Hi, I think that version is still a brute-force solution. The only difference is that it uses EOF (sentinel) so that it can sort the suffixes instead of rotations. However, the big-O complexity is the same. Let's take the rbwt for example:
rbwt xs = let res = sortBy (\(a:as) (b:bs) -> a `compare` b) (zipWith' (:) xs res) in tail . map snd . zip xs $ head res
Here we can see that, although the infinity res is lazy-evaluated, it actually sorts the matrix N times, adding one column per evaluation. each time there are N elements to be sorted and the length of every element grows proportion to N, so the time is O( N * (N^2) * \lg (N^2) ) = O(N^3 \lg N) While my brute-force program provided in previous post is as same as O(N^3 \lg N). However, if the random access time is O(1) (on array) but not O(N) (on list), my 2nd program is much faster: Here is the modified version with Array. (import Data.Array) ibwt'' :: (Ord a) => ([a], Int) -> [a] ibwt'' (r, i) = fst $ iterate f ([], i) !! n where t = listArray (0, n-1) $ map snd $ sort $ zip r [0..] ra = listArray (0, n-1) r f (s, j) = let j' = t ! j in (s++[ra ! j'], j') n = length r This version only sort the input data 1 time, (proportion to O(N * \lg N), after that the transform vector t is generated. Then it iterates N times on t to get the result. so the total time is O(N * \lg N) + O(N) = O(N * \lg N) This should be much better than the brute force one. the idea is that, we can get the result without reconstructing the complete matrix, Only two columns (L & F) are enough. But how to turn the random access idea of transform-vector into purely functional settings? here I mean what if Haskell doesn't provide constant access time array? One idea is to to turn the transform vector T into a function, just like what we've done in KMP implementation in FP way. Does such solution exist? Regards. -- Larry, LIU Xinyu https://github.com/liuxinyu95/AlgoXY On Friday, June 24, 2011 6:50:46 AM UTC+8, Henning Thielemann wrote:
On Wed, 22 Jun 2011, larry.liuxinyu wrote:
Hi,
I read a previous thread about BWT implementation in Haskell: http://www.mail-archive.com/haskell-cafe@haskell.org/msg25609.html and
http://sambangu.blogspot.com/2007/01/burrows-wheeler-transform-in-haskell
They are all in a `brute-force' way, that is implement based on
Burrows-Wheeler's definition like below:
I thought that the knot-tying solution by Bertram Felgenhauer in the same thread was both elegant and efficient: http://www.mail-archive.com/haskell-cafe%40haskell.org/msg25692.html
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