def test_int_payloads(self):
lattice = get_square_lattice(3)
sym = make_number_range_symbol_set(1, 9)
sg = SymbolGrid(lattice, sym)
sc = ShapeConstrainer(lattice, [
Shape([
(Vector(0, 0), 1),
(Vector(0, 1), 2),
(Vector(1, 0), 4),
]),
Shape([
(Vector(0, 1), 3),
(Vector(1, 0), 5),
(Vector(1, 1), 6),
(Vector(2, 1), 9),
]),
Shape([
(Vector(0, 0), 7),
(Vector(0, 1), 8),
]),
],
solver=sg.solver,
complete=True)
for p in lattice.points:
sg.solver.add(sg.cell_is(p, sc.shape_payload_grid[p]))
self.assertTrue(sg.solve())
solved_grid = sg.solved_grid()
for p in lattice.points:
self.assertEqual(solved_grid[p], lattice.point_to_index(p) + 1)
self.assertTrue(sg.is_unique())
def main():
"""SLICY solver example."""
sym = grilops.SymbolSet(["S", "L", "I", "C", "Y", ("W", " ")])
lattice = PointyToppedHexagonalLattice([
areas_row_col_to_point(r, c) for r in range(len(AREAS))
for c in range(len(AREAS[r]))
])
sg = grilops.SymbolGrid(lattice, sym)
rc = grilops.regions.RegionConstrainer(lattice,
solver=sg.solver,
complete=True)
sc = ShapeConstrainer(
lattice,
[
# Note that the example shapes are shown as flat-topped hexagons, so
# you need to turn the page sideways to see them as pointy-topped ones.
Shape([Vector(0, 0),
Vector(1, 1),
Vector(1, 3),
Vector(2, 4)]), # S
Shape([Vector(0, 0),
Vector(0, 2),
Vector(0, 4),
Vector(-1, 5)]), # L
Shape([Vector(0, 0),
Vector(0, 2),
Vector(0, 4),
Vector(0, 6)]), # I
Shape([Vector(0, 0),
Vector(1, 1),
Vector(1, 3),
Vector(0, 4)]), # C
Shape([Vector(0, 0),
Vector(2, 0),
Vector(1, 1),
Vector(1, 3)]), # Y
],
solver=sg.solver,
allow_rotations=True,
allow_reflections=True,
allow_copies=True)
link_symbols_to_shapes(sym, sg, sc)
add_area_constraints(lattice, sc)
add_sea_constraints(sym, sg, rc)
add_adjacent_tetrahex_constraints(lattice, sc)
if sg.solve():
sg.print()
print()
if sg.is_unique():
print("Unique solution")
else:
print("Alternate solution")
sg.print()
print()
else:
print("No solution")
def main():
"""Shape solver example."""
points = []
for y, row in enumerate(GRID):
for x, c in enumerate(row):
if c == "O":
points.append(Point(y, x))
lattice = RectangularLattice(points)
shapes = [
Shape([Vector(0, 0),
Vector(1, 0),
Vector(2, 0),
Vector(3, 0)]), # I
Shape([Vector(0, 0),
Vector(1, 0),
Vector(2, 0),
Vector(2, 1)]), # L
Shape([Vector(0, 1),
Vector(0, 2),
Vector(1, 0),
Vector(1, 1)]), # S
]
sym = grilops.SymbolSet([("B", chr(0x2588) * 2), ("W", " ")])
sg = grilops.SymbolGrid(lattice, sym)
sc = ShapeConstrainer(lattice,
shapes,
sg.solver,
complete=False,
allow_rotations=True,
allow_reflections=True,
allow_copies=False)
for p in points:
sg.solver.add(sg.cell_is(p, sym.W) == (sc.shape_type_grid[p] == -1))
for n in sg.vertex_sharing_neighbors(p):
np = n.location
sg.solver.add(
Implies(
And(sc.shape_type_grid[p] != -1,
sc.shape_type_grid[np] != -1),
sc.shape_type_grid[p] == sc.shape_type_grid[np]))
if sg.solve():
sg.print()
print()
sc.print_shape_types()
print()
if sg.is_unique():
print("Unique solution")
else:
print("Alternate solution")
sg.print()
else:
print("No solution")
def main():
"""LITS solver example."""
