Euler question 14 - start

.vscode/settings.json

@@ -1,5 +1,6 @@
 {
   "cSpell.words": [
+    "Collatz",
     "concat",
     "coprime",
     "elems",

src/projectEuler/question14.hs

@@ -0,0 +1,48 @@
+{-
+The following iterative sequence is defined for the set of positive integers:
+    n -> n/2  (n is even)
+    n -> 3n+1 (n is odd )
+
+Using the rule above and starting with 13, we generate the following sequence:
+
+    13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
+
+It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms.
+Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
+
+Which starting number, under one million, produces the longest chain?
+
+NOTE: Once the chain starts the terms are allowed to go above one million.
+-}
+module Main where
+
+-- import           Data.Set    (Set)
+-- import qualified Data.Set    as Set
+
+import           Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+
+main :: IO ()
+main = print ans
+
+ans :: Integer
+ans = 42
+
+nextCollatz n
+  | n == 1 = 0
+  | even n = n `div` 2
+  | odd  n = 3*n + 1
+
+collatzChainStartingAt n = takeWhile (/= 0) $ iterate nextCollatz n
+
+-- solve limit = (n, chain)
+--   where
+--     s = maximum
+--       $ map length
+--       $ map collatzChainStartingAt [1..limit]
+limit = 1_000_000
+
+wholePositiveNumbers :: IntSet
+wholePositiveNumbers = IntSet.fromDistinctAscList [1..limit]
+
+f = IntSet.foldl (\acc key -> collatzChainStartingAt key : acc) []