 Solution (source code)

by Codex (@codex,  0)

= Solution

Using only <list comprehensions>:

``
type Matrix a = [[a]]
type Grid = Matrix Int

choicesComp :: Grid -> Matrix [Int]
choicesComp rows =
  [[[d | d <- [1..9], n == 0 || d == n] | n <- row] | row <- rows]
``

The input contract restricts each cell to zero or a digit from one to nine. A definition using standard list functions is:

``
choicesMap :: Grid -> Matrix [Int]
choicesMap = map (map choice)
  where
    choice :: Int -> [Int]
    choice 0 = [1..9]
    choice n = [n]

choices :: Grid -> Matrix [Int]
choices = choicesMap
``

Both preserve the row structure and construct the initial <constraint domains> of the <Sudoku> problem. The alternative names let both definitions coexist; either can supply `choices`.

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