Initial data commit

Task/Recamans-sequence/Haskell/recamans-sequence-3.hs

@@ -0,0 +1,47 @@
+import Data.List (find, findIndex, nub)
+import Data.Maybe (fromJust)
+import Data.Set (Set, fromList, insert, isSubsetOf, member)
+
+--- INFINITE STREAM OF RECAMAN SERIES OF GROWING LENGTH --
+rSeries :: [[Int]]
+rSeries =
+  scanl
+    ( \rs@(r : _) i ->
+        let back = r - i
+            nxt
+              | 0 > back || elem back rs = r + i
+              | otherwise = back
+         in nxt : rs
+    )
+    [0]
+    [1 ..]
+
+----------- INFINITE STREAM OF RECAMAN-GENERATED ---------
+--------------- INTEGER SETS OF GROWING SIZE -------------
+rSets :: [(Set Int, Int)]
+rSets =
+  scanl
+    ( \(seen, r) i ->
+        let back = r - i
+            nxt
+              | 0 > back || member back seen = r + i
+              | otherwise = back
+         in (insert nxt seen, nxt)
+    )
+    (fromList [0], 0)
+    [1 ..]
+
+--------------------------- TEST -------------------------
+main :: IO ()
+main = do
+  let setK = fromList [0 .. 1000]
+  (putStrLn . unlines)
+    [ "First 15 Recamans:",
+      show . reverse . fromJust $ find ((15 ==) . length) rSeries,
+      [],
+      "First duplicated Recaman:",
+      show . head . fromJust $ find ((/=) <$> length <*> (length . nub)) rSeries,
+      [],
+      "Length of Recaman series required to include [0..1000]:",
+      show . fromJust $ findIndex (\(setR, _) -> isSubsetOf setK setR) rSets
+    ]