CEGEP computer science: programs and preparation

# Our practice program: number bases and Euclid's algorithm, with a test plan.
DIGITS = "0123456789ABCDEF"

def to_base(n, base):
    """Write a whole number n >= 0 in a base from 2 to 16."""
    if n == 0:
        return "0"
    out = ""
    while n > 0:
        n, r = divmod(n, base)     # repeated division: the remainder is the next digit
        out = DIGITS[r] + out
    return out

def gcd(a, b):
    """Euclid's algorithm: replace (a, b) by (b, a mod b) until b is 0."""
    while b != 0:
        a, b = b, a % b
    return a

# functional test plan: (what we test, call, expected result)
TESTS = [
    ("zero",              lambda: to_base(0, 2),     "0"),
    ("binary",            lambda: to_base(13, 2),    "1101"),
    ("hexadecimal",       lambda: to_base(255, 16),  "FF"),
    ("one digit",         lambda: to_base(7, 8),     "7"),
    ("gcd, common factor", lambda: gcd(84, 36),      12),
    ("gcd, coprime",      lambda: gcd(17, 5),        1),
]

passed = 0
for name, call, expected in TESTS:
    got = call()
    ok = got == expected
    passed += ok
    print(f"{name:20} expected {expected!s:6} got {got!s:6} {'PASS' if ok else 'FAIL'}")
print(passed, "of", len(TESTS), "tests pass")

zero                 expected 0      got 0      PASS
binary               expected 1101   got 1101   PASS
hexadecimal          expected FF     got FF     PASS
one digit            expected 7      got 7      PASS
gcd, common factor   expected 12     got 12     PASS
gcd, coprime         expected 1      got 1      PASS
6 of 6 tests pass

The test plan was written before the functions, as a list of cases with the answers worked out by hand: 13 in binary is 1101 (8 + 4 + 1), 255 in hexadecimal is FF (15 x 16 + 15), and the greatest common divisor of 84 and 36 is 12. Then the code was written to make all six pass.