, 2, 2]], [[1, 2],\
[1, 1, 2]], [[1, 1, 2, 2], [1]], [[1, 2, 2], [1, 1]]]
assert list(multiset_partitions([1,1,2,2], 2)) == [[[1, 1, 2], [2]], \
[[1, 2], [1, 2]], [[1], [1, 2, 2]], [[1, 1], [2, 2]], [[1, 2, 2], [1]]]
assert list(multiset_partitions([1,2,3,4], 2)) == [[[1, 2, 3], [4]], [[1, 3], \
[2, 4]], [[1], [2, 3, 4]], [[1, 2], [3, 4]], [[1, 2, 4], [3]], \
[[1, 4], [2, 3]], [[1, 3, 4], [2]]]
assert list(multiset_partitions([1,2,2], 2)) == [[[1, 2], [2]],
[[1], [2, 2]]]
开发者ID:dyao-vu，项目名称:meta-core，代码行数:21，代码来源:test_iterables.py
示例2: nT
def nT(n, k=None):
"""Return the number of ``k``-sized partitions of ``n`` items.
Possible values for ``n``::
integer - ``n`` identical items
sequence - converted to a multiset internally
multiset - {element: multiplicity}
Note: the convention for ``nT`` is different than that of ``nC`` and``nP`` in that
here an integer indicates ``n`` *identical* items instead of a set of
length ``n``; this is in keepng with the ``partitions`` function which
treats its integer-``n`` input like a list of ``n`` 1s. One can use
``range(n)`` for ``n`` to indicate ``n`` distinct items.
If ``k`` is None then the total number of ways to partition the elements
represented in ``n`` will be returned.
Examples
========
>>> from sympy.functions.combinatorial.numbers import nT
Partitions of the given multiset:
>>> [nT('aabbc', i) for i in range(1, 7)]
[1, 8, 11, 5, 1, 0]
>>> nT('aabbc') == sum(_)
True
(TODO The following can be activated with >>> when
taocp_multiset_permutation is in place.)
>> [nT("mississippi", i) for i in range(1, 12)]
[1, 74, 609, 1521, 1768, 1224, 579, 197, 50, 9, 1]
Partitions when all items are identical:
>>> [nT(5, i) for i in range(1, 6)]
[1, 2, 2, 1, 1]
>>> nT('1'*5) == sum(_)
True
When all items are different:
>>> [nT(range(5), i) for i in range(1, 6)]
[1, 15, 25, 10, 1]
>>> nT(range(5)) == sum(_)
True
References
==========
.. [1] http://undergraduate.csse.uwa.edu.au/units/CITS7209/partition.pdf
See Also
========
sympy.utilities.iterables.partitions
sympy.utilities.iterables.multiset_partitions
"""
from sympy.utilities.iterables import multiset_partitions
if isinstance(n, SYMPY_INTS):
# assert n >= 0
# all the same
if k is None:
return sum(_nT(n, k) for k in range(1, n + 1))
return _nT(n, k)
if not isinstance(n, _MultisetHistogram):
try:
# if n contains hashable items there is some
# quick handling that can be done
u = len(set(n))
if u == 1:
return nT(len(n), k)
elif u == len(n):
n = range(u)
raise TypeError
except TypeError:
n = _multiset_histogram(n)
N = n[_N]
if k is None and N == 1:
return 1
if k in (1, N):
return 1
if k == 2 or N == 2 and k is None:
m, r = divmod(N, 2)
rv = sum(nC(n, i) for i in range(1, m + 1))
if not r:
rv -= nC(n, m)//2
if k is None:
rv += 1 # for k == 1
return rv
if N == n[_ITEMS]:
# all distinct
if k is None:
return bell(N)
return stirling(N, k)
if k is None:
return sum(nT(n, k) for k in range(1, N + 1))
tot = 0
#.........这里部分代码省略.........
