def n_queens(n: int, *args, **kwargs) -> facile.Solution:
queens = [facile.variable(range(n)) for i in range(n)]
diag1 = [queens[i] + i for i in range(n)]
diag2 = [queens[i] - i for i in range(n)]
facile.constraint(facile.alldifferent(queens))
facile.constraint(facile.alldifferent(diag1))
facile.constraint(facile.alldifferent(diag2))
return facile.solve(queens, *args, **kwargs)
def n_queen(n):
"""Solves the n-queen problem. """
queens = [variable(0, n - 1) for i in range(n)]
diag1 = [queens[i] + i for i in range(n)]
diag2 = [queens[i] - i for i in range(n)]
constraint(alldifferent(queens))
constraint(alldifferent(diag1))
constraint(alldifferent(diag2))
if solve(queens):
return [x.value() for x in queens]
else:
return None
def n_queen(n):
"""Solves the n-queen problem. """
queens = [variable(0, n-1) for i in range(n)]
diag1 = [queens[i] + i for i in range(n)]
diag2 = [queens[i] - i for i in range(n)]
constraint(alldifferent(queens))
constraint(alldifferent(diag1))
constraint(alldifferent(diag2))
if solve(queens):
return [x.value() for x in queens]
else:
return None
def n_queen(n):
"""Solves the n-queen problem. """
queens = [variable(range(n)) for i in range(n)]
# prepare for animation
def on_bt(nb_bt):
for i, q in enumerate(queens):
print(i, q.domain())
constraint(alldifferent(queens))
constraint(alldifferent(queens[i] - i for i in range(n)))
constraint(alldifferent(queens[i] + i for i in range(n)))
return solve(queens, strategy=queen_strategy, backtrack=True)
def golomb(n):
# On peut majorer la taille de la règle par 2 ** n. En effet, si
# ticks[i] vaut 2**i alors tous les ticks[i] - ticks[j] = 2**i - 2**j
# = 2**j * (2**(i-j) - 1) qui sont tous différents.
# On a donc au moins cette solution.
n2 = 2 ** n
ticks = [facile.variable(0, n2) for i in range(n)]
# First tick at the start of the ruler
facile.constraint(ticks[0] == 0)
# Ticks are ordered
for i in range(n-1):
facile.constraint(ticks[i] < ticks[i+1])
# All distances
distances = []
for i in range(n-1):
for j in range(i + 1, n):
distances.append(ticks[j] - ticks[i])
facile.constraint(facile.alldifferent(distances))
for d in distances:
facile.constraint(d > 0)
# Breaking the symmetry
size = len(distances)
facile.constraint(distances[size - 1] > distances[0])
return (facile.minimize(ticks, ticks[n-1])[1])
def golomb(n: int) -> facile.Solution:
ticks = [facile.variable(range(2**n)) for i in range(n)]
# First tick at the start of the ruler
facile.constraint(ticks[0] == 0)
# Ticks are ordered
for i in range(n - 1):
facile.constraint(ticks[i] < ticks[i + 1])
# All distances
distances = []
for i in range(n - 1):
for j in range(i + 1, n):
distances.append(facile.variable(ticks[j] - ticks[i]))
facile.constraint(facile.alldifferent(distances))
for d in distances:
facile.constraint(d > 0)
# Breaking the symmetry
size = len(distances)
facile.constraint(distances[size - 1] > distances[0])
return facile.minimize(ticks,
ticks[n - 1],
backtrack=True,
on_solution=print)
def arithmetic(puzzle="SEND+MORE=MONEY", base=10):
problem = re.split("[\s+=]", puzzle)
# remove spaces
problem = list(filter(lambda w: len(w) > 0, problem))
# letters
letters = {l: fcl.variable(range(base)) for l in set("".join(problem))}
# expressions
expr_pb = [[letters[a] for a in word] for word in problem]
words = [reduce(lambda a, b: 10 * a + b, word) for word in expr_pb]
# constraints
fcl.constraint(fcl.alldifferent(letters.values()))
fcl.constraint(sum(words[:-1]) == words[-1])
for word in expr_pb:
fcl.constraint(word[0] > 0)
assert fcl.solve(letters.values())
# print solutions
for word, numbers in zip(problem, expr_pb):
strings = [str(n.value()) for n in numbers]
print(word + " = " + "".join(strings))
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)}")
