Week 5 examples

def even_numbers(limit):
    x = 0
    while x < limit:
        yield x
        x += 2

def factors(x):
    p = 2
    while p <=  x:
        if x % p ==0:
            yield p
        p += 1

def prime_factors(x):
    p = 2
    while p <= x:
        if x % p == 0 and len(factors(x)) == 2:
            yield p
        p += 1

def factorial(x):
    if x == 0:
        return 1
    return factorial(x - 1) * x

def permutation(s, x):
    if len(s) == 1:
        return tuple(s)
    if len(s) == 0:
        return ()
    s = list(s)
    selection = x % len(s)
    head = (s[selection],)
    del s[selection]
    return head + permutation(set(s), x // (len(s)+1))

def permutations(s):
    x = factorial(len(s)) - 1
    while x >= 0:
        yield permutation(s, x)
        x -= 1