Finish question 11 using lazy lists

src/projectEuler/question11.hs

@@ -26,6 +26,7 @@ The product of these numbers is 26x63x78x14 = 1788696.
 
 What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20x20 grid?
 -}
+import           Data.List (genericDrop, genericIndex, genericTake)
 
 grid :: [[Integer]]
 grid =
@@ -50,3 +51,60 @@ grid =
   , [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]
   ]
+
+points :: Integer -> [(Integer, Integer)]
+points n =  [ (x,y) | x <- [1..n], y <- [1..n] ]
+
+allDiagonals :: Integer -> [[(Integer, Integer)]]
+allDiagonals n =
+  [ [(i, j), b, c, d]
+  |  (i, j) <- points n
+  ,  i+3 <= n
+  ,  j+3 <= n
+  ,  b <- [(i + 1, j + 1)]
+  ,  c <- [(i + 2, j + 2)]
+  ,  d <- [(i + 3, j + 3)]
+  ]
+
+allUpDown :: Integer -> [[(Integer, Integer)]]
+allUpDown n =
+  [ [(i, j), b, c, d]
+  |  (i, j) <- points n
+  ,  i   <= n
+  ,  j+3 <= n
+  ,  b <- [(i, j + 1)]
+  ,  c <- [(i, j + 2)]
+  ,  d <- [(i, j + 3)]
+  ]
+
+allLeftRight :: Integer -> [[(Integer, Integer)]]
+allLeftRight n =
+  [ [(i, j), b, c, d]
+  |  (i, j) <- points n
+  ,  i+3 <= n
+  ,  j   <= n
+  ,  b <- [(i + 1, j)]
+  ,  c <- [(i + 2, j)]
+  ,  d <- [(i + 3, j)]
+  ]
+
+allSequences :: Integer -> [[(Integer, Integer)]]
+allSequences n = allDiagonals n ++ allUpDown n ++ allLeftRight n
+
+s20x20 :: [[(Integer, Integer)]]
+s20x20 = allSequences 20
+
+getValue :: [[Integer]] -> (Integer, Integer) -> Integer
+getValue grid (x,y) = row `genericIndex` y'
+  where row = (head . genericDrop (x-1) . genericTake x) grid
+        y'  = y-1 -- compensate for 1 index numbering above
+
+-- |
+-- λ> ans
+-- 51267216
+-- (0.13 secs, 38,281,312 bytes)
+ans :: Integer
+ans = maximum $ map (product . map (getValue grid)) s20x20
+
+main :: IO ()
+main = print ans