import math
from e057 import add_fractions


def get_floor_sqrt(n):
    return math.floor(math.sqrt(n))


def next_expansion_1(current_a, current_nominator,
                     current_denominator, original_number):
    cn = current_nominator
    cd = current_denominator
    cn, cd = cd, (original_number - cd * cd) // cn
    next_a = math.floor((math.sqrt(original_number) + cn) // cd)
    cn = cn - next_a * cd
    cn *= -1

    return next_a, cn, cd


def get_continued_fraction_sequence(n):

    # If number is a square number we return it.
    floor_sqrt = get_floor_sqrt(n)
    if n == floor_sqrt * floor_sqrt:
        return ((floor_sqrt), [])

    # Otherwise, we calculate the next expansion till we
    # encounter a step a second time.
    a = floor_sqrt
    cn = a
    cd = 1
    sequence = []
    previous_steps = []

    while not (a, cn, cd) in previous_steps:
        # print("a: {} cn: {} cd: {}".format(a, cn, cd))
        previous_steps.append((a, cn, cd))
        a, cn, cd = next_expansion_1(a, cd, cn, n)
        sequence.append(a)
    sequence.pop()
    return ((floor_sqrt), sequence)


def next_expansion_2(previous_numerator, previous_denumerator, value):
    if previous_numerator == 0:
        return (value, 1)
    return add_fractions(previous_denumerator, previous_numerator, value, 1)


def get_fractions(n, x):
    # print("get_fractions(n={}, x={})".format(n, x))
    # Get sequence of a_x
    first_value, sequence = get_continued_fraction_sequence(n)
    sequence = [first_value] + math.ceil(x / len(sequence)) * sequence
    sequence = sequence[:x + 1]
    sequence = sequence[::-1]

    n, d = 0, 1
    for s in sequence:
        n, d = next_expansion_2(n, d, s)
    return (n, d)


def get_minimal_solution(d):
    for i in range(0, 100):
        x, y = get_fractions(d, i)
        if x * x - d * y * y == 1:
            return((x, y))


def is_square(n):
    return math.sqrt(n).is_integer()


def euler_066():
    # XXX: This seems really long and complicated. We can do better.
    x_max = 0
    d_max = 0

    for d in range(2, 1001):
        if is_square(d):
            continue

        x, y = get_minimal_solution(d)
        if x > x_max:
            x_max = x
            d_max = d

    print("d: {} x: {}".format(d_max, x_max))
    s = d_max
    return s


if __name__ == "__main__":
    print("e066.py: " + str(euler_066()))
    assert(euler_066() == 661)