-- | -- Module : System.Random.Shuffle -- Copyright : (c) 2009 Oleg Kiselyov, Manlio Perillo -- License : BSD3 (see LICENSE file) -- -- http://okmij.org/ftp/Haskell/perfect-shuffle.txt -- module System.Random.Shuffle ( shuffle , shuffle' ) where import Data.Function (fix) import System.Random (RandomGen, randomR) -- A complete binary tree, of leaves and internal nodes. -- Internal node: Node card l r -- where card is the number of leaves under the node. -- Invariant: card >=2. All internal tree nodes are always full. data Tree a = Leaf {-# UNPACK #-} !a | Node {-# UNPACK #-} !Int !(Tree a) !(Tree a) deriving Show -- Convert a sequence (e1...en) to a complete binary tree buildTree :: [a] -> Tree a buildTree = (fix growLevel) . (map Leaf) where growLevel _ [node] = node growLevel self l = self $ inner l inner [] = [] inner [e] = [e] inner (e1 : e2 : es) = e1 `seq` e2 `seq` (join e1 e2) : inner es join l@(Leaf _) r@(Leaf _) = Node 2 l r join l@(Node ct _ _) r@(Leaf _) = Node (ct + 1) l r join l@(Leaf _) r@(Node ct _ _) = Node (ct + 1) l r join l@(Node ctl _ _) r@(Node ctr _ _) = Node (ctl + ctr) l r -- Given a sequence (e1,...en) to shuffle, and a sequence -- (r1,...r[n-1]) of numbers such that r[i] is an independent sample -- from a uniform random distribution [0..n-i], compute the -- corresponding permutation of the input sequence. shuffle :: [a] -> [Int] -> [a] shuffle elements = shuffleTree (buildTree elements) where shuffleTree (Leaf e) [] = [e] shuffleTree tree (r : rs) = let (b, rest) = extractTree r tree in b : (shuffleTree rest rs) -- Extracts the n-th element from the tree and returns -- that element, paired with a tree with the element -- deleted. -- The function maintains the invariant of the completeness -- of the tree: all internal nodes are always full. -- NOTE: the collection of patterns below is deliberately not -- complete. -- All the missing cases may not occur -- (and if they do, that's an error). extractTree 0 (Node _ (Leaf e) r) = (e, r) extractTree 1 (Node 2 (Leaf l) (Leaf r)) = (r, Leaf l) extractTree n (Node c (Leaf l) r) = let (e, r') = extractTree (n - 1) r in (e, Node (c - 1) (Leaf l) r') extractTree n (Node n' l (Leaf e)) | n + 1 == n' = (e, l) extractTree n (Node c l@(Node cl _ _) r) | n < cl = let (e, l') = extractTree n l in (e, Node (c - 1) l' r) | otherwise = let (e, r') = extractTree (n - cl) r in (e, Node (c - 1) l r') -- Given a sequence (e1,...en) to shuffle, its length, and a random -- generator, compute the corresponding permutation of the input -- sequence. shuffle' :: RandomGen gen => [a] -> Int -> gen -> [a] shuffle' elements len = shuffle elements . rseq len where -- The sequence (r1,...r[n-1]) of numbers such that r[i] is an -- independent sample from a uniform random distribution -- [0..n-i] rseq :: RandomGen gen => Int -> gen -> [Int] rseq n = fst . unzip . rseq' (n - 1) where rseq' :: RandomGen gen => Int -> gen -> [(Int, gen)] rseq' 0 _ = [] rseq' i gen = (j, gen) : rseq' (i - 1) gen' where (j, gen') = randomR (0, i) gen