Mogelijke oplossing
nqueens::Int->[Int]
-------------------
nqueens n = let
list = [1..n]
permlist = perms list
in
getoklist permlist
getoklist::[[Int]]->[Int]
------------------------
getoklist [] = error "geen oplossing"
getoklist (x:xs) | listok x = x
| otherwise = getoklist xs
listok::[Int]->Bool
-------------------
listok [] = True
listok (a:as) = if (listok2 a as 1) == False then False
else listok as
listok2::Int->[Int]->Int->Bool
------------------------------
listok2 _ [] _ = True
listok2 a (b:bs) kol | a == (b+kol) = False
| a == (b-kol) = False
| otherwise = listok2 a bs (kol+1)
--Permuteer de lijst
perms :: [k] -> [[k]]
---------------------
perms [] = [[]]
perms (x:xs) = concat (map (tussen x) (perms xs)) where
tussen e [] = [[e]]
tussen e (y:ys) = (e:y:ys) : map (y:) (tussen e ys)
Een alternatief
nqueens::Int->[Int]
nqueens n =
let
permutaties = permuteer [1..n]
oplossingen = [p | p<-permutaties, (mog_oplossing p) == True]
in head oplossingen
permuteer::[Int]->[[Int]]
permuteer [] = [[]]
permuteer rij = [x:xs | x<-rij, xs<-permuteer (filter (/=x) rij)]
mog_oplossing::[Int]->Bool
mog_oplossing rij =
let
indexen = get_indexen rij 1
in voldoet indexen []
-- nog af te gaan, reeds afgegaan
voldoet::[Int]->[Int]->Bool
voldoet [] _ = True
voldoet (x:xs) rij =
if (elem x rij) then False
else if ((check_diagonaal (x-2) rij) == False) then False
else voldoet xs ([x]++rij)
get_indexen::[Int]->Int->[Int]
get_indexen [] _ = []
get_indexen (x:xs) w =
let
n_x = x + w
in [n_x] ++ (get_indexen xs (w+1))
check_diagonaal::Int->[Int]->Bool
check_diagonaal _ [] = True
check_diagonaal n (x:xs) =
if n == x then False
else check_diagonaal (n-2) xs