[Python]直積

cartesian_product.py

def cartesian_product(X):
    """直積を求める
    直積とは A={a, b, c}, B={d, e}のような2つの集合が与えられたとすると
    A×B={(a,d),(a,e),(b,d),(b,e),(c,d),(c,e)}
    """
    import itertools

    Y = list(itertools.product(*X))
    # >> [(11, 21, 31), (11, 21, 32), (11, 21, 33), (11, 22, 31), (11, 22, 32), (11, 22, 33),
    return Y


def test_cartesian_product():
    X = [
        [11, 12, 13],
        [21, 22, 23],
        [31, 32, 33],
    ]
    x_size = [3, 3, 3]
    x_length = 3 * 3 * 3
    Y = [
        (11, 21, 31),
        (11, 21, 32),
        (11, 21, 33),
        (11, 22, 31),
        (11, 22, 32),
        (11, 22, 33),
        (11, 23, 31),
        (11, 23, 32),
        (11, 23, 33),
        (12, 21, 31),
        (12, 21, 32),
        (12, 21, 33),
        (12, 22, 31),
        (12, 22, 32),
        (12, 22, 33),
        (12, 23, 31),
        (12, 23, 32),
        (12, 23, 33),
        (13, 21, 31),
        (13, 21, 32),
        (13, 21, 33),
        (13, 22, 31),
        (13, 22, 32),
        (13, 22, 33),
        (13, 23, 31),
        (13, 23, 32),
        (13, 23, 33),
    ]
    y_length = len(Y)
    assert y_length == x_length

    ans = make_tree(X)
    assert Y == ans, (ans, Y)
    assert len(Y) == len(ans), (len(Y), len(ans))

    def matched_list(Y1, Y2):
        result = []
        for y1 in Y1:
            for y2 in Y2:
                if y1 == y2:
                    assert y1 == y2, (y1, y2)
                    result.append(y1)
        return result

    Y_matched = matched_list(Y, ans)
    assert len(Y) == len(Y_matched), (y_length, len(Y_matched))


test_cartesian_product()