Problem 11

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

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

The product of these numbers is .

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

訳

以下の の格子において，対角線に沿った四つの数が赤くマークされている（ここでは[ ]で囲みました）．

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

これらの数の積はである．

こののグリッドの任意の方向（上・下・右・左・斜め）の四つの積の最大値を求めよ．

Haskell

左右の斜め・上・下・左・右の積で関数が続くのでまとめてみましたが，あんまりすっきりしません．また，データをファイルから読み取るようにしてみました．

{-
Project Euler Problem 11 e11.hs
-}

import System.Environment


proc :: String -> IO ()
proc filename =  readFile filename 
                 >>=  print . maximum .  prodlist . makedata

makedata::String -> [[Int]]
makedata cs = map (map read) (map words (lines cs))


prodlist::[[Int]]->[Int]
prodlist cs =[(maximum.diagProdr) cs, (maximum.diagProdl) cs, 
              (maximum.downProd)  cs, (maximum.upProd)    cs, 
              (maximum.rightProd) cs, (maximum.leftProd)  cs]

anyDirProd::([Int],[Int])->((Int,Int)->Int->Int->Int) -> [[Int]] -> [Int]
anyDirProd (x,y) func cs =  map (anyDirProd' cs) pts
    where pts = [ (i,j) | i<-x, j<-y ]
          anyDirProd':: [[Int]] -> (Int,Int)-> Int 
          anyDirProd' cs pt = foldl (func pt) 1 [0,1,2,3]

diagProdr::[[Int]] -> [Int]
diagProdr cs = anyDirProd (range,range)  (\pt x y-> x * cs!!(fst pt+y)!!(snd pt+y)) cs
    where range = [0..length cs-4]

diagProdl::[[Int]] -> [Int]
diagProdl cs = anyDirProd (rangex,rangey)  (\pt x y-> x * cs!!(fst pt-y)!!(snd pt+y)) cs
    where m  = length cs-1
          n  = m - 3
          rangex = [3..m]
          rangey = [0..n]

downProd::[[Int]] -> [Int]
downProd cs = anyDirProd (rangex,rangey)  (\pt x y-> x * cs!!(fst pt)!!(snd pt+y)) cs
    where m  = length cs-1
          n  = m - 3
          rangex = [0..m]
          rangey = [0..n]

upProd::[[Int]] -> [Int]
upProd cs = anyDirProd (rangex,rangey)  (\pt x y-> x * cs!!(fst pt)!!(snd pt-y)) cs
    where m  = length cs-1
          rangex = [0..m]
          rangey = [3..m]

rightProd::[[Int]] -> [Int]
rightProd cs = anyDirProd (rangex,rangey)  (\pt x y-> x * cs!!(fst pt+y)!!(snd pt)) cs
    where m  = length cs-1
          n =  m - 3
          rangex = [0..n]
          rangey = [0..m]

leftProd::[[Int]] -> [Int]
leftProd cs = anyDirProd (rangex,rangey)  (\pt x y-> x * cs!!(fst pt-y)!!(snd pt)) cs
    where m  = length cs-1
          rangex = [3..m]
          rangey = [0..m]

main =  getArgs >>=  mapM_ proc

答えは 70600674 であってるかな・・・