{-# OPTIONS_GHC -fglasgow-exts #-} ----------------------------------------------------------------------------- -- | -- Module : Data.Tree.AVL.List -- Copyright : (c) Adrian Hey 2004,2005 -- License : BSD3 -- -- Maintainer : http://homepages.nildram.co.uk/~ahey/em.png -- Stability : stable -- Portability : portable ----------------------------------------------------------------------------- module Data.Tree.AVL.List (-- * List related utilities for AVL trees -- ** Converting AVL trees to Lists (fixed element order). -- | These functions are lazy and allow normal lazy list processing -- style to be used (without necessarily converting the entire tree -- to a list in one gulp). asListL,toListL,asListR,toListR, -- ** Converting Lists to AVL trees (fixed element order) asTreeLenL,asTreeL, asTreeLenR,asTreeR, -- ** Converting unsorted Lists to sorted AVL trees genAsTree, -- ** \"Pushing\" unsorted Lists in sorted AVL trees genPushList, -- * Some analogues of common List functions reverseAVL,mapAVL,mapAVL', mapAccumLAVL ,mapAccumRAVL , mapAccumLAVL' ,mapAccumRAVL' , #ifdef __GLASGOW_HASKELL__ mapAccumLAVL'',mapAccumRAVL'', #endif #if __GLASGOW_HASKELL__ > 604 traverseAVL, #endif replicateAVL, filterAVL,mapMaybeAVL, filterViaList,mapMaybeViaList, partitionAVL, -- ** Folds -- | Note that unlike folds over lists ('foldr' and 'foldl'), there is no -- significant difference between left and right folds in AVL trees, other -- than which side of the tree each starts with. -- Therefore this library provides strict and lazy versions of both. foldrAVL,foldrAVL',foldr1AVL,foldr1AVL',foldr2AVL,foldr2AVL', foldlAVL,foldlAVL',foldl1AVL,foldl1AVL',foldl2AVL,foldl2AVL', foldrAVL_UINT, -- * \"Flattening\" AVL trees -- | These functions can be improve search times by reducing a tree of given size to -- the minimum possible height. flatten, flatReverse,flatMap,flatMap', -- * AVL tree based sorting of Lists -- | Nothing to do with AVL trees really. But using AVL trees do give an O(n.(log n)) sort -- algorithm for free, so here it is. These functions all consume the entire -- input list to construct a sorted AVL tree and then read the elements out as a list (lazily). genSortAscending,genSortDescending, ) where import Prelude -- so haddock finds the symbols there #if __GLASGOW_HASKELL__ > 604 import Control.Applicative hiding (empty) #endif import Data.COrdering import Data.Tree.AVL.Types(AVL(..),empty) import Data.Tree.AVL.Size(size) import Data.Tree.AVL.Push(genPush) import Data.Tree.AVL.Internals.HJoin(spliceH,joinH) import Data.Bits(shiftR,(.&.)) import Data.List(foldl') #ifdef __GLASGOW_HASKELL__ import GHC.Base #include "ghcdefs.h" #else #include "h98defs.h" #endif -- | List AVL tree contents in left to right order. -- The resulting list in ascending order if the tree is sorted. -- -- Complexity: O(n) asListL :: AVL e -> [e] asListL avl = toListL avl [] -- | Join the AVL tree contents to an existing list in left to right order. -- This is a ++ free function which behaves as if defined thusly.. -- -- > avl `toListL` as = (asListL avl) ++ as -- -- Complexity: O(n) toListL :: AVL e -> [e] -> [e] toListL E es = es toListL (N l e r) es = toListL' l e r es toListL (Z l e r) es = toListL' l e r es toListL (P l e r) es = toListL' l e r es toListL' :: AVL e -> e -> AVL e -> [e] -> [e] toListL' l e r es = toListL l (e:(toListL r es)) -- | List AVL tree contents in right to left order. -- The resulting list in descending order if the tree is sorted. -- -- Complexity: O(n) asListR :: AVL e -> [e] asListR avl = toListR avl [] -- | Join the AVL tree contents to an existing list in right to left order. -- This is a ++ free function which behaves as if defined thusly.. -- -- > avl `toListR` as = (asListR avl) ++ as -- -- Complexity: O(n) toListR :: AVL e -> [e] -> [e] toListR E es = es toListR (N l e r) es = toListR' l e r es toListR (Z l e r) es = toListR' l e r es toListR (P l e r) es = toListR' l e r es toListR' :: AVL e -> e -> AVL e -> [e] -> [e] toListR' l