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-- (c) 2000-2005 by Martin Erwig [see file COPYRIGHT]
-- | Minimum-Spanning-Tree Algorithms
module Data.Graph.Inductive.Query.MST (
msTreeAt,msTree,
-- * Path in MST
msPath,
-- * Types used
LRTree
) where
import Data.Graph.Inductive.Graph
import qualified Data.Graph.Inductive.Internal.Heap as H
import Data.Graph.Inductive.Internal.RootPath
newEdges :: LPath b -> Context a b -> [H.Heap b (LPath b)]
newEdges (LP p) (_,_,_,s) = map (\(l,v)->H.unit l (LP ((v,l):p))) s
prim :: (Graph gr,Real b) => H.Heap b (LPath b) -> gr a b -> LRTree b
prim h g | H.isEmpty h || isEmpty g = []
prim h g =
case H.splitMin h of
(_,p@(LP ((v,_):_)),h') ->
case match v g of
(Just c,g') -> p:prim (H.mergeAll (h':newEdges p c)) g'
(Nothing,g') -> prim h' g'
_ -> []
msTreeAt :: (Graph gr,Real b) => Node -> gr a b -> LRTree b
msTreeAt v = prim (H.unit 0 (LP [(v,0)]))
msTree :: (Graph gr,Real b) => gr a b -> LRTree b
msTree g = msTreeAt v g where ((_,v,_,_),_) = matchAny g
msPath :: LRTree b -> Node -> Node -> Path
msPath t a b = joinPaths (getLPathNodes a t) (getLPathNodes b t)
joinPaths :: Path -> Path -> Path
joinPaths p = joinAt (head p) p
joinAt :: Node -> Path -> Path -> Path
joinAt _ (v:vs) (w:ws) | v==w = joinAt v vs ws
joinAt x p q = reverse p++(x:q)
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