Am Donnerstag, 12. Februar 2009 20:19 schrieb Thomas Davie:
On 12 Feb 2009, at 19:33, Brent Yorgey wrote:
On Thu, Feb 12, 2009 at 11:58:21AM -0500, Andrew Wagner wrote:
<rant> It seems everyone has just been reading the first few words of Jan's email and not the actual content. Jan is clearly trying to write a *random list shuffling* function, not a function to generate permutations. Let's try to be helpful, people... </rant>
Agreed, I've been quite confused by this thread. In the spirit of laziness, though, wouldn't it seem like the "right" method is to generate all the permutations lazily, and then choose a random element of that list?
Well, it sounds nice, but it's pretty inefficient. And by "pretty inefficient" I mean "horrendously, terribly inefficient" -- there are n! permutations of a list of length n, so this would take time O(n!) as opposed to O(n); O(n!) is even worse than O(2^n).
Would it? We're talking about lazyness here... it's not gonna compute one it doesn't need, and if you're somewhat cleverer with your permute function than I was, I'm sure you can do as little computation as the imperative version.
Bob
But to find the k-th permutation, it would have to traverse k cons cells containing thunks, wouldn't it? Well, the following is O(n^2), not quite O(n), but at least it's not "horrendously, terribly inefficient". module Permutations where import Data.List (sortBy, genericSplitAt, genericLength) import Data.Ord (comparing) factorialDigits :: Integer -> [Integer] factorialDigits k = go k 2 where go 0 _ = [] go m d = case m `divMod` d of (q,r) -> r:go q (d+1) permIndices :: Integer -> [Integer] permIndices k = go [0] 1 fds where fds = factorialDigits k go acc d [] = acc ++ [d .. ] go acc d (p:ps) = case genericSplitAt (d-p) acc of (front,back) -> go (front ++ d:back) (d+1) ps kthPerm :: Integer -> [a] -> [a] kthPerm k = map snd . sortBy (comparing fst) . zip (permIndices k)