sym = grilops.SymbolSet(["L", "I", "T", "S", ("W", " ")])
lattice = grilops.get_rectangle_lattice(HEIGHT, WIDTH)
sg = grilops.SymbolGrid(lattice, sym)
rc = grilops.regions.RegionConstrainer(lattice, solver=sg.solver)
sc = ShapeConstrainer(
lattice,
[
Shape([Vector(0, 0),
Vector(1, 0),
Vector(2, 0),
Vector(2, 1)]), # L
Shape([Vector(0, 0),
Vector(1, 0),
Vector(2, 0),
Vector(3, 0)]), # I
Shape([Vector(0, 0),
Vector(0, 1),
Vector(0, 2),
Vector(1, 1)]), # T
Shape([Vector(0, 0),
Vector(1, 0),
Vector(1, 1),
Vector(2, 1)]), # S
],
solver=sg.solver,
allow_rotations=True,
allow_reflections=True,
allow_copies=True)
link_symbols_to_shapes(sym, sg, sc)
add_area_constraints(lattice, sc)
add_nurikabe_constraints(sym, sg, rc)
add_adjacent_tetronimo_constraints(lattice, sc)
if sg.solve():
sg.print()
print()
sc.print_shape_types()
print()
sc.print_shape_instances()
print()
if sg.is_unique():
print("Unique solution")
else:
print("Alternate solution")
sg.print()
print()
sc.print_shape_types()
print()
sc.print_shape_instances()
print()
else:
print("No solution")
def main():
"""Status Park (Loop) solver example."""
for row in GIVENS:
for cell in row:
sys.stdout.write(cell)
print()
points = []
for y, row in enumerate(GIVENS):
for x, c in enumerate(row):
if c != X:
points.append(Point(y, x))
lattice = RectangularLattice(points)
sym = grilops.loops.LoopSymbolSet(lattice)
sym.append("EMPTY", " ")
sg = grilops.SymbolGrid(lattice, sym)
grilops.loops.LoopConstrainer(sg, single_loop=True)
sc = ShapeConstrainer(
lattice, [Shape([Vector(y, x) for y, x in shape]) for shape in SHAPES],
solver=sg.solver,
allow_rotations=True,
allow_reflections=True,
allow_copies=False)
for p in points:
if GIVENS[p.y][p.x] == W:
# White circles must be part of the loop.
sg.solver.add(sym.is_loop(sg.grid[p]))
elif GIVENS[p.y][p.x] == B:
# Black circles must be part of a shape.
sg.solver.add(sc.shape_type_grid[p] != -1)
# A cell is part of the loop if and only if it is not part of
# any shape.
sg.solver.add(sym.is_loop(sg.grid[p]) == (sc.shape_type_grid[p] == -1))
# Orthogonally-adjacent cells must be part of the same shape.
for n in sg.edge_sharing_neighbors(p):
np = n.location
sg.solver.add(
Implies(
And(sc.shape_type_grid[p] != -1,
sc.shape_type_grid[np] != -1),
sc.shape_type_grid[p] == sc.shape_type_grid[np]))
if sg.solve():
sg.print()
print()
sc.print_shape_types()
print()
if sg.is_unique():
print("Unique solution")
else:
print("Alternate solution")
sg.print()
else:
print("No solution")
def test_datatype_payloads(self):
lattice = get_square_lattice(3)
sym = make_number_range_symbol_set(0, 2)
row_grid = SymbolGrid(lattice, sym)
col_grid = SymbolGrid(lattice, sym, solver=row_grid.solver)
RowCol = Datatype("RowCol")
RowCol.declare("row_col", ("row", IntSort()), ("col", IntSort()))
RowCol = RowCol.create()
sc = ShapeConstrainer(lattice, [
Shape([
(Vector(0, 0), RowCol.row_col(0, 0)),
(Vector(0, 1), RowCol.row_col(0, 1)),
(Vector(1, 0), RowCol.row_col(1, 0)),
]),
Shape([
(Vector(0, 1), RowCol.row_col(0, 2)),
(Vector(1, 0), RowCol.row_col(1, 1)),
(Vector(1, 1), RowCol.row_col(1, 2)),
(Vector(2, 1), RowCol.row_col(2, 2)),
]),
Shape([
(Vector(0, 0), RowCol.row_col(2, 0)),
(Vector(0, 1), RowCol.row_col(2, 1)),
]),
],
solver=row_grid.solver,
complete=True)
for p in lattice.points:
row_grid.solver.add(
row_grid.cell_is(p, RowCol.row(sc.shape_payload_grid[p])))
col_grid.solver.add(
col_grid.cell_is(p, RowCol.col(sc.shape_payload_grid[p])))
self.assertTrue(row_grid.solve())
solved_row_grid = row_grid.solved_grid()
solved_col_grid = col_grid.solved_grid()
for p in lattice.points:
self.assertEqual(solved_row_grid[p], p.y)
self.assertEqual(solved_col_grid[p], p.x)
self.assertTrue(row_grid.is_unique())
def test_no_payloads(self):
lattice = get_square_lattice(3)
sym = make_number_range_symbol_set(0, 2)
sg = SymbolGrid(lattice, sym)
sc = ShapeConstrainer(lattice, [
Shape([
Vector(0, 0),
Vector(0, 1),
Vector(1, 0),
]),
Shape([
Vector(0, 1),
Vector(1, 0),
Vector(1, 1),
Vector(2, 1),
]),
Shape([
Vector(0, 0),
Vector(0, 1),
]),
],
solver=sg.solver,
complete=True)
for p in lattice.points:
sg.solver.add(sg.cell_is(p, sc.shape_type_grid[p]))
self.assertTrue(sg.solve())
solved_grid = sg.solved_grid()
expected = [
[0, 0, 1],
[0, 1, 1],
[2, 2, 1],
]
for p in lattice.points:
self.assertEqual(solved_grid[p], expected[p.y][p.x])
self.assertTrue(sg.is_unique())
def main():
"""Battleship solver example."""
