def test_factorize(number):
if number == 0:
with pytest.raises(ValueError):
factorize(number)
else:
factors = factorize(number)
product = 1
for factor in factors:
product *= factor
assert product == number
def solve(n): i = 2*n log2 = math.floor(math.log(n, 2)) minSum = n + log2 minSol = () while i > minSum: factors = factorize.factorize(i) if sum(factors) > i: i -= 1 continue if len(factors) <= 1: i -= 1 continue if len(factors) == 2 and sum(factors) + n - 2 != i: i -= 1 continue print i # for factor in factors: # print "\t" + str(factor) if sum(factors) + n - len(factors) == i: minSol = min(minSol, i) print "\tsolution: " + str(i) i -= 1 continue if valid(i, n): minSol = min(minSol, i) print "\tsolution: " + str(i) i -= 1 print "min: " + str(n) + " => " + str(minSol)
def test_factorize_multiplication_property(n):
"""The product of the integers returned by factorize(n) needs to be n."""
factors = factorize(n)
product = 1
for factor in factors:
product *= factor
assert product == n, f"factorize({n}) returned {factors}"
def test_simple_numbers(self):
""" Что для простых чисел 3, 13, 29 возвращается кортеж, содержащий одно данное число. """
cases = [3, 13, 29]
for x in cases:
with self.subTest(x=x):
result = factorize(x)
self.assertEqual(result, (x, ))
def factors_count(n, pfactors=[], primes=[2]):
if pfactors == []:
pfactors = factorize(n, primes)
product = 1
for i in pfactors.keys():
product *= pfactors[i] + 1
return product
def test_zero_and_one_cases(self):
""" Что для числа 0 возвращается кортеж (0,), а для числа 1 кортеж (1,) """
cases = [0, 1]
for x in cases:
with self.subTest(x=x):
result = factorize(x)
self.assertEqual(result, (x, ))
def test_factorize(self):
for n in range(2, 100):
product = reduce(lambda r, f: r * (f[0]**f[1]), factorize(n), 1)
self.assertTrue(
n == product,
"{} != {}, i.e. product of its factorization".format(
n, product))
def test_two_simple_multipliers(self):
""" Что для чисел 6, 26, 121 возвращаются соответственно кортежи (2, 3), (2, 13) и (11, 11). """
cases = {6: (2, 3), 26: (2, 13), 121: (11, 11)}
for x in cases:
with self.subTest(x=x):
result = factorize(x)
self.assertEqual(result, cases[x])
def test_many_multipliers(self):
""" Что для чисел 1001 и 9699690 возвращаются соответственно кортежи (7, 11, 13) и (2, 3, 5, 7, 11, 13, 17,
19). """
cases = {1001: (7, 11, 13), 9699690: (2, 3, 5, 7, 11, 13, 17, 19)}
for x in cases:
with self.subTest(x=x):
result = factorize(x)
self.assertEqual(result, cases[x])
def rsaDecode(cipherBlocks, e, n): factors = factorize.factorize(n) # will be a 2-tuple for RSA phi = (factors[0] - 1) * (factors[1] - 1) d = modInverse(e, phi) plainBlocks = [] for c in cipherBlocks: pb = 1 for i in range(0, d): # up to but not including the power pb = (pb * c) % n plainBlocks.append(pb) return numConvert(blockToNum(plainBlocks))
def smallest(bound):
so_far = 1
primelist = primes2(1000000)
primeset = set(primelist)
for i in xrange(1, len(primeset)):
# i+2 arbitrarily chosen because it happens to give correct answer
for n in combinations_with_replacement(primelist[0:i], i+2):
n = reduce(mul, n)
den = n-1
if n in primeset: num = n-1
else: num = reduce(mul, [(a-1) * a**(len(list(b))-1)
for a,b in groupby(factorize(n), lambda x: x)])
r = num/float(den)
so_far = min(so_far, r)
if so_far == r: print n, bound, r, "%d/%d" % (num,den)
if r < bound: return n
def smallest(bound):
so_far = 1
primelist = primes2(1000000)
primeset = set(primelist)
for i in xrange(1, len(primeset)):
# i+2 arbitrarily chosen because it happens to give correct answer
for n in combinations_with_replacement(primelist[0:i], i + 2):
n = reduce(mul, n)
den = n - 1
if n in primeset: num = n - 1
else:
num = reduce(mul,
[(a - 1) * a**(len(list(b)) - 1)
for a, b in groupby(factorize(n), lambda x: x)])
r = num / float(den)
so_far = min(so_far, r)
if so_far == r: print n, bound, r, "%d/%d" % (num, den)
if r < bound: return n
import factorize max = 0 for factor in factorize.factorize(600851475143): if factor > max: max = factor print factor print "max: " + str(max)
def test_factorize_12():
assert factorize(12) == [2, 2, 3]
def test_factorize_minus_12():
assert factorize(-12) == [-1, 2, 2, 3]
