Return the length of a constant loop given some conditions, an ID, and a given base

recursive_constant_loop.py

def solution(n, b):
    k = len(n)
    xc = sorted(n, reverse=True)
    yc = sorted(n)
    x = ''.join(xc)
    y = ''.join(yc)
    zc = int(x, base=b) - int(y, base=b)
    z = str_base(zc, b)
    if z in a:
        return len(a) - a.index(z)
    else:
        a.append(z)
        return solution(z, b)


def digit_to_char(digit):
    if digit < 10:
        return str(digit)
    return chr(ord('a') + digit - 10)


def str_base(number, base):
    if number < 0:
        return '-' + str_base(-number, base)
    (d, m) = divmod(number, base)
    if d > 0:
        return str_base(d, base) + digit_to_char(m)
    return digit_to_char(m)


a = []