{-# LANGUAGE BangPatterns #-} -- | Functions for finding /lowest common ancestors/ in trees in /O(1)/ time, with /O(n)/ preprocessing. module Data.RangeMin.LCA (Index, lowestCommonAncestor, quickLCA) where import Data.RangeMin.LCA.IndexM import Data.RangeMin import Data.RangeMin.Common.Vector import qualified Data.RangeMin.Mixed as Mix import qualified Data.Vector.Generic as G import qualified Data.Vector.Unboxed as UV import qualified Data.Vector as V import qualified Data.Vector.Fusion.Stream as S import Data.Vector.Fusion.Stream.Size import Data.Tree -- | Labels a tree in depth-first order. dfOrder :: Tree a -> (Tree (Index, a), Int) dfOrder tree = execIndexM $ indexer tree where indexer (Node a ts) = do i <- getIndex ts' <- mapM indexer ts return (Node (i, a) ts') type Depth = Int data Trav a = Trav {-# UNPACK #-} !Depth {-# UNPACK #-} !Index a travel :: (a -> Index) -> Tree a -> [Trav a] -> [Trav a] travel f = trav' 0 where trav' !d (Node x ts) zs = let me = Trav d (f x) x in me:foldr (\ t -> trav' (d+1) t . (me:)) zs ts -- | Takes a tree and indexes it in depth-first order, returning the number of nodes, the indexed -- tree, and the lowest common ancestor function. quickLCA :: Tree a -> (Int, Tree (Index, a), Index -> Index -> (Index, a)) quickLCA tree = case dfOrder tree of (iTree, n) -> (n, iTree, lowestCommonAncestor n fst iTree) -- | @'lowestCommonAncestor' n ix tree@ takes a tree whose nodes are mapped by -- @ix@ to a unique index in the range @0..n-1@, and returns a function -- which takes two indices (corresponding to two nodes in the tree) and returns -- the label of their /lowest common ancestor/. -- -- This takes /O(n)/ preprocessing and answers queries in /O(1)/, as it is an -- application of "Data.RangeMin". -- -- For binary trees, consider using "Data.RangeMin.LCA.Binary". lowestCommonAncestor :: Int -> (a -> Index) -> Tree a -> Index -> Index -> a lowestCommonAncestor !n ix tree = vals `seq` lca where traversal = G.unstream $ S.map (\ (Trav d i a) -> ((d, i), a)) $ S.fromList (travel ix tree []) `S.sized` Max (2 * n - 1) ixs :: UV.Vector Int !ixs = vec n $ S.map (\ (a, b) -> (b, a)) $ S.indexed $ S.map (snd . fst) $ G.stream traversal !(dixs, !vals) = (Mix.unzip :: Mix.MixVector UV.Vector V.Vector (a, b) -> (UV.Vector a, V.Vector b)) traversal (!depths, _) = UV.unzip dixs rM :: Int -> Int -> Int !rM = vecRangeMin depths {-# NOINLINE lca #-} lca !i !j = let iIx = ixs ! i jIx = ixs ! j in vals ! case compare iIx jIx of EQ -> iIx LT -> rM iIx (jIx - iIx + 1) GT -> rM jIx (iIx - jIx + 1)