N-queens in Haskell without list traversal

Question

I searched the web for different solutions to the n-queens problem in Haskell but couldn\'t find any that could check for unsafe positions in O(1) time, like that one that you k

Answer 1

Probably the most straightforward way would be to use a UArray (Int, Int) Bool to record safe/unsafe bits. Although copying this is O(n²), for small values of N this is the fastest method available.

For larger values of N, there are three major options:

• Data.DiffArray removes copy overhead as long as you never use the old values again after modifying them. That is, if you always throw away the old value of the array after mutating it, the modification is O(1). If, however, you access the old value of the array later (even for only a read), the O(N²) is paid then in full.
• Data.Map and Data.Set allow O(lg n) modifications and lookups. This changes the algorithmic complexity, but is often fast enough.
• Data.Array.ST's STUArray s (Int, Int) Bool will give you imperative arrays, allowing you to implement the algorithm in the classic (non-functional) manner.