def test_Linear():
l = Linear([(3, 1), (2, -4), (4, 5)], 12)
l2 = Linear([(3, 1), (2, -4), (4, 5)], 12)
l3 = Linear([(3, 2), (2, -4), (4, 5)], 12)
l4 = Linear([(3, 1), (2, -4), (4, 5)], 11)
assert l == l
assert l == l2
assert l != l3
assert l != l4
assert l.equation == ((2, -4), (3, 1), (4, 5))
assert l.lo == l.hi == l.rhs == 12
assert l.coeffs == [2, 3, 4]
assert l.atoms == [-4, 1, 5]
assert l.total == 9
assert len(l) == 3
# Remember that the equation is sorted
assert l[1:] == Linear([(3, 1), (4, 5)], 12)
assert str(l) == repr(l) == "Linear(((2, -4), (3, 1), (4, 5)), 12)"
l = Linear([(3, 1), (2, -4), (4, 5)], [3, 5])
assert l != l2
assert l != l3
assert l != l4
assert l.equation == ((2, -4), (3, 1), (4, 5))
assert l.lo == 3
assert l.hi == 5
assert l.rhs == [3, 5]
assert l.coeffs == [2, 3, 4]
assert l.atoms == [-4, 1, 5]
assert l.total == 9
assert len(l) == 3
assert l([1, 2, 3, 4, 5]) == False
assert l([1, 2, 3, 4, -5]) == True
assert l([1, 2, 3, -4, -5]) == True
assert l([-1, -2, -3, -4, -5]) == False
assert l([-1, 2, 3, 4, -5]) == False
# Remember that the equation is sorted
assert l[1:] == Linear([(3, 1), (4, 5)], [3, 5])
assert str(l) == repr(l) == "Linear(((2, -4), (3, 1), (4, 5)), [3, 5])"
l = Linear([], [1, 3])
assert l.equation == ()
assert l.lo == 1
assert l.hi == 3
assert l.coeffs == []
assert l.atoms == []
assert l.total == 0
assert l([1, 2, 3]) == False
def test_sorter():
L = [
Linear([(1, 1), (2, 2)], [0, 2]),
Linear([(1, 1), (2, -2)], [0, 2]),
Linear([(1, 1), (2, 2), (3, 3)], [3, 3]),
Linear([(0, 1), (1, 2), (2, 3), (0, 4), (1, 5), (0, 6), (1, 7)],
[0, 2])
]
for l in L:
C = Clauses(max(l.atoms))
m = C.build_sorter(l)
if l.rhs[0]:
x = {(m[l.rhs[0] - 1], ), (-m[l.rhs[1]], )}
nx = {(-m[l.rhs[0] - 1], m[l.rhs[1]])}
else:
x = {(-m[l.rhs[1]], )}
nx = {(m[l.rhs[1]], )}
for sol in my_itersolve(x | C.clauses):
assert l(sol)
for sol in my_itersolve(nx | C.clauses):
assert not l(sol)
l = Linear([(1, 15), (2, 16), (3, 17), (4, 18), (5, 6), (5, 19), (6, 7),
(6, 20), (7, 8), (7, 21), (7, 28), (8, 9), (8, 22), (8, 29),
(8, 41), (9, 10), (9, 23), (9, 30), (9, 42), (10, 1), (10, 11),
(10, 24), (10, 31), (10, 34), (10, 37), (10, 43), (10, 46),
(10, 50), (11, 2), (11, 12), (11, 25), (11, 32), (11, 35),
(11, 38), (11, 44), (11, 47), (11, 51), (12, 3), (12, 4),
(12, 5), (12, 13), (12, 14), (12, 26), (12, 27), (12, 33),
(12, 36), (12, 39), (12, 40), (12, 45), (12, 48), (12, 49),
(12, 52), (12, 53), (12, 54)], [192, 204])
C = Clauses(max(l.atoms))
m = C.build_sorter(l)
if l.rhs[0]:
x = {(m[l.rhs[0] - 1], ), (-m[l.rhs[1]], )}