开发者ID:Zulko，项目名称:sympy，代码行数:101，代码来源:numbers.py
示例3: test_multiset_partitions
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]]]
开发者ID:Acebulf，项目名称:sympy，代码行数:46，代码来源:test_iterables.py
示例4: test_multiset_partitions
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
开发者ID:Krastanov，项目名称:sympy，代码行数:64，代码来源:test_iterables.py
示例5: test_nC_nP_nT
def test_nC_nP_nT():
from sympy.utilities.iterables import (
multiset_permutations, multiset_combinations, multiset_partitions,
partitions, subsets, permutations)
from sympy.functions.combinatorial.numbers import (
nP, nC, nT, stirling, _multiset_histogram, _AOP_product)
from sympy.combinatorics.permutations import Permutation
from sympy.core.numbers import oo
from random import choice
c = string.ascii_lowercase
for i in range(100):
s = ''.join(choice(c) for i in range(7))
u = len(s) == len(set(s))
try:
tot = 0
for i in range(8):
check = nP(s, i)
tot += check
assert len(list(multiset_permutations(s, i))) == check
if u:
assert nP(len(s), i) == check
assert nP(s) == tot
except AssertionError:
print(s, i, 'failed perm test')
raise ValueError()
for i in range(100):
s = ''.join(choice(c) for i in range(7))
u = len(s) == len(set(s))
try:
tot = 0
for i in range(8):
check = nC(s, i)
tot += check
assert len(list(multiset_combinations(s, i))) == check
if u:
assert nC(len(s), i) == check
assert nC(s) == tot
if u:
assert nC(len(s)) == tot
except AssertionError:
print(s, i, 'failed combo test')
raise ValueError()
for i in range(1, 10):
tot = 0
for j in range(1, i + 2):
check = nT(i, j)
tot += check
assert sum(1 for p in partitions(i, j, size=True) if p[0] == j) == check
assert nT(i) == tot
for i in range(1, 10):
tot = 0
for j in range(1, i + 2):
check = nT(range(i), j)
tot += check
assert len(list(multiset_partitions(range(i), j))) == check
assert nT(range(i)) == tot
for i in range(100):
s = ''.join(choice(c) for i in range(7))
u = len(s) == len(set(s))
try:
tot = 0
for i in range(1, 8):
check = nT(s, i)
tot += check
assert len(list(multiset_partitions(s, i))) == check
if u:
assert nT(range(len(s)), i) == check
if u:
assert nT(range(len(s))) == tot
assert nT(s) == tot
except AssertionError:
print(s, i, 'failed partition test')
raise ValueError()
# tests for Stirling numbers of the first kind that are not tested in the
# above
assert [stirling(9, i, kind=1) for i in range(11)] == [
0, 40320, 109584, 118124, 67284, 22449, 4536, 546, 36, 1, 0]
perms = list(permutations(range(4)))
assert [sum(1 for p in perms if Permutation(p).cycles == i)
for i in range(5)] == [0, 6, 11, 6, 1] == [
stirling(4, i, kind=1) for i in range(5)]
# http://oeis.org/A008275
assert [stirling(n, k, signed=1)
for n in range(10) for k in range(1, n + 1)] == [
1, -1,
1, 2, -3,
1, -6, 11, -6,
1, 24, -50, 35, -10,
1, -120, 274, -225, 85, -15,
1, 720, -1764, 1624, -735, 175, -21,
1, -5040, 13068, -13132, 6769, -1960, 322, -28,
1, 40320, -109584, 118124, -67284, 22449, -4536, 546, -36, 1]
# http://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind
assert [stirling(n, k, kind=1)
#.........这里部分代码省略.........
开发者ID:B-Rich，项目名称:sympy，代码行数:101，代码来源:test_comb_numbers.py
示例6: _generate_partitions
def _generate_partitions(self, list_for_par):
for p in multiset_partitions(range(len(list_for_par)), m=len(list_for_par)/2):
# keep partitions of size = 2
if all([(len(k) == 2) for k in p]):
# retrieve index in original list
yield [[list_for_par[i] for i in k] for k in p]
开发者ID:lukauskas，项目名称:means，代码行数:6，代码来源:closure_normal.py
示例7: test_multiset_partitions
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)))
开发者ID:skolwind，项目名称:sympy，代码行数:40，代码来源:test_iterables.py
示例8: test_multiset_partitions
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]]]
开发者ID:rae1，项目名称:sympy，代码行数:52，代码来源:test_iterables.py
注：本文中的sympy.utilities.iterables.multiset_partitions函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。 |
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