def subrange_exercise(mult, lb, ub):
"""Compare filter-based and more optimized subrange implementations
Helper for tests, called with both small and larger multisets.
"""
m = MultisetPartitionTraverser()
assert m.count_partitions(mult) == \
m.count_partitions_slow(mult)
# Note - multiple traversals from the same
# MultisetPartitionTraverser object cannot execute at the same
# time, hence make several instances here.
ma = MultisetPartitionTraverser()
mc = MultisetPartitionTraverser()
md = MultisetPartitionTraverser()
# Several paths to compute just the size two partitions
a_it = ma.enum_range(mult, lb, ub)
b_it = part_range_filter(multiset_partitions_taocp(mult), lb, ub)
c_it = part_range_filter(mc.enum_small(mult, ub), lb, sum(mult))
d_it = part_range_filter(md.enum_large(mult, lb), 0, ub)
for sa, sb, sc, sd in zip_longest(a_it, b_it, c_it, d_it):
assert compare_multiset_states(sa, sb)
assert compare_multiset_states(sa, sc)
assert compare_multiset_states(sa, sd)
def subrange_exercise(mult, lb, ub):
"""Compare filter-based and more optimized subrange implementations
Helper for tests, called with both small and larger multisets.
"""
m = MultisetPartitionTraverser()
assert m.count_partitions(mult) == \
m.count_partitions_slow(mult)
# Note - multiple traversals from the same
# MultisetPartitionTraverser object cannot execute at the same
# time, hence make several instances here.
ma = MultisetPartitionTraverser()
mc = MultisetPartitionTraverser()
md = MultisetPartitionTraverser()
# Several paths to compute just the size two partitions
a_it = ma.enum_range(mult, lb, ub)
b_it = part_range_filter(multiset_partitions_taocp(mult), lb, ub)
c_it = part_range_filter(mc.enum_small(mult, ub), lb, sum(mult))
d_it = part_range_filter(md.enum_large(mult, lb), 0, ub)
for sa, sb, sc, sd in zip_longest(a_it, b_it, c_it, d_it):
assert compare_multiset_states(sa, sb)
assert compare_multiset_states(sa, sc)
assert compare_multiset_states(sa, sd)
def test_multiset_partitions_versions():
"""Compares Knuth-based versions of multiset_partitions"""
multiplicities = [5, 2, 2, 1]
m = MultisetPartitionTraverser()
for s1, s2 in zip_longest(m.enum_all(multiplicities),
multiset_partitions_taocp(multiplicities)):
assert compare_multiset_states(s1, s2)
def test_multiset_partitions_versions():
"""Compares Knuth-based versions of multiset_partitions"""
multiplicities = [5,2,2,1]
m = MultisetPartitionTraverser()
for s1, s2 in zip_longest(m.enum_all(multiplicities),
multiset_partitions_taocp(multiplicities)):
assert compare_multiset_states(s1, s2)
def to_NNF(expr):
"""
Generates the Negation Normal Form of any boolean expression in terms
of AND, OR, and Literal objects.
"""
if isinstance(expr, Not):
arg = expr.args[0]
tmp = to_NNF(arg) # Strategy: negate the NNF of expr
return ~tmp
if isinstance(expr, Or):
return OR(*[to_NNF(x) for x in Or.make_args(expr)])
if isinstance(expr, And):
return AND(*[to_NNF(x) for x in And.make_args(expr)])
if isinstance(expr, Nand):
tmp = AND(*[to_NNF(x) for x in expr.args])
return ~tmp
if isinstance(expr, Nor):
tmp = OR(*[to_NNF(x) for x in expr.args])
return ~tmp
if isinstance(expr, Xor):
cnfs = []
for i in range(0, len(expr.args) + 1, 2):
for neg in combinations(expr.args, i):
clause = [~to_NNF(s) if s in neg else to_NNF(s)
for s in expr.args]
cnfs.append(OR(*clause))
return AND(*cnfs)
if isinstance(expr, Xnor):
cnfs = []
for i in range(0, len(expr.args) + 1, 2):
for neg in combinations(expr.args, i):
clause = [~to_NNF(s) if s in neg else to_NNF(s)
for s in expr.args]
cnfs.append(OR(*clause))
return ~AND(*cnfs)
if isinstance(expr, Implies):
L, R = to_NNF(expr.args[0]), to_NNF(expr.args[1])
return OR(~L, R)
if isinstance(expr, Equivalent):
cnfs = []
for a, b in zip_longest(expr.args, expr.args[1:], fillvalue=expr.args[0]):
a = to_NNF(a)
b = to_NNF(b)
cnfs.append(OR(~a, b))
return AND(*cnfs)
if isinstance(expr, ITE):
L = to_NNF(expr.args[0])
M = to_NNF(expr.args[1])
R = to_NNF(expr.args[2])
return AND(OR(~L, M), OR(L, R))
else:
return Literal(expr)