nx = {(-m[l.rhs[0] - 1], m[l.rhs[1]])}
else:
x = {(-m[l.rhs[1]], )}
nx = {(m[l.rhs[1]], )}
for sol, _ in zip(my_itersolve(x | C.clauses), range(2)):
assert l(sol)
for sol, _ in zip(my_itersolve(nx | C.clauses), range(2)):
assert not l(sol)
l = Linear([(0, 12), (0, 14), (0, 22), (0, 59), (0, 60), (0, 68), (0, 102),
(0, 105), (0, 164), (0, 176), (0, 178), (0, 180), (0, 182),
(1, 9), (1, 13), (1, 21), (1, 58), (1, 67), (1, 101), (1, 104),
(1, 163), (1, 175), (1, 177), (1, 179), (1, 181), (2, 6),
(2, 20), (2, 57), (2, 66), (2, 100), (2, 103), (2, 162),
(2, 174), (3, 11), (3, 19), (3, 56), (3, 65), (3, 99),
(3, 161), (3, 173), (4, 8), (4, 18), (4, 55), (4, 64), (4, 98),
(4, 160), (4, 172), (5, 5), (5, 17), (5, 54), (5, 63), (5, 97),
(5, 159), (5, 171), (6, 10),
(6, 16), (6, 52), (6, 62), (6, 96), (6, 158), (6, 170), (7, 7),
(7, 15), (7, 50), (7, 61), (7, 95), (7, 157), (7, 169), (8, 4),
(8, 48), (8, 94), (8, 156), (8, 168), (9, 3), (9, 46), (9, 93),
(9, 155), (9, 167), (10, 2), (10, 53), (10, 92), (10, 154),
(10, 166), (11, 1), (11, 51), (11, 91), (11, 152), (11, 165),
(12, 49), (12, 90), (12, 150), (13, 47), (13, 89), (13, 148),
(14, 45), (14, 88), (14, 146), (15, 39), (15, 87), (15, 144),
(16, 38), (16, 86), (16, 142), (17, 37), (17, 85), (17, 140),
(18, 44), (18, 84), (18, 138), (19, 43), (19, 83), (19, 153),
(20, 42), (20, 82), (20, 151), (21, 41), (21, 81), (21, 149),
(22, 40), (22, 80), (22, 147), (23, 36), (23, 79), (23, 145),
(24, 32), (24, 70), (24, 143), (25, 35), (25, 78), (25, 141),
(26, 34), (26, 77), (26, 139), (27, 31), (27, 76), (27, 137),
(28, 30), (28, 75), (28, 136), (29, 33), (29, 74), (29, 135),
(30, 29), (30, 73), (30, 134), (31, 28), (31, 72), (31, 133),
(32, 27), (32, 71), (32, 132), (33, 25), (33, 69), (33, 131),
(34, 24), (34, 130), (35, 26), (35, 129), (36, 23), (36, 128),
(37, 125), (38, 124), (39, 123), (40, 122), (41, 121),
(42, 120), (43, 119), (44, 118), (45, 117), (46, 116),
(47, 115), (48, 114), (49, 113), (50, 127), (51, 126),
(52, 112), (53, 111), (54, 110), (55, 109), (56, 108),
(57, 107), (58, 106)], [21, 40])
C = Clauses(max(l.atoms))
print('building sorter')
m = C.build_sorter(l)
if l.rhs[0]:
x = {(m[l.rhs[0] - 1], ), (-m[l.rhs[1]], )}
nx = {(-m[l.rhs[0] - 1], m[l.rhs[1]])}
else:
x = {(-m[l.rhs[1]], )}
nx = {(m[l.rhs[1]], )}
print('checking positive solutions')
for sol, _ in zip(my_itersolve(x | C.clauses), range(2)):
assert l(sol)
print('checking negative solutions')
for sol, _ in zip(my_itersolve(nx | C.clauses), range(2)):
assert not l(sol)
C = Clauses(0)
assert C.build_sorter([]) == []
assert not C.clauses
