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 remove_interval_up(original, s):
r = Robdd.false()
for i, b in enumerate(s):
if b == '0':
current_var = Robdd.make_x(i)
r = synth(r, Bdd.OR, current_var)
return synth(original, Bdd.AND, r)
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 add_negated(s):
r = Robdd.false()
for i, b in enumerate(s):
# if i == 0:
# continue
# if i >= 8:
# continue
if b == '0':
current_var = Robdd.make_x(i)
else:
current_var = Robdd.make_not_x(i)
r = synth(r, Bdd.OR, current_var)
return r
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))
