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## Inhoud

#### 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]

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
```

#### nog een alternatief

(alle oplossingen)

```nqueens::Int->[[Int]]
nqueens n = [opl | opl<-(permuteer [1..n]), (safe opl) == True]

permuteer::[Int]->[[Int]]
permuteer [] = [[]]
permuteer rij = [x:xs | x<-rij, xs<-permuteer (filter (/=x) rij)]

safe [] = True
safe (x:xs) = (no_attack x xs 1) && (safe xs)

no_attack _ [] _ = True
no_attack x (l:ls) n = not (x == n + l) && not (l==x+n) && not (x==l) && no_attack x ls (n+1)
```

#### Ik heb nog iets korters gevonden

```--Eerste argument is het aantal queens, het tweede de grootte van het bord
queens 0 _ = [[]]
queens n b = [x:y | y <- queens (n-1) b, x <- [1..b], safe x y 1]
where 	safe x [] n = True
safe x (c:y) n = and [x/=c,x/=c+n,x/=c-n,safe x y (n+1)]
```