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PureScript solution to Project Euler problem 11

2018-Aug-01 09:18
purescriptproject-euler

Problem details at Project Euler problem 11 page.

Test

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module Euler011Test (euler11suite) where
 
import Prelude
 
import Data.Maybe (Maybe(..))
import Euler011 (euler11)
import Test.Unit (TestSuite, suite, test)
import Test.Unit.Assert as Assert
 
gridWarmup :: String
gridWarmup = """
  08 02 22 97
  49 49 99 40
  81 49 31 73
  52 70 95 23
"""
 
gridReal :: String
gridReal = """
  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
"""
 
euler11suite :: forall e. TestSuite e
euler11suite =
  suite "Euler 11" do
    test "Warmup" do
      Assert.equal (Just 24468444) (euler11 gridWarmup)
    test "Real" do
      Assert.equal (Just 70600674) (euler11 gridReal)

Solution

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module Euler011 (euler11) where
 
import Prelude
 
import Data.Array (catMaybes, concat, drop, filter, head, length, null, range, reverse, take, zip, (:))
import Data.Foldable (maximum, product)
import Data.Int (fromString)
import Data.Maybe (Maybe, maybe)
import Data.String (Pattern(..), split, trim)
import Data.Tuple (Tuple(..))
 
lines :: String -> Array String
lines = split (Pattern "\n") <<< trim
 
words :: String -> Array String
words = split (Pattern " ") <<< trim
 
type Mat a = Array (Array a)
 
toMat :: String -> Mat Int
toMat s = catMaybes <$> map fromString <$> words <$> lines s
 
filterEmpty :: forall a. Mat a -> Mat a
filterEmpty m = filter (not <<< null) m
 
visit1 :: forall a. (Mat a -> Mat a) -> Mat a -> Mat a
visit1 f m = filterEmpty (concat $ f <$> tails m)
 
visit :: forall a. (Mat a -> Mat a) -> Mat a -> Mat a
visit _ [] = []
visit f m = visit1 f m <> visit f (filterEmpty $ drop 1 <$> m)
 
transpose :: forall a. Mat a -> Mat a
transpose m = visit f m
  where f x = take 1 <$> x
 
flipVer :: forall a. Mat a -> Mat a
flipVer = liftA1 reverse
 
tails :: forall a. Mat a -> Array (Mat a)
tails [] = []
tails m = m : tails (drop 1 m)
 
horiz :: Int -> Mat Int -> Array Int
horiz n m = maybe [] (take n) (head m)
 
diag :: Int -> Mat Int -> Array Int
diag n m =
  let ts = zip (range 0 (n - 1)) (take n m)
      f (Tuple i a) = drop i a
      sm = f <$> ts
  in catMaybes $ head <$> sm
 
hordi :: Int -> Mat Int -> Mat Int
hordi n m = filter f [horiz n m, diag n m]
  where f e = length e == n
 
euler11 :: String -> Maybe Int
euler11 s =
  let m = toMat s
      ms = [m, flipVer m, transpose m]
      f = hordi 4
      vs = concat $ visit f <$> ms
      ps = product <$> vs
  in maximum ps