# recursive algorithm for balls in numbered boxes

Dr. Phillip M. Feldman Phillip.M.Feldman at gmail.com
Sun Sep 11 21:41:33 CEST 2011

```Hello Peter,

When I run my code, I get the same 14 configurations that your code
produces; the only different that I can see in the output is that the
configurations are produced in a different order.  Note that your code is
not creating an iterator, so thus doesn't do what I want.  Also, generating
the product set and then testing whether the total number of balls is
correct will potentially consider a huge number of cases that must be
rejected because the sum is wrong; this is too inefficient.

Phillip

In [2]: list(balls_in_numbered_boxes(10,[4,3,2,1,2]))
Out[2]:
[(4, 3, 2, 1, 0),
(4, 3, 2, 0, 1),
(4, 3, 1, 1, 1),
(4, 3, 1, 0, 2),
(4, 3, 0, 1, 2),
(4, 2, 2, 1, 1),
(4, 2, 2, 0, 2),
(4, 2, 1, 1, 2),
(4, 1, 2, 1, 2),
(3, 3, 2, 1, 1),
(3, 3, 2, 0, 2),
(3, 3, 1, 1, 2),
(3, 2, 2, 1, 2),
(2, 3, 2, 1, 2)]
--
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```