def recursive_fib(n):
    if n <= 1:
        return n
    return recursive_fib(n - 2) + recursive_fib(n - 1)


def memoized_fib(n):
    f = [0] * (n + 1)
    f[0] = 0
    f[1] = 1
    for i in range(2, n + 1):
        f[i] = f[i - 2] + f[i - 1]
    return f[n]


@lru_cache(maxsize=None)
def memoized_recursive_fib(n):
    if n <= 1:
        return n
    return memoized_recursive_fib(n - 2) + memoized_recursive_fib(n - 1)


def last_digit_fib(n):
    return memoized_fib(n) % 10


def improved_last_digit_fib(n):
    f = [0] * (n + 1)
    f[0] = 0
    f[1] = 1
    for i in range(2, n + 1):
        f[i] = (f[i - 2] + f[i - 1]) % 10
    return f[n]