def test_rgs():
pytest.raises(ValueError, lambda: RGS_unrank(-1, 3))
pytest.raises(ValueError, lambda: RGS_unrank(3, 0))
pytest.raises(ValueError, lambda: RGS_unrank(10, 1))
pytest.raises(ValueError, lambda: Partition.from_rgs(list(range(3)), list(range(2))))
pytest.raises(ValueError, lambda: Partition.from_rgs(list(range(1, 3)), list(range(2))))
assert RGS_enum(-1) == 0
assert RGS_enum(1) == 1
assert RGS_unrank(7, 5) == [0, 0, 1, 0, 2]
assert RGS_unrank(23, 14) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2]
assert RGS_rank(RGS_unrank(40, 100)) == 40
def test_partitions():
ans = [[{}], [(0, {})]]
for i in range(2):
assert list(partitions(0, size=i)) == ans[i]
assert list(partitions(1, 0, size=i)) == ans[i]
assert list(partitions(6, 2, 2, size=i)) == ans[i]
assert list(partitions(6, 2, None, size=i)) != ans[i]
assert list(partitions(6, None, 2, size=i)) != ans[i]
assert list(partitions(6, 2, 0, size=i)) == ans[i]
assert [p.copy() for p in partitions(6, k=2)] == [
{2: 3}, {1: 2, 2: 2}, {1: 4, 2: 1}, {1: 6}]
assert [p.copy() for p in partitions(6, k=3)] == [
{3: 2}, {1: 1, 2: 1, 3: 1}, {1: 3, 3: 1}, {2: 3}, {1: 2, 2: 2},
{1: 4, 2: 1}, {1: 6}]
assert [p.copy() for p in partitions(8, k=4, m=3)] == [
{4: 2}, {1: 1, 3: 1, 4: 1}, {2: 2, 4: 1}, {2: 1, 3: 2}] == [
i.copy() for i in partitions(8, k=4, m=3) if all(k <= 4 for k in i)
and sum(i.values()) <= 3]
assert [p.copy() for p in partitions(Integer(3), m=2)] == [
{3: 1}, {1: 1, 2: 1}]
assert [i.copy() for i in partitions(4, k=3)] == [
{1: 1, 3: 1}, {2: 2}, {1: 2, 2: 1}, {1: 4}] == [
i.copy() for i in partitions(4) if all(k <= 3 for k in i)]
# Consistency check on output of _partitions and RGS_unrank.
# This provides a sanity test on both routines. Also verifies that
# the total number of partitions is the same in each case.
# (from pkrathmann2)
for n in range(2, 6):
i = 0
for m, q in _set_partitions(n):
assert q == RGS_unrank(i, n)
i += 1
assert i == RGS_enum(n)
def test_partitions():
assert [p.copy() for p in partitions(6, k=2)] == [{
2: 3
}, {
1: 2,
2: 2
}, {
1: 4,
2: 1
}, {
1: 6
}]
assert [p.copy() for p in partitions(6, k=3)] == [{
3: 2
}, {
1: 1,
2: 1,
3: 1
}, {
1: 3,
3: 1
}, {
2: 3
}, {
1: 2,
2: 2
}, {
1: 4,
2: 1
}, {
1: 6
}]
assert [p.copy() for p in partitions(6, k=2, m=2)] == []
assert [p.copy() for p in partitions(8, k=4, m=3)] == [{
4: 2
}, {
1: 1,
3: 1,
4: 1
}, {
2: 2,
4: 1
}, {
2: 1,
3: 2
}] == [
i.copy() for i in partitions(8, k=4, m=3)
if all(k <= 4 for k in i) and sum(i.values()) <= 3
]
assert [p.copy() for p in partitions(Integer(3), m=2)] == [{
3: 1
}, {
1: 1,
2: 1
}]
assert [i.copy() for i in partitions(4, k=3)] == [{
1: 1,
3: 1
}, {
2: 2
}, {
1: 2,
2: 1
}, {
1: 4
}] == [i.copy() for i in partitions(4) if all(k <= 3 for k in i)]
pytest.raises(ValueError, lambda: list(partitions(3, 0)))
# Consistency check on output of _partitions and RGS_unrank.
# This provides a sanity test on both routines. Also verifies that
# the total number of partitions is the same in each case.
# (from pkrathmann2)
for n in range(2, 6):
i = 0
for m, q in _set_partitions(n):
assert q == RGS_unrank(i, n)
i = i + 1
assert i == RGS_enum(n)