I apologize for replying to my own message, but I just realized that I
must choose to either maximize the columns or maximize the rows... not
both. So let's say I wish to maximize the columns. It appears that the
three tied answers are still valid.
Thanks again!
-- Glenn
Glenn M. Lewis wrote:
Hi all!
Say I have a table with shape 'm n' (m rows, n columns) populated
with ones and zeros.
Let's say I would like to create the largest table possible by
selecting the most rows and the most columns where all intersections
of said rows and columns consist of all ones.
I'm having difficulties coming up with an expression that gives me
two lists... one for the rows and one for the columns that 'selects'
the rows/columns that would make up this maximal table.
Wow... I probably didn't explain that very well. Let me try an
example.
t =. 6 10 $ 0 1 1 0 0 1
t
0 1 1 0 0 1 0 1 1 0
0 1 0 1 1 0 0 1 0 1
1 0 0 1 0 1 1 0 0 1
0 1 1 0 0 1 0 1 1 0
0 1 0 1 1 0 0 1 0 1
1 0 0 1 0 1 1 0 0 1
By inspection, it appears that one of three solutions is possible
that all tie for the maximum-sized table of all-ones (in this case, a
shape '2 5' table.
rows 0 and 3 with columns 1,2,5,7,8 or in J:
(< 0 3 ; 1 2 5 7 8) { t
1 1 1 1 1
1 1 1 1 1
or
(< 1 4 ; 1 3 4 7 9) { t
1 1 1 1 1
1 1 1 1 1
or
(< 2 5 ; 0 3 5 6 9) { t
1 1 1 1 1
1 1 1 1 1
The problem I'm having is coming up with these lists
algorithmically...
Any ideas on how to solve this?
Thanks!
-- Glenn Lewis
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