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Diffstat (limited to '80-89/83.hs')
-rw-r--r-- | 80-89/83.hs | 52 |
1 files changed, 52 insertions, 0 deletions
diff --git a/80-89/83.hs b/80-89/83.hs new file mode 100644 index 0000000..f9d9038 --- /dev/null +++ b/80-89/83.hs @@ -0,0 +1,52 @@ +import qualified Data.Map as Map +import Data.Map (Map) +import Data.List (foldl') +import Data.Maybe (fromJust) +import Control.Monad (foldM, mapM) + +data Graph a = Graph [a] [(a, a)] + deriving (Show, Eq) + +k4 = Graph ['a', 'b', 'c', 'd'] + [('a', 'b'), ('b', 'c'), ('c', 'd'), + ('d', 'a'), ('a', 'c'), ('b', 'd')] + +newElem :: Ord a => Map a a -> a -> Maybe (Map a a) +findLead :: Ord a => Map a a -> a -> Maybe (Map a a, a) +unionSet :: Ord a => Map a a -> a -> a -> Maybe (Map a a) + +newElem m v = Just (Map.insert v v m) +findLead m v = do pv <- Map.lookup v m + if pv == v then return (m, v) else do + (m', v') <- findLead m pv + return (Map.adjust (\_ -> v') v m', v') +unionSet m u v = do (m', lu) <- findLead m u + (m'', lv) <- findLead m' v + return (Map.adjust (\_ -> lv) lu m'') + +-- The above lines implement a monadic union-find-set, e.g: +-- z = do m <- newElem Map.empty 1 +-- m1 <- newElem m 2 +-- m2 <- newElem m1 3 +-- m3 <- newElem m2 4 +-- m4 <- unionSet m3 1 2 +-- m5 <- unionSet m4 3 4 +-- m6 <- unionSet m5 2 3 +-- (m7, _) <- findLead m6 1 +-- return m7 + +spantree :: Ord a => Graph a -> Maybe Int + +spantree (Graph v e) = span e $ foldM (\acc u -> newElem acc u) Map.empty v + where span [] comp0 = do comp <- comp0 + lu <- mapM (\u -> do (_, l) <- findLead comp u + return l) v + return (if all (== head lu) lu then 1 else 0) + span ((u, v):es) comp0 = do comp <- comp0 + (comp', lu) <- findLead comp u + (comp'', lv) <- findLead comp' v + l <- span es $ return comp + if lu == lv then return l else do + comp''' <- unionSet comp'' u v + r <- span es $ return comp''' + return (l + r) |