Data commit

Task/Motzkin-numbers/Haskell/motzkin-numbers.hs

@@ -0,0 +1,31 @@
+import Control.Monad.Memo (Memo, memo, startEvalMemo)
+import Math.NumberTheory.Primes.Testing (isPrime)
+import System.Environment (getArgs)
+import Text.Printf (printf)
+
+type I = Integer
+
+-- The n'th Motzkin number, where n is assumed to be ≥ 0.  We memoize the
+-- computations using MonadMemo.
+motzkin :: I -> Memo I I I
+motzkin 0 = return 1
+motzkin 1 = return 1
+motzkin n = do
+  m1 <- memo motzkin (n-1)
+  m2 <- memo motzkin (n-2)
+  return $ ((2*n+1)*m1 + (3*n-3)*m2) `div` (n+2)
+
+-- The first n+1 Motzkin numbers, starting at 0.
+motzkins :: I -> [I]
+motzkins = startEvalMemo . mapM motzkin . enumFromTo 0
+
+-- For i = 0 to n print i, the i'th Motzkin number, and if it's a prime number.
+printMotzkins :: I -> IO ()
+printMotzkins n = mapM_ prnt $ zip [0 :: I ..] (motzkins n)
+  where prnt (i, m) = printf "%2d %20d %s\n" i m $ prime m
+        prime m = if isPrime m then "prime" else ""
+
+main :: IO ()
+main = do
+  [n] <- map read <$> getArgs
+  printMotzkins n