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
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