{-# LANGUAGE GeneralizedNewtypeDeriving #-}
module Control.Monad.Trans.UnionFind
  ( UnionFindT, runUnionFind
  , Point, fresh, repr, descriptor, union, equivalent
  ) where

import Control.Applicative (Applicative)
import Control.Monad.Trans.Class (MonadTrans(..))
import Control.Monad.Trans.State (StateT(..), evalStateT)
import Data.UnionFind.IntMap (Point)
import qualified Control.Monad.Trans.State as State
import qualified Data.UnionFind.IntMap as UF

-- | A monad transformer that adds union find operations.
--
-- The @p@ parameter is the type of points.  Uses the
-- "Data.UnionFind.IntMap" as the underlying union-find
-- implementation.
newtype UnionFindT p m a = UnionFindT {
  forall p (m :: * -> *) a.
UnionFindT p m a -> StateT (PointSupply p) m a
unUnionFindT :: StateT (UF.PointSupply p) m a
  } deriving ((forall a b. (a -> b) -> UnionFindT p m a -> UnionFindT p m b)
-> (forall a b. a -> UnionFindT p m b -> UnionFindT p m a)
-> Functor (UnionFindT p m)
forall a b. a -> UnionFindT p m b -> UnionFindT p m a
forall a b. (a -> b) -> UnionFindT p m a -> UnionFindT p m b
forall p (m :: * -> *) a b.
Functor m =>
a -> UnionFindT p m b -> UnionFindT p m a
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(a -> b) -> UnionFindT p m a -> UnionFindT p m b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
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$c<$ :: forall p (m :: * -> *) a b.
Functor m =>
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Functor (UnionFindT p m)
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    (a -> b -> c)
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-> Applicative (UnionFindT p m)
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forall {p} {m :: * -> *}. Monad m => Functor (UnionFindT p m)
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Monad m =>
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UnionFindT p m a -> UnionFindT p m b -> UnionFindT p m b
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(a -> b -> c)
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Functor f
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UnionFindT p m (a -> b) -> UnionFindT p m a -> UnionFindT p m b
$cliftA2 :: forall p (m :: * -> *) a b c.
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UnionFindT p m a -> UnionFindT p m b -> UnionFindT p m b
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UnionFindT p m a -> UnionFindT p m b -> UnionFindT p m b
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UnionFindT p m a -> UnionFindT p m b -> UnionFindT p m a
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Applicative (UnionFindT p m)
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MonadTrans)

runUnionFind :: Monad m => UnionFindT p m a -> m a
runUnionFind :: forall (m :: * -> *) p a. Monad m => UnionFindT p m a -> m a
runUnionFind = (StateT (PointSupply p) m a -> PointSupply p -> m a
forall (m :: * -> *) s a. Monad m => StateT s m a -> s -> m a
`evalStateT` PointSupply p
forall a. PointSupply a
UF.newPointSupply) (StateT (PointSupply p) m a -> m a)
-> (UnionFindT p m a -> StateT (PointSupply p) m a)
-> UnionFindT p m a
-> m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. UnionFindT p m a -> StateT (PointSupply p) m a
forall p (m :: * -> *) a.
UnionFindT p m a -> StateT (PointSupply p) m a
unUnionFindT

swap :: (a, b) -> (b, a)
swap :: forall a b. (a, b) -> (b, a)
swap (a
x, b
y) = (b
y, a
x)

-- | Create a new point with the given descriptor.  The returned is
-- only equivalent to itself.
--
-- Note that a 'Point' has its own identity.  That is, if two points
-- are equivalent then their descriptors are equal, but not vice
-- versa.
--
fresh :: Monad m => p -> UnionFindT p m (Point p)
fresh :: forall (m :: * -> *) p. Monad m => p -> UnionFindT p m (Point p)
fresh p
x = StateT (PointSupply p) m (Point p) -> UnionFindT p m (Point p)
forall p (m :: * -> *) a.
StateT (PointSupply p) m a -> UnionFindT p m a
UnionFindT (StateT (PointSupply p) m (Point p) -> UnionFindT p m (Point p))
-> ((PointSupply p -> m (Point p, PointSupply p))
    -> StateT (PointSupply p) m (Point p))
-> (PointSupply p -> m (Point p, PointSupply p))
-> UnionFindT p m (Point p)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (PointSupply p -> m (Point p, PointSupply p))
-> StateT (PointSupply p) m (Point p)
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 -> UnionFindT p m (Point p))
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swap ((PointSupply p, Point p) -> (Point p, PointSupply p))
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flip PointSupply p -> p -> (PointSupply p, Point p)
forall a. PointSupply a -> a -> (PointSupply a, Point a)
UF.fresh p
x

