Data commit

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

@@ -0,0 +1,33 @@
+import Control.Monad (forM_)
+
+import Data.List (permutations)
+
+-- Compute all derangements of a list
+derangements
+  :: Eq a
+  => [a] -> [[a]]
+derangements = (\x -> filter (and . zipWith (/=) x)) <*> permutations
+
+-- Compute the number of derangements of n elements
+subfactorial
+  :: (Eq a, Num a)
+  => a -> a
+subfactorial 0 = 1
+subfactorial 1 = 0
+subfactorial n = (n - 1) * (subfactorial (n - 1) + subfactorial (n - 2))
+
+main :: IO ()
+main
+-- Generate and show all the derangements of four integers
+ = do
+  print $ derangements [1 .. 4]
+  putStrLn ""
+  -- Print the count of derangements vs subfactorial
+  forM_ [1 .. 9] $
+    \i ->
+       putStrLn $
+       mconcat
+         [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)]