# Project Euler #011

In the 20 × 20 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 26 × 63 × 78 × 14 = 1788696. What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 20 × 20 grid?

```//In the 2020 grid below, four numbers along a diagonal line have been marked in red.
//What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 2020 grid?
module E011

let data =
["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 matrix = data |> List.map (fun vector -> vector.Split(' ') |> Seq.map (fun number -> System.Int32.Parse(number)) |> Seq.toList)

// Reorder the matrix so that it reads from top to bottom instead
let vertical_matrix (matrix:list<list<int>>) = [0..(matrix.Length - 1)] |> List.map (fun x -> [0..(matrix.Length - 1)] |> List.map (fun y -> matrix.[y].[x]))

// Rotate the matrix so that the bottom left corder appears on top, all rows diagonal
let diagonalmatrixbottomlefttotopright (matrix:list<list<int>>) =
let max = matrix.Length - 1
([0..max] |> List.map (fun x -> [(max - x)..max] |> List.mapi (fun i y -> [i;y]))) @ ([1..max] |> List.map (fun x -> [0..(max - x)] |> List.map (fun y -> [(x + y);y]))) // Get the coords
|> List.map (fun row -> row |> List.map (fun coord -> matrix.[coord.[1]].[coord.[0]])) // Map coords to matrix

// Rotate the matrix so that the top left corder appears at the top, all rows diagonal
let diagonalmatrixtoplefttobottomright (matrix:list<list<int>>) =
let max = matrix.Length - 1
([0..max] |> List.map (fun x -> [0..x] |> List.mapi (fun i y -> [i;(x - y)]))) @ ([1..max] |> List.map (fun x -> [0..(max - x)] |> List.mapi (fun i y -> [(y + x);(max - i)]))) // Get the coords
|> List.map (fun row -> row |> List.map (fun coord -> matrix.[coord.[1]].[coord.[0]])) // Map coords to matrix

let rec Take (vector:list<int>) n =
vector |> List.toSeq |> Seq.take n |> Seq.toList

let rec findlargestproduct (vector:list<int>) numberofparts result =
if vector.Length >= numberofparts then
let product = Take vector numberofparts |> List.fold (fun acc x -> acc * x) 1
if (product > result) then
findlargestproduct vector.Tail numberofparts product
else
findlargestproduct vector.Tail numberofparts result
else
result

let rec findlargestproductinmatrix matrix numberofparts result =
match matrix with
let subproduct = findlargestproduct head numberofparts 0
if  subproduct > result then
findlargestproductinmatrix tail numberofparts subproduct
else
findlargestproductinmatrix tail numberof_parts result
| [] -> result

let solution = lazy ([
findlargestproductinmatrix matrix 4 0;
findlargestproductinmatrix (verticalmatrix matrix) 4 0;
findlargestproductinmatrix (diagonalmatrixbottomlefttotopright matrix) 4 0;
findlargestproductinmatrix (diagonalmatrixtoplefttobottom_right matrix) 4 0
] |> List.max)
```