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-rw-r--r--lore/System/Random/Shuffle.hs122
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diff --git a/lore/System/Random/Shuffle.hs b/lore/System/Random/Shuffle.hs
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--- a/lore/System/Random/Shuffle.hs
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-{- |
-Module : System.Random.Shuffle
-Copyright : (c) 2009 Oleg Kiselyov, Manlio Perillo
-License : BSD3 (see LICENSE file)
-
-<http://okmij.org/ftp/Haskell/perfect-shuffle.txt>
-
-
-Example:
-
- import System.Random (newStdGen)
- import System.Random.Shuffle (shuffle')
-
- main = do
- rng <- newStdGen
- let xs = [1,2,3,4,5]
- print $ shuffle' xs (length xs) rng
--}
-{-# OPTIONS_GHC -funbox-strict-fields #-}
-
-module System.Random.Shuffle
- ( shuffle
- , shuffle'
- , shuffleM
- )
-where
-
-import Data.Function ( fix )
-import System.Random ( RandomGen
- , randomR
- )
-import Control.Monad ( liftM
- , liftM2
- )
-import Control.Monad.Random ( MonadRandom
- , getRandomR
- )
-
-
--- | 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 !a
- | Node !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)
- shuffleTree _ _ = error "[shuffle] called with lists of different lengths"
-
- -- 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.
- 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')
- extractTree _ _ = error "[extractTree] impossible"
-
--- |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
-
--- |shuffle' wrapped in a random monad
-shuffleM :: (MonadRandom m) => [a] -> m [a]
-shuffleM elements
- | null elements = return []
- | otherwise = liftM (shuffle elements) (rseqM (length elements - 1))
- where
- rseqM :: (MonadRandom m) => Int -> m [Int]
- rseqM 0 = return []
- rseqM i = liftM2 (:) (getRandomR (0, i)) (rseqM (i - 1))