from lib_prime import primes
from functools import lru_cache 


def euler_077():

    def get_prime_sequence_dict(n_max):
        """ Returns a dict that maps a
        current prime to the following prime. """
        ps = primes(n_max)
        ps_current = ps[0]
        ps_dict = {}

        for p in ps[1:]:
            ps_dict[ps_current] = p
            ps_current = p

        return ps_dict

    prime_dict = get_prime_sequence_dict(10000)

    @lru_cache(maxsize=1000000)
    def possible_sums(n, n_orig, d):
        if d == n_orig:
            return 0
        if n == 0:
            return 1
        if n < 0:
            return 0
        if d > n:
            return 0

        s_1 = possible_sums(n - d, n_orig, d)
        s_2 = possible_sums(n, n_orig, prime_dict[d])
        return s_1 + s_2

    for n in range(1000):
        if possible_sums(n, n, 2) > 5000:
            return n


if __name__ == "__main__":
    print("e077.py: " + str(euler_077()))
    assert(euler_077() == 71)