Data commit

Task/Mertens-function/Haskell/mertens-function.hs

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+import           Data.List.Split          (chunksOf)
+import qualified Data.MemoCombinators  as Memo
+import           Math.NumberTheory.Primes (unPrime, factorise)
+import           Text.Printf              (printf)
+
+moebius :: Integer -> Int
+moebius = product . fmap m . factorise
+  where
+    m (p, e)
+      | unPrime p == 0 = 0
+      | e == 1 = -1
+      | otherwise = 0
+
+mertens :: Integer -> Int
+mertens = Memo.integral (\n -> sum $ fmap moebius [1..n])
+
+countZeros :: [Integer] -> Int
+countZeros = length . filter ((==0) . mertens)
+
+crossesZero :: [Integer] -> Int
+crossesZero = length . go . fmap mertens
+  where
+    go (x:y:xs)
+      | y == 0 && x /= 0 = y : go (y:xs)
+      | otherwise        = go (y:xs)
+    go _ = []
+
+main :: IO ()
+main = do
+  printf "The first 99 terms for M(1..99):\n\n   "
+  mapM_ (printf "%3d" . mertens) [1..9] >> printf "\n"
+  mapM_ (\row -> mapM_ (printf "%3d" . mertens) row >> printf "\n") $ chunksOf 10 [10..99]
+  printf "\nM(n) is zero %d times for 1 <= n <= 1000.\n" $ countZeros [1..1000]
+  printf "M(n) crosses zero %d times for 1 <= n <= 1000.\n" $ crossesZero [1..1000]