import unittest
from math import floor

################################################################################
# Solution
################################################################################

# change_possibilities :: Int -> [Int] -> Int
def change_possibilities(n, xs):
    combinations = [0] * (n + 1)
    combinations[0] = 1

    for x in xs:
        for i in range(len(combinations)):
            if i >= x:
                combinations[i] += combinations[i - x]

    return combinations[n]


################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):

    def test_sample_input(self):
        actual = change_possibilities(4, (1, 2, 3))
        expected = 4
        self.assertEqual(actual, expected)

    def test_one_way_to_make_zero_cents(self):
        actual = change_possibilities(0, (1, 2))
        expected = 1
        self.assertEqual(actual, expected)

    def test_no_ways_if_no_coins(self):
        actual = change_possibilities(1, ())
        expected = 0
        self.assertEqual(actual, expected)

    def test_big_coin_value(self):
        actual = change_possibilities(5, (25, 50))
        expected = 0
        self.assertEqual(actual, expected)

    def test_big_target_amount(self):
        actual = change_possibilities(50, (5, 10))
        expected = 6
        self.assertEqual(actual, expected)

    def test_change_for_one_dollar(self):
        actual = change_possibilities(100, (1, 5, 10, 25, 50))
        expected = 292
        self.assertEqual(actual, expected)


unittest.main(verbosity=2)