def test_BDD():
L = [
Linear([(1, 1), (2, 2)], [0, 2]),
Linear([(1, 1), (2, -2)], [0, 2]),
Linear([(1, 1), (2, 2), (3, 3)], [3, 3]),
Linear([(0, 1), (1, 2), (2, 3), (0, 4), (1, 5), (0, 6), (1, 7)],
[0, 2])
]
for l in L:
Cr = Clauses(max(l.atoms))
Crneg = Clauses(max(l.atoms))
Crpos = Clauses(max(l.atoms))
xr = Cr.build_BDD_recursive(l)
xrneg = Crneg.build_BDD_recursive(l, polarity=False)
xrpos = Crpos.build_BDD_recursive(l, polarity=True)
C = Clauses(max(l.atoms))
Cneg = Clauses(max(l.atoms))
Cpos = Clauses(max(l.atoms))
x = C.build_BDD(l)
xneg = Cneg.build_BDD(l, polarity=False)
xpos = Cpos.build_BDD(l, polarity=True)
assert x == xr
assert xneg == xrneg
assert xpos == xrpos
assert C.clauses == Cr.clauses
assert Cneg.clauses == Crneg.clauses
assert Cpos.clauses == Crpos.clauses
for sol in chain(my_itersolve({(x, )} | C.clauses),
my_itersolve({(xpos, )} | Cpos.clauses)):
assert l(sol)
for sol in chain(my_itersolve({(-x, )} | C.clauses),
my_itersolve({(-xneg, )} | Cneg.clauses)):
assert not l(sol)
# Real life example. There are too many solutions to check them all, just
# check that building the BDD doesn't take forever
l = Linear([(1, 15), (2, 16), (3, 17), (4, 18), (5, 6), (5, 19), (6, 7),
(6, 20), (7, 8), (7, 21), (7, 28), (8, 9), (8, 22), (8, 29),
(8, 41), (9, 10), (9, 23), (9, 30), (9, 42), (10, 1), (10, 11),
(10, 24), (10, 31), (10, 34), (10, 37), (10, 43), (10, 46),
(10, 50), (11, 2), (11, 12), (11, 25), (11, 32), (11, 35),
(11, 38), (11, 44), (11, 47), (11, 51), (12, 3), (12, 4),
(12, 5), (12, 13), (12, 14), (12, 26), (12, 27), (12, 33),
(12, 36), (12, 39), (12, 40), (12, 45), (12, 48), (12, 49),
(12, 52), (12, 53), (12, 54)], [192, 204])
Cr = Clauses(max(l.atoms))
Crneg = Clauses(max(l.atoms))
Crpos = Clauses(max(l.atoms))
xr = Cr.build_BDD_recursive(l)
xrneg = Crneg.build_BDD_recursive(l, polarity=False)
xrpos = Crpos.build_BDD_recursive(l, polarity=True)
C = Clauses(max(l.atoms))
Cneg = Clauses(max(l.atoms))
Cpos = Clauses(max(l.atoms))
x = C.build_BDD(l)
xneg = Cneg.build_BDD(l, polarity=False)
xpos = Cpos.build_BDD(l, polarity=True)
assert x == xr
assert xneg == xrneg
assert xpos == xrpos
assert C.clauses == Cr.clauses
assert Cneg.clauses == Crneg.clauses
assert Cpos.clauses == Crpos.clauses
for _, sol in zip(range(20), my_itersolve({(x, )} | C.clauses)):
assert l(sol)
for _, sol in zip(range(20), my_itersolve({(-x, )} | C.clauses)):
assert not l(sol)
for _, sol in zip(range(20), my_itersolve({(xpos, )} | Cpos.clauses)):
assert l(sol)
for _, sol in zip(range(20), my_itersolve({(-xneg, )} | Cneg.clauses)):
assert not l(sol)
