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

In general you are probably going to be stuck paying the O(log n) complexity tax for a functional non-destructive implementation or you'll have to relent and use an (IO|ST|STM)UArray.

Strict pure languages may have to pay an O(log n) tax over an impure language that can write to references by implementing references through a map-like structure; lazy languages can sometimes dodge this tax, although there is no proof either way whether or not the extra power offered by laziness is sufficient to always dodge this tax -- even if it is strongly suspected that laziness isn't powerful enough.

In this case it is hard to see a mechanism by which laziness could be exploited to avoid the reference tax. And, after all that is why we have the ST monad in the first place. ;)

That said, you might investigate whether or not some kind of board-diagonal zipper could be used to exploit locality of updates -- exploiting locality in a zipper is a common way to try to drop a logarithmic term.