Heh, didn't know what else to title this sort of scrapbook/notebook entry. Basically I hadn’t looked at Codewars for a long time, so I went back and tried the next “Kata”.
Problem: Given two integers m, n (1 <= m <= n) we want to find all integers between m and n whose sum of squared divisors is itself a square.
(E.g. 42 has divisors: 1,2,3,6,7,14,21,42, the squares of which are 1,4,9,3649,196,441,1764, and sum to 2500, which is a square)
I wrote my trivial solution, tried it and the submission failed because it timed out. So I hacked away, and uglified my solution, until it was using “memoized” divisors.
I ran it locally and it seemed faster, then I submitted it, and … it timed out again. I gave up, and moved on. I guess the lesson to be learnt is that it's always easy to code yourself into a corner?
module Codewars.G964.Sumdivsq where import Data.List import Data.Map as M intSqrt :: Int -> Int intSqrt = floor . sqrt . fromIntegral isSquare :: Int -> Bool isSquare x = x == (intSqrt x)^2 sumSq :: [Int] -> Int sumSq list = sum [x^2 | x <- list] multiply :: Int -> [Int] -> [Int] multiply factor oldDivlist = factor : oldDivlist ++ (Data.List.map (* factor) oldDivlist) divisorHelper :: Int -> Int -> Int -> (Map Int [Int]) -> [Int] -> (Map Int [Int], [Int]) divisorHelper n lower upper knownDivs listDivs = if lower > upper then (M.insert n listDivs knownDivs, listDivs) else let otherDiv = n `div` lower in if (n `rem` lower /= 0) then -- Keep going till we can divide divisorHelper n (lower+1) upper knownDivs listDivs else if otherDiv == lower then -- Special case: we reach a square divisor (M.insert n (lower : listDivs) knownDivs, lower : listDivs) -- Ok, we need to know if we've seen the bigger number before else case M.lookup otherDiv knownDivs of Just oldDivlist -> -- We're done! let newDivlist = nub $ (lower : listDivs) ++ (multiply lower oldDivlist) in (M.insert n newDivlist knownDivs, newDivlist) Nothing -> divisorHelper n (lower+1) (otherDiv-1) knownDivs (lower : otherDiv : listDivs) divisors :: Int -> (Map Int [Int]) -> (Map Int [Int], [Int]) divisors n knownDivs = divisorHelper n 1 n knownDivs  listSquaredHelper :: Int -> Int -> Map Int [Int] -> [(Int, Int)] -> [(Int, Int)] listSquaredHelper lower upper knownDivs sqList = if lower > upper then sqList else let (newKnownDivs, divs) = divisors lower knownDivs s = sumSq divs in if isSquare s then listSquaredHelper (lower+1) upper newKnownDivs ((lower,s):sqList) else listSquaredHelper (lower+1) upper newKnownDivs sqList listSquared :: Int -> Int -> [(Int, Int)] listSquared m n = reverse $ listSquaredHelper m n M.empty 
I clearly have a long way to go in understanding the “why” of Haskell performance. My initial solution was much, uh ... simpler. I didn't save it but I translated that into Clojure, which looks something like this:
(ns sumdivsq.core) (defn is-square [n] (== n (Math/pow (int (Math/sqrt n)) 2))) (defn sum-sq [lst] (int (reduce + (map #(Math/pow % 2) lst)))) (defn divisors [n] (if (== n 1)  (conj (filter #(== 0 (mod n %)) (range 1 (inc (/ n 2)))) n))) (defn list-squared [m n] (letfn [(lfh [n] (let [ssq (sum-sq (divisors n))] (when (is-square ssq) [n, ssq])))] (keep #(lfh %) (range m n))))
Certainly looks very nice, and it passed all the tests, but I was too impatient to begin optimizing it, and left this one behind too ...