From e6e3cfbccc8233d22dc7d99ee59f28b4ba571c2a Mon Sep 17 00:00:00 2001
From: Bill Ewanick <bill@ewanick.com>
Date: Tue, 19 Sep 2023 16:31:12 -0400
Subject: [PATCH] Euler question 14 - start

---
 .vscode/settings.json          |  1 +
 src/projectEuler/question14.hs | 48 ++++++++++++++++++++++++++++++++++
 2 files changed, 49 insertions(+)
 create mode 100644 src/projectEuler/question14.hs

diff --git a/.vscode/settings.json b/.vscode/settings.json
index d113012..9700597 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -1,5 +1,6 @@
 {
   "cSpell.words": [
+    "Collatz",
     "concat",
     "coprime",
     "elems",
diff --git a/src/projectEuler/question14.hs b/src/projectEuler/question14.hs
new file mode 100644
index 0000000..c8a4a8e
--- /dev/null
+++ b/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) []