import facile
import functools
# The list comprehension mechanism is always helpful!
[s, e, n, d, m, o, r, y] = [facile.variable(range(10)) for i in range(8)]
# A shortcut
letters = [s, e, n, d, m, o, r, y]
# Constraints
facile.constraint(s > 0)
facile.constraint(m > 0)
facile.constraint(facile.alldifferent(letters))
send = functools.reduce(lambda x, y: 10 * x + y, [s, e, n, d])
more = functools.reduce(lambda x, y: 10 * x + y, [m, o, r, e])
money = functools.reduce(lambda x, y: 10 * x + y, [m, o, n, e, y])
facile.constraint(send + more == money)
if facile.solve(letters):
[vs, ve, vn, vd, vm, vo, vr, vy] = [x.value() for x in letters]
print("Solution found :")
print
print(" %d%d%d%d" % (vs, ve, vn, vd))
print("+ %d%d%d%d" % (vm, vo, vr, ve))
print("------")
print(" %d%d%d%d%d" % (vm, vo, vn, ve, vy))
else:
print("No solution found")
# -*- coding: utf-8 -*-
"""
Basic examples of CSP problems:
- a ≠ b
- alldifferent(a, b, c) and a + b <= 2c
"""
from facile import variable, constraint, solve, alldifferent
a = variable(0, 1)
b = variable(0, 1)
constraint(a != b)
if solve([a, b]):
print("Solution found a=%d and b=%d" % (a.value(), b.value()))
a = variable(0, 2)
b = variable(0, 2)
c = variable(0, 2)
constraint(alldifferent([a, b, c]))
constraint(a + b <= 2 * c)
if solve([a, b, c]):
print("Solution found a=%d, b=%d and c=%d" %
(a.value(), b.value(), c.value()))
people = [variable(range(1, 6)) for i in range(5)] englishman, spaniard, japanese, ukrainian, norwegian = people names = ["Englishman", "Spaniard", "Japanese", "Ukrainian", "Norwegian"] animals = [variable(range(1, 6)) for i in range(5)] dog, snails, fox, zebra, horse = animals drinks = [variable(range(1, 6)) for i in range(5)] tea, coffee, water, milk, fruit_juice = drinks cigarettes = [variable(range(1, 6)) for i in range(5)] old_gold, kools, chesterfields, lucky_strike, parliaments = cigarettes constraint(alldifferent(colors)) constraint(alldifferent(people)) constraint(alldifferent(animals)) constraint(alldifferent(drinks)) constraint(alldifferent(cigarettes)) constraint(englishman == red) constraint(spaniard == dog) constraint(coffee == green) constraint(ukrainian == tea) constraint(green == ivory + 1) constraint(old_gold == snails) constraint(kools == yellow) constraint(milk == 3) constraint(norwegian == 1) constraint(abs(fox - chesterfields) == 1)
def test_overconstrained() -> None:
a, b, c = [facile.variable(0, 1) for _ in range(3)]
with pytest.raises(ValueError, match="The problem is overconstrained"):
facile.constraint(facile.alldifferent([a, b, c]))
# -*- coding: utf-8 -*-
"""
Basic examples of CSP problems:
- a ≠ b
- alldifferent(a, b, c) and a + b <= 2c
"""
from facile import variable, constraint, solve, alldifferent
a = variable(0, 1)
b = variable(0, 1)
constraint(a != b)
if solve([a, b]):
print ("Solution found a=%d and b=%d" % (a.value(), b.value()))
a = variable(0, 2)
b = variable(0, 2)
c = variable(0, 2)
constraint(alldifferent([a, b, c]))
constraint(a + b <= 2 * c)
if solve([a, b, c]):
print ("Solution found a=%d, b=%d and c=%d" %
(a.value(), b.value(), c.value()))
