tasks a-s

Task/Permutations-Derangements/Haskell/permutations-derangements-1.hs

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+import Control.Monad
+import Data.List
+
+-- Compute all derangements of a list
+derangements xs = filter (and . zipWith (/=) xs) $ permutations xs
+
+-- Compute the number of derangements of n elements
+subfactorial 0 = 0
+subfactorial 1 = 0
+subfactorial 2 = 1
+subfactorial n = (n-1) * (subfactorial (n-1) + subfactorial (n-2))
+
+main = do
+  -- Generate and show all the derangements of four integers
+  print $ derangements [1..4]
+  putStrLn ""
+
+  -- Print the count of derangements vs subfactorial
+  forM_ [1..9] $ \i ->
+      putStrLn $ show (length (derangements [1..i])) ++ " " ++
+                 show (subfactorial i)
+  putStrLn ""
+
+  -- Print the number of derangements in a list of 20 items
+  print $ subfactorial 20

Task/Permutations-Derangements/Haskell/permutations-derangements-2.hs

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+derangements xs = loop xs xs
+    where loop [] [] = [[]]
+          loop (h:hs) xs = [x:ys | x <- xs, x /= h, ys <- loop hs (delete x xs)]