HaskellでNクイーン問題

N_Queen.hs

import Data.List
import System.Environment

main :: IO ()
main = do
    [n] <- getArgs
    let ans = solves (read n)
    mapM_ print ans
    print $ length ans

type Queens = [Int]
type State = (Queens,[[Int]])

solves :: Int -> [Queens]
solves n = solve n ([],[possible n []])

solve :: Int -> State -> [Queens]
solve n (qs,[]) = []
solve n (qs,ss) | length qs == n = qs:(solve n $ back (qs,ss))
                | otherwise = solve n $ next n (qs,ss)

gen :: Int -> Queens -> [Int]
gen i [] = []
gen i (q:qs) = [q-i,q,q+i] ++ (gen (i+1) qs)

possible :: Int -> Queens -> [Int]
possible n qs = [1..n] \\ (gen 1 qs)

back :: State -> State
back ((q:qs),([]:ss)) = back (qs,ss)
back ((q:qs),(s:ss)) = ((head s):qs,(tail s):ss)
back (_,_) = ([],[])

next :: Int -> State -> State
next n ([],(s:ss)) = ([head s],(tail s):ss)
next n (qs,ss) = let ps = possible n qs
                in if null ps
                      then back (qs,ss)
                      else ((head ps):qs,(tail ps):ss)