problem11.fsx

(* Project Euler Problem 11
 * By Weisi Dai <weisi@x-research.com>
 *)

let ubound = 20

let groupLen = 4

let matrixString = """
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
"""

let matrixStrings = matrixString.Split('\n').[1 .. ubound]

let makeArray lineNumber = 
    let strVector = matrixStrings.[lineNumber]
    Array.map int (strVector.Split(' '))

let matrix = Array.init ubound makeArray

let matrixElement x y (deltaX, deltaY) = 
    matrix.[x + deltaX].[y + deltaY]

let inRange x a b = 
    (a <= x) && (x <= b)

let outOfRange x a b = 
    inRange x a b |> not

let foldProduct prod x = 
    prod * x

let computeProduct x y delta =
    let group = Array.map (matrixElement x y) delta
    Array.fold foldProduct 1 group

let productHorizontal x y =
    if outOfRange x 0 (ubound - 1) then 0 else
    if outOfRange y 0 (ubound - groupLen - 1) then 0 else
    computeProduct x y [| (0,0); (0,1); (0,2); (0,3) |]

let productVertical x y =
    if outOfRange x 0 (ubound - groupLen - 1) then 0 else
    if outOfRange y 0 (ubound - 1) then 0 else
    computeProduct x y [| (0,0); (1,0); (2,0); (3,0) |]

let productDiagonal1 x y =
    if outOfRange y 0 (ubound - groupLen - 1) then 0 else
    if outOfRange x 0 (ubound - groupLen - 1) then 0 else
    computeProduct x y [| (0,0); (1,1); (2,2); (3,3) |]

let productDiagonal2 x y =
    if outOfRange y 0 (ubound - groupLen - 1) then 0 else
    if outOfRange x 0 (ubound - groupLen - 1) then 0 else
    computeProduct x y [| (0,3); (1,2); (2,1); (3,0) |]

let products = [| productHorizontal;
                  productVertical;
                  productDiagonal1;
                  productDiagonal2 |]

let allProducts = seq {
    for i in 0 .. ubound - 1 do
        for j in 0 .. ubound - 1 do
            for product in products do
                yield product i j
}

let problem11 = Seq.max allProducts
    
let main = printfn "The answer is %d." (problem11)

main