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@gilles-leblanc
Created September 3, 2017 19:43
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Board.fs
module Board
type Value =
| Locked of int
| Possible of int List
type BoardSolved =
| Solved
| InvalidSolution
| BoardUnlocked
// Get a series of board elements defined by the function eFunc
let private getLinearElements eFunc start end' (board:Value[,]) : Value list =
[start..end'] |> List.fold (eFunc) []
// Get the Values at row rowNum
let row rowNum (board:Value[,]) : Value list =
getLinearElements (fun acc e -> board.[rowNum, e] :: acc) 0 8 board
// Get the values at column colNum
let column colNum (board:Value[,]) : Value list =
getLinearElements (fun acc e -> board.[e, colNum] :: acc) 0 8 board
// Get the values at box boxNum. A box is a 3x3 square of which there are 9 in the Sudoku board.
// The squares are at fixed position and are numbered sequentially from 0 to 8 with 0 being the top left corner
// and 8 and the bottom right corner.
let box boxNum (board:Value[,]) : Value list =
let startX, endX, startY, endY = match boxNum with
| 0 -> 0, 2, 0, 2
| 1 -> 3, 5, 0, 2
| 2 -> 6, 8, 0, 2
| 3 -> 0, 2, 3, 5
| 4 -> 3, 5, 3, 5
| 5 -> 6, 8, 3, 5
| 6 -> 0, 2, 6, 8
| 7 -> 3, 5, 6, 8
| 8 -> 6, 8, 6, 8
| _ -> failwith "Invalid box values. range: 0-8"
[startY..endY]
|> List.fold (fun acc x -> (getLinearElements (fun acc e -> board.[x, e] :: acc) startX endX board) @ acc) []
let containsDuplicates list : bool =
List.length list <> (list |> List.distinct |> List.length)
// Check if a particular board is solved by returning it's BoardSolved status.
let boardSolved (board:Value[,]) : BoardSolved =
let makeLists func =
List.init 1 (fun x -> List.init 9 (fun y -> func y board))
// check that all squares are locked
let allLocked = board |> Seq.cast<Value>
|> Seq.forall (fun e -> match e with
| Locked _ -> true
| _ -> false)
match allLocked with
| false -> BoardUnlocked
// check for duplicates
| true -> match makeLists row |> List.exists (fun x -> x |> List.exists (containsDuplicates)) with
| true -> InvalidSolution
| false -> match makeLists column |> List.exists (fun x -> x |> List.exists (containsDuplicates)) with
| true -> InvalidSolution
| false -> match makeLists box |> List.exists (fun x -> x |> List.exists (containsDuplicates)) with
| true -> InvalidSolution
| false -> Solved
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