def part2():
with ManyLineInput('./input.txt', Ingredient) as data:
answer = max([
product2(list(zip(data, partition)))
for partition in partitions(len(data), 100)
])
print(f"part 2: {answer}")
def describe_moment_polynomial(syms, moments_x, moment_y, alpha, b):
"""
Computes the moment polynomial for E[x^alpha, y^b]
"""
D = len(syms)
expr = -moment_y
coeffs = sp.ntheory.multinomial_coefficients(D, b)
for beta in partitions(D, b):
expr += coeffs[beta] * monomial(syms, beta) * moments_x[tuple_add(alpha, beta)]
return expr
def describe_moment_polynomial(syms, moments_x, moment_y, alpha, b):
"""
Computes the moment polynomial for E[x^alpha, y^b]
"""
D = len(syms)
expr = -moment_y
coeffs = sp.ntheory.multinomial_coefficients(D, b)
for beta in partitions(D, b):
expr += coeffs[beta] * monomial(syms, beta) * moments_x[tuple_add(
alpha, beta)]
return expr
def compute_exact_y_moments(ws, pis, moments_x, alpha, b):
"""
Compute the exact moments E[x^a y^b] using coefficients ws, pis and moments_x.
"""
D, _ = ws.shape
coeffs = sp.ntheory.multinomial_coefficients(D, b)
ret = 0.
for beta in partitions(D, b):
ret += coeffs[beta] * evaluate_mixture(ws, pis, beta) * moments_x[tuple_add(alpha, beta)]
return ret
def compute_exact_y_moments(ws, pis, moments_x, alpha, b):
"""
Compute the exact moments E[x^a y^b] using coefficients ws, pis and moments_x.
"""
D, _ = ws.shape
coeffs = sp.ntheory.multinomial_coefficients(D, b)
ret = 0.
for beta in partitions(D, b):
ret += coeffs[beta] * evaluate_mixture(
ws, pis, beta) * moments_x[tuple_add(alpha, beta)]
return ret
def test_partitions():
try:
partitions([1, 2, 3, 4], 0)
raise AssertionError("Expected ValueError")
except ValueError:
pass
try:
partitions([1, 2, 3, 4], -1)
raise AssertionError("Expected ValueError")
except ValueError:
pass
# strings
assert partitions("abcd", 1) == 4
assert partitions("abcd", 2) == 2
assert partitions("abcd", 3) == 2
assert partitions("_ä__", 2) == 2
assert partitions("", 1) == 0
# lists
assert partitions([1, 2, 3, 4], 1) == 4
assert partitions([1, 2, 3, 4], 2) == 2
assert partitions([1, 2, 3, 4], 3) == 2
assert partitions([], 1) == 0
