def require_different_values(x0, y0, x1, y1, n):
formulas = []
# TODO: return a list of logic formulas that together implement the rule
# "The values of cells (x0,y0) and (x1,y1) must be different"
for d in range(1, n + 1):
formulas.append(
Or([
And(value(x0, y0, d), Not(value(x1, y1, d))),
And(Not(value(x0, y0, d)), value(x1, y1, d))
]))
formulas = [Or(formulas)]
return formulas
def alternative_solution_finder(n=9):
formulas = []
# TODO: Return a list of formulas that, given
# a sudoku puzzle defined by clue(x,y,v) atoms and
# a solution to the puzzle defined by origvalue(x,y,v) atoms,
# finds a different solution to the sudoku expressed using value(x,y,v) atoms.
# You can assume that clue(x,y,v) -> origvalue(x,y,v) holds true.
list = []
k = int(math.sqrt(n))
for x in range(1, n + 1):
for y in range(1, n + 1):
formulas += value_exists(x, y, n)
formulas += unique_value(x, y, n)
for x0 in range(1, n + 1):
for y0 in range(1, n + 1):
for x1 in range(x0, n + 1):
for y1 in range(1, n + 1):
if x0 == x1 and y0 >= y1:
continue
if (same_row(x0, y0, x1, y1) or same_col(x0, y0, x1, y1)
or same_box(x0, y0, x1, y1, k)):
formulas += require_different_values(x0, y0, x1, y1, n)
for x in range(1, n + 1):
for y in range(1, n + 1):
for v in range(1, n + 1):
list.append(
And([
value(x, y, v),
Implies(clue(x, y, v), value(x, y, v)),
Implies(value(x, y, v), Not(origvalue(x, y, v)))
]))
formulas.append(Or(list))
return formulas
def unique_value(x, y, n):
formulas = []
# TODO: return a list of logic formulas that together implement the rule
# "There can be at most one value at position (x,y)".
for v1 in range(1, n):
for v2 in range(v1 + 1, n + 1):
formulas.append(Or([Not(value(x, y, v1)), Not(value(x, y, v2))]))
return formulas
def unique_value(x, y, n):
formulas = []
# TODO: return a list of logic formulas that together implement the rule
# "There can be at most one value at position (x,y)".
list = []
for i in range(1, n + 1):
for j in range(i + 1, n + 1):
list.append(Or(Not(value(x, y, i)), Not(value(x, y, j))))
formulas += [And(list)]
return formulas
def value_exists(x, y, n):
# Returns a list of logic formulas that together implement the rule
# "There must exist a value (between 1 and n) at position (x,y)"
# list=[Or([value(x,y,v) for v in range(1,n+1)])]
# print(list)
return [Or([value(x, y, v) for v in range(1, n + 1)])]