{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FunctionalDependencies, TypeFamilies #-}

{-
  This module is part of Antisplice.
  Copyleft (c) 2014 Marvin Cohrs

  All wrongs reversed. Sharing is an act of love, not crime.
  Please share Antisplice with everyone you like.

  Antisplice is free software: you can redistribute it and/or modify
  it under the terms of the GNU Affero General Public License as published by
  the Free Software Foundation, either version 3 of the License, or
  (at your option) any later version.

  Antisplice is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
  GNU Affero General Public License for more details.

  You should have received a copy of the GNU Affero General Public License
  along with Antisplice. If not, see <http://www.gnu.org/licenses/>.
-}

-- | Provides a typeclass for all binary search trees and an unbalanced implementation
module Game.Antisplice.Utils.BST where

import Game.Antisplice.Utils.None

-- | Only instances of Indexable may be saved in a BST
class Ord o => Indexable i o v | i -> o, i -> v where
  type IndexOf i
  type ValueOf i
  -- | Extract the index
  indexOf :: i -> o
  -- | Extract the value
  valueOf :: i -> v

instance Indexable Int Int Int where
  type IndexOf Int = Int
  type ValueOf Int = Int
  indexOf = id
  valueOf = id

instance Ord o => Indexable (o,a) o a where
  type IndexOf (o,a) = o
  type ValueOf (o,a) = a
  indexOf = fst
  valueOf = snd

instance Ord o => Indexable (o,a,b) o (a,b) where
  type IndexOf (o,a,b) = o
  type ValueOf (o,a,b) = (a,b)
  indexOf (o,_,_) = o
  valueOf (_,a,b) = (a,b)

instance Ord o => Indexable (o,a,b,c) o (a,b,c) where
  type IndexOf (o,a,b,c) = o
  type ValueOf (o,a,b,c) = (a,b,c)
  indexOf (o,_,_,_) = o
  valueOf (_,a,b,c) = (a,b,c)

-- | Typeclass for all BSTs that store the given Indexable
class Indexable i o v => AnyBST t i o v where
  -- | Insert into the tree
  anyBstInsert :: i -> t i -> t i
  -- | Remove from the tree
  anyBstRemove :: o -> t i -> t i
  -- | Get the greatest element
  anyBstMax :: t i -> Maybe i
  -- | Get the least element
  anyBstMin :: t i -> Maybe i
  -- | Lookup a given key
  anyBstLookup :: o -> t i -> Maybe v
  -- | An empty tree
  anyBstEmpty :: t i
  -- | The root of the tree
  anyBstHead :: t i -> Maybe i
  -- | Traverse the tree in order
  anyBstInorder :: t i -> [i]

instance Indexable i o v => AnyBST BST i o v where
  anyBstInsert = bstInsert
  anyBstRemove = bstRemove
  anyBstMax = bstMax
  anyBstMin =  bstMin
  anyBstLookup = bstLookup
  anyBstEmpty = EmptyBST
  anyBstHead = bstHead
  anyBstInorder = bstInorder

instance None (BST a) where
  none = EmptyBST

-- | An unbalanced binary search tree
data BST a = EmptyBST | BST a !(BST a) !(BST a)

-- | Insert into the BST
bstInsert :: Indexable i o v => i -> BST i -> BST i
bstInsert i EmptyBST = BST i EmptyBST EmptyBST
bstInsert i (BST a l r)
  | indexOf i < indexOf a = BST a (bstInsert i l) r
  | indexOf i > indexOf a = BST a l (bstInsert i r)
  | otherwise = BST i l r

-- | Remove from the BST
bstRemove :: Indexable i o v => o -> BST i -> BST i
bstRemove o EmptyBST = EmptyBST
bstRemove o (BST a EmptyBST r) | indexOf a == o = r
bstRemove o (BST a l EmptyBST) | indexOf a == o = l
bstRemove o (BST a l r)
  | indexOf a < o = BST a (bstRemove o l) r
  | indexOf a > o = BST a l (bstRemove o r)
  | otherwise = let (Just m) = bstMax l in BST m (bstRemove (indexOf m) l) r

-- | Get the greatest element
bstMax :: BST i -> Maybe i
bstMax EmptyBST = Nothing
bstMax (BST a _ EmptyBST) = Just a
bstMax (BST _ _ r) = bstMax r

-- | Get the least element
bstMin :: BST i -> Maybe i
bstMin EmptyBST = Nothing
bstMin (BST a EmptyBST _) = Just a
bstMin (BST _ l _) = bstMin l

-- | Lookup a given key
bstLookup :: Indexable i o v => o -> BST i -> Maybe v
bstLookup _ EmptyBST = Nothing
bstLookup o (BST a l r)
  | o == indexOf a = Just $ valueOf a
  | o < indexOf a = bstLookup o l
  | o > indexOf a = bstLookup o r

-- | Return the tree's root
bstHead :: Indexable i o v => BST i -> Maybe i
bstHead EmptyBST = Nothing
bstHead (BST a _ _) = Just a

-- | Traverse the tree in order
bstInorder :: Indexable i o v => BST i -> [i]
bstInorder EmptyBST = []
bstInorder (BST a l r) = bstInorder l ++ [a] ++ bstInorder r