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{- This is the n Queens problem. -}
module Main where
queens :: Int -> [[Int]]
queens size = queens' size size
queens' :: Int -> Int -> [[Int]]
queens' 0 _ = [[]]
queens' (n+1) size = [q:qs | qs <- queens' n size, q <- [1..size],
not (threatens q qs)]
threatens :: Int -> [Int] -> Bool
threatens q qs = q `elem` qs || q `elem` (diagonals 1 qs)
diagonals :: Int -> [Int] -> [Int]
diagonals _ [] = []
diagonals n (q:qs) = (q+n) : (q-n) : diagonals (n+1) qs
main = appendChan stdout "Enter board size: " abort $
readChan stdin abort $ \input ->
let line1 : ~(line2 : _) = lines input
size = read line1
solns = read line2
in if size == 0 then done else -- This causes the size to actually read
appendChan stdout "Number of solutions: " abort $
appendChan stdout (concat (map (\x -> showBoard size x)
(take solns (queens size))))
abort done
showBoard :: Int -> [Int] -> String
showBoard size pos =
concat (map showRow pos) ++ "\n"
where
showRow n = concat [if i == n then "Q " else ". " | i <- [1..size]]
++ "\n"
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