[Jprogramming] J expression question

[Glenn M. Lewis]

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