def test_prime_factorization(self):
values = Arithmetic.prime_factorization(1)
msg = 'Prime factorization for 1'
exp = np.array([])
self.assertListEqual(list(exp), list(values), msg)
values = Arithmetic.prime_factorization(3)
msg = 'Prime factorization for 3'
exp = np.array([3])
self.assertListEqual(list(exp), list(values), msg)
values = Arithmetic.prime_factorization(6)
msg = 'Prime factorization for 3'
exp = np.array([2, 3])
self.assertListEqual(list(exp), list(values), msg)
values = Arithmetic.prime_factorization(10)
msg = 'Prime factorization for 3'
exp = np.array([2, 5])
self.assertListEqual(list(exp), list(values), msg)
values = Arithmetic.prime_factorization(15)
msg = 'Prime factorization for 3'
exp = np.array([3, 5])
self.assertListEqual(list(exp), list(values), msg)
def find_solution(self):
"""
This method contains the guts of finding the solution.
The timer starts just prior to calling this method
and stops just after returning the solution's value.
"""
# What number to we want to include up to.
up_to = 20
# Initialize the prime factors for the solution
factors = np.array([])
# Starting at 1 and going up to the up_to limit,
# Calculate the prime factorization for each item
# If the facotrs have already been accounted for, we're
# all set.
#
# Ex: from 2 to 7 the factors array would include
# [ 2, 2, 3, 5, 7 ]
# The prime factorization for 8 is 2 * 2 * 2.
# The factors array already has 2's but not three
# of them so add one more.
# [ 2, 2, 2, 3, 5, 7 ]
for item in range(2, up_to + 1):
# Get the prime factorization for "item"
primes = Arithmetic.prime_factorization(item)
for factor in primes:
# if the factor is not present or there are not enough
# of them append another one on
if sum(factors == factor) < sum(primes == factor):
factors = np.append(factors, factor)
# Final answer is the product of the accumulated primes
return np.prod(factors)
def find_solution(self):
"""
This method contains the guts of finding the solution.
The timer starts just prior to calling this method
and stops just after returning the solution's value.
"""
value = 600851475143
factors = Arithmetic.prime_factorization(value)
if not np.prod(factors) == value:
print 'ERROR'
return "%d" % factors[-1]