e r es = toListR r (e:(toListR l es)) -- | The AVL equivalent of 'foldr' on lists. This is a the lazy version (as lazy as the folding function -- anyway). Using this version with a function that is strict in it's second argument will result in O(n) -- stack use. See 'foldrAVL'' for a strict version. -- -- It behaves as if defined.. -- -- > foldrAVL f a avl = foldr f a (asListL avl) -- -- For example, the 'asListL' function could be defined.. -- -- > asListL = foldrAVL (:) [] -- -- Complexity: O(n) foldrAVL :: (e -> a -> a) -> a -> AVL e -> a foldrAVL f = foldU where foldU a E = a foldU a (N l e r) = foldV a l e r foldU a (Z l e r) = foldV a l e r foldU a (P l e r) = foldV a l e r foldV a l e r = foldU (f e (foldU a r)) l -- | The strict version of 'foldrAVL', which is useful for functions which are strict in their second -- argument. The advantage of this version is that it reduces the stack use from the O(n) that the lazy -- version gives (when used with strict functions) to O(log n). -- -- Complexity: O(n) foldrAVL' :: (e -> a -> a) -> a -> AVL e -> a foldrAVL' f = foldU where foldU a E = a foldU a (N l e r) = foldV a l e r foldU a (Z l e r) = foldV a l e r foldU a (P l e r) = foldV a l e r foldV a l e r = let a' = foldU a r a'' = f e a' in a' `seq` a'' `seq` foldU a'' l -- | The AVL equivalent of 'foldr1' on lists. This is a the lazy version (as lazy as the folding function -- anyway). Using this version with a function that is strict in it's second argument will result in O(n) -- stack use. See 'foldr1AVL'' for a strict version. -- -- > foldr1AVL f avl = foldr1 f (asListL avl) -- -- This function raises an error if the tree is empty. -- -- Complexity: O(n) foldr1AVL :: (e -> e -> e) -> AVL e -> e foldr1AVL f = foldU where foldU E = error "foldr1AVL: Empty Tree" foldU (N l e r) = foldV l e r -- r can't be E foldU (Z l e r) = foldW l e r -- r might be E foldU (P l e r) = foldW l e r -- r might be E -- Use this when r can't be E foldV l e r = foldrAVL f (f e (foldU r)) l -- Use this when r might be E foldW l e E = foldrAVL f e l foldW l e (N rl re rr) = foldrAVL f (f e (foldV rl re rr)) l -- rr can't be E foldW l e (Z rl re rr) = foldX l e rl re rr -- rr might be E foldW l e (P rl re rr) = foldX l e rl re rr -- rr might be E -- Common code for foldW (Z and P cases) foldX l e rl re rr = foldrAVL f (f e (foldW rl re rr)) l -- | The strict version of 'foldr1AVL', which is useful for functions which are strict in their second -- argument. The advantage of this version is that it reduces the stack use from the O(n) that the lazy -- version gives (when used with strict functions) to O(log n). -- -- Complexity: O(n) foldr1AVL' :: (e -> e -> e) -> AVL e -> e foldr1AVL' f = foldU where foldU E = error "foldr1AVL': Empty Tree" foldU (N l e r) = foldV l e r -- r can't be E foldU (Z l e r) = foldW l e r -- r might be E foldU (P l e r) = foldW l e r -- r might be E -- Use this when r can't be E foldV l e r = let a = foldU r a' = f e a in a `seq` a' `seq` foldrAVL' f a' l -- Use this when r might be E foldW l e E = foldrAVL' f e l foldW l e (N rl re rr) = let a = foldV rl re rr -- rr can't be E a' = f e a in a `seq` a' `seq` foldrAVL' f a' l foldW l e (Z rl re rr) = foldX l e rl re rr -- rr might be E foldW l e (P rl re rr) = foldX l e rl re rr -- rr might be E -- Common code for foldW (Z and P cases) foldX l e rl re rr = let a = foldW rl re rr a' = f e a in a `seq` a' `seq` foldrAVL' f a' l -- | This fold is a hybrid between 'foldrAVL' and 'foldr1AVL'. As with 'foldr1AVL', it requires -- a non-empty tree, but instead of treating the rightmost element as an initial value, it applies -- a function to it (second function argument) and uses the result instead. This allows -- a more flexible type for the main folding function (same type as that used by 'foldrAVL'). -- As with 'foldrAVL' and 'foldr1AVL', this function is lazy, so it's best not to use it with functions -- that are strict in their second argument. See 'foldr2AVL'' for a strict