euler-011.fs

#light

let groupSize = 4;
let gridSize = 20;

let grid =
    @"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" |>
    String.split(['\n']) |> 
    List.map (fun sl -> sl |> String.split([' ']) |> List.map (fun sv -> System.Int32.Parse(sv)) |> List.to_array) |> 
    List.to_array
    
let forwardStartIdxs = {0 .. gridSize - groupSize}
let backwardStartIdxs = {gridSize - 1 .. -1 .. groupSize-1}

let horizontalIdxs = 
    { for i in 0 .. gridSize-1 do
          for j in forwardStartIdxs do
              let is = {for v in 1..groupSize -> i}
              let js = {j .. (j + groupSize - 1)}
              let ijs = Seq.zip is js
              yield ijs
    }                                                

let verticalIdxs = 
    { for i in forwardStartIdxs do
          for j in 0 .. gridSize-1 do
              let is = {i .. (i + groupSize - 1)}
              let js = {for v in 1..groupSize -> j}
              let ijs = Seq.zip is js
              yield ijs
    }
    
let leftSlashIdxs = 
    { for i in forwardStartIdxs do
          for j in forwardStartIdxs do
              let is = {i .. (i + groupSize - 1)}
              let js = {j .. (j + groupSize - 1)}
              let ijs = Seq.zip is js
              yield ijs
    }
    
let rigthSlashIdxs = 
    { for i in backwardStartIdxs do
          for j in forwardStartIdxs do
              let is = {i .. -1 .. (i - groupSize + 1)}
              let js = {j .. (j + groupSize - 1)}
              let ijs = Seq.zip is js
              yield ijs
    }    
                
let allIdxs = horizontalIdxs |> Seq.append verticalIdxs |> Seq.append leftSlashIdxs |> Seq.append rigthSlashIdxs

let answer =
    allIdxs |> 
    Seq.map (fun s -> s |> Seq.map (fun (i,j) -> grid.[i].[j])) |>
    Seq.map (fun s -> s |> Seq.fold ( * ) 1) |>
    Seq.fold (fun a v -> if v > a then v else a) 0

printfn "Greatest product of four numbers on the same straight line is %d" answer