[Jprogramming] A.

[David Ward Lambert]

   Note ' http://projecteuler.net/index.php?section=problems&id=345 '
Please consider brutish solution to the example (quoted below)
The algorithm rotates all  !5  possible values into column
0 , and finds the maximum sum.  This being j, and having
rotated entire rows, it is easy to consider all columns.
Since some of the permutations involve whole matrix rotations
(a constant plus the permutation vector P,  5 | (i.5) +/ P )
the result appears once in each column.  Specifically which
!4  of all  !5  rotations did I need?
What is the answer in general?

Thank you, Dave---not yet a master of A.`C. (or of other stuffs).

"We define  the Matrix Sum  of a matrix  as the maximum sum  of matrix
elements  with  each  element  being  the  only one  in  his  row  and
column. For example, the Matrix Sum of the matrix below equals 3315 (=
863 + 383 + 343 + 959 + 767)"
)

   a=:     7  53 183 439 863
   a=:a,:497 383 563  79 973
   a=:a, 287  63 343 169 583
   a=:a, 627 343 773 959 943
   $a=:a,767 473 103 699 303
5 5
   $b=: ((i.!5) A. i.5)|."0 1"1 _ a
120 5 5
   $c=: +/"2 b
120 5
   >./,c         	     NB. solution
3315
   3315 +/ . = ,c   	     NB. number of occurrences
5