Python/maths/3n+1.py

from typing import Tuple, List


def n31(a: int) -> Tuple[List[int], int]:
    """
    Returns the Collatz sequence and its length of any postiver integer.
    >>> n31(4)
    ([4, 2, 1], 3)
    """

    if not isinstance(a, int):
        raise TypeError("Must be int, not {0}".format(type(a).__name__))
    if a < 1:
        raise ValueError("Given integer must be greater than 1, not {0}".format(a))

    path = [a]
    while a != 1:
        if a % 2 == 0:
            a = a // 2
        else:
            a = 3 * a + 1
        path += [a]
    return path, len(path)


def test_n31():
    """
    >>> test_n31()
    """
    assert n31(4) == ([4, 2, 1], 3)
    assert n31(11) == ([11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1], 15)
    assert n31(31) == ([31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1], 107)


if __name__ == "__main__":
    num = 4
    path, length = n31(num)
    print(f"The Collatz sequence of {num} took {length} steps. \nPath: {path}")