-- | /O(1)/. @repr point@ returns the representative point of
-- @point@'s equivalence class.
repr :: Monad m => Point p -> UnionFindT p m (Point p)
repr :: forall (m :: * -> *) p.
Monad m =>
Point p -> UnionFindT p m (Point p)
repr = StateT (PointSupply p) m (Point p) -> UnionFindT p m (Point p)
forall p (m :: * -> *) a.
StateT (PointSupply p) m a -> UnionFindT p m a
UnionFindT (StateT (PointSupply p) m (Point p) -> UnionFindT p m (Point p))
-> (Point p -> StateT (PointSupply p) m (Point p))
-> Point p
-> UnionFindT p m (Point p)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (PointSupply p -> Point p) -> StateT (PointSupply p) m (Point p)
forall (m :: * -> *) s a. Monad m => (s -> a) -> StateT s m a
State.gets ((PointSupply p -> Point p) -> StateT (PointSupply p) m (Point p))
-> (Point p -> PointSupply p -> Point p)
-> Point p
-> StateT (PointSupply p) m (Point p)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (PointSupply p -> Point p -> Point p)
-> Point p -> PointSupply p -> Point p
forall a b c. (a -> b -> c) -> b -> a -> c
flip PointSupply p -> Point p -> Point p
forall a. PointSupply a -> Point a -> Point a
UF.repr

-- | Return the descriptor of the 
descriptor :: Monad m => Point p -> UnionFindT p m p
descriptor :: forall (m :: * -> *) p. Monad m => Point p -> UnionFindT p m p
descriptor = StateT (PointSupply p) m p -> UnionFindT p m p
forall p (m :: * -> *) a.
StateT (PointSupply p) m a -> UnionFindT p m a
UnionFindT (StateT (PointSupply p) m p -> UnionFindT p m p)
-> (Point p -> StateT (PointSupply p) m p)
-> Point p
-> UnionFindT p m p
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (PointSupply p -> p) -> StateT (PointSupply p) m p
forall (m :: * -> *) s a. Monad m => (s -> a) -> StateT s m a
State.gets ((PointSupply p -> p) -> StateT (PointSupply p) m p)
-> (Point p -> PointSupply p -> p)
-> Point p
-> StateT (PointSupply p) m p
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (PointSupply p -> Point p -> p) -> Point p -> PointSupply p -> p
forall a b c. (a -> b -> c) -> b -> a -> c
flip PointSupply p -> Point p -> p
forall a. PointSupply a -> Point a -> a
UF.descriptor

-- | Join the equivalence classes of the points.  The resulting
-- equivalence class will get the descriptor of the second argument.
union :: Monad m => Point p -> Point p -> UnionFindT p m ()
union :: forall (m :: * -> *) p.
Monad m =>
Point p -> Point p -> UnionFindT p m ()
union Point p
p1 Point p
p2 = StateT (PointSupply p) m () -> UnionFindT p m ()
forall p (m :: * -> *) a.
StateT (PointSupply p) m a -> UnionFindT p m a
UnionFindT (StateT (PointSupply p) m () -> UnionFindT p m ())
-> ((PointSupply p -> PointSupply p)
    -> StateT (PointSupply p) m ())
-> (PointSupply p -> PointSupply p)
-> UnionFindT p m ()
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (PointSupply p -> PointSupply p) -> StateT (PointSupply p) m ()
forall (m :: * -> *) s. Monad m => (s -> s) -> StateT s m ()
State.modify ((PointSupply p -> PointSupply p) -> UnionFindT p m ())
-> (PointSupply p -> PointSupply p) -> UnionFindT p m ()
forall a b. (a -> b) -> a -> b
$ \PointSupply p
x -> PointSupply p -> Point p -> Point p -> PointSupply p
forall a. PointSupply a -> Point a -> Point a -> PointSupply a
UF.union PointSupply p
x Point p
p1 Point p
p2

-- | Test if the two elements are in the same equivalence class.
-- 
-- @
-- liftA2 (==) (repr x) (repr y)
-- @
equivalent :: Monad m => Point p -> Point p -> UnionFindT p m Bool
equivalent :: forall (m :: * -> *) p.
Monad m =>
Point p -> Point p -> UnionFindT p m Bool
equivalent Point p
p1 Point p
p2 = StateT (PointSupply p) m Bool -> UnionFindT p m Bool
forall p (m :: * -> *) a.
StateT (PointSupply p) m a -> UnionFindT p m a
UnionFindT (StateT (PointSupply p) m Bool -> UnionFindT p m Bool)
-> ((PointSupply p -> Bool) -> StateT (PointSupply p) m Bool)
-> (PointSupply p -> Bool)
-> UnionFindT p m Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (PointSupply p -> Bool) -> StateT (PointSupply p) m Bool
forall (m :: * -> *) s a. Monad m => (s -> a) -> StateT s m a
State.gets ((PointSupply p -> Bool) -> UnionFindT p m Bool)
-> (PointSupply p -> Bool) -> UnionFindT p m Bool
forall a b. (a -> b) -> a -> b
$ \PointSupply p
x -> PointSupply p -> Point p -> Point p -> Bool
forall a. PointSupply a -> Point a -> Point a -> Bool
UF.equivalent PointSupply p
x Point p
p1 Point p
p2