{-# LANGUAGE BangPatterns, MagicHash #-} module Data.RangeMin.Cartesian (buildDepths) where import Data.RangeMin.Common.Types import qualified Data.Vector.Generic as G import qualified Data.Vector.Primitive as PV import qualified Data.Vector as V import qualified Data.RangeMin.Fusion as F -- import qualified Data.RangeMin.Fusion.Stream as S -- import qualified Data.Vector.Fusion.Stream.Monadic as SM -- import Data.Vector.Fusion.Stream (Step (..), Stream) -- import qualified Data.Vector.Fusion.Stream as S import Data.RangeMin.Common.Vector import Data.RangeMin.Cartesian.STInt import Prelude hiding (read) -- | A 'CartesianTree' is a tree, specified in the following format: the -- @i@th entry of the vector is the parent of node @i@, or is @-1@ for the -- root. type CartesianTree = PV.Vector Int data IL = IL {-# UNPACK #-} !Int IL | Nil {-# INLINE buildDepths #-} -- | /O(n)/. Given a comparison function and a vector, this function constructs a -- @'PV.Vector' 'Int'@ with the property that the minimum index between @i@ and @j@ -- in the result vector is the same as the minimum index between @i@ and @j@ in the -- original vector. (In both cases, ties are broken by which index comes first.) -- -- This allows us to use the specialized range-min implementation on @'PV.Vector' 'Int'@, -- even for other 'Vector' implementations, other element types, and other comparison -- functions. -- -- Internally, this function constructs the Cartesian tree of the input vector -- (implicitly, to save memory and stack space), and returns the vector of the -- depth of each element in the tree. buildDepths :: Vector v a => LEq a -> v a -> PV.Vector Int buildDepths (<=?) xs = makeDepths (makeTree (<=?) (G.length xs) (xs !)) -- | This method takes as input a tree, specified as an array in which the -- @i@th entry is the parent of node @i@, or @-1@ for the root. It returns -- the vector of the depths of each node. makeDepths :: CartesianTree -> PV.Vector Int makeDepths !parents = inlineCreate $ do let !n = PV.length parents !dest <- newWith n (-1) let depth !i = toSTInt $ do d0 <- read dest i case d0 of -1 -> case parents ! i of -- this node has not been visited -1 -> do -- this is the root of the entire tree write dest i 0 return 0 p -> do -- recurse to this node's parent !d' <- runSTInt (depth p) let !d = d' + 1 write dest i d return d _ -> return d0 -- this node has been visited mapM_ (runSTInt . depth) [0..n-1] return dest {-# INLINE makeTree #-} -- | This method constructs the cartesian tree of the input. makeTree :: LEq a -> Int -> (Int -> a) -> CartesianTree makeTree (<=?) !n look = inlineCreate $ do !dest <- new n F.unsafeUpdate dest (vmap (\ (IP i j) -> (i, j)) (vmapAccumL suc Nil rightScan)) let parent (i, l) = do r <- read dest i write dest i $ case (l, r) of (-1, -1) -> -1 (-1, r) -> r (l, -1) -> l (l, r) -> if look l <=? look r then r else l F.mapM_ parent (vmap (\ (IP i j) -> (i, j)) (vmapAccumL suc Nil leftScan)) return dest where vmapAccumL = F.mapAccumL :: (b -> a -> (c, b)) -> b -> V.Vector a -> V.Vector c vmap = F.map :: (a -> b) -> V.Vector a -> V.Vector b rightScan = F.unfoldN n (\ !i -> if i == 0 then Nothing else let !i' = i - 1 xi' = look i' in Just ((i', xi'), i')) n leftScan = F.generate n (\ !i -> (i, look i)) suc stk (!i, xi) = let run Nil = (IP i (-1), IL i Nil) run stk0@(IL j stk) | not (xi <=? look j) = (IP i j, IL i stk0) | otherwise = run stk in run stk {-# RULES "buildDepths" buildDepths = \ (<=?) xs -> makeDepths (makeTree (<=?) (G.length xs) (xs !)); #-}