def testSums(self):
"""Check that all outputs are partitions of the input."""
for n in range(len(self.counts)):
for p in mckay(n):
self.assertEqual(n, sum(p))
for p in revlex_partitions(n):
self.assertEqual(n, sum(p))
for p in lex_partitions(n):
self.assertEqual(n, sum(p))
def testRevLex(self):
"""Check that the revlex generators' outputs are in revlex order."""
for n in range(len(self.counts)):
last = [n + 1]
for p in mckay(n):
self.assertGreater(last, p)
last = list(p) # make less-mutable copy
last = [n + 1]
for p in revlex_partitions(n):
self.assertGreater(last, p)
last = list(p) # make less-mutable copy
def testFixedLength(self):
"""Check that the fixed length partition outputs are correct."""
for n in range(len(self.counts)):
pn = [list(p) for p in revlex_partitions(n)]
pn.sort()
np = 0
for L in range(n + 1):
pnL = [list(p) for p in fixed_length_partitions(n, L)]
pnL.sort()
np += len(pnL)
self.assertEqual(pnL, [p for p in pn if len(p) == L])
self.assertEqual(np, len(pn))
def testRange(self):
"""Check that all numbers in output partitions are in range."""
for n in range(len(self.counts)):
for p in mckay(n):
for x in p:
self.assertLess(0, x)
self.assertLessEqual(x, n)
for p in lex_partitions(n):
for x in p:
self.assertLess(0, x)
self.assertLessEqual(x, n)
for p in revlex_partitions(n):
for x in p:
self.assertLess(0, x)
self.assertLessEqual(x, n)
def testCounts(self):
"""Check that each generator has the right number of outputs."""
for n in range(len(self.counts)):
self.assertEqual(self.counts[n], len(list(mckay(n))))
self.assertEqual(self.counts[n], len(list(lex_partitions(n))))
self.assertEqual(self.counts[n], len(list(revlex_partitions(n))))