version. -- -- Complexity: O(n) foldr2AVL :: (e -> a -> a) -> (e -> a) -> AVL e -> a foldr2AVL f g = foldU where foldU E = error "foldr2AVL: Empty Tree" foldU (N l e r) = foldV l e r -- r can't be E foldU (Z l e r) = foldW l e r -- r might be E foldU (P l e r) = foldW l e r -- r might be E -- Use this when r can't be E foldV l e r = foldrAVL f (f e (foldU r)) l -- Use this when r might be E foldW l e E = foldrAVL f (g e) l foldW l e (N rl re rr) = foldrAVL f (f e (foldV rl re rr)) l -- rr can't be E foldW l e (Z rl re rr) = foldX l e rl re rr -- rr might be E foldW l e (P rl re rr) = foldX l e rl re rr -- rr might be E -- Common code for foldW (Z and P cases) foldX l e rl re rr = foldrAVL f (f e (foldW rl re rr)) l -- | The strict version of 'foldr2AVL', which is useful for functions which are strict in their second -- argument. The advantage of this version is that it reduces the stack use from the O(n) that the lazy -- version gives (when used with strict functions) to O(log n). -- -- Complexity: O(n) foldr2AVL' :: (e -> a -> a) -> (e -> a) -> AVL e -> a foldr2AVL' f g = foldU where foldU E = error "foldr2AVL': Empty Tree" foldU (N l e r) = foldV l e r -- r can't be E foldU (Z l e r) = foldW l e r -- r might be E foldU (P l e r) = foldW l e r -- r might be E -- Use this when r can't be E foldV l e r = let a = foldU r a' = f e a in a `seq` a' `seq` foldrAVL' f a' l -- Use this when r might be E foldW l e E = let a = g e in a `seq` foldrAVL' f a l foldW l e (N rl re rr) = let a = foldV rl re rr -- rr can't be E a' = f e a in a `seq` a' `seq` foldrAVL' f a' l foldW l e (Z rl re rr) = foldX l e rl re rr -- rr might be E foldW l e (P rl re rr) = foldX l e rl re rr -- rr might be E -- Common code for foldW (Z and P cases) foldX l e rl re rr = let a = foldW rl re rr a' = f e a in a `seq` a' `seq` foldrAVL' f a' l -- | The AVL equivalent of 'foldl' on lists. This is a the lazy version (as lazy as the folding function -- anyway). Using this version with a function that is strict in it's first argument will result in O(n) -- stack use. See 'foldlAVL'' for a strict version. -- -- > foldlAVL f a avl = foldl f a (asListL avl) -- -- For example, the 'asListR' function could be defined.. -- -- > asListR = foldlAVL (flip (:)) [] -- -- Complexity: O(n) foldlAVL :: (a -> e -> a) -> a -> AVL e -> a foldlAVL f = foldU where foldU a E = a foldU a (N l e r) = foldV a l e r foldU a (Z l e r) = foldV a l e r foldU a (P l e r) = foldV a l e r foldV a l e r = foldU (f (foldU a l) e) r -- | The strict version of 'foldlAVL', which is useful for functions which are strict in their first -- argument. The advantage of this version is that it reduces the stack use from the O(n) that the lazy -- version gives (when used with strict functions) to O(log n). -- -- Complexity: O(n) foldlAVL' :: (a -> e -> a) -> a -> AVL e -> a foldlAVL' f = foldU where foldU a E = a foldU a (N l e r) = foldV a l e r foldU a (Z l e r) = foldV a l e r foldU a (P l e r) = foldV a l e r foldV a l e r = let a' = foldU a l a'' = f a' e in a' `seq` a'' `seq` foldU a'' r -- | The AVL equivalent of 'foldl1' on lists. This is a the lazy version (as lazy as the folding function -- anyway). Using this version with a function that is strict in it's first argument will result in O(n) -- stack use. See 'foldl1AVL'' for a strict version. -- -- > foldl1AVL f avl = foldl1 f (asListL avl) -- -- This function raises an error if the tree is empty. -- -- Complexity: O(n) foldl1AVL :: (e -> e -> e) -> AVL e -> e foldl1AVL f = foldU where foldU E = error "foldl1AVL: Empty Tree" foldU (N l e r) = foldW l e r -- l might be E foldU (Z l e r) = foldW l e r -- l might be E foldU (P l e r) = foldV l e r -- l can't be E -- Use this when l can't be E foldV l e r = foldlAVL f (f (foldU l) e) r -- Use this when l might be E foldW E e r = foldlAVL f e r foldW (N ll le lr) e r = foldX ll le lr e r -- ll might be E foldW (Z ll le lr) e r = foldX ll le lr e r -- ll might be E foldW (P ll le lr) e r = foldlAVL f (f (foldV ll le lr) e) r -- ll can't be E -- Common code for foldW (Z and P cases) foldX ll le lr e r = foldlAVL f (f (foldW ll le lr) e) r -- | The strict version of 'foldl1AVL', which is useful for functions which are strict in their first -- argument. The advantage of this version is that it reduces the stack use from the O(n) that the lazy -- version gives (when used with strict functions) to O(log n). -- -- Complexity: O(n) foldl1AVL' :: (e -> e -> e) -> AVL e -> e foldl1AVL' f = foldU where foldU E = error "foldl1AVL': Empty Tree" foldU (N l e r) = foldW l e r -- l might be E foldU (Z l e r) = foldW l e r -- l might be E foldU (P l e r) = foldV l e r -- l can't be E -- Use this when l can't be E foldV l e r = let a = foldU l a' = f a e in a `seq` a' `seq` foldlAVL' f a' r -- Use this when l might be E foldW E e r = foldlAVL' f e r foldW (N ll le lr) e r = foldX ll le lr e r -- ll might be E foldW (Z ll le lr) e r = foldX ll le lr e r -- ll might be E foldW (P ll le lr) e r = let a = foldV ll le lr -- ll can't be E a' = f a e in a `seq` a' `seq` foldlAVL' f a' r -- Common code for foldW (Z and P cases) foldX ll le lr e r = let a = foldW ll le lr a' = f a e in a `seq` a' `seq` foldlAVL' f a' r -- | This fold is a hybrid between 'foldlAVL' and 'foldl1AVL'. As with 'foldl1AVL', it requires -- a non-empty tree, but instead of treating the leftmost element as an initial value, it applies -- a function to it (second function argument) and uses the result instead. This allows -- a more flexible type for the main folding function (same type as that used by 'foldlAVL'). -- As with 'foldlAVL' and 'foldl1AVL', this function is lazy, so it's best not to use it with functions -- that are strict in their first argument. See 'foldl2AVL'' for a strict version. -- -- Complexity: O(n) foldl2AVL :: (a -> e -> a) -> (e -> a) -> AVL e -> a foldl2AVL f g = foldU where foldU E = error "foldl2AVL: Empty Tree" foldU (N l e r) = foldW l e r -- l might be E foldU (Z l e r) = foldW l e r -- l might be E foldU (P l e r) = foldV l e r -- l can't be E -- Use this when l can't be E foldV l e r = foldlAVL f (f (foldU l) e) r -- Use this when l might be E foldW E e r = foldlAVL f (g e) r foldW (N ll le lr) e r = foldX ll le lr e r -- ll might be E foldW (Z ll le lr) e r = foldX ll le lr e r -- ll might be E foldW (P ll le lr) e r = foldlAVL f (f (foldV ll le lr) e) r -- ll can't be E -- Common code for foldW (Z and P cases) foldX ll le lr e r = foldlAVL f (f (foldW ll le lr) e) r -- | The strict version of 'foldl2AVL', which is useful for functions which are strict in their first -- argument. The advantage of this version is that it reduces the stack use from the O(n) that the lazy -- version gives (when used with strict functions) to O(log n). -- -- Complexity: O(n) foldl2AVL' :: (a -> e -> a) -> (e -> a) -> AVL e -> a foldl2AVL' f g = foldU where foldU E = error "foldl2AVL': Empty Tree" foldU (N l e r) = foldW l e r -- l might be E foldU (Z l e r) = foldW l e r -- l might be E foldU (P l e r) = foldV l e r -- l can't be E -- Use this when l can't be E foldV l e r = let a = foldU l a' = f a e in a `seq` a' `seq` foldlAVL' f a' r -- Use this when l might be E foldW E e r = let a = g e in a `seq` foldlAVL' f a r foldW (N ll le lr) e r = foldX ll le lr e r -- ll might be E foldW (Z ll le lr) e r = foldX ll le lr e r -- ll might be E foldW (P ll le lr) e r = let a = foldV ll le lr -- ll can't be E a' = f a e in a `seq` a' `seq` foldlAVL' f a' r -- Common code for foldW (Z and P cases) foldX ll le lr e r = let a = foldW ll le lr a' = f a e in a `seq` a' `seq` foldlAVL' f a' r -- | This is a specialised version of 'foldrAVL'' for use with an -- /unboxed/ Int accumulator (with GHC). Defaults to boxed Int -- for other Haskells. -- -- Complexity: O(n) foldrAVL_UINT :: (e -> UINT -> UINT) -> UINT -> AVL e -> UINT #ifdef __GLASGOW_HASKELL__ foldrAVL_UINT f = foldU where foldU a E = a foldU a (N l e r) = foldV a l e r foldU a (Z l e r) = foldV a l e r foldU a (P l e