Project: Multiply with recursion

Write a recursive function named multiply that takes two positive integers and returns their product. It cannot use the * operator. It has to find the answer by adding. This shows the idea:

7 * 4 = 7 + (7 * 3)
7 * 3 = 7 + (7 * 2)
7 * 2 = 7 + (7 * 1)
7 * 1 = 7
So, 7 * 4 = 7 + (7 + (7 + (7)))

Your function cannot use a loop.

Save the file as multiply_recur.py.

Show a solution

Try the project on your own first. This is one working solution, followed by its tests. Press Run to run the tests. Read them to see what thorough testing looks like, then change the solution and run again to watch a test fail.

def multiply(first: int, second: int) -> int:
    """Multiply two positive integers using only addition and recursion."""
    if second == 1:
        return first
    return first + multiply(first, second - 1)

# ---- Tests ----
import sys
import unittest

class TestMultiply(unittest.TestCase):
    def test_multiplying_by_one_returns_the_first_number(self):
        self.assertEqual(multiply(9, 1), 9)

def test_one_times_one_is_one(self):
        self.assertEqual(multiply(1, 1), 1)

def test_multiplying_one_by_a_number_returns_that_number(self):
        self.assertEqual(multiply(1, 9), 9)

def test_the_example_from_the_project(self):
        self.assertEqual(multiply(7, 4), 28)

def test_two_equal_numbers(self):
        self.assertEqual(multiply(12, 12), 144)

def test_the_order_of_the_numbers_does_not_change_the_answer(self):
        self.assertEqual(multiply(3, 8), multiply(8, 3))

def test_a_small_product(self):
        self.assertEqual(multiply(2, 3), 6)

def test_the_second_number_counts_how_many_times_to_add(self):
        self.assertEqual(multiply(5, 2), 10)
        self.assertEqual(multiply(5, 3), 15)

# ---- Run the tests ----
loader = unittest.defaultTestLoader
suite = unittest.TestSuite(loader.loadTestsFromTestCase(case) for case in [TestMultiply])
unittest.TextTestRunner(stream=sys.stdout, verbosity=2).run(suite)

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