def verify(passcode, rule):
    """
    Passcode is a string of numbers. Rule is two character string "ab". Verify
    returns False if "a" occurs and never comes before "b" at some point in
    the passcode and True otherwise.
    """
    a, b = rule
    if a == b:
        return True
    a_found = False
    b_found = False
    result = True
    for c in passcode:
        if a == c:
            a_found = True
        if b == c:
            b_found = True
        if b_found and c == a:
            result = False
        if a_found and c == b:
            return True
    return result


def verify_all(passcode, rules):
    for rule in rules:
        if not verify(passcode, rule):
            return False
    return True


def tests():
    passcode = "abcded"
    assert(verify(passcode, "ab"))
    assert(verify(passcode, "cz"))
    assert(verify(passcode, "zc"))
    assert(verify(passcode, "bb"))
    assert(verify(passcode, "ed"))
    assert(verify(passcode, "fg"))
    assert(verify(passcode, "ac"))
    assert(verify(passcode, "de"))
    assert(verify(passcode, "ca") is False)
    assert(verify(passcode, "dc") is False)


def get_rules(passcodes):
    rules = []
    for p in passcodes:
        for i in range(len(p) - 1):
            rules.append(p[i:i + 2])
    return rules


def get_digits(passcodes):
    r = []
    for p in passcodes:
        for d in p:
            if d not in r:
                r.append(d)
    return r


def add_single_digit(code, digit):
    # print("add_single_digit({}, {})".format(code, digit))
    r = []
    for i in range(len(code) + 1):
        new_code = code[:i] + str(digit) + code[i:]
        r.append(new_code)
    return r


def euler_079():
    tests()
    with open("../txt/e079.txt", "r") as f:
        passcodes = sorted(list(set([line.strip() for line in f])))

    codes = [""]
    rules = get_rules(passcodes)

    for d in get_digits(passcodes):
        temp_codes = []
        for code in codes:
            if d not in code:
                for new_code in add_single_digit(code, d):
                    if verify_all(new_code, rules):
                        temp_codes.append(new_code)
        codes = temp_codes
    return int(codes[0])


if __name__ == "__main__":
    print("e079.py: " + str(euler_079()))
    assert(euler_079() == 73162890)