On 05/31/2010 08:54 PM, Andrei Alexandrescu wrote:
On 05/31/2010 08:07 PM, Simen kjaeraas wrote:
Andrei Alexandrescu <seewebsiteforem...@erdani.org> wrote:
Yah, there's no argument that infinite ranges must be allowed by a
n-way cross-product. It reminds one of Cantor's diagonalization, just
in several dimensions. Shouldn't be very difficult, but it only works
if all ranges except one are forward ranges (one can be an input range).
Might I coerce you into indulging some more detail on this idea? I'm
afraid my knowledge of the diagonal method is sadly lacking, and some
reading on the subject did not give me satisfactory understanding of
its application in the discussed problem.
Way I thought of doing it is save the highest position this far of each
range, then in popFront see if we're past it. If we are, reset this
range, and pop from the next range up, recursively.
I thought about this some more, and it's more difficult and more
interesting than I thought.
Cantor enumerated rational numbers the following way: first come all
fractions that have numerator + denominator = 1. That's only one
rational number, 1/1. Then come all fractions that have num + denom = 2.
That gives 1/2 and 2/1. Then come all fractions that have num + denom =
3, and so on.
I'm off by one there, but you got the idea :o).
Andrei
