{- 
  
  Euler #11 in Haskell

  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 program was created by Hakan Kjellerstrand (hakank@gmail.com)
  Also see my Haskell page: http://hakank.org/haskell/
  
  
-}

import Data.List
import HakankUtils

p11 = [[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]]


-- Running prod over a list of lists (i.e. a matrix)
runningProd2 n a = maximum $ maximum $ map (runningProd n) a

euler11a = maximum [max1,max2,max3,max4]
           where
             -- rows
             max1 = runningProd2 4 p11 
             -- columns
             max2 = runningProd2 4 (transpose p11)
             -- diag down
             max3 = runningProd2 4 (diagonals3 p11)
             -- diag up
             max4 = runningProd2 4 (diagonals4 p11)             

-- This does not feel especially Curry/Haskell like...
-- (It's a port from my Picat program euler11.pi)
-- diagonals3 m = [ [m !! (a+i) !! (a+j) | a <- [0..3] ] | i <- [0..16], j <- [0..16] ]
-- diagonals4 m = [ [m !! (i-a) !! (j+a) | a <- [0..3] ] | i <- [3..19], j <- [0..16] ]            
diagonals3 m = [ [matrixElement m (a+i) (a+j) | a <- [0..3] ] | i <- [0..16], j <- [0..16] ]
diagonals4 m = [ [matrixElement m (i-a) (j+a) | a <- [0..3] ] | i <- [3..19], j <- [0..16] ]            

main = do
         print euler11a -- 0.02 secs