def test_cubed():
assert_equals(factorize(27), [3, 3, 3])
def test_two():
assert_equals(factorize(2), [2])
def sigma(n):
pfactors = factorize(n)
product = 1
for i in pfactors.keys():
product *= (i ** (pfactors[i] + 1) - 1) / (i - 1)
return product
def test_factorize(n, expected):
assert factorize(n) == expected
def test_simple_numbers(self):
test_cases = (3, 13, 29)
for x in test_cases:
with self.subTest(x=x):
self.assertEqual(factorize(x), (x, ))
def test_two_simple_multipliers(self):
test_cases = ((6, (2, 3)), (26, (2, 13)), (121, (11, 11)))
for x, exp in test_cases:
with self.subTest(x=x):
self.assertEqual(factorize(x), exp)
def test_prime():
assert_equals(factorize(5), [5])
#
# from src/factoriz.c
#
# void factorize(int) to factorize
# factorize to factorizeG
# factorize to factorizeL
#
from factorize import factorize, factorizeG, factorizeL
for i in range(1, 101):
print("{0:5d} = ".format(i), end="")
factorize(i)
print("{0:5d} = ".format(i), end="")
print(" * ".join(map(str, factorizeG(i))))
print("{0:5d} = ".format(i), end="")
print(" * ".join(factorizeG(i, fmt=str)))
print("{0:5d} = ".format(i), end="")
print(" * ".join(map(str, factorizeL(i))))
print("{0:5d} = ".format(i), end="")
print(" * ".join(factorizeL(i, fmt=str)))
def test_single_factor():
assert_equals(factorize(9), [3, 3])
def test_multi_factor():
assert_equals(factorize(21), [3, 7])
def test_multi_factor_repeats():
assert_equals(factorize(147), [3, 7, 7])
def totient(n):
t = n
f = factorize.factorize(n, p_list)
for (p, r) in f:
t = t // p * (p - 1)
return t
def test_many_multipliers(self):
test_cases = (1001, (7, 11, 13), (9699690, (2, 3, 5, 7, 11, 13, 17,
19)))
for x, exp in test_cases:
with self.subTest(x=x):
self.assertEqual(factorize(x), exp)
from factorize import primes, factorize
print(list(primes(5)))
# prints [2, 3, 5, 7, 11]
print(list(primes(limit=100)))
# prints [2, 3, ..., 89, 97]
start = time()
for factor in factorize(2595925957847039):
print(factor, time() - start)
# prints something like this:
# 38047 0.641836404800415
# 140281 6.760272264480591
# 486377 6.760589838027954
# Factors are generated on the fly, so it takes some time until each of them is
# ready to process
def test_wrong_types_raise_exception(self):
test_cases = (1.5, 'string')
for x in test_cases:
with self.subTest(x=x):
with self.assertRaises(TypeError):
factorize(x)
def test_factorize():
assert factorize(99) == {11: 1, 3: 2}
assert factorize(90) == {2: 1, 3: 2, 5: 1}
from pandas import DataFrame
import retrieve_data, grapher, subset, factorize, neural.solve
from keras.utils import to_categorical
# datavoter = retrieve_data.getData("./data/ncvoter_Statewide.txt", "./data/ncvoter_Statewide.pickle",
# filt=['county_desc', 'status_cd', 'voter_status_desc', 'reason_cd', 'voter_status_reason_desc',
# 'mail_city', 'ethnic_code', 'party_cd', 'gender_code', 'birth_age', 'birth_state', 'drivers_lic',
# 'precinct_abbrv', 'municipality_abbrv', 'cong_dist_abbrv', 'super_court_abbrv',
# 'judic_dist_abbrv', 'nc_senate_abbrv', 'nc_house_abbrv',
# 'munic_dist_abbrv', 'dist_1_abbrv', 'birth_year', 'vtd_abbrv'])
filt = [
'county_id', 'birth_age', 'party_cd', 'gender_code', 'race_code',
'birth_state'
]
datavoter = factorize.factorize(
retrieve_data.getData("./data/ncvoter_Statewide.txt",
"./data/ncvoter_Statewide.pickle",
filt=filt))
print("Done!")
parties = [1, 2]
X = datavoter[datavoter.party_cd.isin(parties)][[
'county_id', 'birth_age', 'gender_code', 'race_code', 'birth_state'
]]
y = datavoter[datavoter.party_cd.isin(parties)]['party_cd'] - 1
print(X, y)
neural.solve.train(X, y)
# this is a dictionary. Key = name. Value = count
def test_negative(self):
test_cases = (-1, -10, -100)
for x in test_cases:
with self.subTest(x=x):
with self.assertRaises(ValueError):
factorize(x)
def test_larger_prime():
assert_equals(factorize(13), [13])
def coprime_count(n,factors=[],primes=[2]): if factors == []: factors = factorize(n,primes=primes) for i in factors.iterkeys(): n = int(n*(1-1.0/i)) return n
def test_zero_and_one_cases(self):
test_cases = (0, 1)
for x in test_cases:
with self.subTest(x=x):
self.assertEqual(factorize(x), (x, ))
