APL and Bit Matrices Are For the Birds R. G. Selfridge Introduction The problem to be tackled here has two parts, both of which sound simple on the face of it. Here they are: P 1 Given two vectors, R and C, the row sums and column sums. create a bit matrix (i.e. ^/m~je0,1) with those row and eolunm sums. P2 For a given R, C generate as many different bit matrices as desired with a reasonable hope that these matrices have a fiat distribution across solution space. This is similar to the hope that a 'fiat' random number generator provides a 'fiat' distribution of numbers over the desired range, but I cannot easily prove or 'test' the claims. (This problem will become more obvious as the algorithms are developed.) (I must add that the algorithm described in that article does indeed have back-tracking, but far more emphasis on Knights Tour than was ever warranted. The problem is to outline what back-tracking is for an audience with a limited knowledge or understanding of algorithms, back-tracking or recursion.) These bit matrices have also been studied as mathematical objects, with connections to graphs and trees, and the lemma below earl
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APL and bit matrices are for the birds
Selfridge, R. G.
Follow ACM SIGAPL APL Quote Quad
, Volume 33 (1)
Association for Computing Machinery – Sep 1, 2002
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