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import qualified Data.Map as Map
import Data.Map (Map)
import Data.List (foldl', sortBy)
import Control.Monad (foldM, mapM)
data Graph a b = Graph [a] [(a, a, b)] deriving (Show, Eq)
graph = Graph [1,2,3,4,5] [(1,2,12),(1,3,34),(1,5,78),(2,4,55),
(2,5,32),(3,4,61),(3,5,44),(4,5,93)]
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
kruskal :: (Ord a, Ord b, Num b) => Graph a b -> Maybe b
kruskal (Graph [] _) = Nothing
kruskal (Graph v e) = span (sortBy (\(_, _, c) (_, _, c') -> c `compare` c') e)
(foldM (\acc u -> newElem acc u) Map.empty v) 0
where span [] comp0 cost = return cost
span ((u, v, c):es) comp0 cost =
do comp <- comp0
(comp', lu) <- findLead comp u
(comp'', lv) <- findLead comp' v
comp''' <- unionSet comp'' u v
let (compf, cost') = if lu == lv then (comp'', cost)
else (comp''', cost + c)
span es (return compf) cost'
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