Un-cached implementation of Project Euler problem 14. Fails to meet the "under a minute" time requirement.

problem14_nocache.py

#! `env python` -t
def seq(n):
    """
    Generate the sequence for Project Euler problem 14.
    ===================================================

    n is a positive integer that is the first number in the sequence.

    I'm told that although it hasn't been proven, that it is believed that
    regardless of the starting number, the sequence eventually gets to 1,
    which is where we stop.
             1         2          3         4         5         6         7         8
    123456789012345678901234567989012345678901234567890123456789012345678901234567890
    """

    while True:
        if n % 2 == 0:
            next=n/2
        else:
            next=3*n+1
        yield n
        if n == 1:
            return
        n=next

# end seq


def runlen(n):
    """
    runlen returns the length of the sequence
    generated by seq(n)
    """

    count=0
    for s in seq(n):
        count += 1
    # end "for s"
    return count
#end runlen

def main():
    longest=0
    basis=0
    for i in xrange(1, 1000000):
        r=runlen(i)
        if r > longest:
            basis=i
            longest=r
        # print 'runlen(', i,')=', runlen(i)
        #   end "for i"
    print "longest=", longest,\
        "generated from", basis
    return basis
# end main