sg = grilops.SymbolGrid(LATTICE, SYM)
sc = ShapeConstrainer(LATTICE, [
Shape([Vector(0, i) for i in range(4)]),
Shape([Vector(0, i) for i in range(3)]),
Shape([Vector(0, i) for i in range(3)]),
Shape([Vector(0, i) for i in range(2)]),
Shape([Vector(0, i) for i in range(2)]),
Shape([Vector(0, i) for i in range(2)]),
Shape([Vector(0, i) for i in range(1)]),
Shape([Vector(0, i) for i in range(1)]),
Shape([Vector(0, i) for i in range(1)]),
],
solver=sg.solver,
allow_rotations=True)
# Constrain the given ship segment counts and ship segments.
for y, count in enumerate(GIVENS_Y):
sg.solver.add(
PbEq([(Not(sg.cell_is(Point(y, x), SYM.X)), 1)
for x in range(WIDTH)], count))
for x, count in enumerate(GIVENS_X):
sg.solver.add(
PbEq([(Not(sg.cell_is(Point(y, x), SYM.X)), 1)
for y in range(HEIGHT)], count))
for p, s in GIVENS.items():
sg.solver.add(sg.cell_is(p, s))
for p in LATTICE.points:
shape_type = sc.shape_type_grid[p]
shape_id = sc.shape_instance_grid[p]
touching_types = [
n.symbol
for n in LATTICE.vertex_sharing_neighbors(sc.shape_type_grid, p)
]
touching_ids = [
n.symbol for n in LATTICE.vertex_sharing_neighbors(
sc.shape_instance_grid, p)
]
# Link the X symbol to the absence of a ship segment.
sg.solver.add((sc.shape_type_grid[p] == -1) == sg.cell_is(p, SYM.X))
# Ship segments of different ships may not touch.
and_terms = []
for touching_id in touching_ids:
and_terms.append(
Implies(shape_id >= 0,
Or(touching_id == shape_id, touching_id == -1)))
sg.solver.add(And(*and_terms))
# Choose the correct symbol for each ship segment.
touching_count_terms = [(c == shape_type, 1) for c in touching_types]
sg.solver.add(
Implies(And(shape_type >= 0, PbEq(touching_count_terms, 2)),
sg.cell_is(p, SYM.B)))
sg.solver.add(
Implies(And(shape_type >= 0, PbEq(touching_count_terms, 0)),
sg.cell_is(p, SYM.O)))
for n in sg.edge_sharing_neighbors(p):
sg.solver.add(
Implies(
And(shape_type >= 0, PbEq(touching_count_terms, 1),
sc.shape_type_grid[n.location] == shape_type),
sg.cell_is(p, DIR_TO_OPPOSITE_SYM[n.direction])))
if sg.solve():
sg.print()
print()
sc.print_shape_instances()
print()
if sg.is_unique():
print("Unique solution")
else:
print("Alternate solution")
sg.print()
print()
sc.print_shape_instances()
print()
else:
print("No solution")
LetterColor.declare("letter_color", ("letter", IntSort()),
("color", IntSort()))
LetterColor = LetterColor.create()
def letter_color(letter: str, color: Color) -> ExprRef:
"""Creates a LetterColor z3 constant."""
return LetterColor.letter_color(SYM[letter],
color.value) # type: ignore[attr-defined]
SHAPES: List[Shape] = [
Shape([
(Vector(0, 1), letter_color("R", Color.BLUE)),
(Vector(1, 0), letter_color("R", Color.BLUE)),
(Vector(1, 1), letter_color("E", Color.BLUE)),
(Vector(1, 2), letter_color("V", Color.BLUE)),
(Vector(2, 1), letter_color("R", Color.BLUE)),
]),
Shape([
(Vector(0, 0), letter_color("E", Color.WHITE)),
(Vector(0, 1), letter_color("R", Color.WHITE)),
(Vector(0, 2), letter_color("S", Color.YELLOW)),
(Vector(1, 0), letter_color("A", Color.BLUE)),
(Vector(1, 2), letter_color("O", Color.BLUE)),
]),
Shape([
(Vector(0, 0), letter_color("C", Color.YELLOW)),
(Vector(0, 1), letter_color("L", Color.YELLOW)),
(Vector(1, 1), letter_color("F", Color.YELLOW)),
(Vector(1, 2), letter_color("E", Color.BLUE)),