# Another real-life example. This one is too big to be built recursively
# unless the recursion limit is increased.
l = Linear([(0, 12), (0, 14), (0, 22), (0, 59), (0, 60), (0, 68), (0, 102),
(0, 105), (0, 164), (0, 176), (0, 178), (0, 180), (0, 182),
(1, 9), (1, 13), (1, 21), (1, 58), (1, 67), (1, 101), (1, 104),
(1, 163), (1, 175), (1, 177), (1, 179), (1, 181), (2, 6),
(2, 20), (2, 57), (2, 66), (2, 100), (2, 103), (2, 162),
(2, 174), (3, 11), (3, 19), (3, 56), (3, 65), (3, 99),
(3, 161), (3, 173), (4, 8), (4, 18), (4, 55), (4, 64), (4, 98),
(4, 160), (4, 172), (5, 5), (5, 17), (5, 54), (5, 63), (5, 97),
(5, 159), (5, 171), (6, 10),
(6, 16), (6, 52), (6, 62), (6, 96), (6, 158), (6, 170), (7, 7),
(7, 15), (7, 50), (7, 61), (7, 95), (7, 157), (7, 169), (8, 4),
(8, 48), (8, 94), (8, 156), (8, 168), (9, 3), (9, 46), (9, 93),
(9, 155), (9, 167), (10, 2), (10, 53), (10, 92), (10, 154),
(10, 166), (11, 1), (11, 51), (11, 91), (11, 152), (11, 165),
(12, 49), (12, 90), (12, 150), (13, 47), (13, 89), (13, 148),
(14, 45), (14, 88), (14, 146), (15, 39), (15, 87), (15, 144),
(16, 38), (16, 86), (16, 142), (17, 37), (17, 85), (17, 140),
(18, 44), (18, 84), (18, 138), (19, 43), (19, 83), (19, 153),
(20, 42), (20, 82), (20, 151), (21, 41), (21, 81), (21, 149),
(22, 40), (22, 80), (22, 147), (23, 36), (23, 79), (23, 145),
(24, 32), (24, 70), (24, 143), (25, 35), (25, 78), (25, 141),
(26, 34), (26, 77), (26, 139), (27, 31), (27, 76), (27, 137),
(28, 30), (28, 75), (28, 136), (29, 33), (29, 74), (29, 135),
(30, 29), (30, 73), (30, 134), (31, 28), (31, 72), (31, 133),
(32, 27), (32, 71), (32, 132), (33, 25), (33, 69), (33, 131),
(34, 24), (34, 130), (35, 26), (35, 129), (36, 23), (36, 128),
(37, 125), (38, 124), (39, 123), (40, 122), (41, 121),
(42, 120), (43, 119), (44, 118), (45, 117), (46, 116),
(47, 115), (48, 114), (49, 113), (50, 127), (51, 126),
(52, 112), (53, 111), (54, 110), (55, 109), (56, 108),
(57, 107), (58, 106)], [21, 40])
C = Clauses(max(l.atoms))
Cpos = Clauses(max(l.atoms))
Cneg = Clauses(max(l.atoms))
x = C.build_BDD(l)
xpos = Cpos.build_BDD(l, polarity=True)
xneg = Cneg.build_BDD(l, polarity=False)
for _, sol in zip(range(20), my_itersolve({(x, )} | C.clauses)):
assert l(sol)
for _, sol in zip(range(20), my_itersolve({(-x, )} | C.clauses)):
assert not l(sol)
for _, sol in zip(range(20), my_itersolve({(xpos, )} | Cpos.clauses)):
assert l(sol)
for _, sol in zip(range(20), my_itersolve({(-xneg, )} | Cneg.clauses)):
assert not l(sol)