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import unittest
################################################################################
# Solution
################################################################################
# f :: [Int] -> Int
def highest_product_of_3(xs):
"""Here we're greedily storing:
- current max
- largest product of two
- largest positive number
- second largest positive number
- largest negative number
"""
if len(xs) < 3:
raise Exception
cm = None
ld = xs[0] * xs[1]
l2 = min(xs[0], xs[1])
if xs[0] < 0 or xs[1] < 0:
ln = min(xs[0], xs[1])
else:
ln = 1
l = max(xs[0], xs[1])
for x in xs[2:]:
if not cm:
cm = max(x * ln * l, ld * x, x * l * l2) # beware
ld = max(ld, x * ln, x * l)
ln = min(ln, x)
l = max(l, x)
if x < l:
l2 = max(l2, x)
else:
cm = max(cm, x * ln * l, x * ld, x * l * l2)
ld = max(ld, x * ln, x * l)
ln = min(ln, x)
l = max(l, x)
if x < l:
l2 = max(l2, x)
return cm
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_short_list(self):
actual = highest_product_of_3([1, 2, 3, 4])
expected = 24
self.assertEqual(actual, expected)
def test_longer_list(self):
actual = highest_product_of_3([6, 1, 3, 5, 7, 8, 2])
expected = 336
self.assertEqual(actual, expected)
def test_list_has_one_negative(self):
actual = highest_product_of_3([-5, 4, 8, 2, 3])
expected = 96
self.assertEqual(actual, expected)
def test_list_has_two_negatives(self):
actual = highest_product_of_3([-10, 1, 3, 2, -10])
expected = 300
self.assertEqual(actual, expected)
def test_list_is_all_negatives(self):
actual = highest_product_of_3([-5, -1, -3, -2])
expected = -6
self.assertEqual(actual, expected)
def test_error_with_empty_list(self):
with self.assertRaises(Exception):
highest_product_of_3([])
def test_error_with_one_number(self):
with self.assertRaises(Exception):
highest_product_of_3([1])
def test_error_with_two_numbers(self):
with self.assertRaises(Exception):
highest_product_of_3([1, 1])
unittest.main(verbosity=2)
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