# pydemo2.py                                      David MacQuigg  ece175  5/2/08
'''Python demo2 program
   More cool stuff.
~ '''

# Recursion and automatic conversion to long integer for large results
#
def factorial(n):
    '''Returns an integer n factorial, a long integer if > (2**31 - 1).
    
    >>> factorial(13)
    6227020800L
    '''
    if n<=1: return 1
    return n * factorial(n-1)

# List comprehensions are elegant (think of set notation).
#
def factors(n):
    '''Return a list of positive integers x <= n, such that n is
    divisible by x.

    >>> factors(1000)
    [1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000]
    '''
    return [x for x in range(1, n+1) if n%x==0]

def isprime(n):
    '''Return True if n has only two factors.

    >>> isprime(17)
    True
    '''
    return len(factors(n)) == 2  # len is a built-in function

def primes(a, b):
    '''Return a list of prime numbers in range(a, b+1)

>>> primes(100, 200)
[101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, \
167, 173, 179, 181, 191, 193, 197, 199]
    '''
    return [n for n in range(a, b+1) if isprime(n)]

# You can always "unroll" a list conprehension:
#
def primes_rev1(a, b):

    result = []                # an empty list

    for n in range(a, b+1):
        if isprime(n):
            result.append(n)

    return result

###
#
if __name__ == '__main__':

    from doctest import testmod
    testmod(verbose=True)