Am 14.04.2011 12:29, schrieb Dmitri O.Kondratiev:
3n+1 is the first, "warm-up" problem at Programming Chalenges site: http://www.programming-challenges.com/pg.php?page=downloadproblem&probid=110101&format=html http://www.programming-challenges.com/pg.php?page=downloadproblem&probid=110101&format=html
(This problem illustrates Collatz conjecture: http://en.wikipedia.org/wiki/3n_%2B_1#Program_to_calculate_Collatz_sequences)
As long as the judge on this site takes only C and Java solutions, I submitted in Java some add-hock code (see at the end of this message) where I used recursion and a cache of computed cycles. Judge accepted my code and measured 0.292 sec with best overall submissions of 0.008 sec to solve the problem.
*** Question: I wonder how to implement cache for this problem in Haskell? At the moment, I am not so much interested in the speed of the code, as in nice implementation.
I'ld use something like: import qualified Data.Map as Map addToMap :: Integer -> Map.Map Integer Integer -> Map.Map Integer Integer addToMap n m = case Map.lookup n m of Nothing -> let l = if even n then div n 2 else 3 * n + 1 p = addToMap l m Just s = Map.lookup l p in Map.insert n (s + 1) p Just _ -> m addRangeToMap :: Integer -> Integer -> Map.Map Integer Integer -> Map.Map Integer Integer addRangeToMap i j m = if j < i then m else addRangeToMap i (j - 1) $ addToMap j m getMaxLength :: Integer -> Integer -> Map.Map Integer Integer -> Integer getMaxLength i j = Map.foldWithKey (\ k l -> if i > k || k > j then id else max l) 0 -- putting it all togeter getRangeMax :: Integer -> Integer -> Integer getRangeMax i j = getMaxLength i j $ addRangeToMap i j $ Map.singleton 1 1