Lah numbers: Difference between revisions

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 <lang haskell>import Text.Printf (printf)
 import Control.Monad (when)
+import Control.Applicative (liftA2)
-factorial :: Integral n => n -> n
+factorial
+  :: Integral n
+  => n -> n
 factorial 0 = 1
-factorial n = product [1..n]
+factorial n = product [1 .. n]
+lah
-lah :: Integral n => n -> n -> n
+  :: Integral n
+  => n -> n -> n
 lah n k
   | k == 1 = factorial n
   | k == n = 1
-  | k > n  = 0
+  | k > n = 0
   | k < 1 || n < 1 = 0
-  | otherwise = (factorial n * factorial (pred n)) `div`
+  | otherwise = f n `div` f k `div` factorial (n - k)
+  where
-                (factorial k * factorial (pred k)) `div`
-                factorial (n - k)
+    f = (*) . factorial <*> (factorial . pred)
 printLah :: (Word, Word) -> IO ()
@@ Line 492: / Line 497: @@
   mapM_ (printf "%11d") zeroToTwelve
   mapM_ printLah $ (,) <$> zeroToTwelve <*> zeroToTwelve
+  printf
-  printf "\nMaximum value from the L(100, *) row:\n%d\n"
-    (maximum $ lah 100 <$> ([0..100] :: [Integer]))
+    "\nMaximum value from the L(100, *) row:\n%d\n"
+    (maximum $ lah 100 <$> ([0 .. 100] :: [Integer]))
-  where zeroToTwelve = [0..12]</lang>
+  where
+    zeroToTwelve = [0 .. 12]</lang>
 {{out}}
 <pre>Unsigned Lah numbers: L(n, k):