b4689761d9
Write a function that returns the highest product of three integers within a list of integers. This solution uses a greedy algorithm that solves for the answer in linear time. The space complexity is constant.
81 lines
2.1 KiB
Python
81 lines
2.1 KiB
Python
import unittest
|
|
import sys
|
|
import trace
|
|
|
|
|
|
def highest_product_of_3(xs):
|
|
if len(xs) < 3:
|
|
raise Exception("List needs to contain at least three elements.")
|
|
hp3 = xs[0] * xs[1] * xs[2]
|
|
hp2 = xs[0] * xs[1]
|
|
lp2 = xs[0] * xs[1]
|
|
hn = max(xs[0], xs[1])
|
|
ln = min(xs[0], xs[1])
|
|
for x in xs[2:]:
|
|
hp3 = max(hp3, hp2 * x, lp2 * x)
|
|
hp2 = max(hp2, hn * x, ln * x)
|
|
lp2 = min(lp2, hn * x, ln * x)
|
|
hn = max(hn, x)
|
|
ln = min(ln, x)
|
|
return hp3
|
|
|
|
|
|
# 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])
|
|
|
|
def test_custom(self):
|
|
actual = highest_product_of_3([9, 5, 2, 1, 7, 3])
|
|
expected = 9 * 7 * 5
|
|
self.assertEqual(actual, expected)
|
|
|
|
|
|
unittest.main(verbosity=2)
|
|
|
|
|
|
def main():
|
|
highest_product_of_3([-5, -1, -3, -2])
|
|
|
|
|
|
tracer = trace.Trace(ignoredirs=[sys.prefix, sys.exec_prefix],
|
|
trace=0,
|
|
count=1)
|
|
|
|
tracer.run('main()')
|
|
r = tracer.results()
|
|
r.write_results(show_missing=True, coverdir=".")
|