def queen_conditions(not_x, i, j, n):
queen = Robdd.make_x(index_of(i, j))
# creates the rule "none in the same column"
a = Robdd.true()
for y in range(1, n + 1):
if y == j: continue
a_ = synth(queen, Bdd.IMPL, not_x[(i, y)])
a = synth(a, Bdd.AND, a_)
# creates the rule "none in the same line"
b = Robdd.true()
for x in range(1, n + 1):
if x == i: continue
b_ = synth(queen, Bdd.IMPL, not_x[(x, j)])
b = synth(b, Bdd.AND, b_)
# creates the rule "none in the diagonals"
c = Robdd.true()
x = 1
while (i - x) > 0 and (j - x) > 0:
c_ = synth(queen, Bdd.IMPL, not_x[(i - x, j - x)])
c = synth(c, Bdd.AND, c_)
x += 1
x = 1
while (i + x) <= n and (j + x) <= n:
c_ = synth(queen, Bdd.IMPL, not_x[(i + x, j + x)])
c = synth(c, Bdd.AND, c_)
x += 1
d = Robdd.true()
x = 1
while (i - x) > 0 and (j + x) <= n:
d_ = synth(queen, Bdd.IMPL, not_x[(i - x, j + x)])
d = synth(d, Bdd.AND, d_)
x += 1
x = 1
while (i + x) <= n and (j - x) > 0:
d_ = synth(queen, Bdd.IMPL, not_x[(i + x, j - x)])
d = synth(d, Bdd.AND, d_)
x += 1
return synth(synth(a, Bdd.AND, b), Bdd.AND, synth(c, Bdd.AND, d))
def queen_conditions(not_x, i, j, n) :
queen = Robdd.make_x(index_of(i, j))
# creates the rule "none in the same column"
a = Robdd.true()
for y in range(1, n + 1) :
if y == j : continue
a_ = synth(queen, Bdd.IMPL, not_x[(i, y)])
a = synth(a, Bdd.AND, a_)
# creates the rule "none in the same line"
b = Robdd.true()
for x in range(1, n + 1) :
if x == i : continue
b_ = synth(queen, Bdd.IMPL, not_x[(x, j)])
b = synth(b, Bdd.AND, b_)
# creates the rule "none in the diagonals"
c = Robdd.true()
x = 1
while (i - x) > 0 and (j - x) > 0 :
c_ = synth(queen, Bdd.IMPL, not_x[(i - x, j - x)])
c = synth(c, Bdd.AND, c_)
x += 1
x = 1
while (i + x) <= n and (j + x) <= n :
c_ = synth(queen, Bdd.IMPL, not_x[(i + x, j + x)])
c = synth(c, Bdd.AND, c_)
x += 1
d = Robdd.true()
x = 1
while (i - x) > 0 and (j + x) <= n :
d_ = synth(queen, Bdd.IMPL, not_x[(i - x, j + x)])
d = synth(d, Bdd.AND, d_)
x += 1
x = 1
while (i + x) <= n and (j - x) > 0 :
d_ = synth(queen, Bdd.IMPL, not_x[(i + x, j - x)])
d = synth(d, Bdd.AND, d_)
x += 1
return synth(synth(a, Bdd.AND, b), Bdd.AND, synth(c, Bdd.AND, d))
def queens(n):
solution = Robdd.true()
# create the rule "there must be at least one queen at each line"
for j in range(1, n + 1):
line = Robdd.false()
for i in range(1, n + 1):
queen = Robdd.make_x(index_of(i, j))
line = synth(line, Bdd.OR, queen)
solution = synth(solution, Bdd.AND, line)
# create a list of "NOT" expressions
not_expressions = {}
for j in range(1, n + 1):
for i in range(1, n + 1):
not_expressions[(i, j)] = Robdd.make_not_x(index_of(i, j))
# create conditions for each position
for j in range(1, n + 1):
for i in range(1, n + 1):
queen = queen_conditions(not_expressions, i, j, n)
solution = synth(solution, Bdd.AND, queen)
return solution
def queens(n):
solution = Robdd.true()
# create the rule "there must be at least one queen at each line"
for j in range(1, n + 1):
line = Robdd.false()
for i in range(1, n + 1):
queen = Robdd.make_x(index_of(i, j))
line = synth(line, Bdd.OR, queen)
solution = synth(solution, Bdd.AND, line)
# create a list of "NOT" expressions
not_expressions = {}
for j in range(1, n + 1):
for i in range(1, n + 1):
not_expressions[(i, j)] = Robdd.make_not_x(index_of(i, j))
# create conditions for each position
for j in range(1, n + 1):
for i in range(1, n + 1):
queen = queen_conditions(not_expressions, i, j, n)
solution = synth(solution, Bdd.AND, queen)
return solution
def negate_bdd(bdd):
neg_bdd = synthesize(bdd, Bdd.AND, Robdd.true())
for i in xrange(len(neg_bdd.items)):
neg_bdd.items[i] = tuple((neg_bdd.items[i][0],
not neg_bdd.items[i][1] if neg_bdd.items[i][1] in (True, False) else neg_bdd.items[i][
1],
not neg_bdd.items[i][2] if neg_bdd.items[i][2] in (True, False) else neg_bdd.items[i][
2]))
# invert root, if root is a leaf
if neg_bdd.root in (0, 1):
neg_bdd.root ^= 1
return neg_bdd
def negate_bdd(bdd):
neg_bdd = synthesize(bdd, Bdd.AND, Robdd.true())
for i in xrange(len(neg_bdd.items)):
neg_bdd.items[i] = tuple(
(neg_bdd.items[i][0], not neg_bdd.items[i][1]
if neg_bdd.items[i][1] in (True, False) else neg_bdd.items[i][1],
not neg_bdd.items[i][2]
if neg_bdd.items[i][2] in (True, False) else neg_bdd.items[i][2]))
# invert root, if root is a leaf
if neg_bdd.root in (0, 1):
neg_bdd.root ^= 1
return neg_bdd
def add_restriction(s):
r = Robdd.true()
for i, b in enumerate(s):
# if i == 0:
# continue
# if i >= 8 :
# continue
if b == '1':
current_var = Robdd.make_x(i)
else:
current_var = Robdd.make_not_x(i)
r = synth(r, Bdd.AND, current_var)
return r
def test_evaluate_should_always_return_true(self):
robdd = Robdd.true()
self.assertTrue(robdd.evaluate([0]))
self.assertTrue(robdd.evaluate([1]))
self.assertTrue(robdd.evaluate([0, 0]))
self.assertTrue(robdd.evaluate([0, 1, 1, 0]))
