Question

I am trying to build a Sudoku solver for a project I am working on. I have a 9×9 grid with each position numbered 0..80, left to right, top to bottom

e.g.:

0 1 2 3 4 5 6 7 8

9 10 …

I am trying to return a list of Int’s that represent the 3×3 grid that a position falls in. For example for position 1, which is in grid (0,0) it would return [0,1,2,9,10,11,18,19,20] and for position 8, which is in grid (0,2) it would return [6,7,8,15,16,17,24,25,26].

I have written a function which returns the required 3×3 grid, on a 9×9 Sudoku:

getBlock :: Int -> Int -> [[Int]]
getBlock x y = [[((x * sudokuSizeSq + 0) * sudokuSize) + (y * sudokuSizeSq + 0),((x * sudokuSizeSq + 0) * sudokuSize) + (y * sudokuSizeSq + 1)..((x * sudokuSizeSq + 0) * sudokuSize) + (y * sudokuSizeSq + (sudokuSizeSq-1))],[((x * sudokuSizeSq + 1) * sudokuSize) + (y * sudokuSizeSq + 0),((x * sudokuSizeSq + 1) * sudokuSize) + (y * sudokuSizeSq + 1)..((x * sudokuSizeSq + 1) * sudokuSize) + (y * sudokuSizeSq + (sudokuSizeSq-1))],[((x * sudokuSizeSq + 2) * sudokuSize) + (y * sudokuSizeSq + 0),((x * sudokuSizeSq + 2) * sudokuSize) + (y * sudokuSizeSq + 1)..((x * sudokuSizeSq + 2) * sudokuSize) + (y * sudokuSizeSq + (sudokuSizeSq-1))]]

Where:
sudokuSizeSq is the square of the width (3)
sudokuSize is the width (9)

x and y represent the possible grids.

This works, however I would like to increase it so it will work for larger grids. I changed my code to the follow but it seems then wont load the function.

getBlock :: Int -> Int -> [[Int]]
getBlock x y = [[((x * sudokuSizeSq + 0) * sudokuSize) + (y * sudokuSizeSq + 0),((x * sudokuSizeSq + 0) * sudokuSize) + (y * sudokuSizeSq + 1)..((x * sudokuSizeSq + 0) * sudokuSize) + (y * sudokuSizeSq + (sudokuSizeSq-1))],[((x * sudokuSizeSq + 1) * sudokuSize) + (y * sudokuSizeSq + 0),((x * sudokuSizeSq + 1) * sudokuSize) + (y * sudokuSizeSq + 1)..((x * sudokuSizeSq + 1) * sudokuSize) + (y * sudokuSizeSq + (sudokuSizeSq-1))]..[((x * sudokuSizeSq + (sudokuSizeSq-1)) * sudokuSize) + (y * sudokuSizeSq + 0),((x * sudokuSizeSq + (sudokuSizeSq-1)) * sudokuSize) + (y * sudokuSizeSq + 1)..((x * sudokuSizeSq + (sudokuSizeSq-1)) * sudokuSize) + (y * sudokuSizeSq + (sudokuSizeSq-1))]]

The way I’m doing it seems very cumbersome, is there a better way to do this or a way to fix the problem I’m having. Thanks.

Answer 1

[ a + b
| a <- take sudokuSizeSq $ map (sudokuSize *) [x * sudokuSizeSq .. ]
, b <- take sudokuSizeSq [y * sudokuSizeSq ..] ]