def exactly_one(lx, ly, lnb, whole):
""" Returns a Logics object that represents a set of logics formulas which only allows one of all cases (x,y,nb) ,x in lx, y in ly and nb in lnb to be right. If whole is False, it will only return 2 clauses for incompatibilities """
logics = Logics()
#Global clause (at least 1)
if whole:
c = Clause([])
for x in lx:
for y in ly:
for nb in lnb:
v = Var(x, y, nb)
c.add(Literal(v, 1))
logics += c
#Specific clauses (minus than 1)
for x in lx:
for x2 in lx:
for y in ly:
for y2 in ly:
for nb in lnb:
for nb2 in lnb:
if (x, y, nb) > (x2, y2, nb2):
v1 = Var(x, y, nb)
v2 = Var(x2, y2, nb2)
l1 = Literal(v1, -1)
l2 = Literal(v2, -1)
c = Clause([l1, l2])
logics += c
return logics
def get_grid_logics_data(self):
logics = Logics()
#Use grid data
for y, line in enumerate(self.grid):
for x, nb in enumerate(line):
if nb != 0:
logics += Clause([Literal(Var(x, y, nb - 1), 1)])
return logics
def get_logics(self):
logics = Logics()
#Cases
for i in range(9):
for j in range(9):
logics += exactly_one([i], [j], range(0, 9), True)
#Lines
for j in range(9):
for nb in range(0, 9):
logics += exactly_one(range(9), [j], [nb], False)
#Column
for i in range(9):
for nb in range(0, 9):
logics += exactly_one([i], range(9), [nb], False)
#Square
for s in range(3):
for s2 in range(3):
for nb in range(0, 9):
logics += exactly_one(range(3 * s, 3 * (s + 1)),
range(3 * s2, 3 * (s2 + 1)), [nb],
False)
return logics + self.get_grid_logics_data()
