Iteration of a randomized algorithm in fixed space and linear time

Question

I used to ask a similar question once. Now I\'ll be more specific. The purpose is to learn a Haskell idiom to write iterative algorithms with monadic results. In particular,

Answer 1

Importing Control.Monad.State.Strict instead of Control.Monad.State yields a significant performance improvement. Not sure what you're looking for in terms of asymptotics, but this might get you there.

Additionally, you get a performance increase by swapping the iterateM and the mapM so that you don't keep traversing the list, you don't have to hold on to the head of the list, and you don't need to deepseq through the list, but just force the individual results. I.e.:

let end = flip evalState rnd $ mapM (iterateM iters randStep) start

If you do so, then you can change iterateM to be much more idiomatic as well:

iterateM 0 _ x = return x
iterateM n f !x = f x >>= iterateM (n-1) f

This of course requires the bang patterns language extension.