/* 

  Euler #11 in Picat.

  Problem 11
  """
  In the 2020 grid below, four numbers along a diagonal line have 
  been marked in red.

  ...

  The product of these numbers is 26 x 63 x 78 x 14 = 1788696.

  What is the greatest product of four adjacent numbers in any direction 
  (up, down, left, right, or diagonally) in the 20 x 20 grid?
  """


*/

% This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
% See also my Picat page: http://www.hakank.org/picat/
%

import util.

main => time(go).

go => euler11.


% Euler 11

p11(Mat) => Mat = 
     [[08,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,08],
      [49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00],
      [81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65],
      [52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91],
      [22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80],
      [24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50],
      [32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70],
      [67,26,20,68,02,62,12,20,95,63,94,39,63,08,40,91,66,49,94,21],
      [24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72],
      [21,36,23,09,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95],
      [78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,09,53,56,92],
      [16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57],
      [86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58],
      [19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40],
      [04,52,08,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66],
      [88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69],
      [04,42,16,73,38,25,39,11,24,94,72,18,08,46,29,32,40,62,76,36],
      [20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16],
      [20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54],
      [01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48]].


euler11 => 
  p11(M),

  % rows
  Max1 = max([max(running_prod(Row, 4)) : Row in M]),
  % columns
  Max2 = max([max(running_prod(Column, 4)) : Column in M.transpose()]),   
  % diag down
  Max3 = max([max([prod([M[A+I,A+J] : A in 0..3]) : I in 1..17]) : J in 1..17]),
  % diag up
  Max4 = max([max([prod([M[I-A,J+A] : A in 0..3]) : I in 4..20]) : J in 1..17]),
  % writeln([Max1,Max2,Max3,Max4]),
  writeln(max([Max1,Max2,Max3,Max4])).

%
% Using rows() and columns() from the utils module,
% and skips all the intermediate max'es.
%
euler11b => 
  p11(M),
  writeln(max(([running_prod(Row, 4) : Row in M.rows()] ++
               [running_prod(Column, 4) : Column in M.columns()] ++
               [[prod([M[A+I,A+J] : A in 0..3]) : I in 1..17] : J in 1..17] ++
               [[prod([M[I-A,J+A] : A in 0..3]) : I in 4..20] : J in 1..17]
              ).flatten())).


%
% slices an array A [...] into slices of length SliceLen
% and returns a list List
%
array_slice(A, SliceLen) = List =>
  List = [A2 : I in 1..A.length-SliceLen,
               A2 = [ A[J] : J in I..I+SliceLen-1] ].

% running prod of a list L1 with slice length RLen -> L2
running_prod(L1, RLen) = L2 =>
  Slices = array_slice(L1, RLen),
  L2 =  [Prod : LL in Slices, Prod = prod(LL)].