def dpll(circ: Circuit, assigns: Assignment = {}) -> Solution:
if len(circ) is 0:
return True, assigns
if any(len(clse) == 0 for clse in circ):
return False, {}
# do resolution
unit_a, unit_circ = unit_clause_resolution(circ)
pure_a, resolved_circ = pure_literal_elimination(unit_circ)
assigns = {**assigns, **pure_a, **unit_a}
# did resolution solve the problem
if len(resolved_circ) is 0:
return True, assigns
v = Term(circ[0][0].variable)
new_circ = rm_term(rm_clse(resolved_circ, v), -v)
sat, pot_assign = dpll(new_circ, {**assigns, **{v.variable: True}})
if sat:
return sat, pot_assign
new_circ = rm_term(rm_clse(resolved_circ, -v), v)
sat, pot_assign = dpll(new_circ, {**assigns, **{v.variable: False}})
if sat:
return sat, pot_assign
return False, {}
def random_circuit(n_vars: int, n_clause: int) -> Circuit:
variables = [f"x_{i}" for i in range(n_vars)]
circ = []
for i in range(n_clause):
vs = rd.choices(variables, k=3)
signs = rd.choices([1, -1], k=3)
circ.append(tuple(s * Term(v) for v, s in zip(vs, signs)))
return circ
def simple_dpll(circ: Circuit, assigns: Assignment = {}) -> Solution:
if len(circ) is 0:
return True, assigns
if any(len(clse) is 0 for clse in circ):
return False, {}
v = Term(circ[0][0].variable)
new_circ = rm_term(rm_clse(circ, v), -v)
sat, pot_assign = simple_dpll(new_circ, {**assigns, **{v.variable: True}})
if sat:
return sat, pot_assign
new_circ = rm_term(rm_clse(circ, -v), v)
sat, pot_assign = simple_dpll(new_circ, {**assigns, **{v.variable: False}})
if sat:
return sat, pot_assign
return False, {}
fmt = '|'.join(['%s' * n] * n)
sep = '+'.join(['-' * n] * n)
for i in range(n):
for j in range(n):
offset = (i * n + j) * n**2
print(fmt % tuple(sudoku[offset:offset+n**2]))
if i != n - 1:
print(sep)
if __name__ == "__main__":
circ = []
for point in points:
circ += exactly_one_of([Term(point + value) for value in values])
for group in groups:
for value in values:
circ += exactly_one_of([Term(point + value) for point in group])
sudoku = '53..7....6..195....98....6.8...6...34..8.3..17...2...6.6....28....419..5....8..79'
for p, s in zip(points, sudoku):
if s is not ".":
circ.append((Term(p + s), ))
with open("sudoku/sudoku_circuit.txt", "w") as f:
for c in circ:
f.write(" ".join(map(str, c)) + "\n")
def make_circ(txt: str) -> Circuit:
return [tuple(Term(t) for t in clse.split()) for clse in txt]