euclidian.py

def E(h, n):
    """
    Generates a euclidian rhythm.

    Arguments:
        k : The number of ones in the sequence.
        n : The number of steps in the sequence.

    See http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf
    """
    if h > n:
        raise ValueError("h must be <= n")

    # The number of elements in the second group
    t = n-h
    head = [1]
    tail = [0]

    while True:
        if t > h:
            t = t - h
            head = head + tail
        else:
            h, t = t, h - t
            head, tail = head + tail, head

        if t <= 1:
            break

    return ''.join(['X' if a else '.' for a in head * h + tail * t])


def test(fn):
    """
    tests = [
        """

    tests = [
        ((1, 2), 'X.'),
        ((1, 3), 'X..'),
        ((1, 4), 'X...'),
        ((4, 12), 'X..X..X..X..'),
        ((2, 3), 'X.X'),
        ((2, 5), 'X.X..'),
        ((3, 4), 'X.XX'),
        ((3, 5), 'X.X.X'),
        ((3, 7), 'X.X.X..'),
        ((3, 8), 'X..X..X.'),
        ((4, 7), 'X.X.X.X'),
        ((4, 9), 'X.X.X.X..'),
        ((4, 11), 'X..X..X..X.'),
        ((4, 16), 'X...X...X...X...'),
        ((5, 6), 'X.XXXX'),
        ((5, 7), 'X.XX.XX'),
        ((5, 8), 'X.XX.XX.'),
        ((5, 9), 'X.X.X.X.X'),
        ((5, 11), 'X.X.X.X.X..'),
        ((5, 12), 'X..X.X..X.X.'),
        ((5, 16), 'X..X..X..X..X...'),
        ((7, 8), 'X.XXXXXX'),
        ((7, 12), 'X.XX.X.XX.X.'),
        ((7, 16), 'X..X.X.X..X.X.X.'),
        ((9, 16), 'X.XX.X.X.XX.X.X.'),
        ((11, 24), 'X..X.X.X.X.X..X.X.X.X.X.'),
        ((13, 24), 'X.XX.X.X.X.X.XX.X.X.X.X.'),
    ]
    passed = failed = 0
    for test in tests:
        inp = test[0]
        exp = test[1]
        try:
            out = fn(*inp)
            assert out == exp
            passed += 1
        except AssertionError:
            failed += 1
            print '%s != %s: %s' % (inp, exp, out)

    print "%s passed, %s failed" % (passed, failed)

if __name__ == "__main__":
    test(E)
    #test(E1)
    #test(E2)

gistfile1.txt

E(13, 24):

13, 11 - [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
11, 2  - [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [1, 1]
2, 9   - [101, 101], [10, 10, 10, 10, 10, 10, 10, 10, 10]
2, 7   - [10110, 10110], [10, 10, 10, 10, 10, 10, 10]
2, 5   - [1011010, 1011010], [10, 10, 10, 10, 10]
2, 3   - [101101010, 101101010], [10, 10, 10]
2, 1   - [10110101010, 10110101010], [10]