def smallest_continuous_multiple(max_multiple):
"""
Function takes an int, and returns the smallest natural number evenly divisible by all numbers
less than or equal to the input max_multiple.
REQ: max_multiple >= 0 and whole
:param max_multiple: {int}
:return: smallest natural number evenly divisible by all number less than or equal to input
Function reduces time complexity by iteratively removing redundant factors from the
check_list, ie. suppose 12 exists in the list, then 6, 4, 3, 2 and 1 will have been removed.
This check is done to remove the factors of every int, to reduce the lookup time later.
"""
# all numbers less than or equal to 2 are evenly divisible by themselves and below
if max_multiple <= 2:
return max_multiple
check_list = []
# make a list of all ints from 1 to input
for i in range(max_multiple):
check_list.append(i + 1)
# loop through check list backwards
for i in reversed(check_list):
# get factors of i without i included
temp_factors = get_factors(i)
temp_factors.remove(i)
# loop through the remaining factors, removing them from the check_list
for j in temp_factors:
try:
check_list.remove(j)
except ValueError:
pass
temp_num = max_multiple
# loop indefinitely until find smallest int that that satisfies exit condition
while True:
# if all factors less than max_multiple divide evenly into curr, return
if all(temp_num % n == 0 for n in check_list):
return temp_num
else:
temp_num += max_multiple
def test_input_zero(self):
self.assertEqual(get_factors(0), None)
def test_large_non_prime(self):
self.assertEqual(get_factors(100), {1, 2, 4, 5, 10, 20, 25, 50, 100})
def test_small_non_prime(self):
self.assertEqual(get_factors(12), {1, 2, 3, 4, 6, 12})
def test_large_prime(self):
self.assertEqual(get_factors(97), {1, 97})
def test_small_prime(self):
self.assertEqual(get_factors(7), {1, 7})
def test_input_one(self):
self.assertEqual(get_factors(1), {1})