I am starting to doubt if my plan of getting into Haskell and functional programming by using Haskell for my next course on algorithms is a good one.
To get some Haskell lines under my belt I started trying to implement some simple algos. First: Gale-Shapley for the Stable Marriage Problem. Having not yet gotten into monads, all that mutable state looks daunting, so instead I used the characterization of stable matchings as fixed-points of a mapping on the lattice of semi-matchings. It was fun, but its no longer Gale-Shapley and the complexity isn’t nice (those chains in the lattice can get pretty long apparently 🙂
Next up I have the algorithm for Closest Pair of points in the plane, but am stuck on getting the usual O(n*log n) complexity because I can’t work out how to get a set-like data structure with O(1) checking for membership.
So my question is: Can one in general implement most algorithms eg. Dijkstra, Ford-Fulkerson (Gale-Shapley !?) getting the complexities from procedural implementations if one gets a better command of Haskell and functional programming in general ?
This probably can’t be answered in general. A lot of standard algorithms are designed around mutability, and translations exist in some cases, not in others. Sometimes alternate algorithms exist that give equivalent performance characteristics, sometimes you really do need mutability.
A good place to start, if you want understanding of how to approach algorithms in this setting, is Chris Okasaki’s book Purely Functional Data Structures. The book is an expanded version of his thesis, which is available online in PDF format.
If you want help with specific algorithms, such as the O(1) membership checking (which is actually misleading–there’s no such thing, such data structures usually have something like O(k) where k is the size of elements being stored) you’d be better off asking that as a specific, single question instead of a very general question like this.