from lib_misc import sum_proper_divisors


def euler_095():
    NO_CHAIN = set()
    PROPER_DIVISOR_CACHE = {}

    def sum_proper_divisors_cached(n):
        if n in PROPER_DIVISOR_CACHE:
            return PROPER_DIVISOR_CACHE[n]
        r = sum_proper_divisors(n)
        PROPER_DIVISOR_CACHE[n] = r
        return r

    def chain(n):
        chain = []
        next_number = n

        while next_number not in chain:
            if next_number >= 10**6 or next_number == 0 or next_number in NO_CHAIN:
                for c in chain:
                    NO_CHAIN.add(c)
                return None
            chain.append(next_number)
            next_number = sum_proper_divisors_cached(next_number)
        chain.append(next_number)
        return chain

    chains = [[]]
    for i in range(1, 10**6 + 1):
        c = chain(i)
        if c and c[0] == c[-1]:
            if len(c) == len(chains[0]):
                # There might be multiple different chains with the same length
                # so keep all of them to get the smalles element.
                chains.append(c)
            elif len(c) > len(chains[0]):
                chains = [c]

    elems = [e for c in chains for e in c]
    return min(elems)


if __name__ == "__main__":
    solution = euler_095()
    print("e095.py: " + str(solution))
    assert(solution == 14316)