Programming challenge: wildcard exclusion in cartesian products

wkehowski at wkehowski at
Sat Mar 18 18:53:11 CET 2006

The cardinality of excluding '*a*b*' from S^n should be
(m-1)^(n-1)*(m+n-1), where m=|S|. For m=5 this becomes 4^(n-1)*(n+4),
and your table fits this formula. As far as generating and testing, an
'ideal' solution would be to 'start from the ground up', as in
excluding length 2 wc, and then length 3, etc, until all wc's have been
excluded. The 'ideal' solution would intrinsically exclude wc's and not
test against a background generation of all of S^n. Does that make

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