r) = foldV a l e r foldV a l e r = foldU (f e (foldU a r)) l #else foldrAVL_UINT = foldrAVL' -- Strict version! {-# INLINE foldrAVL_UINT #-} #endif -- | The AVL equivalent of 'Data.List.mapAccumL' on lists. -- It behaves like a combination of 'mapAVL' and 'foldlAVL'. -- It applies a function to each element of a tree, passing an accumulating parameter from -- left to right, and returning a final value of this accumulator together with the new tree. -- -- Using this version with a function that is strict in it's first argument will result in -- O(n) stack use. See 'mapAccumLAVL'' for a strict version. -- -- Complexity: O(n) mapAccumLAVL :: (z -> a -> (z, b)) -> z -> AVL a -> (z, AVL b) mapAccumLAVL f z ta = case mapAL z ta of UBT2(zt,tb) -> (zt,tb) where mapAL z_ E = UBT2(z_,E) mapAL z_ (N la a ra) = mapAL' z_ N la a ra mapAL z_ (Z la a ra) = mapAL' z_ Z la a ra mapAL z_ (P la a ra) = mapAL' z_ P la a ra {-# INLINE mapAL' #-} mapAL' z' c la a ra = case mapAL z' la of UBT2(zl,lb) -> let (za,b) = f zl a in case mapAL za ra of UBT2(zr,rb) -> UBT2(zr, c lb b rb) -- | This is a strict version of 'mapAccumLAVL', which is useful for functions which -- are strict in their first argument. The advantage of this version is that it reduces -- the stack use from the O(n) that the lazy version gives (when used with strict functions) -- to O(log n). -- -- Complexity: O(n) mapAccumLAVL' :: (z -> a -> (z, b)) -> z -> AVL a -> (z, AVL b) mapAccumLAVL' f z ta = case mapAL z ta of UBT2(zt,tb) -> (zt,tb) where mapAL z_ E = UBT2(z_,E) mapAL z_ (N la a ra) = mapAL' z_ N la a ra mapAL z_ (Z la a ra) = mapAL' z_ Z la a ra mapAL z_ (P la a ra) = mapAL' z_ P la a ra {-# INLINE mapAL' #-} mapAL' z' c la a ra = case mapAL z' la of UBT2(zl,lb) -> case f zl a of (za,b) -> case mapAL za ra of UBT2(zr,rb) -> UBT2(zr, c lb b rb) -- | The AVL equivalent of 'Data.List.mapAccumR' on lists. -- It behaves like a combination of 'mapAVL' and 'foldrAVL'. -- It applies a function to each element of a tree, passing an accumulating parameter from -- right to left, and returning a final value of this accumulator together with the new tree. -- -- Using this version with a function that is strict in it's first argument will result in -- O(n) stack use. See 'mapAccumRAVL'' for a strict version. -- -- Complexity: O(n) mapAccumRAVL :: (z -> a -> (z, b)) -> z -> AVL a -> (z, AVL b) mapAccumRAVL f z ta = case mapAR z ta of UBT2(zt,tb) -> (zt,tb) where mapAR z_ E = UBT2(z_,E) mapAR z_ (N la a ra) = mapAR' z_ N la a ra mapAR z_ (Z la a ra) = mapAR' z_ Z la a ra mapAR z_ (P la a ra) = mapAR' z_ P la a ra {-# INLINE mapAR' #-} mapAR' z' c la a ra = case mapAR z' ra of UBT2(zr,rb) -> let (za,b) = f zr a in case mapAR za la of UBT2(zl,lb) -> UBT2(zl, c lb b rb) -- | This is a strict version of 'mapAccumRAVL', which is useful for functions which -- are strict in their first argument. The advantage of this version is that it reduces -- the stack use from the O(n) that the lazy version gives (when used with strict functions) -- to O(log n). -- -- Complexity: O(n) mapAccumRAVL' :: (z -> a -> (z, b)) -> z -> AVL a -> (z, AVL b) mapAccumRAVL' f z ta = case mapAR z ta of UBT2(zt,tb) -> (zt,tb) where mapAR z_ E = UBT2(z_,E) mapAR z_ (N la a ra) = mapAR' z_ N la a ra mapAR z_ (Z la a ra) = mapAR' z_ Z la a ra mapAR z_ (P la a ra) = mapAR' z_ P la a ra {-# INLINE mapAR' #-} mapAR' z' c la a ra = case mapAR z' ra of UBT2(zr,rb) -> case f zr a of (za,b) -> case mapAR za la of UBT2(zl,lb) -> UBT2(zl, c lb b rb) ------------------------------------------------------------------------------------------------ -- These two functions attempt to make the strict mapAccums more efficient and reduce heap -- burn rate with ghc by using an accumulating function that returns an unboxed pair. ------------------------------------------------------------------------------------------------ #ifdef __GLASGOW_HASKELL__ -- | Glasgow Haskell only. Similar to 'mapAccumLAVL'' but uses an unboxed pair in the -- accumulating