def partition(start, end, step):
    '''
    Partitions the interval [start, end) into 'k' intervals [a_i, a_{i+1}).
    '''
    from itertools import takewhile, chain, islice, tee

    # itertools.count does not work with datetime.
    def count(firstval=0, step=1):
        x = firstval
        while 1:
            yield x
            x += step

    assert(start_date < end_date)

    a_i = takewhile(lambda x: x < end, count(start, step))
    a_i = tee(a_i)
    a_ip1 = chain(islice(a_i[0], 1, None), [end])
    return zip(a_i[1], a_ip1)