{-# OPTIONS_GHC -fglasgow-exts #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.Tree.AVL.Types
-- Copyright : (c) Adrian Hey 2004,2005
-- License : BSD3
--
-- Maintainer : http://homepages.nildram.co.uk/~ahey/em.png
-- Stability : stable
-- Portability : portable
--
-- AVL Tree data type definition and a few simple utility functions.
-----------------------------------------------------------------------------
module Data.Tree.AVL.Types
( -- * Types.
AVL(..),
-- * Simple AVL related utilities.
empty,isEmpty,isNonEmpty,singleton,pair,tryGetSingleton,
) where
import Prelude -- so haddock finds the symbols there
import Data.Typeable
#if __GLASGOW_HASKELL__ > 604
import Data.Foldable
import Data.Monoid
#endif
-- | AVL tree data type.
--
-- The balance factor (BF) of an 'AVL' tree node is defined as the difference between the height of
-- the left and right sub-trees. An 'AVL' tree is ALWAYS height balanced, such that |BF| <= 1.
-- The functions in this library ("Data.Tree.AVL") are designed so that they never construct
-- an unbalanced tree (well that's assuming they're not broken). The 'AVL' tree type defined here
-- has the BF encoded the constructors.
--
-- Some functions in this library return 'AVL' trees that are also \"flat\", which (in the context
-- of this library) means that the sizes of left and right sub-trees differ by at most one and
-- are also flat. Flat sorted trees should give slightly shorter searches than sorted trees which
-- are merely height balanced. Whether or not flattening is worth the effort depends on the number
-- of times the tree will be searched and the cost of element comparison.
--
-- In cases where the tree elements are sorted, all the relevant 'AVL' functions follow the
-- convention that the leftmost tree element is least and the rightmost tree element is
-- the greatest. Bear this in mind when defining general comparison functions. It should
-- also be noted that all functions in this library for sorted trees require that the tree
-- does not contain multiple elements which are \"equal\" (according to whatever criterion
-- has been used to sort the elements).
--
-- It is important to be consistent about argument ordering when defining general purpose
-- comparison functions (or selectors) for searching a sorted tree, such as ..
--
-- @
-- myComp :: (k -> e -> Ordering)
-- -- or..
-- myCComp :: (k -> e -> COrdering a)
-- @
--
-- In these cases the first argument is the search key and the second argument is an element of
-- the 'AVL' tree. For example..
--
-- @
-- key \`myCComp\` element -> Lt implies key < element, proceed down the left sub-tree
-- key \`myCComp\` element -> Gt implies key > element, proceed down the right sub-tree
-- @
--
-- This convention is same as that used by the overloaded 'compare' method from 'Ord' class.
--
-- WARNING: The constructors of this data type are exported from this module but not from
-- the top level 'AVL' wrapper ("Data.Tree.AVL"). Don't try to construct your own 'AVL'
-- trees unless you're sure you know what your doing. If you end up creating and using
-- 'AVL' trees that aren't you'll break most of the functions in this library.
--
-- Controlling Strictness.
--
-- The 'AVL' data type is declared as non-strict in all it's fields,
-- but all the functions in this library behave as though it is strict in its
-- recursive fields (left and right sub-trees). Strictness in the element field is
-- controlled either by using the strict variants of functions (defined in this library
-- where appropriate), or using strict variants of the combinators defined in "Data.COrdering",
-- or using 'seq' etc. in your own code (in any combining comparisons you define, for example).
--
-- A note about 'Eq' and 'Ord' class instances.
--
-- For 'AVL' trees the defined instances of 'Ord' and 'Eq' are based on the lists that are produced using
-- the 'Data.Tree.AVL.List.asListL' function (it could just as well have been 'Data.Tree.AVL.List.asListR',
-- the choice is arbitrary but I can only chose one). This means that two trees which contain the same elements
-- in the same order are equal regardless of detailed tree structure. The same principle has been applied to
-- the instances of 'Read' and 'Show'. Unfortunately, this has the undesirable and non-intuitive effect
-- of making \"equal\" trees potentially distinguishable using some functions (such as height).
-- All such functions have been placed in the Data.Tree.AVL.Internals modules, which are not
-- included in the main "Data.Tree.AVL" wrapper. For all \"normal\" functions (f) exported by "Data.Tree.AVL"
-- it is safe to assume that if a and b are 'AVL' trees then (a == b) implies (f a == f b), provided the same
-- is true for the tree elements.
--
data AVL e = E -- ^ Empty Tree
| N (AVL e) e (AVL e) -- ^ BF=-1 (right height > left height)
| Z (AVL e) e (AVL e) -- ^ BF= 0
| P (AVL e) e (AVL e) -- ^ BF=+1 (left height > right height)
-- A name for the AVL type constructor, fully qualified
avlTyConName :: String
avlTyConName = "Data.Tree.AVL.AVL"
-- A Typeable1 instance
instance Typeable1 AVL where
typeOf1 _ = mkTyConApp (mkTyCon avlTyConName) []
#ifndef __GLASGOW_HASKELL__
-- A Typeable instance (not needed by ghc, but Haddock fails to document this instance)
instance Typeable e => Typeable (AVL e) where
typeOf = typeOfDefault
#endif
#if __GLASGOW_HASKELL__ > 604
instance Foldable AVL where
foldMap _f E = mempty
foldMap f (N l v r) = foldMap f l `mappend` f v `mappend` foldMap f r
foldMap f (Z l v r) = foldMap f l `mappend` f v `mappend` foldMap f r
foldMap f (P l v r) = foldMap f l `mappend` f v `mappend` foldMap f r
#endif
-- | The empty AVL tree.
{-# INLINE empty #-}
empty :: AVL e
empty = E
-- | Returns 'True' if an AVL tree is empty.
--
-- Complexity: O(1)
{-# INLINE isEmpty #-}
isEmpty :: AVL e -> Bool
isEmpty E = True
isEmpty _ = False
-- | Returns 'True' if an AVL tree is non-empty.
--
-- Complexity: O(1)
{-# INLINE isNonEmpty #-}
isNonEmpty :: AVL e -> Bool
isNonEmpty E = False
isNonEmpty _ = True
-- | Creates an AVL tree with just one element.
--
-- Complexity: O(1)
{-# INLINE singleton #-}
singleton :: e -> AVL e
singleton e = Z E e E
-- | Create an AVL tree of two elements, occuring in same order as the arguments.
{-# INLINE pair #-}
pair :: e -> e -> AVL e
pair e0 e1 = P (Z E e0 E) e1 E
-- | If the AVL tree is a singleton (has only one element @e@) then this function returns @('Just' e)@.
-- Otherwise it returns Nothing.
--
-- Complexity: O(1)
{-# INLINE tryGetSingleton #-}
tryGetSingleton :: AVL e -> Maybe e
tryGetSingleton (Z E e _) = Just e -- Right subtree must be E too, but no need to waste time checking
tryGetSingleton _ = Nothing