What optimizations can be made to this Haskell code?

Question

--Returns last N elements in list
lastN :: Int -> [a] -> [a]
lastN n xs = let m = length xs in drop (m-n) xs

--create contiguous array starting from index b within list a
produceContiguous :: [a] -> Int -> [[a]]
produceContiguous [] _ = [[]]  
produceContiguous arr ix = scanl (\acc x -> acc ++ [x]) [arr !! ix] inset
    where inset = lastN (length arr - (ix + 1)) arr

--Find maximum sum of all possible contiguous sub arrays, modulo [n]
--d is dummy data
let d = [1,2,3,10,6,3,1,47,10]
let maxResult = maximum $ map (\s -> maximum s) $ map (\c -> map (\ac -> (sum ac )`mod` (last n)) c ) $ map (\n -> produceContiguous d n ) [0..(length d) -1]

I'm a Haskell newb - just a few days into it .. If I'm doing something obviously wrong, whoopsies

Answer 1

You can improve the runtime a lot by observing that map sum (produceContiguous dn) (which has runtime Ω(m^2), m the length of drop nd -- possibly O(m^3) time because you're appending to the end of acc on each iteration) can be collapsed to scanl (+) 0 (drop nd) (which has runtime O(m)). There are plenty of other stylistic changes I would make as well, but that's the main algorithmic one I can think of.

Cleaning up all the stylistic stuff, I would probably write:

import Control.Monad
import Data.List
addMod n x y = (x+y) `mod` n
maxResult n = maximum . (scanl (addMod n) 0 <=< tails)

In ghci:

*Main> jaggedGoofyMax 100 [1..1000]
99
(12.85 secs, 24,038,973,096 bytes)
*Main> dmwitMax 100 [1..1000]
99
(0.42 secs, 291,977,440 bytes)

Not shown here is the version of jaggedGoofyMax that has only the optimization I mentioned in my first paragraph applied, which has slightly better runtime/memory usage stats to dmwitMax when run in ghci (but basically identical to dmwitMax when both are compiled with -O2 ). So you can see that for even modest input sizes this optimization can make a big difference.