function. -- -- Complexity: O(n) mapAccumLAVL'' :: (z -> a -> UBT2(z, b)) -> z -> AVL a -> (z, AVL b) mapAccumLAVL'' f z ta = case mapAL z ta of UBT2(zt,tb) -> (zt,tb) where mapAL z_ E = UBT2(z_,E) mapAL z_ (N la a ra) = mapAL' z_ N la a ra mapAL z_ (Z la a ra) = mapAL' z_ Z la a ra mapAL z_ (P la a ra) = mapAL' z_ P la a ra {-# INLINE mapAL' #-} mapAL' z' c la a ra = case mapAL z' la of UBT2(zl,lb) -> case f zl a of UBT2(za,b) -> case mapAL za ra of UBT2(zr,rb) -> UBT2(zr, c lb b rb) -- | Glasgow Haskell only. Similar to 'mapAccumRAVL'' but uses an unboxed pair in the -- accumulating function. -- -- Complexity: O(n) mapAccumRAVL'' :: (z -> a -> UBT2(z, b)) -> z -> AVL a -> (z, AVL b) mapAccumRAVL'' f z ta = case mapAR z ta of UBT2(zt,tb) -> (zt,tb) where mapAR z_ E = UBT2(z_,E) mapAR z_ (N la a ra) = mapAR' z_ N la a ra mapAR z_ (Z la a ra) = mapAR' z_ Z la a ra mapAR z_ (P la a ra) = mapAR' z_ P la a ra {-# INLINE mapAR' #-} mapAR' z' c la a ra = case mapAR z' ra of UBT2(zr,rb) -> case f zr a of UBT2(za,b) -> case mapAR za la of UBT2(zl,lb) -> UBT2(zl, c lb b rb) #endif ------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------ -- | Convert a list of known length into an AVL tree, such that the head of the list becomes -- the leftmost tree element. The resulting tree is flat (and also sorted if the supplied list -- is sorted in ascending order). -- -- If the actual length of the list is not the same as the supplied length then -- an error will be raised. -- -- Complexity: O(n) asTreeLenL :: Int -> [e] -> AVL e asTreeLenL n es = case subst (replicateAVL n ()) es of UBT2(tree,es_) -> case es_ of [] -> tree _ -> error "asTreeLenL: List too long." where -- Substitute template values for real values taken from the list subst E as = UBT2(E,as) subst (N l _ r) as = subst' N l r as subst (Z l _ r) as = subst' Z l r as subst (P l _ r) as = subst' P l r as {-# INLINE subst' #-} subst' f l r as = case subst l as of UBT2(l_,xs) -> case xs of a:as' -> case subst r as' of UBT2(r_,as__) -> let t_ = f l_ a r_ in t_ `seq` UBT2(t_,as__) [] -> error "asTreeLenL: List too short." -- | As 'asTreeLenL', except the length of the list is calculated internally, not supplied -- as an argument. -- -- Complexity: O(n) asTreeL :: [e] -> AVL e asTreeL es = asTreeLenL (length es) es -- | Convert a list of known length into an AVL tree, such that the head of the list becomes -- the rightmost tree element. The resulting tree is flat (and also sorted if the supplied list -- is sorted in descending order). -- -- If the actual length of the list is not the same as the supplied length then -- an error will be raised. -- -- Complexity: O(n) asTreeLenR :: Int -> [e] -> AVL e asTreeLenR n es = case subst (replicateAVL n ()) es of UBT2(tree,es_) -> case es_ of [] -> tree _ -> error "asTreeLenR: List too long." where -- Substitute template values for real values taken from the list subst E as = UBT2(E,as) subst (N l _ r) as = subst' N l r as subst (Z l _ r) as = subst' Z l r as subst (P l _ r) as = subst' P l r as {-# INLINE subst' #-} subst' f l r as = case subst r as of UBT2(r_,xs) -> case xs of a:as' -> case subst l as' of UBT2(l_,as__) -> let t_ = f l_ a r_ in t_ `seq` UBT2(t_,as__) [] -> error "asTreeLenR: List too short." -- | As 'asTreeLenR', except the length of the list is calculated internally, not supplied -- as an argument. -- -- Complexity: O(n) asTreeR :: [e] -> AVL e asTreeR es = asTreeLenR (length es) es -- | Reverse an AVL tree (swaps and reverses left and right sub-trees). -- The resulting tree is the mirror image of the original. -- -- Complexity: O(n) reverseAVL :: AVL e -> AVL e reverseAVL E = E reverseAVL (N l e r) = let l' = reverseAVL l r' = reverseAVL r in l' `seq` r' `seq` P r' e l' reverseAVL (Z l e r) = let l' = reverseAVL l r' = reverseAVL r in l' `seq` r' `seq` Z r' e l' reverseAVL (P l e r) = let l' = reverseAVL l r' = reverseAVL r in l' `seq` r' `seq` N r' e l' -- | Apply a function to every element in an AVL tree. This function preserves the tree shape. -- There is also a strict version of this function ('mapAVL''). -- -- N.B. If the tree is sorted the result of this operation will only be sorted if -- the applied function preserves ordering (for some suitable ordering definition). -- -- Complexity: O(n) mapAVL :: (a -> b) -> AVL a -> AVL b mapAVL f = map' where map' E = E map' (N l a r) = let l' = map' l r' = map' r in l' `seq` r' `seq` N l' (f a) r' map' (Z l a r) = let l' = map' l r' = map' r in l' `seq` r' `seq` Z l' (f a) r' map' (P l a r) = let l' = map' l r' = map' r in l' `seq` r' `seq` P l' (f a) r' -- | Similar to 'mapAVL', but the supplied function is applied strictly. -- -- Complexity: O(n) mapAVL' :: (a -> b) -> AVL a -> AVL b mapAVL' f = map' where map' E = E map' (N l a r) = let l' = map' l r' = map' r b = f a in b `seq` l' `seq` r' `seq` N l' b r' map' (Z l a r) = let l' = map' l r' = map' r b = f a in b `seq` l' `seq` r' `seq` Z l' b r' map' (P l a r) = let l' = map' l r' = map' r b = f a in b `seq` l' `seq` r' `seq` P l' b r' #if __GLASGOW_HASKELL__ > 604 traverseAVL :: Applicative f => (a -> f b) -> AVL a -> f (AVL b) traverseAVL _f E = pure E traverseAVL f (N l v r) = N <$> traverseAVL f l <*> f v <*> traverseAVL f r traverseAVL f (Z l v r) = Z <$> traverseAVL f l <*> f v <*> traverseAVL f r traverseAVL f (P l v r) = P <$> traverseAVL f l <*> f v <*> traverseAVL f r #endif -- | Construct a flat AVL tree of size n (n>=0), where all elements are identical. -- -- Complexity: O(log n) replicateAVL :: Int -> e -> AVL e replicateAVL m e = rep m where -- Functional spaghetti follows :-) rep n | odd n = repOdd n -- n is odd , >=1 rep n = repEvn n -- n is even, >=0 -- n is known to be odd (>=1), so left and right sub-trees are identical repOdd n = let sub = rep (n `shiftR` 1) in sub `seq` Z sub e sub -- n is known to be even (>=0) repEvn n | n .&. (n-1) == 0 = repP2 n -- treat exact powers of 2 specially, traps n=0 too repEvn n = let nl = n `shiftR` 1 -- size of left subtree (odd or even) nr = nl - 1 -- size of right subtree (even or odd) in if odd nr then let l = repEvn nl -- right sub-tree is odd , so left is even (>=2) r = repOdd nr in l `seq` r `seq` Z l e r else let l = repOdd nl -- right sub-tree is even, so left is odd (>=2) r = repEvn nr in l `seq` r `seq` Z l e r -- n is an exact power of 2 (or 0), I.E. 0,1,2,4,8,16.. repP2 0 = E repP2 1 = Z E e E repP2 n = let nl = n `shiftR` 1 -- nl is also an exact power of 2 nr = nl - 1 -- nr is one less that an exact power of 2 l = repP2 nl r = repP2M1 nr in l `seq` r `seq` P l e r -- BF=+1 -- n is one less than an exact power of 2, I.E. 0,1,3,7,15.. repP2M1 0 = E repP2M1 n = let sub = repP2M1 (n `shiftR` 1) in sub `seq` Z sub e sub -- | Flatten an AVL tree, preserving the ordering of the tree elements. -- -- Complexity: O(n) flatten :: AVL e -> AVL e flatten t = asTreeLenL (size t) (asListL t) -- | Similar to 'flatten', but the tree elements are reversed. This function has higher constant -- factor overhead than 'reverseAVL'. -- -- Complexity: O(n) flatReverse :: AVL e -> AVL e flatReverse t = asTreeLenL (size t) (asListR t) -- | Similar to 'mapAVL', but the resulting tree is flat. -- This function has higher constant factor overhead than 'mapAVL'. -- -- Complexity: O(n) flatMap :: (a -> b) -> AVL a -> AVL b flatMap f t = asTreeLenL (size t) (map f (asListL t)) -- | Same as 'flatMap', but the supplied function is applied strictly. -- -- Complexity: O(n) flatMap' :: (a -> b) -> AVL a -> AVL b flatMap' f t = asTreeLenL (size t) (map' f (asListL t)) where map' _ [] = [] map' g (a:as) = let b = g a in b `seq` (b : map' f as) -- | Remove all AVL tree elements which do not satisfy the supplied predicate. -- Element ordering is preserved. The resulting tree is flat. -- See 'filterAVL' for an alternative implementation which is probably more efficient. -- -- Complexity: O(n) filterViaList :: (e -> Bool) -> AVL e -> AVL e filterViaList p t = filter' [] 0 (asListR t) where filter' se n [] = asTreeLenL n se filter' se n (e:es) = if p e then let n'=n+1 in n' `seq` filter' (e:se) n' es else filter' se n es -- | Remove all AVL tree elements which do not satisfy the supplied predicate. -- Element ordering is preserved. -- -- Complexity: O(n) filterAVL :: (e -> Bool) -> AVL e -> AVL e filterAVL p t0 = case filter_ L(0) t0 of UBT3(_,t_,_) -> t_ -- Work with relative heights!! where filter_ h t = case t of E -> UBT3(False,E,h) N l e r -> f l DECINT2(h) e r DECINT1(h) Z l e r -> f l DECINT1(h) e r DECINT1(h) P l e r -> f l DECINT1(h) e r DECINT2(h) where f l hl e r hr = case filter_ hl l of UBT3(bl,l_,hl_) -> case filter_ hr r of UBT3(br,r_,hr_) -> if p e then if bl || br then case spliceH l_ hl_ e r_ hr_ of UBT2(t_,h_) -> UBT3(True,t_,h_) else UBT3(False,t,h) else case joinH l_ hl_ r_ hr_ of UBT2(t_,h_) -> UBT3(True,t_,h_) -- | Partition an AVL tree using the supplied predicate. The first AVL tree in the -- resulting pair contains all elements for which the predicate is True, the second -- contains all those for which the predicate is False. Element ordering is preserved. -- Both of the resulting trees are flat. -- -- Complexity: O(n) partitionAVL :: (e -> Bool) -> AVL e -> (AVL e, AVL e) partitionAVL p t = part 0 [] 0 [] (asListR t) where part nT lstT nF lstF [] = let avlT = asTreeLenL nT lstT avlF = asTreeLenL nF lstF in (avlT,avlF) -- Non strict in avlT, avlF !! part nT lstT nF lstF (e:es) = if p e then let nT'=nT+1 in nT' `seq` part nT' (e:lstT) nF lstF es else let nF'=nF+1 in nF' `seq` part nT lstT nF' (e:lstF) es -- | Remove all AVL tree elements for which the supplied function returns 'Nothing'. -- Element ordering is preserved. The resulting tree is flat. -- See 'mapMaybeAVL' for an alternative implementation which is probably more efficient. -- -- Complexity: O(n) mapMaybeViaList :: (a -> Maybe b) -> AVL a -> AVL b mapMaybeViaList f t = map' [] 0 (asListR t) where map' sb n [] = asTreeLenL n sb map' sb n (a:as) = case f a of Just b -> let n'=n+1 in n' `seq` map' (b:sb) n' as Nothing -> map' sb n as -- | Remove all AVL tree elements for which the supplied function returns 'Nothing'. -- Element ordering is preserved. -- -- Complexity: O(n) mapMaybeAVL :: (a -> Maybe b) -> AVL a -> AVL b mapMaybeAVL f t0 = case mapMaybe_ L(0) t0 of UBT2(t_,_) -> t_ -- Work with relative heights!! where mapMaybe_ h t = case t of E -> UBT2(E,h) N l a r -> m l DECINT2(h) a r DECINT1(h) Z l a r -> m l DECINT1(h) a r DECINT1(h) P l a r -> m l DECINT1(h) a r DECINT2(h) where m l hl a r hr = case mapMaybe_ hl l of UBT2(l_,hl_) -> case mapMaybe_ hr r of UBT2(r_,hr_) -> case f a of Just b -> spliceH l_ hl_ b r_ hr_ Nothing -> joinH l_ hl_ r_ hr_ -- | Invokes 'genPushList' on the empty AVL tree. -- -- Complexity: O(n.(log n)) {-# INLINE genAsTree #-} genAsTree :: (e -> e -> COrdering e) -> [e] -> AVL e genAsTree c = genPushList c empty -- | Push the elements of an unsorted List in a sorted AVL tree using the supplied combining comparison. -- -- Complexity: O(n.(log (m+n))) where n is the list length, m is the tree size. genPushList :: (e -> e -> COrdering e) -> AVL e -> [e] -> AVL e genPushList c avl = foldl' addElem avl where addElem t e = genPush (c e) e t -- | Uses the supplied combining comparison to sort list elements into ascending order. -- Multiple occurences of the same element are eliminated (they are combined in some way). -- -- @'genSortAscending' c = 'asListL' . 'genAsTree' c@ -- -- Complexity: O(n.(log n)) {-# INLINE genSortAscending #-} genSortAscending :: (e -> e -> COrdering e) -> [e] -> [e] genSortAscending c = asListL . genAsTree c -- | Uses the supplied combining comparison to sort list elements into descending order. -- Multiple occurences of the same element are eliminated (they are combined in some way). -- -- @'genSortDescending' c = 'asListR' . 'genAsTree' c@ -- -- Complexity: O(n.(log n)) {-# INLINE genSortDescending #-} genSortDescending :: (e -> e -> COrdering e) -> [e] -> [e] genSortDescending c = asListR . genAsTree c