Hi
I see two issues. The first is present behaviour. The second is alternative
ways of ordering the elements of a Cartesian product.
Here's an example of the present behaviour.
>>> iter_range = iter(range(100))
>>> prod = itertools.product(iter_range, "abcdef")
>>> next(iter_range)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
StopIteration
It's not what I expected before I read this thread, and it is what I
expected after I read this thread. I regard it as a bug. I expect iterators
to be lazy rather than greedy when consuming input. This helps make for
efficient and non-blocking pipelines. I see no reason for the product to
consume any items until it has been asked to yield a member of the product.
The second issue is that there are at least three sensible ways to iterate
a Cartesian product. The itertools.product function is, as said in the
docs, equivalent to nested for loops. On ordered input it's equivalent to
lexicographic ordering.
The squares on a chessboard are labelled a1, a2, a3, .... b1, b2, b3, ... ,
g7, g8 (using lexicographic order. There are as many fractions as there are
counting numbers. The usual way to prove this is to order unsimplified
fractions p/q via the TRIPLE (p + q, p, q). This gives a diagonal ordering.
The third order is via subsquares. In other words order via the TRIPLE
(max(p,q), p, q).
I suggest on the basis of batteries included that all three methods be
included in itertools, perhaps with names lexicproduct, diagproduct and
maxproduct. Finally, product is a synonym for lexicproduct. This allows the
programmer to say without writing a comment that they've considered the
alternatives and chosen the function also known as product.
with best regards
Jonathan
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