def arithmetic(puzzle="SEND+MORE=MONEY", base=10) -> None:
problem = re.split(r"[\s+=]", puzzle)
# remove spaces
problem = list(filter(lambda w: len(w) > 0, problem))
letters = {
letter: facile.variable(range(base))
for letter in set("".join(problem))
}
# expressions
expr_pb = [[letters[a] for a in word] for word in problem]
def horner(a: Expression, b: Expression):
return 10 * a + b
words = [reduce(horner, word) for word in expr_pb]
# constraints
facile.constraint(facile.alldifferent(letters.values()))
facile.constraint(facile.sum(words[:-1]) == words[-1])
for word in expr_pb:
facile.constraint(word[0] > 0)
assert facile.solve(letters.values())
# print solutions
for word, numbers in zip(problem, expr_pb):
strings = [str(n.value()) for n in numbers]
print(f"{word} = {''.join(strings)}")
def print_current(sol):
print("Solution after {} backtracks:".format(sol.backtrack))
for i, x in enumerate(sol.solution):
if x == 0:
continue
print(" {} × {:<20} : {:>5}".format(x, products[i], x * price[i]))
total = sum(x * price[i] for i, x in enumerate(sol.solution))
print(" Total : {:>5}".format(total))
def test_magical() -> None:
array = [facile.variable(range(10)) for i in range(10)]
for i in range(10):
sum_ = facile.sum(x == i for x in array)
facile.constraint(sum_ == array[i])
solution = facile.solve(array)
assert solution.solved
assert solution.solution == [6, 2, 1, 0, 0, 0, 1, 0, 0, 0]
def coins(values, maxval) -> Optional[Solution]:
"""
Which coins do you need to give back change for any amount between 0 and
maxval, using coins from values?
"""
# How many coin types
n = len(values)
nb_min_coins = [variable(range(maxval // values[i])) for i in range(n)]
for val in range(maxval):
# How many coins per type
nb_coins = [variable(range(maxval // values[i])) for i in range(n)]
mysum = sum([x[0] * x[1] for x in zip(values, nb_coins)])
constraint(mysum == val)
for j in range(len(nb_coins)):
constraint(nb_coins[j] <= nb_min_coins[j])
total = variable(sum(nb_min_coins))
return minimize(nb_min_coins, total)
import facile
# Magical sequence!
# The value inside array[i] is equal to the number of i in array
array = [facile.variable(range(10)) for i in range(10)]
for i in range(10):
facile.constraint(facile.sum(x == i for x in array) == array[i])
if facile.solve(array):
print([v.value() for v in array])
# Agatha hates everybody except the butler.
constraint(hates[agatha, charles] == 1)
constraint(hates[agatha, agatha] == 1)
constraint(hates[agatha, butler] == 0)
# The butler hates everyone not richer than Aunt Agatha.
# (richer[i, agatha] = 0) => (hates[butler, i] = 1),
for i in range(n):
constraint((richer[i, agatha] == 0) <= (hates[butler, i] == 1))
# The butler hates everyone whom Agatha hates.
# (hates[agatha, i] = 1) => (hates[butler, i] = 1),
for i in range(n):
constraint((hates[agatha, i] == 1) <= (hates[butler, i] == 1))
# No one hates everyone.
# (sum j: hates[i, j]) <= 2,
for i in range(n):
constraint(sum([hates[i, j] for j in range(n)]) <= 2)
# Who killed Agatha?
constraint(victim == agatha)
assert solve(list(hates) + list(richer) + [victim, killer])
killer_value = killer.value()
assert killer_value is not None
msg = "{} killed Agatha."
print(msg.format(["Agatha", "The butler", "Charles"][killer_value]))
buckets = [
[variable(range(capacity[b] + 1)) for b in range(nb)] for i in range(steps)
]
constraint(buckets[0][0] == 8)
constraint(buckets[0][1] == 0)
constraint(buckets[0][2] == 0)
constraint(buckets[steps - 1][0] == 4)
constraint(buckets[steps - 1][1] == 4)
constraint(buckets[steps - 1][2] == 0)
for i in range(steps - 1):
# we change the contents of two buckets at a time
sum_buckets = sum([buckets[i][b] != buckets[i + 1][b] for b in range(nb)])
constraint(sum_buckets == 2)
# we play with a constant amount of water
sum_water = sum([buckets[i][b] for b in range(nb)])
constraint(sum_water == 8)
for b1 in range(nb):
for b2 in range(b1):
constraint(
# either the content of the bucket does not change
(buckets[i][b1] == buckets[i + 1][b1])
| (buckets[i][b2] == buckets[i + 1][b2])
|
# or the bucket ends up empty or full
(buckets[i + 1][b1] == 0)
| (buckets[i + 1][b1] == capacity[b1])
| (buckets[i + 1][b2] == 0)
for i in range(nb_weeks):
# [1] Use a Sorting Constraint (redundant with [2])
s = groups[i, :].sort()
for j in range(nb_golfers):
facile.constraint(s[j] == j // size_group)
# [2] Use a Global Cardinality Constraint (redundant with [1])
gcc = groups[i, :].gcc([(size_group, i) for i in range(nb_groups)])
facile.constraint(gcc)
# Two golfers do not play in the same group more than once
for g1 in range(nb_golfers):
for g2 in range(g1 + 1, nb_golfers):
g1_with_g2 = [groups[w, g1] == groups[w, g2] for w in range(nb_weeks)]
facile.constraint(facile.sum(g1_with_g2) <= 1)
# Breaking the symmetries
# - 0 always in the first group, 1 in a group less than 1, ...
# - First week (0) a priori chosen
for w in range(nb_weeks):
for g in range(nb_groups):
facile.constraint(groups[w, g] <= g)
for g in range(nb_golfers):
facile.constraint(groups[0, g] == g // size_group)
if not facile.solve(list(groups)):
print("No solution found")
else:
price = [215, 275, 335, 355, 420, 580]
total = 1505
products = [
"mixed fruit",
"french fries",
"side salad",
"host wings",
"mozzarella sticks",
"samples place",
]
# how many items of each dish
quantity = [variable(range(10)) for p in price]
constraint(sum(q * p for q, p in zip(quantity, price)) == total)
def print_current(sol):
print("Solution after {} backtracks:".format(sol.backtrack))
for i, x in enumerate(sol.solution):
if x == 0:
continue
print(" {} × {:<20} : {:>5}".format(x, products[i], x * price[i]))
total = sum(x * price[i] for i, x in enumerate(sol.solution))
print(" Total : {:>5}".format(total))
res = solve_all(quantity, backtrack=True, on_solution=print_current)
print("Total of {} backtracks".format(res[-1].backtrack))
information.
"""
from facile import Variable, constraint, sum
row_sums = [0, 0, 8, 2, 6, 4, 5, 3, 7, 0, 0]
col_sums = [0, 0, 7, 1, 6, 3, 4, 5, 2, 7, 0, 0]
rows = len(row_sums)
cols = len(col_sums)
x = [[Variable.binary() for j in col_sums] for i in row_sums]
for i in range(rows):
constraint(sum(x[i][j] for j in range(cols)) == row_sums[i])
for j in range(cols):
constraint(sum(x[i][j] for i in range(rows)) == col_sums[j])
def print_solution():
print(" ", end=" ")
for j in range(cols):
print(col_sums[j], end=" ")
print()
for i in range(rows):
print(row_sums[i], end=" ")
for j in range(cols):
if x[i][j].value() == 1:
print("#", end=" ")
else: