1 {-# OPTIONS -cpp -fglasgow-exts #-}
2 -----------------------------------------------------------------------------
3 -- Module : Data.IntMap
4 -- Copyright : (c) Daan Leijen 2002
6 -- Maintainer : libraries@haskell.org
7 -- Stability : provisional
8 -- Portability : portable
10 -- An efficient implementation of maps from integer keys to values.
12 -- This module is intended to be imported @qualified@, to avoid name
13 -- clashes with "Prelude" functions. eg.
15 -- > import Data.IntMap as Map
17 -- The implementation is based on /big-endian patricia trees/. This data
18 -- structure performs especially well on binary operations like 'union'
19 -- and 'intersection'. However, my benchmarks show that it is also
20 -- (much) faster on insertions and deletions when compared to a generic
21 -- size-balanced map implementation (see "Data.Map" and "Data.FiniteMap").
23 -- * Chris Okasaki and Andy Gill, \"/Fast Mergeable Integer Maps/\",
24 -- Workshop on ML, September 1998, pages 77-86,
25 -- <http://www.cse.ogi.edu/~andy/pub/finite.htm>
27 -- * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve
28 -- Information Coded In Alphanumeric/\", Journal of the ACM, 15(4),
29 -- October 1968, pages 514-534.
31 -- Many operations have a worst-case complexity of /O(min(n,W))/.
32 -- This means that the operation can become linear in the number of
33 -- elements with a maximum of /W/ -- the number of bits in an 'Int'
35 -----------------------------------------------------------------------------
39 IntMap, Key -- instance Eq,Show
57 , insertWith, insertWithKey, insertLookupWithKey
114 , fromDistinctAscList
126 , isSubmapOf, isSubmapOfBy
127 , isProperSubmapOf, isProperSubmapOfBy
135 import Prelude hiding (lookup,map,filter,foldr,foldl,null)
138 import qualified Data.IntSet as IntSet
143 import qualified Prelude
144 import Debug.QuickCheck
145 import List (nub,sort)
146 import qualified List
149 #if __GLASGOW_HASKELL__
150 import Text.Read (Lexeme(Ident), lexP, parens, prec, readPrec)
151 import Data.Generics.Basics
152 import Data.Generics.Instances
155 #if __GLASGOW_HASKELL__ >= 503
157 import GHC.Exts ( Word(..), Int(..), shiftRL# )
158 #elif __GLASGOW_HASKELL__
160 import GlaExts ( Word(..), Int(..), shiftRL# )
165 infixl 9 \\{-This comment teaches CPP correct behaviour -}
167 -- A "Nat" is a natural machine word (an unsigned Int)
170 natFromInt :: Key -> Nat
171 natFromInt i = fromIntegral i
173 intFromNat :: Nat -> Key
174 intFromNat w = fromIntegral w
176 shiftRL :: Nat -> Key -> Nat
177 #if __GLASGOW_HASKELL__
178 {--------------------------------------------------------------------
179 GHC: use unboxing to get @shiftRL@ inlined.
180 --------------------------------------------------------------------}
181 shiftRL (W# x) (I# i)
184 shiftRL x i = shiftR x i
187 {--------------------------------------------------------------------
189 --------------------------------------------------------------------}
191 -- | /O(min(n,W))/. Find the value at a key.
192 -- Calls 'error' when the element can not be found.
194 (!) :: IntMap a -> Key -> a
197 -- | /O(n+m)/. See 'difference'.
198 (\\) :: IntMap a -> IntMap b -> IntMap a
199 m1 \\ m2 = difference m1 m2
201 {--------------------------------------------------------------------
203 --------------------------------------------------------------------}
204 -- | A map of integers to values @a@.
206 | Tip {-# UNPACK #-} !Key a
207 | Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !(IntMap a) !(IntMap a)
213 #if __GLASGOW_HASKELL__
215 {--------------------------------------------------------------------
217 --------------------------------------------------------------------}
219 -- This instance preserves data abstraction at the cost of inefficiency.
220 -- We omit reflection services for the sake of data abstraction.
222 instance Data a => Data (IntMap a) where
223 gfoldl f z im = z fromList `f` (toList im)
224 toConstr _ = error "toConstr"
225 gunfold _ _ = error "gunfold"
226 dataTypeOf _ = mkNorepType "Data.IntMap.IntMap"
230 {--------------------------------------------------------------------
232 --------------------------------------------------------------------}
233 -- | /O(1)/. Is the map empty?
234 null :: IntMap a -> Bool
238 -- | /O(n)/. Number of elements in the map.
239 size :: IntMap a -> Int
242 Bin p m l r -> size l + size r
246 -- | /O(min(n,W))/. Is the key a member of the map?
247 member :: Key -> IntMap a -> Bool
253 -- | /O(min(n,W))/. Lookup the value at a key in the map.
254 lookup :: Key -> IntMap a -> Maybe a
256 = let nk = natFromInt k in seq nk (lookupN nk t)
258 lookupN :: Nat -> IntMap a -> Maybe a
262 | zeroN k (natFromInt m) -> lookupN k l
263 | otherwise -> lookupN k r
265 | (k == natFromInt kx) -> Just x
266 | otherwise -> Nothing
269 find' :: Key -> IntMap a -> a
272 Nothing -> error ("IntMap.find: key " ++ show k ++ " is not an element of the map")
276 -- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@
277 -- returns the value at key @k@ or returns @def@ when the key is not an
278 -- element of the map.
279 findWithDefault :: a -> Key -> IntMap a -> a
280 findWithDefault def k m
285 {--------------------------------------------------------------------
287 --------------------------------------------------------------------}
288 -- | /O(1)/. The empty map.
293 -- | /O(1)/. A map of one element.
294 singleton :: Key -> a -> IntMap a
298 {--------------------------------------------------------------------
300 --------------------------------------------------------------------}
301 -- | /O(min(n,W))/. Insert a new key\/value pair in the map.
302 -- If the key is already present in the map, the associated value is
303 -- replaced with the supplied value, i.e. 'insert' is equivalent to
304 -- @'insertWith' 'const'@.
305 insert :: Key -> a -> IntMap a -> IntMap a
309 | nomatch k p m -> join k (Tip k x) p t
310 | zero k m -> Bin p m (insert k x l) r
311 | otherwise -> Bin p m l (insert k x r)
314 | otherwise -> join k (Tip k x) ky t
317 -- right-biased insertion, used by 'union'
318 -- | /O(min(n,W))/. Insert with a combining function.
319 insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
321 = insertWithKey (\k x y -> f x y) k x t
323 -- | /O(min(n,W))/. Insert with a combining function.
324 insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
325 insertWithKey f k x t
328 | nomatch k p m -> join k (Tip k x) p t
329 | zero k m -> Bin p m (insertWithKey f k x l) r
330 | otherwise -> Bin p m l (insertWithKey f k x r)
332 | k==ky -> Tip k (f k x y)
333 | otherwise -> join k (Tip k x) ky t
337 -- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@)
338 -- is a pair where the first element is equal to (@'lookup' k map@)
339 -- and the second element equal to (@'insertWithKey' f k x map@).
340 insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
341 insertLookupWithKey f k x t
344 | nomatch k p m -> (Nothing,join k (Tip k x) p t)
345 | zero k m -> let (found,l') = insertLookupWithKey f k x l in (found,Bin p m l' r)
346 | otherwise -> let (found,r') = insertLookupWithKey f k x r in (found,Bin p m l r')
348 | k==ky -> (Just y,Tip k (f k x y))
349 | otherwise -> (Nothing,join k (Tip k x) ky t)
350 Nil -> (Nothing,Tip k x)
353 {--------------------------------------------------------------------
355 [delete] is the inlined version of [deleteWith (\k x -> Nothing)]
356 --------------------------------------------------------------------}
357 -- | /O(min(n,W))/. Delete a key and its value from the map. When the key is not
358 -- a member of the map, the original map is returned.
359 delete :: Key -> IntMap a -> IntMap a
364 | zero k m -> bin p m (delete k l) r
365 | otherwise -> bin p m l (delete k r)
371 -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
372 -- a member of the map, the original map is returned.
373 adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
375 = adjustWithKey (\k x -> f x) k m
377 -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
378 -- a member of the map, the original map is returned.
379 adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
381 = updateWithKey (\k x -> Just (f k x)) k m
383 -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
384 -- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
385 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
386 update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
388 = updateWithKey (\k x -> f x) k m
390 -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
391 -- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is
392 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
393 updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
398 | zero k m -> bin p m (updateWithKey f k l) r
399 | otherwise -> bin p m l (updateWithKey f k r)
401 | k==ky -> case (f k y) of
407 -- | /O(min(n,W))/. Lookup and update.
408 updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a)
409 updateLookupWithKey f k t
412 | nomatch k p m -> (Nothing,t)
413 | zero k m -> let (found,l') = updateLookupWithKey f k l in (found,bin p m l' r)
414 | otherwise -> let (found,r') = updateLookupWithKey f k r in (found,bin p m l r')
416 | k==ky -> case (f k y) of
417 Just y' -> (Just y,Tip ky y')
418 Nothing -> (Just y,Nil)
419 | otherwise -> (Nothing,t)
423 {--------------------------------------------------------------------
425 --------------------------------------------------------------------}
426 -- | The union of a list of maps.
427 unions :: [IntMap a] -> IntMap a
429 = foldlStrict union empty xs
431 -- | The union of a list of maps, with a combining operation
432 unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a
434 = foldlStrict (unionWith f) empty ts
436 -- | /O(n+m)/. The (left-biased) union of two maps.
437 -- It prefers the first map when duplicate keys are encountered,
438 -- i.e. (@'union' == 'unionWith' 'const'@).
439 union :: IntMap a -> IntMap a -> IntMap a
440 union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
441 | shorter m1 m2 = union1
442 | shorter m2 m1 = union2
443 | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
444 | otherwise = join p1 t1 p2 t2
446 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
447 | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
448 | otherwise = Bin p1 m1 l1 (union r1 t2)
450 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
451 | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
452 | otherwise = Bin p2 m2 l2 (union t1 r2)
454 union (Tip k x) t = insert k x t
455 union t (Tip k x) = insertWith (\x y -> y) k x t -- right bias
459 -- | /O(n+m)/. The union with a combining function.
460 unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
462 = unionWithKey (\k x y -> f x y) m1 m2
464 -- | /O(n+m)/. The union with a combining function.
465 unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
466 unionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
467 | shorter m1 m2 = union1
468 | shorter m2 m1 = union2
469 | p1 == p2 = Bin p1 m1 (unionWithKey f l1 l2) (unionWithKey f r1 r2)
470 | otherwise = join p1 t1 p2 t2
472 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
473 | zero p2 m1 = Bin p1 m1 (unionWithKey f l1 t2) r1
474 | otherwise = Bin p1 m1 l1 (unionWithKey f r1 t2)
476 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
477 | zero p1 m2 = Bin p2 m2 (unionWithKey f t1 l2) r2
478 | otherwise = Bin p2 m2 l2 (unionWithKey f t1 r2)
480 unionWithKey f (Tip k x) t = insertWithKey f k x t
481 unionWithKey f t (Tip k x) = insertWithKey (\k x y -> f k y x) k x t -- right bias
482 unionWithKey f Nil t = t
483 unionWithKey f t Nil = t
485 {--------------------------------------------------------------------
487 --------------------------------------------------------------------}
488 -- | /O(n+m)/. Difference between two maps (based on keys).
489 difference :: IntMap a -> IntMap b -> IntMap a
490 difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
491 | shorter m1 m2 = difference1
492 | shorter m2 m1 = difference2
493 | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
496 difference1 | nomatch p2 p1 m1 = t1
497 | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
498 | otherwise = bin p1 m1 l1 (difference r1 t2)
500 difference2 | nomatch p1 p2 m2 = t1
501 | zero p1 m2 = difference t1 l2
502 | otherwise = difference t1 r2
504 difference t1@(Tip k x) t2
508 difference Nil t = Nil
509 difference t (Tip k x) = delete k t
512 -- | /O(n+m)/. Difference with a combining function.
513 differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
514 differenceWith f m1 m2
515 = differenceWithKey (\k x y -> f x y) m1 m2
517 -- | /O(n+m)/. Difference with a combining function. When two equal keys are
518 -- encountered, the combining function is applied to the key and both values.
519 -- If it returns 'Nothing', the element is discarded (proper set difference).
520 -- If it returns (@'Just' y@), the element is updated with a new value @y@.
521 differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
522 differenceWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
523 | shorter m1 m2 = difference1
524 | shorter m2 m1 = difference2
525 | p1 == p2 = bin p1 m1 (differenceWithKey f l1 l2) (differenceWithKey f r1 r2)
528 difference1 | nomatch p2 p1 m1 = t1
529 | zero p2 m1 = bin p1 m1 (differenceWithKey f l1 t2) r1
530 | otherwise = bin p1 m1 l1 (differenceWithKey f r1 t2)
532 difference2 | nomatch p1 p2 m2 = t1
533 | zero p1 m2 = differenceWithKey f t1 l2
534 | otherwise = differenceWithKey f t1 r2
536 differenceWithKey f t1@(Tip k x) t2
537 = case lookup k t2 of
538 Just y -> case f k x y of
543 differenceWithKey f Nil t = Nil
544 differenceWithKey f t (Tip k y) = updateWithKey (\k x -> f k x y) k t
545 differenceWithKey f t Nil = t
548 {--------------------------------------------------------------------
550 --------------------------------------------------------------------}
551 -- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys).
552 intersection :: IntMap a -> IntMap b -> IntMap a
553 intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
554 | shorter m1 m2 = intersection1
555 | shorter m2 m1 = intersection2
556 | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
559 intersection1 | nomatch p2 p1 m1 = Nil
560 | zero p2 m1 = intersection l1 t2
561 | otherwise = intersection r1 t2
563 intersection2 | nomatch p1 p2 m2 = Nil
564 | zero p1 m2 = intersection t1 l2
565 | otherwise = intersection t1 r2
567 intersection t1@(Tip k x) t2
570 intersection t (Tip k x)
574 intersection Nil t = Nil
575 intersection t Nil = Nil
577 -- | /O(n+m)/. The intersection with a combining function.
578 intersectionWith :: (a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
579 intersectionWith f m1 m2
580 = intersectionWithKey (\k x y -> f x y) m1 m2
582 -- | /O(n+m)/. The intersection with a combining function.
583 intersectionWithKey :: (Key -> a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
584 intersectionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
585 | shorter m1 m2 = intersection1
586 | shorter m2 m1 = intersection2
587 | p1 == p2 = bin p1 m1 (intersectionWithKey f l1 l2) (intersectionWithKey f r1 r2)
590 intersection1 | nomatch p2 p1 m1 = Nil
591 | zero p2 m1 = intersectionWithKey f l1 t2
592 | otherwise = intersectionWithKey f r1 t2
594 intersection2 | nomatch p1 p2 m2 = Nil
595 | zero p1 m2 = intersectionWithKey f t1 l2
596 | otherwise = intersectionWithKey f t1 r2
598 intersectionWithKey f t1@(Tip k x) t2
599 = case lookup k t2 of
600 Just y -> Tip k (f k x y)
602 intersectionWithKey f t1 (Tip k y)
603 = case lookup k t1 of
604 Just x -> Tip k (f k x y)
606 intersectionWithKey f Nil t = Nil
607 intersectionWithKey f t Nil = Nil
610 {--------------------------------------------------------------------
612 --------------------------------------------------------------------}
613 -- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
614 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
615 isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
616 isProperSubmapOf m1 m2
617 = isProperSubmapOfBy (==) m1 m2
619 {- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
620 The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
621 @m1@ and @m2@ are not equal,
622 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
623 applied to their respective values. For example, the following
624 expressions are all 'True':
626 > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
627 > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
629 But the following are all 'False':
631 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
632 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
633 > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
635 isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
636 isProperSubmapOfBy pred t1 t2
637 = case submapCmp pred t1 t2 of
641 submapCmp pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
643 | shorter m2 m1 = submapCmpLt
644 | p1 == p2 = submapCmpEq
645 | otherwise = GT -- disjoint
647 submapCmpLt | nomatch p1 p2 m2 = GT
648 | zero p1 m2 = submapCmp pred t1 l2
649 | otherwise = submapCmp pred t1 r2
650 submapCmpEq = case (submapCmp pred l1 l2, submapCmp pred r1 r2) of
656 submapCmp pred (Bin p m l r) t = GT
657 submapCmp pred (Tip kx x) (Tip ky y)
658 | (kx == ky) && pred x y = EQ
659 | otherwise = GT -- disjoint
660 submapCmp pred (Tip k x) t
662 Just y | pred x y -> LT
663 other -> GT -- disjoint
664 submapCmp pred Nil Nil = EQ
665 submapCmp pred Nil t = LT
667 -- | /O(n+m)/. Is this a submap?
668 -- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
669 isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
671 = isSubmapOfBy (==) m1 m2
674 The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if
675 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
676 applied to their respective values. For example, the following
677 expressions are all 'True':
679 > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
680 > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
681 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
683 But the following are all 'False':
685 > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
686 > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
687 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
690 isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
691 isSubmapOfBy pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
692 | shorter m1 m2 = False
693 | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubmapOfBy pred t1 l2
694 else isSubmapOfBy pred t1 r2)
695 | otherwise = (p1==p2) && isSubmapOfBy pred l1 l2 && isSubmapOfBy pred r1 r2
696 isSubmapOfBy pred (Bin p m l r) t = False
697 isSubmapOfBy pred (Tip k x) t = case lookup k t of
700 isSubmapOfBy pred Nil t = True
702 {--------------------------------------------------------------------
704 --------------------------------------------------------------------}
705 -- | /O(n)/. Map a function over all values in the map.
706 map :: (a -> b) -> IntMap a -> IntMap b
708 = mapWithKey (\k x -> f x) m
710 -- | /O(n)/. Map a function over all values in the map.
711 mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
714 Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r)
715 Tip k x -> Tip k (f k x)
718 -- | /O(n)/. The function @'mapAccum'@ threads an accumulating
719 -- argument through the map in ascending order of keys.
720 mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
722 = mapAccumWithKey (\a k x -> f a x) a m
724 -- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
725 -- argument through the map in ascending order of keys.
726 mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
727 mapAccumWithKey f a t
730 -- | /O(n)/. The function @'mapAccumL'@ threads an accumulating
731 -- argument through the map in ascending order of keys.
732 mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
735 Bin p m l r -> let (a1,l') = mapAccumL f a l
736 (a2,r') = mapAccumL f a1 r
737 in (a2,Bin p m l' r')
738 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
742 -- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
743 -- argument throught the map in descending order of keys.
744 mapAccumR :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
747 Bin p m l r -> let (a1,r') = mapAccumR f a r
748 (a2,l') = mapAccumR f a1 l
749 in (a2,Bin p m l' r')
750 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
753 {--------------------------------------------------------------------
755 --------------------------------------------------------------------}
756 -- | /O(n)/. Filter all values that satisfy some predicate.
757 filter :: (a -> Bool) -> IntMap a -> IntMap a
759 = filterWithKey (\k x -> p x) m
761 -- | /O(n)/. Filter all keys\/values that satisfy some predicate.
762 filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
766 -> bin p m (filterWithKey pred l) (filterWithKey pred r)
772 -- | /O(n)/. partition the map according to some predicate. The first
773 -- map contains all elements that satisfy the predicate, the second all
774 -- elements that fail the predicate. See also 'split'.
775 partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
777 = partitionWithKey (\k x -> p x) m
779 -- | /O(n)/. partition the map according to some predicate. The first
780 -- map contains all elements that satisfy the predicate, the second all
781 -- elements that fail the predicate. See also 'split'.
782 partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
783 partitionWithKey pred t
786 -> let (l1,l2) = partitionWithKey pred l
787 (r1,r2) = partitionWithKey pred r
788 in (bin p m l1 r1, bin p m l2 r2)
790 | pred k x -> (t,Nil)
791 | otherwise -> (Nil,t)
795 -- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@
796 -- where all keys in @map1@ are lower than @k@ and all keys in
797 -- @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@.
798 split :: Key -> IntMap a -> (IntMap a,IntMap a)
802 | nomatch k p m -> if k>p then (t,Nil) else (Nil,t)
803 | zero k m -> let (lt,gt) = split k l in (lt,union gt r)
804 | otherwise -> let (lt,gt) = split k r in (union l lt,gt)
808 | otherwise -> (Nil,Nil)
811 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
812 -- key was found in the original map.
813 splitLookup :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
817 | nomatch k p m -> if k>p then (t,Nothing,Nil) else (Nil,Nothing,t)
818 | zero k m -> let (lt,found,gt) = splitLookup k l in (lt,found,union gt r)
819 | otherwise -> let (lt,found,gt) = splitLookup k r in (union l lt,found,gt)
821 | k>ky -> (t,Nothing,Nil)
822 | k<ky -> (Nil,Nothing,t)
823 | otherwise -> (Nil,Just y,Nil)
824 Nil -> (Nil,Nothing,Nil)
826 {--------------------------------------------------------------------
828 --------------------------------------------------------------------}
829 -- | /O(n)/. Fold the values in the map, such that
830 -- @'fold' f z == 'Prelude.foldr' f z . 'elems'@.
833 -- > elems map = fold (:) [] map
835 fold :: (a -> b -> b) -> b -> IntMap a -> b
837 = foldWithKey (\k x y -> f x y) z t
839 -- | /O(n)/. Fold the keys and values in the map, such that
840 -- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
843 -- > keys map = foldWithKey (\k x ks -> k:ks) [] map
845 foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
849 foldr :: (Key -> a -> b -> b) -> b -> IntMap a -> b
852 Bin p m l r -> foldr f (foldr f z r) l
856 {--------------------------------------------------------------------
858 --------------------------------------------------------------------}
860 -- Return all elements of the map in the ascending order of their keys.
861 elems :: IntMap a -> [a]
863 = foldWithKey (\k x xs -> x:xs) [] m
865 -- | /O(n)/. Return all keys of the map in ascending order.
866 keys :: IntMap a -> [Key]
868 = foldWithKey (\k x ks -> k:ks) [] m
870 -- | /O(n*min(n,W))/. The set of all keys of the map.
871 keysSet :: IntMap a -> IntSet.IntSet
872 keysSet m = IntSet.fromDistinctAscList (keys m)
875 -- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
876 assocs :: IntMap a -> [(Key,a)]
881 {--------------------------------------------------------------------
883 --------------------------------------------------------------------}
884 -- | /O(n)/. Convert the map to a list of key\/value pairs.
885 toList :: IntMap a -> [(Key,a)]
887 = foldWithKey (\k x xs -> (k,x):xs) [] t
889 -- | /O(n)/. Convert the map to a list of key\/value pairs where the
890 -- keys are in ascending order.
891 toAscList :: IntMap a -> [(Key,a)]
893 = -- NOTE: the following algorithm only works for big-endian trees
894 let (pos,neg) = span (\(k,x) -> k >=0) (foldr (\k x xs -> (k,x):xs) [] t) in neg ++ pos
896 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs.
897 fromList :: [(Key,a)] -> IntMap a
899 = foldlStrict ins empty xs
901 ins t (k,x) = insert k x t
903 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
904 fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
906 = fromListWithKey (\k x y -> f x y) xs
908 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
909 fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
911 = foldlStrict ins empty xs
913 ins t (k,x) = insertWithKey f k x t
915 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
916 -- the keys are in ascending order.
917 fromAscList :: [(Key,a)] -> IntMap a
921 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
922 -- the keys are in ascending order, with a combining function on equal keys.
923 fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
927 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
928 -- the keys are in ascending order, with a combining function on equal keys.
929 fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
930 fromAscListWithKey f xs
931 = fromListWithKey f xs
933 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
934 -- the keys are in ascending order and all distinct.
935 fromDistinctAscList :: [(Key,a)] -> IntMap a
936 fromDistinctAscList xs
940 {--------------------------------------------------------------------
942 --------------------------------------------------------------------}
943 instance Eq a => Eq (IntMap a) where
944 t1 == t2 = equal t1 t2
945 t1 /= t2 = nequal t1 t2
947 equal :: Eq a => IntMap a -> IntMap a -> Bool
948 equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
949 = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
950 equal (Tip kx x) (Tip ky y)
951 = (kx == ky) && (x==y)
955 nequal :: Eq a => IntMap a -> IntMap a -> Bool
956 nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
957 = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
958 nequal (Tip kx x) (Tip ky y)
959 = (kx /= ky) || (x/=y)
960 nequal Nil Nil = False
963 {--------------------------------------------------------------------
965 --------------------------------------------------------------------}
967 instance Ord a => Ord (IntMap a) where
968 compare m1 m2 = compare (toList m1) (toList m2)
970 {--------------------------------------------------------------------
972 --------------------------------------------------------------------}
974 instance Functor IntMap where
977 {--------------------------------------------------------------------
979 --------------------------------------------------------------------}
981 instance Show a => Show (IntMap a) where
982 showsPrec d m = showParen (d > 10) $
983 showString "fromList " . shows (toList m)
985 showMap :: (Show a) => [(Key,a)] -> ShowS
989 = showChar '{' . showElem x . showTail xs
991 showTail [] = showChar '}'
992 showTail (x:xs) = showChar ',' . showElem x . showTail xs
994 showElem (k,x) = shows k . showString ":=" . shows x
996 {--------------------------------------------------------------------
998 --------------------------------------------------------------------}
999 instance (Read e) => Read (IntMap e) where
1000 #ifdef __GLASGOW_HASKELL__
1001 readPrec = parens $ prec 10 $ do
1002 Ident "fromList" <- lexP
1004 return (fromList xs)
1006 readsPrec p = readParen (p > 10) $ \ r -> do
1007 ("fromList",s) <- lex
1009 return (fromList xs,t)
1012 {--------------------------------------------------------------------
1014 --------------------------------------------------------------------}
1016 #include "Typeable.h"
1017 INSTANCE_TYPEABLE1(IntMap,intMapTc,"IntMap")
1019 {--------------------------------------------------------------------
1021 --------------------------------------------------------------------}
1022 -- | /O(n)/. Show the tree that implements the map. The tree is shown
1023 -- in a compressed, hanging format.
1024 showTree :: Show a => IntMap a -> String
1026 = showTreeWith True False s
1029 {- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
1030 the tree that implements the map. If @hang@ is
1031 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
1032 @wide@ is 'True', an extra wide version is shown.
1034 showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
1035 showTreeWith hang wide t
1036 | hang = (showsTreeHang wide [] t) ""
1037 | otherwise = (showsTree wide [] [] t) ""
1039 showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS
1040 showsTree wide lbars rbars t
1043 -> showsTree wide (withBar rbars) (withEmpty rbars) r .
1044 showWide wide rbars .
1045 showsBars lbars . showString (showBin p m) . showString "\n" .
1046 showWide wide lbars .
1047 showsTree wide (withEmpty lbars) (withBar lbars) l
1049 -> showsBars lbars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1050 Nil -> showsBars lbars . showString "|\n"
1052 showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS
1053 showsTreeHang wide bars t
1056 -> showsBars bars . showString (showBin p m) . showString "\n" .
1057 showWide wide bars .
1058 showsTreeHang wide (withBar bars) l .
1059 showWide wide bars .
1060 showsTreeHang wide (withEmpty bars) r
1062 -> showsBars bars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1063 Nil -> showsBars bars . showString "|\n"
1066 = "*" -- ++ show (p,m)
1069 | wide = showString (concat (reverse bars)) . showString "|\n"
1072 showsBars :: [String] -> ShowS
1076 _ -> showString (concat (reverse (tail bars))) . showString node
1079 withBar bars = "| ":bars
1080 withEmpty bars = " ":bars
1083 {--------------------------------------------------------------------
1085 --------------------------------------------------------------------}
1086 {--------------------------------------------------------------------
1088 --------------------------------------------------------------------}
1089 join :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
1091 | zero p1 m = Bin p m t1 t2
1092 | otherwise = Bin p m t2 t1
1094 m = branchMask p1 p2
1097 {--------------------------------------------------------------------
1098 @bin@ assures that we never have empty trees within a tree.
1099 --------------------------------------------------------------------}
1100 bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
1103 bin p m l r = Bin p m l r
1106 {--------------------------------------------------------------------
1107 Endian independent bit twiddling
1108 --------------------------------------------------------------------}
1109 zero :: Key -> Mask -> Bool
1111 = (natFromInt i) .&. (natFromInt m) == 0
1113 nomatch,match :: Key -> Prefix -> Mask -> Bool
1120 mask :: Key -> Mask -> Prefix
1122 = maskW (natFromInt i) (natFromInt m)
1125 zeroN :: Nat -> Nat -> Bool
1126 zeroN i m = (i .&. m) == 0
1128 {--------------------------------------------------------------------
1129 Big endian operations
1130 --------------------------------------------------------------------}
1131 maskW :: Nat -> Nat -> Prefix
1133 = intFromNat (i .&. (complement (m-1) `xor` m))
1135 shorter :: Mask -> Mask -> Bool
1137 = (natFromInt m1) > (natFromInt m2)
1139 branchMask :: Prefix -> Prefix -> Mask
1141 = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
1143 {----------------------------------------------------------------------
1144 Finding the highest bit (mask) in a word [x] can be done efficiently in
1146 * convert to a floating point value and the mantissa tells us the
1147 [log2(x)] that corresponds with the highest bit position. The mantissa
1148 is retrieved either via the standard C function [frexp] or by some bit
1149 twiddling on IEEE compatible numbers (float). Note that one needs to
1150 use at least [double] precision for an accurate mantissa of 32 bit
1152 * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
1153 * use processor specific assembler instruction (asm).
1155 The most portable way would be [bit], but is it efficient enough?
1156 I have measured the cycle counts of the different methods on an AMD
1157 Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
1159 highestBitMask: method cycles
1166 highestBit: method cycles
1173 Wow, the bit twiddling is on today's RISC like machines even faster
1174 than a single CISC instruction (BSR)!
1175 ----------------------------------------------------------------------}
1177 {----------------------------------------------------------------------
1178 [highestBitMask] returns a word where only the highest bit is set.
1179 It is found by first setting all bits in lower positions than the
1180 highest bit and than taking an exclusive or with the original value.
1181 Allthough the function may look expensive, GHC compiles this into
1182 excellent C code that subsequently compiled into highly efficient
1183 machine code. The algorithm is derived from Jorg Arndt's FXT library.
1184 ----------------------------------------------------------------------}
1185 highestBitMask :: Nat -> Nat
1187 = case (x .|. shiftRL x 1) of
1188 x -> case (x .|. shiftRL x 2) of
1189 x -> case (x .|. shiftRL x 4) of
1190 x -> case (x .|. shiftRL x 8) of
1191 x -> case (x .|. shiftRL x 16) of
1192 x -> case (x .|. shiftRL x 32) of -- for 64 bit platforms
1193 x -> (x `xor` (shiftRL x 1))
1196 {--------------------------------------------------------------------
1198 --------------------------------------------------------------------}
1202 (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
1205 {--------------------------------------------------------------------
1207 --------------------------------------------------------------------}
1208 testTree :: [Int] -> IntMap Int
1209 testTree xs = fromList [(x,x*x*30696 `mod` 65521) | x <- xs]
1210 test1 = testTree [1..20]
1211 test2 = testTree [30,29..10]
1212 test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
1214 {--------------------------------------------------------------------
1216 --------------------------------------------------------------------}
1221 { configMaxTest = 500
1222 , configMaxFail = 5000
1223 , configSize = \n -> (div n 2 + 3)
1224 , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
1228 {--------------------------------------------------------------------
1229 Arbitrary, reasonably balanced trees
1230 --------------------------------------------------------------------}
1231 instance Arbitrary a => Arbitrary (IntMap a) where
1232 arbitrary = do{ ks <- arbitrary
1233 ; xs <- mapM (\k -> do{ x <- arbitrary; return (k,x)}) ks
1234 ; return (fromList xs)
1238 {--------------------------------------------------------------------
1239 Single, Insert, Delete
1240 --------------------------------------------------------------------}
1241 prop_Single :: Key -> Int -> Bool
1243 = (insert k x empty == singleton k x)
1245 prop_InsertDelete :: Key -> Int -> IntMap Int -> Property
1246 prop_InsertDelete k x t
1247 = not (member k t) ==> delete k (insert k x t) == t
1249 prop_UpdateDelete :: Key -> IntMap Int -> Bool
1250 prop_UpdateDelete k t
1251 = update (const Nothing) k t == delete k t
1254 {--------------------------------------------------------------------
1256 --------------------------------------------------------------------}
1257 prop_UnionInsert :: Key -> Int -> IntMap Int -> Bool
1258 prop_UnionInsert k x t
1259 = union (singleton k x) t == insert k x t
1261 prop_UnionAssoc :: IntMap Int -> IntMap Int -> IntMap Int -> Bool
1262 prop_UnionAssoc t1 t2 t3
1263 = union t1 (union t2 t3) == union (union t1 t2) t3
1265 prop_UnionComm :: IntMap Int -> IntMap Int -> Bool
1266 prop_UnionComm t1 t2
1267 = (union t1 t2 == unionWith (\x y -> y) t2 t1)
1270 prop_Diff :: [(Key,Int)] -> [(Key,Int)] -> Bool
1272 = List.sort (keys (difference (fromListWith (+) xs) (fromListWith (+) ys)))
1273 == List.sort ((List.\\) (nub (Prelude.map fst xs)) (nub (Prelude.map fst ys)))
1275 prop_Int :: [(Key,Int)] -> [(Key,Int)] -> Bool
1277 = List.sort (keys (intersection (fromListWith (+) xs) (fromListWith (+) ys)))
1278 == List.sort (nub ((List.intersect) (Prelude.map fst xs) (Prelude.map fst ys)))
1280 {--------------------------------------------------------------------
1282 --------------------------------------------------------------------}
1284 = forAll (choose (5,100)) $ \n ->
1285 let xs = [(x,()) | x <- [0..n::Int]]
1286 in fromAscList xs == fromList xs
1288 prop_List :: [Key] -> Bool
1290 = (sort (nub xs) == [x | (x,()) <- toAscList (fromList [(x,()) | x <- xs])])